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# -*- coding: utf-8 -*-
"""
Script to execute example covarying MMGP regression forecasting model
with full Krhh.
Inputs: Data training and test sets (dictionary pickle)
Data for example:
- normalised solar data for 25 sites for 15 minute forecast
- N_train = 4200, N_test = 2276, P = 25, D = 51
- Xtr[:, :50] 2 recent lagged observations for each site in order
- Xtr[:, 50] time index
- link inputs is a 25x2 array (link inputs repeated for every group)
with normalised lat,long for each site in order
Model Options:
- Sparse or full x-function covariance prior Krhh (set bool SPARSE_PRIOR)
- Diagonal or Kronecker-structured variational posterior covariance Sr (set bool DIAG_POST)
- Sparse or full posterior covariance (when Kronecker posterior; set bool SPARSE_POST)
Current Settings (sparse covarying mmgp model with sparse Kronecker posterior):
DIAG_POST = False
SPARSE_PRIOR = False # set True for equivalent sparse scmmgp model
SPARSE_POST = True
Note on specifying group structure for F:
Grouping occurs via block_struct, a nested list of grouping order
Where functions [i] are independent i.e. in own block, set link_kernel[i] = link_inputs[i] = 1.0
See model class preamble and example below for further details.
"""
import os
import numpy as np
import pickle
import pandas as pd
import traceback
import time
import sklearn.cluster
import csv
import sys
import mmgp
from mmgp import likelihoods
from mmgp import kernels
import tensorflow as tf
from mmgp import datasets
from mmgp import losses
from mmgp import util
dpath = '/experiments/datasets/'
dfile = 'p25_inputsdict.pickle'
dlinkfile = 'p25_linkinputsarray.pickle'
outdir = '/experiments/results/p25_nonsparse_cmmgp/'
try:
os.makedirs(outdir)
except FileExistsError:
pass
def get_inputs():
"""
inputsdict contains {'Yte': Yte, 'Ytr': Ytr, 'Xtr': Xtr, 'Xte': Xte} where values are np.arrays
np. arrays are truncated to evenly split into batches of size = batchsize
returns inputsdict, Xtr_link (ndarray, shape = [P, D_link_features])
"""
with open(os.path.join(dpath, dfile), 'rb') as f:
d_all = pickle.load(f)
with open(os.path.join(dpath, dlinkfile), 'rb') as f:
d_link = pickle.load(f)
return d_all, d_link
def init_z(train_inputs, num_inducing):
# Initialize inducing points using clustering.
mini_batch = sklearn.cluster.MiniBatchKMeans(num_inducing)
cluster_indices = mini_batch.fit_predict(train_inputs)
inducing_locations = mini_batch.cluster_centers_
return inducing_locations
FLAGS = util.util.get_flags()
BATCH_SIZE = FLAGS.batch_size
LEARNING_RATE = FLAGS.learning_rate
DISPLAY_STEP = FLAGS.display_step
EPOCHS = FLAGS.n_epochs
NUM_SAMPLES = FLAGS.mc_train
PRED_SAMPLES = FLAGS.mc_test
NUM_INDUCING = FLAGS.n_inducing
NUM_COMPONENTS = FLAGS.num_components
IS_ARD = FLAGS.is_ard
TOL = FLAGS.opt_tol
VAR_STEPS = FLAGS.var_steps
DIAG_POST = False
SPARSE_PRIOR = False
SPARSE_POST = True # option for non-diag post
MAXTIME = 1200
print("settings done")
# define GPRN P and Q
output_dim = 25 #P
node_dim = 25 #Q
lag_dim = 2
save_nlpds = False # If True saves samples of nlpds for n,p,s
# extract dataset
d, d_link = get_inputs()
Ytr, Yte, Xtr, Xte = d['Ytr'], d['Yte'], d['Xtr'], d['Xte']
data = datasets.DataSet(Xtr.astype(np.float32), Ytr.astype(np.float32), shuffle=False)
test = datasets.DataSet(Xte.astype(np.float32), Yte.astype(np.float32), shuffle=False)
print("dataset created")
# model config block rows (where P=Q): block all w.1, w.2 etc, leave f independent
# order of block_struct is rows, node functions
# lists required: block_struct, link_inputs, kern_link, kern
#block_struct nested list of grouping order
weight_struct = [[] for _ in range(output_dim)]
for i in range(output_dim):
row = list(range(i, i+output_dim*(node_dim-1)+1, output_dim))
row_0 = row.pop(i) # bring diag to pivot position
weight_struct[i] = [row_0] + row
nodes = [[x] for x in list(range(output_dim * node_dim, output_dim * node_dim + output_dim))]
block_struct = weight_struct + nodes
# create link inputs (link inputs used repeatedly but can have link input per group)
# permute to bring diagonal to first position
link_inputs = [[] for _ in range(output_dim)]
for i in range(output_dim):
idx = list(range(d_link.shape[0]))
link_inputs[i] = d_link[[idx.pop(i)] + idx, :]
link_inputs = link_inputs + [1.0 for i in range(output_dim)] # for full W row blocks, independent nodes
# create 'between' kernel list
klink_rows = [kernels.CompositeKernel('mul',[kernels.RadialBasis(2, std_dev=2.0, lengthscale=1.0, white=0.01, input_scaling = IS_ARD),
kernels.CompactSlice(2, active_dims=[0,1], lengthscale = 2.0, input_scaling = IS_ARD)] )
for i in range(output_dim) ]
klink_f = [1.0 for i in range(node_dim)]
kernlink = klink_rows + klink_f
# create 'within' kernel
# kern
lag_active_dims_s = [ [] for _ in range(output_dim)]
for i in range(output_dim):
lag_active_dims_s[i] = list(range(lag_dim*i, lag_dim*(i+1)))
k_rows = [kernels.CompositeKernel('mul',[kernels.RadialBasisSlice(lag_dim, active_dims=lag_active_dims_s[i],
std_dev = 1.0, white = 0.01, input_scaling = IS_ARD),
kernels.PeriodicSliceFixed(1, active_dims=[Xtr.shape[1]-1],
lengthscale=0.5, std_dev=1.0, period = 144) ])
for i in range(output_dim)]
k_f = [kernels.RadialBasisSlice(lag_dim, active_dims=lag_active_dims_s[i], std_dev = 1.0, white = 0.01, input_scaling = IS_ARD)
for i in range(output_dim)]
kern = k_rows + k_f
print('len link_inputs ',len(link_inputs))
print('len kernlink ',len(kernlink))
print('len kern ', len(kern))
print('no. groups = ', len(block_struct), 'no. latent functions =', len([i for b in block_struct for i in b]))
print('number latent functions', node_dim*(output_dim+1))
likelihood = likelihoods.CovaryingRegressionNetwork(output_dim, node_dim, std_dev = 0.2) # p, q, lik_noise
print("likelihood and kernels set")
Z = init_z(data.X, NUM_INDUCING)
print('inducing points set')
m = mmgp.ExplicitSCMMGP(output_dim, likelihood, kern, kernlink, block_struct, Z, link_inputs,
num_components=NUM_COMPONENTS, diag_post=DIAG_POST, sparse_prior=SPARSE_PRIOR,
sparse_post=SPARSE_POST, num_samples=NUM_SAMPLES, predict_samples=PRED_SAMPLES)
print("model set")
# initialise losses and logging
error_rate = losses.RootMeanSqError(data.Dout)
os.chdir(outdir)
with open("log_results.csv", 'w', newline='') as f:
csv.writer(f).writerow(['epoch', 'fit_runtime', 'nelbo', error_rate.get_name(),'generalised_nlpd'])
with open("log_params.csv", 'w', newline='') as f:
csv.writer(f).writerow(['epoch', 'raw_kernel_params', 'raw_kernlink_params', 'raw_likelihood_params', 'raw_weights'])
with open("log_comp_time.csv", 'w', newline='') as f:
csv.writer(f).writerow(['epoch', 'batch_time', 'nelbo_time', 'pred_time', 'gen_nlpd_time', error_rate.get_name()+'_time'])
# optimise
o = tf.train.AdamOptimizer(LEARNING_RATE, beta1=0.9,beta2=0.99)
print("start time = ", time.strftime('%X %x %Z'))
m.fit(data, o, var_steps = VAR_STEPS, epochs = EPOCHS, batch_size = BATCH_SIZE, display_step=DISPLAY_STEP,
test = test, loss = error_rate, tolerance = TOL, max_time=MAXTIME )
print("optimisation complete")
# export final predicted values and loss metrics
ypred = m.predict(test.X, batch_size = BATCH_SIZE) #same batchsize used for convenience
np.savetxt("predictions.csv", np.concatenate(ypred, axis=1), delimiter=",")
if save_nlpds == True:
nlpd_samples, nlpd_meanvar = m.nlpd_samples(test.X, test.Y, batch_size = BATCH_SIZE)
try:
np.savetxt("nlpd_meanvar.csv", nlpd_meanvar, delimiter=",") # N x 2P as for predictions
except:
print('nlpd_meanvar export fail')
try:
np.savetxt("nlpd_samples.csv", nlpd_samples, delimiter=",") # NP x S (NxS concat for P tasks)
except:
print('nlpd_samples export fail')
print("Final " + error_rate.get_name() + "=" + "%.4f" % error_rate.eval(test.Y, ypred[0]))
print("Final " + "generalised_nlpd" + "=" + "%.4f" % m.nlpd_general(test.X, test.Y, batch_size = BATCH_SIZE))
error_rate_end = [losses.MeanAbsError(data.Dout)] # any extra accuracy measures at end of routine
print("Final ", [e.get_name() for e in error_rate_end])
print([e.eval(test.Y, ypred[0]) for e in error_rate_end])
predvar = [np.mean( | np.mean(ypred[1]) | numpy.mean |
# Credit to https://medium.com/emergent-future/simple-reinforcement-learning-with-tensorflow-part-0-q-learning-with-tables-and-neural-networks-d195264329d0
import gym
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
env = gym.make('FrozenLake-v0')
# NEURAL NETWORK IMPLEMENTATION
tf.reset_default_graph()
# Feature vector for current state representation
input1 = tf.placeholder(shape=[1, env.observation_space.n], dtype=tf.float32)
# tf.Variable(<initial-value>, name=<optional-name>)
# tf.random_uniform(shape, minval=0, maxval=None, dtype=tf.float32, seed=None, name=None)
# Weighting W vector in range 0 - 0.01 (like the way Andrew Ng did with *0.01
W = tf.Variable(tf.random_uniform([env.observation_space.n, env.action_space.n], 0, 0.01))
# Qout with shape [1, env.action_space.n] - Action state value for Q[s, a] with every a available at a state
Qout = tf.matmul(input1, W)
# Greedy action at a state
predict = tf.argmax(Qout, axis=1)
# Feature vector for next state representation
nextQ = tf.placeholder(shape=[1, env.action_space.n], dtype=tf.float32)
# Entropy loss
loss = tf.reduce_sum(tf.square(Qout - nextQ))
trainer = tf.train.GradientDescentOptimizer(learning_rate=0.1)
updateModel = trainer.minimize(loss)
# TRAIN THE NETWORK
init = tf.global_variables_initializer()
# Set learning parameters
y = 0.99
e = 0.1
number_episodes = 2000
# List to store total rewards and steps per episode
jList = []
rList = []
with tf.Session() as sess:
sess.run(init)
for i in range(number_episodes):
print("Episode #{} is running!".format(i))
# First state
s = env.reset()
rAll = 0
d = False
j = 0
# Q network
while j < 200: # or While not d:
j += 1
# Choose action by epsilon (e) greedy
# print("s = ", s," --> Identity s:s+1: ", np.identity(env.observation_space.n)[s:s+1])
# s = 0 --> Identity s: s + 1: [[1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]
# s = 1 --> Identity s: s + 1: [[0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]
# Identity [s:s+1] is a one-hot vector
# Therefore W is the actual Q value
a, allQ = sess.run([predict, Qout], feed_dict={input1: np.identity(env.observation_space.n)[s:s+1]})
if np.random.rand(1) < e:
a[0] = env.action_space.sample()
s1, r, d, _ = env.step(a[0])
# Obtain next state Q value by feeding the new state throughout the network
Q1 = sess.run(Qout, feed_dict={input1: np.identity(env.observation_space.n)[s1:s1+1]})
maxQ1 = | np.max(Q1) | numpy.max |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
min_1_y_time = minima_x[-1] * np.ones_like(min_1_y)
dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101)
dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Characteristic Wave Effects Example')
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10))
plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10))
plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4,
label=textwrap.fill('Coughlin maximum', 14))
plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4,
label=textwrap.fill('Coughlin minimum', 14))
plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4,
label=textwrap.fill('Average maximum', 14))
plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4,
label=textwrap.fill('Average minimum', 14))
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14))
plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14))
plt.plot(max_2_x_time, max_2_x, 'k-')
plt.plot(max_2_x_time_side, max_2_x, 'k-')
plt.plot(min_2_x_time, min_2_x, 'k-')
plt.plot(min_2_x_time_side, min_2_x, 'k-')
plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--')
plt.text(5.16 * np.pi, 0.85, r'$2a_2$')
plt.plot(max_2_y_time, max_2_y, 'k-')
plt.plot(max_2_y_time, max_2_y_side, 'k-')
plt.plot(min_2_y_time, min_2_y, 'k-')
plt.plot(min_2_y_time, min_2_y_side, 'k-')
plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--')
plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$')
plt.plot(max_1_x_time, max_1_x, 'k-')
plt.plot(max_1_x_time_side, max_1_x, 'k-')
plt.plot(min_1_x_time, min_1_x, 'k-')
plt.plot(min_1_x_time_side, min_1_x, 'k-')
plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--')
plt.text(5.42 * np.pi, -0.1, r'$2a_1$')
plt.plot(max_1_y_time, max_1_y, 'k-')
plt.plot(max_1_y_time, max_1_y_side, 'k-')
plt.plot(min_1_y_time, min_1_y, 'k-')
plt.plot(min_1_y_time, min_1_y_side, 'k-')
plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--')
plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$')
plt.xlim(3.9 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_characteristic_wave.png')
plt.show()
# plot 6
t = np.linspace(5, 95, 100)
signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200)
util_nn = emd_utils.Utility(time=t, time_series=signal_orig)
maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()]
minima = signal_orig[util_nn.min_bool_func_1st_order_fd()]
cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima)
cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima)
time = np.linspace(0, 5 * np.pi, 1001)
lsq_signal = np.cos(time) + np.cos(5 * time)
knots = | np.linspace(0, 5 * np.pi, 101) | numpy.linspace |
'''
-------------------------------------------------------------------------------------------------
This code accompanies the paper titled "Human injury-based safety decision of automated vehicles"
Author: <NAME>, <NAME>, <NAME>, <NAME>
Corresponding author: <NAME> (<EMAIL>)
-------------------------------------------------------------------------------------------------
'''
import torch
import numpy as np
from torch import nn
from torch.nn.utils import weight_norm
__author__ = "<NAME>"
def Collision_cond(veh_striking_list, V1_v, V2_v, delta_angle, veh_param):
''' Estimate the collision condition. '''
(veh_l, veh_w, veh_cgf, veh_cgs, veh_k, veh_m) = veh_param
delta_angle_2 = np.arccos(np.abs( | np.cos(delta_angle) | numpy.cos |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = | np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) | numpy.linspace |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = | np.linspace(maxima_y[-1], minima_y[-2], 101) | numpy.linspace |
from abc import ABCMeta, abstractmethod
import os
from vmaf.tools.misc import make_absolute_path, run_process
from vmaf.tools.stats import ListStats
__copyright__ = "Copyright 2016-2018, Netflix, Inc."
__license__ = "Apache, Version 2.0"
import re
import numpy as np
import ast
from vmaf import ExternalProgramCaller, to_list
from vmaf.config import VmafConfig, VmafExternalConfig
from vmaf.core.executor import Executor
from vmaf.core.result import Result
from vmaf.tools.reader import YuvReader
class FeatureExtractor(Executor):
"""
FeatureExtractor takes in a list of assets, and run feature extraction on
them, and return a list of corresponding results. A FeatureExtractor must
specify a unique type and version combination (by the TYPE and VERSION
attribute), so that the Result generated by it can be identified.
A derived class of FeatureExtractor must:
1) Override TYPE and VERSION
2) Override _generate_result(self, asset), which call a
command-line executable and generate feature scores in a log file.
3) Override _get_feature_scores(self, asset), which read the feature
scores from the log file, and return the scores in a dictionary format.
For an example, follow VmafFeatureExtractor.
"""
__metaclass__ = ABCMeta
@property
@abstractmethod
def ATOM_FEATURES(self):
raise NotImplementedError
def _read_result(self, asset):
result = {}
result.update(self._get_feature_scores(asset))
executor_id = self.executor_id
return Result(asset, executor_id, result)
@classmethod
def get_scores_key(cls, atom_feature):
return "{type}_{atom_feature}_scores".format(
type=cls.TYPE, atom_feature=atom_feature)
@classmethod
def get_score_key(cls, atom_feature):
return "{type}_{atom_feature}_score".format(
type=cls.TYPE, atom_feature=atom_feature)
def _get_feature_scores(self, asset):
# routine to read the feature scores from the log file, and return
# the scores in a dictionary format.
log_file_path = self._get_log_file_path(asset)
atom_feature_scores_dict = {}
atom_feature_idx_dict = {}
for atom_feature in self.ATOM_FEATURES:
atom_feature_scores_dict[atom_feature] = []
atom_feature_idx_dict[atom_feature] = 0
with open(log_file_path, 'rt') as log_file:
for line in log_file.readlines():
for atom_feature in self.ATOM_FEATURES:
re_template = "{af}: ([0-9]+) ([a-zA-Z0-9.-]+)".format(af=atom_feature)
mo = re.match(re_template, line)
if mo:
cur_idx = int(mo.group(1))
assert cur_idx == atom_feature_idx_dict[atom_feature]
# parse value, allowing NaN and inf
val = float(mo.group(2))
if np.isnan(val) or np.isinf(val):
val = None
atom_feature_scores_dict[atom_feature].append(val)
atom_feature_idx_dict[atom_feature] += 1
continue
len_score = len(atom_feature_scores_dict[self.ATOM_FEATURES[0]])
assert len_score != 0
for atom_feature in self.ATOM_FEATURES[1:]:
assert len_score == len(atom_feature_scores_dict[atom_feature]), \
"Feature data possibly corrupt. Run cleanup script and try again."
feature_result = {}
for atom_feature in self.ATOM_FEATURES:
scores_key = self.get_scores_key(atom_feature)
feature_result[scores_key] = atom_feature_scores_dict[atom_feature]
return feature_result
class VmafFeatureExtractor(FeatureExtractor):
TYPE = "VMAF_feature"
# VERSION = '0.1' # vmaf_study; Anush's VIF fix
# VERSION = '0.2' # expose vif_num, vif_den, adm_num, adm_den, anpsnr
# VERSION = '0.2.1' # expose vif num/den of each scale
# VERSION = '0.2.2' # adm abs-->fabs, corrected border handling, uniform reading with option of offset for input YUV, updated VIF corner case
# VERSION = '0.2.2b' # expose adm_den/num_scalex
# VERSION = '0.2.3' # AVX for VMAF convolution; update adm features by folding noise floor into per coef
# VERSION = '0.2.4' # Fix a bug in adm feature passing scale into dwt_quant_step
# VERSION = '0.2.4b' # Modify by adding ADM noise floor outside cube root; add derived feature motion2
VERSION = '0.2.4c' # Modify by moving motion2 to c code
ATOM_FEATURES = ['vif', 'adm', 'ansnr', 'motion', 'motion2',
'vif_num', 'vif_den', 'adm_num', 'adm_den', 'anpsnr',
'vif_num_scale0', 'vif_den_scale0',
'vif_num_scale1', 'vif_den_scale1',
'vif_num_scale2', 'vif_den_scale2',
'vif_num_scale3', 'vif_den_scale3',
'adm_num_scale0', 'adm_den_scale0',
'adm_num_scale1', 'adm_den_scale1',
'adm_num_scale2', 'adm_den_scale2',
'adm_num_scale3', 'adm_den_scale3',
]
DERIVED_ATOM_FEATURES = ['vif_scale0', 'vif_scale1', 'vif_scale2', 'vif_scale3',
'vif2', 'adm2', 'adm3',
'adm_scale0', 'adm_scale1', 'adm_scale2', 'adm_scale3',
]
ADM2_CONSTANT = 0
ADM_SCALE_CONSTANT = 0
def _generate_result(self, asset):
# routine to call the command-line executable and generate feature
# scores in the log file.
quality_width, quality_height = asset.quality_width_height
log_file_path = self._get_log_file_path(asset)
yuv_type=self._get_workfile_yuv_type(asset)
ref_path=asset.ref_workfile_path
dis_path=asset.dis_workfile_path
w=quality_width
h=quality_height
logger = self.logger
ExternalProgramCaller.call_vmaf_feature(yuv_type, ref_path, dis_path, w, h, log_file_path, logger)
@classmethod
def _post_process_result(cls, result):
# override Executor._post_process_result
result = super(VmafFeatureExtractor, cls)._post_process_result(result)
# adm2 =
# (adm_num + ADM2_CONSTANT) / (adm_den + ADM2_CONSTANT)
adm2_scores_key = cls.get_scores_key('adm2')
adm_num_scores_key = cls.get_scores_key('adm_num')
adm_den_scores_key = cls.get_scores_key('adm_den')
result.result_dict[adm2_scores_key] = list(
(np.array(result.result_dict[adm_num_scores_key]) + cls.ADM2_CONSTANT) /
(np.array(result.result_dict[adm_den_scores_key]) + cls.ADM2_CONSTANT)
)
# vif_scalei = vif_num_scalei / vif_den_scalei, i = 0, 1, 2, 3
vif_num_scale0_scores_key = cls.get_scores_key('vif_num_scale0')
vif_den_scale0_scores_key = cls.get_scores_key('vif_den_scale0')
vif_num_scale1_scores_key = cls.get_scores_key('vif_num_scale1')
vif_den_scale1_scores_key = cls.get_scores_key('vif_den_scale1')
vif_num_scale2_scores_key = cls.get_scores_key('vif_num_scale2')
vif_den_scale2_scores_key = cls.get_scores_key('vif_den_scale2')
vif_num_scale3_scores_key = cls.get_scores_key('vif_num_scale3')
vif_den_scale3_scores_key = cls.get_scores_key('vif_den_scale3')
vif_scale0_scores_key = cls.get_scores_key('vif_scale0')
vif_scale1_scores_key = cls.get_scores_key('vif_scale1')
vif_scale2_scores_key = cls.get_scores_key('vif_scale2')
vif_scale3_scores_key = cls.get_scores_key('vif_scale3')
result.result_dict[vif_scale0_scores_key] = list(
(np.array(result.result_dict[vif_num_scale0_scores_key])
/ np.array(result.result_dict[vif_den_scale0_scores_key]))
)
result.result_dict[vif_scale1_scores_key] = list(
(np.array(result.result_dict[vif_num_scale1_scores_key])
/ np.array(result.result_dict[vif_den_scale1_scores_key]))
)
result.result_dict[vif_scale2_scores_key] = list(
(np.array(result.result_dict[vif_num_scale2_scores_key])
/ np.array(result.result_dict[vif_den_scale2_scores_key]))
)
result.result_dict[vif_scale3_scores_key] = list(
(np.array(result.result_dict[vif_num_scale3_scores_key])
/ np.array(result.result_dict[vif_den_scale3_scores_key]))
)
# vif2 =
# ((vif_num_scale0 / vif_den_scale0) + (vif_num_scale1 / vif_den_scale1) +
# (vif_num_scale2 / vif_den_scale2) + (vif_num_scale3 / vif_den_scale3)) / 4.0
vif_scores_key = cls.get_scores_key('vif2')
result.result_dict[vif_scores_key] = list(
(
(np.array(result.result_dict[vif_num_scale0_scores_key])
/ np.array(result.result_dict[vif_den_scale0_scores_key])) +
(np.array(result.result_dict[vif_num_scale1_scores_key])
/ np.array(result.result_dict[vif_den_scale1_scores_key])) +
(np.array(result.result_dict[vif_num_scale2_scores_key])
/ | np.array(result.result_dict[vif_den_scale2_scores_key]) | numpy.array |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
min_1_y_time = minima_x[-1] * np.ones_like(min_1_y)
dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101)
dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Characteristic Wave Effects Example')
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10))
plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10))
plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4,
label=textwrap.fill('Coughlin maximum', 14))
plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4,
label=textwrap.fill('Coughlin minimum', 14))
plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4,
label=textwrap.fill('Average maximum', 14))
plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4,
label=textwrap.fill('Average minimum', 14))
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14))
plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14))
plt.plot(max_2_x_time, max_2_x, 'k-')
plt.plot(max_2_x_time_side, max_2_x, 'k-')
plt.plot(min_2_x_time, min_2_x, 'k-')
plt.plot(min_2_x_time_side, min_2_x, 'k-')
plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--')
plt.text(5.16 * np.pi, 0.85, r'$2a_2$')
plt.plot(max_2_y_time, max_2_y, 'k-')
plt.plot(max_2_y_time, max_2_y_side, 'k-')
plt.plot(min_2_y_time, min_2_y, 'k-')
plt.plot(min_2_y_time, min_2_y_side, 'k-')
plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--')
plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$')
plt.plot(max_1_x_time, max_1_x, 'k-')
plt.plot(max_1_x_time_side, max_1_x, 'k-')
plt.plot(min_1_x_time, min_1_x, 'k-')
plt.plot(min_1_x_time_side, min_1_x, 'k-')
plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--')
plt.text(5.42 * np.pi, -0.1, r'$2a_1$')
plt.plot(max_1_y_time, max_1_y, 'k-')
plt.plot(max_1_y_time, max_1_y_side, 'k-')
plt.plot(min_1_y_time, min_1_y, 'k-')
plt.plot(min_1_y_time, min_1_y_side, 'k-')
plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--')
plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$')
plt.xlim(3.9 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_characteristic_wave.png')
plt.show()
# plot 6
t = np.linspace(5, 95, 100)
signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200)
util_nn = emd_utils.Utility(time=t, time_series=signal_orig)
maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()]
minima = signal_orig[util_nn.min_bool_func_1st_order_fd()]
cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima)
cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima)
time = np.linspace(0, 5 * np.pi, 1001)
lsq_signal = np.cos(time) + np.cos(5 * time)
knots = np.linspace(0, 5 * np.pi, 101)
time_extended = time_extension(time)
time_series_extended = np.zeros_like(time_extended) / 0
time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal
neural_network_m = 200
neural_network_k = 100
# forward ->
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))]
P[-1, col] = 1 # for additive constant
t = lsq_signal[-neural_network_m:]
# test - top
seed_weights = np.ones(neural_network_k) / neural_network_k
weights = 0 * seed_weights.copy()
train_input = P[:-1, :]
lr = 0.01
for iterations in range(1000):
output = np.matmul(weights, train_input)
error = (t - output)
gradients = error * (- train_input)
# guess average gradients
average_gradients = np.mean(gradients, axis=1)
# steepest descent
max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients)))
adjustment = - lr * average_gradients
# adjustment = - lr * max_gradient_vector
weights += adjustment
# test - bottom
weights_right = np.hstack((weights, 0))
max_count_right = 0
min_count_right = 0
i_right = 0
while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1):
time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \
sum(weights_right * np.hstack((time_series_extended[
int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right):
int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1)))
i_right += 1
if i_right > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_right += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_right += 1
# backward <-
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)]
P[-1, col] = 1 # for additive constant
t = lsq_signal[:neural_network_m]
vx = cvx.Variable(int(neural_network_k + 1))
objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary
prob = cvx.Problem(objective)
result = prob.solve(verbose=True, solver=cvx.ECOS)
weights_left = np.array(vx.value)
max_count_left = 0
min_count_left = 0
i_left = 0
while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1):
time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \
2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left):
int(len(lsq_signal) - 1 - i_left + neural_network_k)],
1))) + 1
i_left += 1
if i_left > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_left += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_left += 1
lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal)
utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended)
maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()]
maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()]
maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()]
minima_time = time[lsq_utils.min_bool_func_1st_order_fd()]
minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Single Neuron Neural Network Example')
plt.plot(time, lsq_signal, zorder=2, label='Signal')
plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12))
plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima')
plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima')
plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3,
label=textwrap.fill('Extrapolated maxima', 12))
plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4,
label=textwrap.fill('Extrapolated minima', 12))
plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k',
label=textwrap.fill('Neural network inputs', 13))
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='k')
plt.plot( | np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100) | numpy.linspace |
import numpy as np
import sys
import os
from PIL import Image
from visu.helper_functions import save_image
from scipy.spatial.transform import Rotation as R
from helper import re_quat
import copy
import torch
import numpy as np
import k3d
class Visualizer():
def __init__(self, p_visu, writer=None):
if p_visu[-1] != '/':
p_visu = p_visu + '/'
self.p_visu = p_visu
self.writer = writer
if not os.path.exists(self.p_visu):
os.makedirs(self.p_visu)
def plot_estimated_pose(self, tag, epoch, img, points, trans=[[0, 0, 0]], rot_mat=[[1, 0, 0], [0, 1, 0], [0, 0, 1]], cam_cx=0, cam_cy=0, cam_fx=0, cam_fy=0, store=False, jupyter=False, w=2):
"""
tag := tensorboard tag
epoch := tensorboard epoche
store := ture -> stores the image to standard path
path := != None creats the path and store to it path/tag.png
img:= original_image, [widht,height,RGB]
points:= points of the object model [length,x,y,z]
trans: [1,3]
rot: [3,3]
"""
img_d = copy.deepcopy(img)
points = np.dot(points, rot_mat.T)
points = | np.add(points, trans[0, :]) | numpy.add |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
min_1_y_time = minima_x[-1] * np.ones_like(min_1_y)
dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101)
dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Characteristic Wave Effects Example')
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10))
plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10))
plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4,
label=textwrap.fill('Coughlin maximum', 14))
plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4,
label=textwrap.fill('Coughlin minimum', 14))
plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4,
label=textwrap.fill('Average maximum', 14))
plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4,
label=textwrap.fill('Average minimum', 14))
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14))
plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14))
plt.plot(max_2_x_time, max_2_x, 'k-')
plt.plot(max_2_x_time_side, max_2_x, 'k-')
plt.plot(min_2_x_time, min_2_x, 'k-')
plt.plot(min_2_x_time_side, min_2_x, 'k-')
plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--')
plt.text(5.16 * np.pi, 0.85, r'$2a_2$')
plt.plot(max_2_y_time, max_2_y, 'k-')
plt.plot(max_2_y_time, max_2_y_side, 'k-')
plt.plot(min_2_y_time, min_2_y, 'k-')
plt.plot(min_2_y_time, min_2_y_side, 'k-')
plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--')
plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$')
plt.plot(max_1_x_time, max_1_x, 'k-')
plt.plot(max_1_x_time_side, max_1_x, 'k-')
plt.plot(min_1_x_time, min_1_x, 'k-')
plt.plot(min_1_x_time_side, min_1_x, 'k-')
plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--')
plt.text(5.42 * np.pi, -0.1, r'$2a_1$')
plt.plot(max_1_y_time, max_1_y, 'k-')
plt.plot(max_1_y_time, max_1_y_side, 'k-')
plt.plot(min_1_y_time, min_1_y, 'k-')
plt.plot(min_1_y_time, min_1_y_side, 'k-')
plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--')
plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$')
plt.xlim(3.9 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_characteristic_wave.png')
plt.show()
# plot 6
t = np.linspace(5, 95, 100)
signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200)
util_nn = emd_utils.Utility(time=t, time_series=signal_orig)
maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()]
minima = signal_orig[util_nn.min_bool_func_1st_order_fd()]
cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima)
cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima)
time = np.linspace(0, 5 * np.pi, 1001)
lsq_signal = np.cos(time) + np.cos(5 * time)
knots = np.linspace(0, 5 * np.pi, 101)
time_extended = time_extension(time)
time_series_extended = np.zeros_like(time_extended) / 0
time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal
neural_network_m = 200
neural_network_k = 100
# forward ->
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))]
P[-1, col] = 1 # for additive constant
t = lsq_signal[-neural_network_m:]
# test - top
seed_weights = np.ones(neural_network_k) / neural_network_k
weights = 0 * seed_weights.copy()
train_input = P[:-1, :]
lr = 0.01
for iterations in range(1000):
output = np.matmul(weights, train_input)
error = (t - output)
gradients = error * (- train_input)
# guess average gradients
average_gradients = np.mean(gradients, axis=1)
# steepest descent
max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients)))
adjustment = - lr * average_gradients
# adjustment = - lr * max_gradient_vector
weights += adjustment
# test - bottom
weights_right = np.hstack((weights, 0))
max_count_right = 0
min_count_right = 0
i_right = 0
while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1):
time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \
sum(weights_right * np.hstack((time_series_extended[
int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right):
int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1)))
i_right += 1
if i_right > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_right += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_right += 1
# backward <-
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)]
P[-1, col] = 1 # for additive constant
t = lsq_signal[:neural_network_m]
vx = cvx.Variable(int(neural_network_k + 1))
objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary
prob = cvx.Problem(objective)
result = prob.solve(verbose=True, solver=cvx.ECOS)
weights_left = np.array(vx.value)
max_count_left = 0
min_count_left = 0
i_left = 0
while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1):
time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \
2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left):
int(len(lsq_signal) - 1 - i_left + neural_network_k)],
1))) + 1
i_left += 1
if i_left > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_left += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_left += 1
lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal)
utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended)
maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()]
maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()]
maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()]
minima_time = time[lsq_utils.min_bool_func_1st_order_fd()]
minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Single Neuron Neural Network Example')
plt.plot(time, lsq_signal, zorder=2, label='Signal')
plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12))
plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima')
plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima')
plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3,
label=textwrap.fill('Extrapolated maxima', 12))
plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4,
label=textwrap.fill('Extrapolated minima', 12))
plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k',
label=textwrap.fill('Neural network inputs', 13))
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k')
plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k')
plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed',
label=textwrap.fill('Neural network targets', 13))
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray')
plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray',
linestyle='dashed')
plt.xlim(3.4 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/neural_network.png')
plt.show()
# plot 6a
np.random.seed(0)
time = np.linspace(0, 5 * np.pi, 1001)
knots_51 = np.linspace(0, 5 * np.pi, 51)
time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time)
noise = np.random.normal(0, 1, len(time_series))
time_series += noise
advemdpy = EMD(time=time, time_series=time_series)
imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_31 = np.linspace(0, 5 * np.pi, 31)
imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_11 = np.linspace(0, 5 * np.pi, 11)
imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1,
edge_effect='symmetric_anchor', verbose=False)[:3]
fig, axs = plt.subplots(3, 1)
plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40))
plt.subplots_adjust(hspace=0.1)
axs[0].plot(time, time_series, label='Time series')
axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21))
print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}')
for knot in knots_51:
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[0].set_xticklabels(['', '', '', '', '', ''])
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[1].plot(time, time_series, label='Time series')
axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19))
axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19))
print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}')
for knot in knots_31:
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[1].set_xticklabels(['', '', '', '', '', ''])
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[1].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[1].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
axs[2].plot(time, time_series, label='Time series')
axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots')
axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots')
axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots')
print(f'DFA fluctuation with 11 knots: {np.round(np.var(time_series - imfs_51[3, :]), 3)}')
for knot in knots_11:
axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[2].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[2].set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$', r'$5\pi$'])
box_2 = axs[2].get_position()
axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height])
axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[2].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[2].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
plt.savefig('jss_figures/DFA_different_trends.png')
plt.show()
# plot 6b
fig, axs = plt.subplots(3, 1)
plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences Zoomed Region', 40))
plt.subplots_adjust(hspace=0.1)
axs[0].plot(time, time_series, label='Time series')
axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21))
for knot in knots_51:
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[0].set_xticklabels(['', '', '', '', '', ''])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[0].set_ylim(-5.5, 5.5)
axs[0].set_xlim(0.95 * np.pi, 1.55 * np.pi)
axs[1].plot(time, time_series, label='Time series')
axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19))
axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19))
for knot in knots_31:
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[1].set_xticklabels(['', '', '', '', '', ''])
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[1].set_ylim(-5.5, 5.5)
axs[1].set_xlim(0.95 * np.pi, 1.55 * np.pi)
axs[2].plot(time, time_series, label='Time series')
axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots')
axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots')
axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots')
for knot in knots_11:
axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[2].set_xticks([np.pi, (3 / 2) * np.pi])
axs[2].set_xticklabels([r'$\pi$', r'$\frac{3}{2}\pi$'])
box_2 = axs[2].get_position()
axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height])
axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[2].set_ylim(-5.5, 5.5)
axs[2].set_xlim(0.95 * np.pi, 1.55 * np.pi)
plt.savefig('jss_figures/DFA_different_trends_zoomed.png')
plt.show()
hs_ouputs = hilbert_spectrum(time, imfs_51, hts_51, ifs_51, max_frequency=12, plot=False)
# plot 6c
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Simple Sinusoidal Time Seres with Added Noise', 50))
x_hs, y, z = hs_ouputs
z_min, z_max = 0, np.abs(z).max()
ax.pcolormesh(x_hs, y, np.abs(z), cmap='gist_rainbow', vmin=z_min, vmax=z_max)
ax.plot(x_hs[0, :], 8 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 8$', Linewidth=3)
ax.plot(x_hs[0, :], 4 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 4$', Linewidth=3)
ax.plot(x_hs[0, :], 2 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 2$', Linewidth=3)
ax.set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi])
ax.set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$'])
plt.ylabel(r'Frequency (rad.s$^{-1}$)')
plt.xlabel('Time (s)')
box_0 = ax.get_position()
ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.85, box_0.height * 0.9])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/DFA_hilbert_spectrum.png')
plt.show()
# plot 6c
time = np.linspace(0, 5 * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
knots = np.linspace(0, 5 * np.pi, 51)
fluc = Fluctuation(time=time, time_series=time_series)
max_unsmoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='maxima', smooth=False)
max_smoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='maxima', smooth=True)
min_unsmoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='minima', smooth=False)
min_smoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='minima', smooth=True)
util = Utility(time=time, time_series=time_series)
maxima = util.max_bool_func_1st_order_fd()
minima = util.min_bool_func_1st_order_fd()
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title(textwrap.fill('Plot Demonstrating Unsmoothed Extrema Envelopes if Schoenberg–Whitney Conditions are Not Satisfied', 50))
plt.plot(time, time_series, label='Time series', zorder=2, LineWidth=2)
plt.scatter(time[maxima], time_series[maxima], c='r', label='Maxima', zorder=10)
plt.scatter(time[minima], time_series[minima], c='b', label='Minima', zorder=10)
plt.plot(time, max_unsmoothed[0], label=textwrap.fill('Unsmoothed maxima envelope', 10), c='darkorange')
plt.plot(time, max_smoothed[0], label=textwrap.fill('Smoothed maxima envelope', 10), c='red')
plt.plot(time, min_unsmoothed[0], label=textwrap.fill('Unsmoothed minima envelope', 10), c='cyan')
plt.plot(time, min_smoothed[0], label=textwrap.fill('Smoothed minima envelope', 10), c='blue')
for knot in knots[:-1]:
plt.plot(knot * np.ones(101), np.linspace(-3.0, -2.0, 101), '--', c='grey', zorder=1)
plt.plot(knots[-1] * | np.ones(101) | numpy.ones |
# -*- coding: utf-8 -*-
"""
Created on Thu Nov 28 12:10:11 2019
@author: Omer
"""
## File handler
## This file was initially intended purely to generate the matrices for the near earth code found in: https://public.ccsds.org/Pubs/131x1o2e2s.pdf
## The values from the above pdf were copied manually to a txt file, and it is the purpose of this file to parse it.
## The emphasis here is on correctness, I currently do not see a reason to generalise this file, since matrices will be saved in either json or some matrix friendly format.
import numpy as np
from scipy.linalg import circulant
#import matplotlib.pyplot as plt
import scipy.io
import common
import hashlib
import os
projectDir = os.environ.get('LDPC')
if projectDir == None:
import pathlib
projectDir = pathlib.Path(__file__).parent.absolute()
## <NAME>: added on 01/12/2020, need to make sure this doesn't break anything.
import sys
sys.path.insert(1, projectDir)
FILE_HANDLER_INT_DATA_TYPE = np.int32
GENERAL_CODE_MATRIX_DATA_TYPE = np.int32
NIBBLE_CONVERTER = np.array([8, 4, 2, 1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
def nibbleToHex(inputArray):
n = NIBBLE_CONVERTER.dot(inputArray)
if n == 10:
h = 'A'
elif n== 11:
h = 'B'
elif n== 12:
h = 'C'
elif n== 13:
h = 'D'
elif n== 14:
h = 'E'
elif n== 15:
h = 'F'
else:
h = str(n)
return h
def binaryArraytoHex(inputArray):
d1 = len(inputArray)
assert (d1 % 4 == 0)
outputArray = np.zeros(d1//4, dtype = str)
outputString = ''
for j in range(d1//4):
nibble = inputArray[4 * j : 4 * j + 4]
h = nibbleToHex(nibble)
outputArray[j] = h
outputString = outputString + h
return outputArray, outputString
def hexStringToBinaryArray(hexString):
outputBinary = np.array([], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
for i in hexString:
if i == '0':
nibble = np.array([0,0,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '1':
nibble = np.array([0,0,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '2':
nibble = np.array([0,0,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '3':
nibble = np.array([0,0,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '4':
nibble = np.array([0,1,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '5':
nibble = np.array([0,1,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '6':
nibble = np.array([0,1,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '7':
nibble = np.array([0,1,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '8':
nibble = np.array([1,0,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '9':
nibble = np.array([1,0,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == 'A':
nibble = np.array([1,0,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == 'B':
nibble = np.array([1,0,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == 'C':
nibble = np.array([1,1,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == 'D':
nibble = np.array([1,1,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == 'E':
nibble = np.array([1,1,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == 'F':
nibble = np.array([1,1,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
else:
#print('Error, 0-9 or A-F')
pass
nibble = np.array([], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
outputBinary = np.hstack((outputBinary, nibble))
return outputBinary
def hexToCirculant(hexStr, circulantSize):
binaryArray = hexStringToBinaryArray(hexStr)
if len(binaryArray) < circulantSize:
binaryArray = np.hstack(np.zeros(circulantSize-len(binaryArray), dtype = GENERAL_CODE_MATRIX_DATA_TYPE))
else:
binaryArray = binaryArray[1:]
circulantMatrix = circulant(binaryArray)
circulantMatrix = circulantMatrix.T
return circulantMatrix
def hotLocationsToCirculant(locationList, circulantSize):
generatingVector = np.zeros(circulantSize, dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
generatingVector[locationList] = 1
newCirculant = circulant(generatingVector)
newCirculant = newCirculant.T
return newCirculant
def readMatrixFromFile(fileName, dim0, dim1, circulantSize, isRow = True, isHex = True, isGenerator = True ):
# This function assumes that each line in the file contains the non zero locations of the first row of a circulant.
# Each line in the file then defines a circulant, and the order in which they are defined is top to bottom left to right, i.e.:
# line 0 defines circulant 0,0
with open(fileName) as fid:
lines = fid.readlines()
if isGenerator:
for i in range((dim0 // circulantSize) ):
bLeft = hexToCirculant(lines[2 * i], circulantSize)
bRight = hexToCirculant(lines[2 * i + 1], circulantSize)
newBlock = np.hstack((bLeft, bRight))
if i == 0:
accumulatedBlock = newBlock
else:
accumulatedBlock = np.vstack((accumulatedBlock, newBlock))
newMatrix = np.hstack((np.eye(dim0, dtype = GENERAL_CODE_MATRIX_DATA_TYPE), accumulatedBlock))
else:
for i in range((dim1 // circulantSize)):
locationList1 = list(lines[ i].rstrip('\n').split(','))
locationList1 = list(map(int, locationList1))
upBlock = hotLocationsToCirculant(locationList1, circulantSize)
if i == 0:
accumulatedUpBlock1 = upBlock
else:
accumulatedUpBlock1 = np.hstack((accumulatedUpBlock1, upBlock))
for i in range((dim1 // circulantSize)):
locationList = list(lines[(dim1 // circulantSize) + i].rstrip('\n').split(','))
locationList = list(map(int, locationList))
newBlock = hotLocationsToCirculant(locationList, circulantSize)
if i == 0:
accumulatedBlock2 = newBlock
else:
accumulatedBlock2 = | np.hstack((accumulatedBlock2, newBlock)) | numpy.hstack |
# coding: utf-8
# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Test the Logarithmic Units and Quantities
"""
from __future__ import (absolute_import, unicode_literals, division,
print_function)
from ...extern import six
from ...extern.six.moves import zip
import pickle
import itertools
import pytest
import numpy as np
from numpy.testing.utils import assert_allclose
from ...tests.helper import assert_quantity_allclose
from ... import units as u, constants as c
lu_units = [u.dex, u.mag, u.decibel]
lu_subclasses = [u.DexUnit, u.MagUnit, u.DecibelUnit]
lq_subclasses = [u.Dex, u.Magnitude, u.Decibel]
pu_sample = (u.dimensionless_unscaled, u.m, u.g/u.s**2, u.Jy)
class TestLogUnitCreation(object):
def test_logarithmic_units(self):
"""Check logarithmic units are set up correctly."""
assert u.dB.to(u.dex) == 0.1
assert u.dex.to(u.mag) == -2.5
assert u.mag.to(u.dB) == -4
@pytest.mark.parametrize('lu_unit, lu_cls', zip(lu_units, lu_subclasses))
def test_callable_units(self, lu_unit, lu_cls):
assert isinstance(lu_unit, u.UnitBase)
assert callable(lu_unit)
assert lu_unit._function_unit_class is lu_cls
@pytest.mark.parametrize('lu_unit', lu_units)
def test_equality_to_normal_unit_for_dimensionless(self, lu_unit):
lu = lu_unit()
assert lu == lu._default_function_unit # eg, MagUnit() == u.mag
assert lu._default_function_unit == lu # and u.mag == MagUnit()
@pytest.mark.parametrize('lu_unit, physical_unit',
itertools.product(lu_units, pu_sample))
def test_call_units(self, lu_unit, physical_unit):
"""Create a LogUnit subclass using the callable unit and physical unit,
and do basic check that output is right."""
lu1 = lu_unit(physical_unit)
assert lu1.physical_unit == physical_unit
assert lu1.function_unit == lu1._default_function_unit
def test_call_invalid_unit(self):
with pytest.raises(TypeError):
u.mag([])
with pytest.raises(ValueError):
u.mag(u.mag())
@pytest.mark.parametrize('lu_cls, physical_unit', itertools.product(
lu_subclasses + [u.LogUnit], pu_sample))
def test_subclass_creation(self, lu_cls, physical_unit):
"""Create a LogUnit subclass object for given physical unit,
and do basic check that output is right."""
lu1 = lu_cls(physical_unit)
assert lu1.physical_unit == physical_unit
assert lu1.function_unit == lu1._default_function_unit
lu2 = lu_cls(physical_unit,
function_unit=2*lu1._default_function_unit)
assert lu2.physical_unit == physical_unit
assert lu2.function_unit == u.Unit(2*lu2._default_function_unit)
with pytest.raises(ValueError):
lu_cls(physical_unit, u.m)
def test_predefined_magnitudes():
assert_quantity_allclose((-21.1*u.STmag).physical,
1.*u.erg/u.cm**2/u.s/u.AA)
assert_quantity_allclose((-48.6*u.ABmag).physical,
1.*u.erg/u.cm**2/u.s/u.Hz)
assert_quantity_allclose((0*u.M_bol).physical, c.L_bol0)
assert_quantity_allclose((0*u.m_bol).physical,
c.L_bol0/(4.*np.pi*(10.*c.pc)**2))
def test_predefined_reinitialisation():
assert u.mag('ST') == u.STmag
assert u.mag('AB') == u.ABmag
assert u.mag('Bol') == u.M_bol
assert u.mag('bol') == u.m_bol
def test_predefined_string_roundtrip():
"""Ensure roundtripping; see #5015"""
with u.magnitude_zero_points.enable():
assert u.Unit(u.STmag.to_string()) == u.STmag
assert u.Unit(u.ABmag.to_string()) == u.ABmag
assert u.Unit(u.M_bol.to_string()) == u.M_bol
assert u.Unit(u.m_bol.to_string()) == u.m_bol
def test_inequality():
"""Check __ne__ works (regresssion for #5342)."""
lu1 = u.mag(u.Jy)
lu2 = u.dex(u.Jy)
lu3 = u.mag(u.Jy**2)
lu4 = lu3 - lu1
assert lu1 != lu2
assert lu1 != lu3
assert lu1 == lu4
class TestLogUnitStrings(object):
def test_str(self):
"""Do some spot checks that str, repr, etc. work as expected."""
lu1 = u.mag(u.Jy)
assert str(lu1) == 'mag(Jy)'
assert repr(lu1) == 'Unit("mag(Jy)")'
assert lu1.to_string('generic') == 'mag(Jy)'
with pytest.raises(ValueError):
lu1.to_string('fits')
lu2 = u.dex()
assert str(lu2) == 'dex'
assert repr(lu2) == 'Unit("dex(1)")'
assert lu2.to_string() == 'dex(1)'
lu3 = u.MagUnit(u.Jy, function_unit=2*u.mag)
assert str(lu3) == '2 mag(Jy)'
assert repr(lu3) == 'MagUnit("Jy", unit="2 mag")'
assert lu3.to_string() == '2 mag(Jy)'
lu4 = u.mag(u.ct)
assert lu4.to_string('generic') == 'mag(ct)'
assert lu4.to_string('latex') == ('$\\mathrm{mag}$$\\mathrm{\\left( '
'\\mathrm{ct} \\right)}$')
assert lu4._repr_latex_() == lu4.to_string('latex')
class TestLogUnitConversion(object):
@pytest.mark.parametrize('lu_unit, physical_unit',
itertools.product(lu_units, pu_sample))
def test_physical_unit_conversion(self, lu_unit, physical_unit):
"""Check various LogUnit subclasses are equivalent and convertible
to their non-log counterparts."""
lu1 = lu_unit(physical_unit)
assert lu1.is_equivalent(physical_unit)
assert lu1.to(physical_unit, 0.) == 1.
assert physical_unit.is_equivalent(lu1)
assert physical_unit.to(lu1, 1.) == 0.
pu = u.Unit(8.*physical_unit)
assert lu1.is_equivalent(physical_unit)
assert lu1.to(pu, 0.) == 0.125
assert pu.is_equivalent(lu1)
assert_allclose(pu.to(lu1, 0.125), 0., atol=1.e-15)
# Check we round-trip.
value = np.linspace(0., 10., 6)
assert_allclose(pu.to(lu1, lu1.to(pu, value)), value, atol=1.e-15)
# And that we're not just returning True all the time.
pu2 = u.g
assert not lu1.is_equivalent(pu2)
with pytest.raises(u.UnitsError):
lu1.to(pu2)
assert not pu2.is_equivalent(lu1)
with pytest.raises(u.UnitsError):
pu2.to(lu1)
@pytest.mark.parametrize('lu_unit', lu_units)
def test_container_unit_conversion(self, lu_unit):
"""Check that conversion to logarithmic units (u.mag, u.dB, u.dex)
is only possible when the physical unit is dimensionless."""
values = np.linspace(0., 10., 6)
lu1 = lu_unit(u.dimensionless_unscaled)
assert lu1.is_equivalent(lu1.function_unit)
assert_allclose(lu1.to(lu1.function_unit, values), values)
lu2 = lu_unit(u.Jy)
assert not lu2.is_equivalent(lu2.function_unit)
with pytest.raises(u.UnitsError):
lu2.to(lu2.function_unit, values)
@pytest.mark.parametrize(
'flu_unit, tlu_unit, physical_unit',
itertools.product(lu_units, lu_units, pu_sample))
def test_subclass_conversion(self, flu_unit, tlu_unit, physical_unit):
"""Check various LogUnit subclasses are equivalent and convertible
to each other if they correspond to equivalent physical units."""
values = np.linspace(0., 10., 6)
flu = flu_unit(physical_unit)
tlu = tlu_unit(physical_unit)
assert flu.is_equivalent(tlu)
assert_allclose(flu.to(tlu), flu.function_unit.to(tlu.function_unit))
assert_allclose(flu.to(tlu, values),
values * flu.function_unit.to(tlu.function_unit))
tlu2 = tlu_unit(u.Unit(100.*physical_unit))
assert flu.is_equivalent(tlu2)
# Check that we round-trip.
assert_allclose(flu.to(tlu2, tlu2.to(flu, values)), values, atol=1.e-15)
tlu3 = tlu_unit(physical_unit.to_system(u.si)[0])
assert flu.is_equivalent(tlu3)
assert_allclose(flu.to(tlu3, tlu3.to(flu, values)), values, atol=1.e-15)
tlu4 = tlu_unit(u.g)
assert not flu.is_equivalent(tlu4)
with pytest.raises(u.UnitsError):
flu.to(tlu4, values)
def test_unit_decomposition(self):
lu = u.mag(u.Jy)
assert lu.decompose() == u.mag(u.Jy.decompose())
assert lu.decompose().physical_unit.bases == [u.kg, u.s]
assert lu.si == u.mag(u.Jy.si)
assert lu.si.physical_unit.bases == [u.kg, u.s]
assert lu.cgs == u.mag(u.Jy.cgs)
assert lu.cgs.physical_unit.bases == [u.g, u.s]
def test_unit_multiple_possible_equivalencies(self):
lu = u.mag(u.Jy)
assert lu.is_equivalent(pu_sample)
class TestLogUnitArithmetic(object):
def test_multiplication_division(self):
"""Check that multiplication/division with other units is only
possible when the physical unit is dimensionless, and that this
turns the unit into a normal one."""
lu1 = u.mag(u.Jy)
with pytest.raises(u.UnitsError):
lu1 * u.m
with pytest.raises(u.UnitsError):
u.m * lu1
with pytest.raises(u.UnitsError):
lu1 / lu1
for unit in (u.dimensionless_unscaled, u.m, u.mag, u.dex):
with pytest.raises(u.UnitsError):
lu1 / unit
lu2 = u.mag(u.dimensionless_unscaled)
with pytest.raises(u.UnitsError):
lu2 * lu1
with pytest.raises(u.UnitsError):
lu2 / lu1
# But dimensionless_unscaled can be cancelled.
assert lu2 / lu2 == u.dimensionless_unscaled
# With dimensionless, normal units are OK, but we return a plain unit.
tf = lu2 * u.m
tr = u.m * lu2
for t in (tf, tr):
assert not isinstance(t, type(lu2))
assert t == lu2.function_unit * u.m
with u.set_enabled_equivalencies(u.logarithmic()):
with pytest.raises(u.UnitsError):
t.to(lu2.physical_unit)
# Now we essentially have a LogUnit with a prefactor of 100,
# so should be equivalent again.
t = tf / u.cm
with u.set_enabled_equivalencies(u.logarithmic()):
assert t.is_equivalent(lu2.function_unit)
assert_allclose(t.to(u.dimensionless_unscaled, np.arange(3.)/100.),
lu2.to(lu2.physical_unit, np.arange(3.)))
# If we effectively remove lu1, a normal unit should be returned.
t2 = tf / lu2
assert not isinstance(t2, type(lu2))
assert t2 == u.m
t3 = tf / lu2.function_unit
assert not isinstance(t3, type(lu2))
assert t3 == u.m
# For completeness, also ensure non-sensical operations fail
with pytest.raises(TypeError):
lu1 * object()
with pytest.raises(TypeError):
slice(None) * lu1
with pytest.raises(TypeError):
lu1 / []
with pytest.raises(TypeError):
1 / lu1
@pytest.mark.parametrize('power', (2, 0.5, 1, 0))
def test_raise_to_power(self, power):
"""Check that raising LogUnits to some power is only possible when the
physical unit is dimensionless, and that conversion is turned off when
the resulting logarithmic unit (such as mag**2) is incompatible."""
lu1 = u.mag(u.Jy)
if power == 0:
assert lu1 ** power == u.dimensionless_unscaled
elif power == 1:
assert lu1 ** power == lu1
else:
with pytest.raises(u.UnitsError):
lu1 ** power
# With dimensionless, though, it works, but returns a normal unit.
lu2 = u.mag(u.dimensionless_unscaled)
t = lu2**power
if power == 0:
assert t == u.dimensionless_unscaled
elif power == 1:
assert t == lu2
else:
assert not isinstance(t, type(lu2))
assert t == lu2.function_unit**power
# also check we roundtrip
t2 = t**(1./power)
assert t2 == lu2.function_unit
with u.set_enabled_equivalencies(u.logarithmic()):
assert_allclose(t2.to(u.dimensionless_unscaled, np.arange(3.)),
lu2.to(lu2.physical_unit, np.arange(3.)))
@pytest.mark.parametrize('other', pu_sample)
def test_addition_subtraction_to_normal_units_fails(self, other):
lu1 = u.mag(u.Jy)
with pytest.raises(u.UnitsError):
lu1 + other
with pytest.raises(u.UnitsError):
lu1 - other
with pytest.raises(u.UnitsError):
other - lu1
def test_addition_subtraction_to_non_units_fails(self):
lu1 = u.mag(u.Jy)
with pytest.raises(TypeError):
lu1 + 1.
with pytest.raises(TypeError):
lu1 - [1., 2., 3.]
@pytest.mark.parametrize(
'other', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m),
u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag)))
def test_addition_subtraction(self, other):
"""Check physical units are changed appropriately"""
lu1 = u.mag(u.Jy)
other_pu = getattr(other, 'physical_unit', u.dimensionless_unscaled)
lu_sf = lu1 + other
assert lu_sf.is_equivalent(lu1.physical_unit * other_pu)
lu_sr = other + lu1
assert lu_sr.is_equivalent(lu1.physical_unit * other_pu)
lu_df = lu1 - other
assert lu_df.is_equivalent(lu1.physical_unit / other_pu)
lu_dr = other - lu1
assert lu_dr.is_equivalent(other_pu / lu1.physical_unit)
def test_complicated_addition_subtraction(self):
"""for fun, a more complicated example of addition and subtraction"""
dm0 = u.Unit('DM', 1./(4.*np.pi*(10.*u.pc)**2))
lu_dm = u.mag(dm0)
lu_absST = u.STmag - lu_dm
assert lu_absST.is_equivalent(u.erg/u.s/u.AA)
def test_neg_pos(self):
lu1 = u.mag(u.Jy)
neg_lu = -lu1
assert neg_lu != lu1
assert neg_lu.physical_unit == u.Jy**-1
assert -neg_lu == lu1
pos_lu = +lu1
assert pos_lu is not lu1
assert pos_lu == lu1
def test_pickle():
lu1 = u.dex(u.cm/u.s**2)
s = pickle.dumps(lu1)
lu2 = pickle.loads(s)
assert lu1 == lu2
def test_hashable():
lu1 = u.dB(u.mW)
lu2 = u.dB(u.m)
lu3 = u.dB(u.mW)
assert hash(lu1) != hash(lu2)
assert hash(lu1) == hash(lu3)
luset = {lu1, lu2, lu3}
assert len(luset) == 2
class TestLogQuantityCreation(object):
@pytest.mark.parametrize('lq, lu', zip(lq_subclasses + [u.LogQuantity],
lu_subclasses + [u.LogUnit]))
def test_logarithmic_quantities(self, lq, lu):
"""Check logarithmic quantities are all set up correctly"""
assert lq._unit_class == lu
assert type(lu()._quantity_class(1.)) is lq
@pytest.mark.parametrize('lq_cls, physical_unit',
itertools.product(lq_subclasses, pu_sample))
def test_subclass_creation(self, lq_cls, physical_unit):
"""Create LogQuantity subclass objects for some physical units,
and basic check on transformations"""
value = np.arange(1., 10.)
log_q = lq_cls(value * physical_unit)
assert log_q.unit.physical_unit == physical_unit
assert log_q.unit.function_unit == log_q.unit._default_function_unit
assert_allclose(log_q.physical.value, value)
with pytest.raises(ValueError):
lq_cls(value, physical_unit)
@pytest.mark.parametrize(
'unit', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m),
u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag),
u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag)))
def test_different_units(self, unit):
q = u.Magnitude(1.23, unit)
assert q.unit.function_unit == getattr(unit, 'function_unit', unit)
assert q.unit.physical_unit is getattr(unit, 'physical_unit',
u.dimensionless_unscaled)
@pytest.mark.parametrize('value, unit', (
(1.*u.mag(u.Jy), None),
(1.*u.dex(u.Jy), None),
(1.*u.mag(u.W/u.m**2/u.Hz), u.mag(u.Jy)),
(1.*u.dex(u.W/u.m**2/u.Hz), u.mag(u.Jy))))
def test_function_values(self, value, unit):
lq = u.Magnitude(value, unit)
assert lq == value
assert lq.unit.function_unit == u.mag
assert lq.unit.physical_unit == getattr(unit, 'physical_unit',
value.unit.physical_unit)
@pytest.mark.parametrize(
'unit', (u.mag(), u.mag(u.Jy), u.mag(u.m), u.MagUnit('', 2.*u.mag),
u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag)))
def test_indirect_creation(self, unit):
q1 = 2.5 * unit
assert isinstance(q1, u.Magnitude)
assert q1.value == 2.5
assert q1.unit == unit
pv = 100. * unit.physical_unit
q2 = unit * pv
assert q2.unit == unit
assert q2.unit.physical_unit == pv.unit
assert q2.to_value(unit.physical_unit) == 100.
assert (q2._function_view / u.mag).to_value(1) == -5.
q3 = unit / 0.4
assert q3 == q1
def test_from_view(self):
# Cannot view a physical quantity as a function quantity, since the
# values would change.
q = [100., 1000.] * u.cm/u.s**2
with pytest.raises(TypeError):
q.view(u.Dex)
# But fine if we have the right magnitude.
q = [2., 3.] * u.dex
lq = q.view(u.Dex)
assert isinstance(lq, u.Dex)
assert lq.unit.physical_unit == u.dimensionless_unscaled
assert np.all(q == lq)
def test_using_quantity_class(self):
"""Check that we can use Quantity if we have subok=True"""
# following issue #5851
lu = u.dex(u.AA)
with pytest.raises(u.UnitTypeError):
u.Quantity(1., lu)
q = u.Quantity(1., lu, subok=True)
assert type(q) is lu._quantity_class
def test_conversion_to_and_from_physical_quantities():
"""Ensures we can convert from regular quantities."""
mst = [10., 12., 14.] * u.STmag
flux_lambda = mst.physical
mst_roundtrip = flux_lambda.to(u.STmag)
# check we return a logquantity; see #5178.
assert isinstance(mst_roundtrip, u.Magnitude)
assert mst_roundtrip.unit == mst.unit
assert_allclose(mst_roundtrip.value, mst.value)
wave = [4956.8, 4959.55, 4962.3] * u.AA
flux_nu = mst.to(u.Jy, equivalencies=u.spectral_density(wave))
mst_roundtrip2 = flux_nu.to(u.STmag, u.spectral_density(wave))
assert isinstance(mst_roundtrip2, u.Magnitude)
assert mst_roundtrip2.unit == mst.unit
assert_allclose(mst_roundtrip2.value, mst.value)
def test_quantity_decomposition():
lq = 10.*u.mag(u.Jy)
assert lq.decompose() == lq
assert lq.decompose().unit.physical_unit.bases == [u.kg, u.s]
assert lq.si == lq
assert lq.si.unit.physical_unit.bases == [u.kg, u.s]
assert lq.cgs == lq
assert lq.cgs.unit.physical_unit.bases == [u.g, u.s]
class TestLogQuantityViews(object):
def setup(self):
self.lq = u.Magnitude(np.arange(10.) * u.Jy)
self.lq2 = u.Magnitude(np.arange(5.))
def test_value_view(self):
lq_value = self.lq.value
assert type(lq_value) is np.ndarray
lq_value[2] = -1.
assert np.all(self.lq.value == lq_value)
def test_function_view(self):
lq_fv = self.lq._function_view
assert type(lq_fv) is u.Quantity
assert lq_fv.unit is self.lq.unit.function_unit
lq_fv[3] = -2. * lq_fv.unit
assert np.all(self.lq.value == lq_fv.value)
def test_quantity_view(self):
# Cannot view as Quantity, since the unit cannot be represented.
with pytest.raises(TypeError):
self.lq.view(u.Quantity)
# But a dimensionless one is fine.
q2 = self.lq2.view(u.Quantity)
assert q2.unit is u.mag
assert np.all(q2.value == self.lq2.value)
lq3 = q2.view(u.Magnitude)
assert type(lq3.unit) is u.MagUnit
assert lq3.unit.physical_unit == u.dimensionless_unscaled
assert np.all(lq3 == self.lq2)
class TestLogQuantitySlicing(object):
def test_item_get_and_set(self):
lq1 = u.Magnitude(np.arange(1., 11.)*u.Jy)
assert lq1[9] == u.Magnitude(10.*u.Jy)
lq1[2] = 100.*u.Jy
assert lq1[2] == u.Magnitude(100.*u.Jy)
with pytest.raises(u.UnitsError):
lq1[2] = 100.*u.m
with pytest.raises(u.UnitsError):
lq1[2] = 100.*u.mag
with pytest.raises(u.UnitsError):
lq1[2] = u.Magnitude(100.*u.m)
assert lq1[2] == u.Magnitude(100.*u.Jy)
def test_slice_get_and_set(self):
lq1 = u.Magnitude(np.arange(1., 10.)*u.Jy)
lq1[2:4] = 100.*u.Jy
assert np.all(lq1[2:4] == u.Magnitude(100.*u.Jy))
with pytest.raises(u.UnitsError):
lq1[2:4] = 100.*u.m
with pytest.raises(u.UnitsError):
lq1[2:4] = 100.*u.mag
with pytest.raises(u.UnitsError):
lq1[2:4] = u.Magnitude(100.*u.m)
assert np.all(lq1[2] == u.Magnitude(100.*u.Jy))
class TestLogQuantityArithmetic(object):
def test_multiplication_division(self):
"""Check that multiplication/division with other quantities is only
possible when the physical unit is dimensionless, and that this turns
the result into a normal quantity."""
lq = u.Magnitude(np.arange(1., 11.)*u.Jy)
with pytest.raises(u.UnitsError):
lq * (1.*u.m)
with pytest.raises(u.UnitsError):
(1.*u.m) * lq
with pytest.raises(u.UnitsError):
lq / lq
for unit in (u.m, u.mag, u.dex):
with pytest.raises(u.UnitsError):
lq / unit
lq2 = u.Magnitude(np.arange(1, 11.))
with pytest.raises(u.UnitsError):
lq2 * lq
with pytest.raises(u.UnitsError):
lq2 / lq
with pytest.raises(u.UnitsError):
lq / lq2
# but dimensionless_unscaled can be cancelled
r = lq2 / u.Magnitude(2.)
assert r.unit == u.dimensionless_unscaled
assert np.all(r.value == lq2.value/2.)
# with dimensionless, normal units OK, but return normal quantities
tf = lq2 * u.m
tr = u.m * lq2
for t in (tf, tr):
assert not isinstance(t, type(lq2))
assert t.unit == lq2.unit.function_unit * u.m
with u.set_enabled_equivalencies(u.logarithmic()):
with pytest.raises(u.UnitsError):
t.to(lq2.unit.physical_unit)
t = tf / (50.*u.cm)
# now we essentially have the same quantity but with a prefactor of 2
assert t.unit.is_equivalent(lq2.unit.function_unit)
assert_allclose(t.to(lq2.unit.function_unit), lq2._function_view*2)
@pytest.mark.parametrize('power', (2, 0.5, 1, 0))
def test_raise_to_power(self, power):
"""Check that raising LogQuantities to some power is only possible when
the physical unit is dimensionless, and that conversion is turned off
when the resulting logarithmic unit (say, mag**2) is incompatible."""
lq = u.Magnitude(np.arange(1., 4.)*u.Jy)
if power == 0:
assert np.all(lq ** power == 1.)
elif power == 1:
assert np.all(lq ** power == lq)
else:
with pytest.raises(u.UnitsError):
lq ** power
# with dimensionless, it works, but falls back to normal quantity
# (except for power=1)
lq2 = u.Magnitude(np.arange(10.))
t = lq2**power
if power == 0:
assert t.unit is u.dimensionless_unscaled
assert np.all(t.value == 1.)
elif power == 1:
assert np.all(t == lq2)
else:
assert not isinstance(t, type(lq2))
assert t.unit == lq2.unit.function_unit ** power
with u.set_enabled_equivalencies(u.logarithmic()):
with pytest.raises(u.UnitsError):
t.to(u.dimensionless_unscaled)
def test_error_on_lq_as_power(self):
lq = u.Magnitude(np.arange(1., 4.)*u.Jy)
with pytest.raises(TypeError):
lq ** lq
@pytest.mark.parametrize('other', pu_sample)
def test_addition_subtraction_to_normal_units_fails(self, other):
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
q = 1.23 * other
with pytest.raises(u.UnitsError):
lq + q
with pytest.raises(u.UnitsError):
lq - q
with pytest.raises(u.UnitsError):
q - lq
@pytest.mark.parametrize(
'other', (1.23 * u.mag, 2.34 * u.mag(),
u.Magnitude(3.45 * u.Jy), u.Magnitude(4.56 * u.m),
5.67 * u.Unit(2*u.mag), u.Magnitude(6.78, 2.*u.mag)))
def test_addition_subtraction(self, other):
"""Check that addition/subtraction with quantities with magnitude or
MagUnit units works, and that it changes the physical units
appropriately."""
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
other_physical = other.to(getattr(other.unit, 'physical_unit',
u.dimensionless_unscaled),
equivalencies=u.logarithmic())
lq_sf = lq + other
assert_allclose(lq_sf.physical, lq.physical * other_physical)
lq_sr = other + lq
assert_allclose(lq_sr.physical, lq.physical * other_physical)
lq_df = lq - other
assert_allclose(lq_df.physical, lq.physical / other_physical)
lq_dr = other - lq
| assert_allclose(lq_dr.physical, other_physical / lq.physical) | numpy.testing.utils.assert_allclose |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * | np.ones_like(anti_symmetric_time) | numpy.ones_like |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
min_1_y_time = minima_x[-1] * np.ones_like(min_1_y)
dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101)
dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Characteristic Wave Effects Example')
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10))
plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10))
plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4,
label=textwrap.fill('Coughlin maximum', 14))
plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4,
label=textwrap.fill('Coughlin minimum', 14))
plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4,
label=textwrap.fill('Average maximum', 14))
plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4,
label=textwrap.fill('Average minimum', 14))
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14))
plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14))
plt.plot(max_2_x_time, max_2_x, 'k-')
plt.plot(max_2_x_time_side, max_2_x, 'k-')
plt.plot(min_2_x_time, min_2_x, 'k-')
plt.plot(min_2_x_time_side, min_2_x, 'k-')
plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--')
plt.text(5.16 * np.pi, 0.85, r'$2a_2$')
plt.plot(max_2_y_time, max_2_y, 'k-')
plt.plot(max_2_y_time, max_2_y_side, 'k-')
plt.plot(min_2_y_time, min_2_y, 'k-')
plt.plot(min_2_y_time, min_2_y_side, 'k-')
plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--')
plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$')
plt.plot(max_1_x_time, max_1_x, 'k-')
plt.plot(max_1_x_time_side, max_1_x, 'k-')
plt.plot(min_1_x_time, min_1_x, 'k-')
plt.plot(min_1_x_time_side, min_1_x, 'k-')
plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--')
plt.text(5.42 * np.pi, -0.1, r'$2a_1$')
plt.plot(max_1_y_time, max_1_y, 'k-')
plt.plot(max_1_y_time, max_1_y_side, 'k-')
plt.plot(min_1_y_time, min_1_y, 'k-')
plt.plot(min_1_y_time, min_1_y_side, 'k-')
plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--')
plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$')
plt.xlim(3.9 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_characteristic_wave.png')
plt.show()
# plot 6
t = np.linspace(5, 95, 100)
signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200)
util_nn = emd_utils.Utility(time=t, time_series=signal_orig)
maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()]
minima = signal_orig[util_nn.min_bool_func_1st_order_fd()]
cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima)
cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima)
time = np.linspace(0, 5 * np.pi, 1001)
lsq_signal = np.cos(time) + np.cos(5 * time)
knots = np.linspace(0, 5 * np.pi, 101)
time_extended = time_extension(time)
time_series_extended = np.zeros_like(time_extended) / 0
time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal
neural_network_m = 200
neural_network_k = 100
# forward ->
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))]
P[-1, col] = 1 # for additive constant
t = lsq_signal[-neural_network_m:]
# test - top
seed_weights = np.ones(neural_network_k) / neural_network_k
weights = 0 * seed_weights.copy()
train_input = P[:-1, :]
lr = 0.01
for iterations in range(1000):
output = np.matmul(weights, train_input)
error = (t - output)
gradients = error * (- train_input)
# guess average gradients
average_gradients = np.mean(gradients, axis=1)
# steepest descent
max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients)))
adjustment = - lr * average_gradients
# adjustment = - lr * max_gradient_vector
weights += adjustment
# test - bottom
weights_right = np.hstack((weights, 0))
max_count_right = 0
min_count_right = 0
i_right = 0
while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1):
time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \
sum(weights_right * np.hstack((time_series_extended[
int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right):
int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1)))
i_right += 1
if i_right > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_right += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_right += 1
# backward <-
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)]
P[-1, col] = 1 # for additive constant
t = lsq_signal[:neural_network_m]
vx = cvx.Variable(int(neural_network_k + 1))
objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary
prob = cvx.Problem(objective)
result = prob.solve(verbose=True, solver=cvx.ECOS)
weights_left = np.array(vx.value)
max_count_left = 0
min_count_left = 0
i_left = 0
while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1):
time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \
2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left):
int(len(lsq_signal) - 1 - i_left + neural_network_k)],
1))) + 1
i_left += 1
if i_left > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_left += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_left += 1
lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal)
utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended)
maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()]
maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()]
maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()]
minima_time = time[lsq_utils.min_bool_func_1st_order_fd()]
minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Single Neuron Neural Network Example')
plt.plot(time, lsq_signal, zorder=2, label='Signal')
plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12))
plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima')
plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima')
plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3,
label=textwrap.fill('Extrapolated maxima', 12))
plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4,
label=textwrap.fill('Extrapolated minima', 12))
plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k',
label=textwrap.fill('Neural network inputs', 13))
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k')
plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k')
plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed',
label=textwrap.fill('Neural network targets', 13))
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray')
plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray',
linestyle='dashed')
plt.xlim(3.4 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/neural_network.png')
plt.show()
# plot 6a
np.random.seed(0)
time = np.linspace(0, 5 * np.pi, 1001)
knots_51 = np.linspace(0, 5 * np.pi, 51)
time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time)
noise = np.random.normal(0, 1, len(time_series))
time_series += noise
advemdpy = EMD(time=time, time_series=time_series)
imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_31 = np.linspace(0, 5 * np.pi, 31)
imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_11 = np.linspace(0, 5 * np.pi, 11)
imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1,
edge_effect='symmetric_anchor', verbose=False)[:3]
fig, axs = plt.subplots(3, 1)
plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40))
plt.subplots_adjust(hspace=0.1)
axs[0].plot(time, time_series, label='Time series')
axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21))
print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}')
for knot in knots_51:
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[0].set_xticklabels(['', '', '', '', '', ''])
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[1].plot(time, time_series, label='Time series')
axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19))
axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19))
print(f'DFA fluctuation with 31 knots: {np.round( | np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])) | numpy.var |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * | np.ones(100) | numpy.ones |
import numpy as np
from typing import Tuple, Union, Optional
from autoarray.structures.arrays.two_d import array_2d_util
from autoarray.geometry import geometry_util
from autoarray import numba_util
from autoarray.mask import mask_2d_util
@numba_util.jit()
def grid_2d_centre_from(grid_2d_slim: np.ndarray) -> Tuple[float, float]:
"""
Returns the centre of a grid from a 1D grid.
Parameters
----------
grid_2d_slim
The 1D grid of values which are mapped to a 2D array.
Returns
-------
(float, float)
The (y,x) central coordinates of the grid.
"""
centre_y = (np.max(grid_2d_slim[:, 0]) + np.min(grid_2d_slim[:, 0])) / 2.0
centre_x = (np.max(grid_2d_slim[:, 1]) + np.min(grid_2d_slim[:, 1])) / 2.0
return centre_y, centre_x
@numba_util.jit()
def grid_2d_slim_via_mask_from(
mask_2d: np.ndarray,
pixel_scales: Union[float, Tuple[float, float]],
sub_size: int,
origin: Tuple[float, float] = (0.0, 0.0),
) -> np.ndarray:
"""
For a sub-grid, every unmasked pixel of its 2D mask with shape (total_y_pixels, total_x_pixels) is divided into
a finer uniform grid of shape (total_y_pixels*sub_size, total_x_pixels*sub_size). This routine computes the (y,x)
scaled coordinates a the centre of every sub-pixel defined by this 2D mask array.
The sub-grid is returned on an array of shape (total_unmasked_pixels*sub_size**2, 2). y coordinates are
stored in the 0 index of the second dimension, x coordinates in the 1 index. Masked coordinates are therefore
removed and not included in the slimmed grid.
Grid2D are defined from the top-left corner, where the first unmasked sub-pixel corresponds to index 0.
Sub-pixels that are part of the same mask array pixel are indexed next to one another, such that the second
sub-pixel in the first pixel has index 1, its next sub-pixel has index 2, and so forth.
Parameters
----------
mask_2d
A 2D array of bools, where `False` values are unmasked and therefore included as part of the calculated
sub-grid.
pixel_scales
The (y,x) scaled units to pixel units conversion factor of the 2D mask array.
sub_size
The size of the sub-grid that each pixel of the 2D mask array is divided into.
origin : (float, flloat)
The (y,x) origin of the 2D array, which the sub-grid is shifted around.
Returns
-------
ndarray
A slimmed sub grid of (y,x) scaled coordinates at the centre of every pixel unmasked pixel on the 2D mask
array. The sub grid array has dimensions (total_unmasked_pixels*sub_size**2, 2).
Examples
--------
mask = np.array([[True, False, True],
[False, False, False]
[True, False, True]])
grid_slim = grid_2d_slim_via_mask_from(mask=mask, pixel_scales=(0.5, 0.5), sub_size=1, origin=(0.0, 0.0))
"""
total_sub_pixels = mask_2d_util.total_sub_pixels_2d_from(mask_2d, sub_size)
grid_slim = np.zeros(shape=(total_sub_pixels, 2))
centres_scaled = geometry_util.central_scaled_coordinate_2d_from(
shape_native=mask_2d.shape, pixel_scales=pixel_scales, origin=origin
)
sub_index = 0
y_sub_half = pixel_scales[0] / 2
y_sub_step = pixel_scales[0] / (sub_size)
x_sub_half = pixel_scales[1] / 2
x_sub_step = pixel_scales[1] / (sub_size)
for y in range(mask_2d.shape[0]):
for x in range(mask_2d.shape[1]):
if not mask_2d[y, x]:
y_scaled = (y - centres_scaled[0]) * pixel_scales[0]
x_scaled = (x - centres_scaled[1]) * pixel_scales[1]
for y1 in range(sub_size):
for x1 in range(sub_size):
grid_slim[sub_index, 0] = -(
y_scaled - y_sub_half + y1 * y_sub_step + (y_sub_step / 2.0)
)
grid_slim[sub_index, 1] = (
x_scaled - x_sub_half + x1 * x_sub_step + (x_sub_step / 2.0)
)
sub_index += 1
return grid_slim
def grid_2d_via_mask_from(
mask_2d: np.ndarray,
pixel_scales: Union[float, Tuple[float, float]],
sub_size: int,
origin: Tuple[float, float] = (0.0, 0.0),
) -> np.ndarray:
"""
For a sub-grid, every unmasked pixel of its 2D mask with shape (total_y_pixels, total_x_pixels) is divided into a
finer uniform grid of shape (total_y_pixels*sub_size, total_x_pixels*sub_size). This routine computes the (y,x)
scaled coordinates at the centre of every sub-pixel defined by this 2D mask array.
The sub-grid is returned in its native dimensions with shape (total_y_pixels*sub_size, total_x_pixels*sub_size).
y coordinates are stored in the 0 index of the second dimension, x coordinates in the 1 index. Masked pixels are
given values (0.0, 0.0).
Grids are defined from the top-left corner, where the first unmasked sub-pixel corresponds to index 0.
Sub-pixels that are part of the same mask array pixel are indexed next to one another, such that the second
sub-pixel in the first pixel has index 1, its next sub-pixel has index 2, and so forth.
Parameters
----------
mask_2d
A 2D array of bools, where `False` values are unmasked and therefore included as part of the calculated
sub-grid.
pixel_scales
The (y,x) scaled units to pixel units conversion factor of the 2D mask array.
sub_size
The size of the sub-grid that each pixel of the 2D mask array is divided into.
origin : (float, flloat)
The (y,x) origin of the 2D array, which the sub-grid is shifted around.
Returns
-------
ndarray
A sub grid of (y,x) scaled coordinates at the centre of every pixel unmasked pixel on the 2D mask
array. The sub grid array has dimensions (total_y_pixels*sub_size, total_x_pixels*sub_size).
Examples
--------
mask = np.array([[True, False, True],
[False, False, False]
[True, False, True]])
grid_2d = grid_2d_via_mask_from(mask=mask, pixel_scales=(0.5, 0.5), sub_size=1, origin=(0.0, 0.0))
"""
grid_2d_slim = grid_2d_slim_via_mask_from(
mask_2d=mask_2d, pixel_scales=pixel_scales, sub_size=sub_size, origin=origin
)
return grid_2d_native_from(
grid_2d_slim=grid_2d_slim, mask_2d=mask_2d, sub_size=sub_size
)
def grid_2d_slim_via_shape_native_from(
shape_native: Tuple[int, int],
pixel_scales: Union[float, Tuple[float, float]],
sub_size: int,
origin: Tuple[float, float] = (0.0, 0.0),
) -> np.ndarray:
"""
For a sub-grid, every unmasked pixel of its 2D mask with shape (total_y_pixels, total_x_pixels) is divided into a
finer uniform grid of shape (total_y_pixels*sub_size, total_x_pixels*sub_size). This routine computes the (y,x)
scaled coordinates at the centre of every sub-pixel defined by this 2D mask array.
The sub-grid is returned in its slimmed dimensions with shape (total_pixels**2*sub_size**2, 2). y coordinates are
stored in the 0 index of the second dimension, x coordinates in the 1 index.
Grid2D are defined from the top-left corner, where the first sub-pixel corresponds to index [0,0].
Sub-pixels that are part of the same mask array pixel are indexed next to one another, such that the second
sub-pixel in the first pixel has index 1, its next sub-pixel has index 2, and so forth.
Parameters
----------
shape_native
The (y,x) shape of the 2D array the sub-grid of coordinates is computed for.
pixel_scales
The (y,x) scaled units to pixel units conversion factor of the 2D mask array.
sub_size
The size of the sub-grid that each pixel of the 2D mask array is divided into.
origin
The (y,x) origin of the 2D array, which the sub-grid is shifted around.
Returns
-------
ndarray
A sub grid of (y,x) scaled coordinates at the centre of every pixel unmasked pixel on the 2D mask
array. The sub grid is slimmed and has dimensions (total_unmasked_pixels*sub_size**2, 2).
Examples
--------
mask = np.array([[True, False, True],
[False, False, False]
[True, False, True]])
grid_2d_slim = grid_2d_slim_via_shape_native_from(shape_native=(3,3), pixel_scales=(0.5, 0.5), sub_size=2, origin=(0.0, 0.0))
"""
return grid_2d_slim_via_mask_from(
mask_2d=np.full(fill_value=False, shape=shape_native),
pixel_scales=pixel_scales,
sub_size=sub_size,
origin=origin,
)
def grid_2d_via_shape_native_from(
shape_native: Tuple[int, int],
pixel_scales: Union[float, Tuple[float, float]],
sub_size: int,
origin: Tuple[float, float] = (0.0, 0.0),
) -> np.ndarray:
"""
For a sub-grid, every unmasked pixel of its 2D mask with shape (total_y_pixels, total_x_pixels) is divided
into a finer uniform grid of shape (total_y_pixels*sub_size, total_x_pixels*sub_size). This routine computes
the (y,x) scaled coordinates at the centre of every sub-pixel defined by this 2D mask array.
The sub-grid is returned in its native dimensions with shape (total_y_pixels*sub_size, total_x_pixels*sub_size).
y coordinates are stored in the 0 index of the second dimension, x coordinates in the 1 index.
Grids are defined from the top-left corner, where the first sub-pixel corresponds to index [0,0].
Sub-pixels that are part of the same mask array pixel are indexed next to one another, such that the second
sub-pixel in the first pixel has index 1, its next sub-pixel has index 2, and so forth.
Parameters
----------
shape_native
The (y,x) shape of the 2D array the sub-grid of coordinates is computed for.
pixel_scales
The (y,x) scaled units to pixel units conversion factor of the 2D mask array.
sub_size
The size of the sub-grid that each pixel of the 2D mask array is divided into.
origin : (float, flloat)
The (y,x) origin of the 2D array, which the sub-grid is shifted around.
Returns
-------
ndarray
A sub grid of (y,x) scaled coordinates at the centre of every pixel unmasked pixel on the 2D mask
array. The sub grid array has dimensions (total_y_pixels*sub_size, total_x_pixels*sub_size).
Examples
--------
grid_2d = grid_2d_via_shape_native_from(shape_native=(3, 3), pixel_scales=(1.0, 1.0), sub_size=2, origin=(0.0, 0.0))
"""
return grid_2d_via_mask_from(
mask_2d=np.full(fill_value=False, shape=shape_native),
pixel_scales=pixel_scales,
sub_size=sub_size,
origin=origin,
)
@numba_util.jit()
def grid_scaled_2d_slim_radial_projected_from(
extent: np.ndarray,
centre: Tuple[float, float],
pixel_scales: Union[float, Tuple[float, float]],
sub_size: int,
shape_slim: Optional[int] = 0,
) -> np.ndarray:
"""
Determine a projected radial grid of points from a 2D region of coordinates defined by an
extent [xmin, xmax, ymin, ymax] and with a (y,x) centre. This functions operates as follows:
1) Given the region defined by the extent [xmin, xmax, ymin, ymax], the algorithm finds the longest 1D distance of
the 4 paths from the (y,x) centre to the edge of the region (e.g. following the positive / negative y and x axes).
2) Use the pixel-scale corresponding to the direction chosen (e.g. if the positive x-axis was the longest, the
pixel_scale in the x dimension is used).
3) Determine the number of pixels between the centre and the edge of the region using the longest path between the
two chosen above.
4) Create a (y,x) grid of radial points where all points are at the centre's y value = 0.0 and the x values iterate
from the centre in increasing steps of the pixel-scale.
5) Rotate these radial coordinates by the input `angle` clockwise.
A schematric is shown below:
-------------------
| |
|<- - - - ->x | x = centre
| | <-> = longest radial path from centre to extent edge
| |
-------------------
Using the centre x above, this function finds the longest radial path to the edge of the extent window.
The returned `grid_radii` represents a radial set of points that in 1D sample the 2D grid outwards from its centre.
This grid stores the radial coordinates as (y,x) values (where all y values are the same) as opposed to a 1D data
structure so that it can be used in functions which require that a 2D grid structure is input.
Parameters
----------
extent
The extent of the grid the radii grid is computed using, with format [xmin, xmax, ymin, ymax]
centre : (float, flloat)
The (y,x) central coordinate which the radial grid is traced outwards from.
pixel_scales
The (y,x) scaled units to pixel units conversion factor of the 2D mask array.
sub_size
The size of the sub-grid that each pixel of the 2D mask array is divided into.
shape_slim
Manually choose the shape of the 1D projected grid that is returned. If 0, the border based on the 2D grid is
used (due to numba None cannot be used as a default value).
Returns
-------
ndarray
A radial set of points sampling the longest distance from the centre to the edge of the extent in along the
positive x-axis.
"""
distance_to_positive_x = extent[1] - centre[1]
distance_to_positive_y = extent[3] - centre[0]
distance_to_negative_x = centre[1] - extent[0]
distance_to_negative_y = centre[0] - extent[2]
scaled_distance = max(
[
distance_to_positive_x,
distance_to_positive_y,
distance_to_negative_x,
distance_to_negative_y,
]
)
if (scaled_distance == distance_to_positive_y) or (
scaled_distance == distance_to_negative_y
):
pixel_scale = pixel_scales[0]
else:
pixel_scale = pixel_scales[1]
if shape_slim == 0:
shape_slim = sub_size * int((scaled_distance / pixel_scale)) + 1
grid_scaled_2d_slim_radii = np.zeros((shape_slim, 2))
grid_scaled_2d_slim_radii[:, 0] += centre[0]
radii = centre[1]
for slim_index in range(shape_slim):
grid_scaled_2d_slim_radii[slim_index, 1] = radii
radii += pixel_scale / sub_size
return grid_scaled_2d_slim_radii
@numba_util.jit()
def grid_pixels_2d_slim_from(
grid_scaled_2d_slim: np.ndarray,
shape_native: Tuple[int, int],
pixel_scales: Union[float, Tuple[float, float]],
origin: Tuple[float, float] = (0.0, 0.0),
) -> np.ndarray:
"""
Convert a slimmed grid of 2d (y,x) scaled coordinates to a slimmed grid of 2d (y,x) pixel coordinate values. Pixel
coordinates are returned as floats such that they include the decimal offset from each pixel's top-left corner
relative to the input scaled coordinate.
The input and output grids are both slimmed and therefore shape (total_pixels, 2).
The pixel coordinate origin is at the top left corner of the grid, such that the pixel [0,0] corresponds to
the highest (most positive) y scaled coordinate and lowest (most negative) x scaled coordinate on the gird.
The scaled grid is defined by an origin and coordinates are shifted to this origin before computing their
1D grid pixel coordinate values.
Parameters
----------
grid_scaled_2d_slim: np.ndarray
The slimmed grid of 2D (y,x) coordinates in scaled units which are converted to pixel value coordinates.
shape_native
The (y,x) shape of the original 2D array the scaled coordinates were computed on.
pixel_scales
The (y,x) scaled units to pixel units conversion factor of the original 2D array.
origin : (float, flloat)
The (y,x) origin of the grid, which the scaled grid is shifted to.
Returns
-------
ndarray
A slimmed grid of 2D (y,x) pixel-value coordinates with dimensions (total_pixels, 2).
Examples
--------
grid_scaled_2d_slim = np.array([[1.0, 1.0], [2.0, 2.0], [3.0, 3.0], [4.0, 4.0]])
grid_pixels_2d_slim = grid_scaled_2d_slim_from(grid_scaled_2d_slim=grid_scaled_2d_slim, shape=(2,2),
pixel_scales=(0.5, 0.5), origin=(0.0, 0.0))
"""
grid_pixels_2d_slim = np.zeros((grid_scaled_2d_slim.shape[0], 2))
centres_scaled = geometry_util.central_scaled_coordinate_2d_from(
shape_native=shape_native, pixel_scales=pixel_scales, origin=origin
)
for slim_index in range(grid_scaled_2d_slim.shape[0]):
grid_pixels_2d_slim[slim_index, 0] = (
(-grid_scaled_2d_slim[slim_index, 0] / pixel_scales[0])
+ centres_scaled[0]
+ 0.5
)
grid_pixels_2d_slim[slim_index, 1] = (
(grid_scaled_2d_slim[slim_index, 1] / pixel_scales[1])
+ centres_scaled[1]
+ 0.5
)
return grid_pixels_2d_slim
@numba_util.jit()
def grid_pixel_centres_2d_slim_from(
grid_scaled_2d_slim: np.ndarray,
shape_native: Tuple[int, int],
pixel_scales: Union[float, Tuple[float, float]],
origin: Tuple[float, float] = (0.0, 0.0),
) -> np.ndarray:
"""
Convert a slimmed grid of 2D (y,x) scaled coordinates to a slimmed grid of 2D (y,x) pixel values. Pixel coordinates
are returned as integers such that they map directly to the pixel they are contained within.
The input and output grids are both slimmed and therefore shape (total_pixels, 2).
The pixel coordinate origin is at the top left corner of the grid, such that the pixel [0,0] corresponds to
the highest (most positive) y scaled coordinate and lowest (most negative) x scaled coordinate on the gird.
The scaled coordinate grid is defined by the class attribute origin, and coordinates are shifted to this
origin before computing their 1D grid pixel indexes.
Parameters
----------
grid_scaled_2d_slim: np.ndarray
The slimmed grid of 2D (y,x) coordinates in scaled units which is converted to pixel indexes.
shape_native
The (y,x) shape of the original 2D array the scaled coordinates were computed on.
pixel_scales
The (y,x) scaled units to pixel units conversion factor of the original 2D array.
origin : (float, flloat)
The (y,x) origin of the grid, which the scaled grid is shifted
Returns
-------
ndarray
A slimmed grid of 2D (y,x) pixel indexes with dimensions (total_pixels, 2).
Examples
--------
grid_scaled_2d_slim = np.array([[1.0, 1.0], [2.0, 2.0], [3.0, 3.0], [4.0, 4.0]])
grid_pixels_2d_slim = grid_scaled_2d_slim_from(grid_scaled_2d_slim=grid_scaled_2d_slim, shape=(2,2),
pixel_scales=(0.5, 0.5), origin=(0.0, 0.0))
"""
grid_pixels_2d_slim = np.zeros((grid_scaled_2d_slim.shape[0], 2))
centres_scaled = geometry_util.central_scaled_coordinate_2d_from(
shape_native=shape_native, pixel_scales=pixel_scales, origin=origin
)
for slim_index in range(grid_scaled_2d_slim.shape[0]):
grid_pixels_2d_slim[slim_index, 0] = int(
(-grid_scaled_2d_slim[slim_index, 0] / pixel_scales[0])
+ centres_scaled[0]
+ 0.5
)
grid_pixels_2d_slim[slim_index, 1] = int(
(grid_scaled_2d_slim[slim_index, 1] / pixel_scales[1])
+ centres_scaled[1]
+ 0.5
)
return grid_pixels_2d_slim
@numba_util.jit()
def grid_pixel_indexes_2d_slim_from(
grid_scaled_2d_slim: np.ndarray,
shape_native: Tuple[int, int],
pixel_scales: Union[float, Tuple[float, float]],
origin: Tuple[float, float] = (0.0, 0.0),
) -> np.ndarray:
"""
Convert a slimmed grid of 2D (y,x) scaled coordinates to a slimmed grid of pixel indexes. Pixel coordinates are
returned as integers such that they are the pixel from the top-left of the 2D grid going rights and then downwards.
The input and output grids are both slimmed and have shapes (total_pixels, 2) and (total_pixels,).
For example:
The pixel at the top-left, whose native index is [0,0], corresponds to slimmed pixel index 0.
The fifth pixel on the top row, whose native index is [0,5], corresponds to slimmed pixel index 4.
The first pixel on the second row, whose native index is [0,1], has slimmed pixel index 10 if a row has 10 pixels.
The scaled coordinate grid is defined by the class attribute origin, and coordinates are shifted to this
origin before computing their 1D grid pixel indexes.
The input and output grids are both of shape (total_pixels, 2).
Parameters
----------
grid_scaled_2d_slim: np.ndarray
The slimmed grid of 2D (y,x) coordinates in scaled units which is converted to slimmed pixel indexes.
shape_native
The (y,x) shape of the original 2D array the scaled coordinates were computed on.
pixel_scales
The (y,x) scaled units to pixel units conversion factor of the original 2D array.
origin : (float, flloat)
The (y,x) origin of the grid, which the scaled grid is shifted.
Returns
-------
ndarray
A grid of slimmed pixel indexes with dimensions (total_pixels,).
Examples
--------
grid_scaled_2d_slim = np.array([[1.0, 1.0], [2.0, 2.0], [3.0, 3.0], [4.0, 4.0]])
grid_pixel_indexes_2d_slim = grid_pixel_indexes_2d_slim_from(grid_scaled_2d_slim=grid_scaled_2d_slim, shape=(2,2),
pixel_scales=(0.5, 0.5), origin=(0.0, 0.0))
"""
grid_pixels_2d_slim = grid_pixel_centres_2d_slim_from(
grid_scaled_2d_slim=grid_scaled_2d_slim,
shape_native=shape_native,
pixel_scales=pixel_scales,
origin=origin,
)
grid_pixel_indexes_2d_slim = np.zeros(grid_pixels_2d_slim.shape[0])
for slim_index in range(grid_pixels_2d_slim.shape[0]):
grid_pixel_indexes_2d_slim[slim_index] = int(
grid_pixels_2d_slim[slim_index, 0] * shape_native[1]
+ grid_pixels_2d_slim[slim_index, 1]
)
return grid_pixel_indexes_2d_slim
@numba_util.jit()
def grid_scaled_2d_slim_from(
grid_pixels_2d_slim: np.ndarray,
shape_native: Tuple[int, int],
pixel_scales: Union[float, Tuple[float, float]],
origin: Tuple[float, float] = (0.0, 0.0),
) -> np.ndarray:
"""
Convert a slimmed grid of 2D (y,x) pixel coordinates to a slimmed grid of 2D (y,x) scaled values.
The input and output grids are both slimmed and therefore shape (total_pixels, 2).
The pixel coordinate origin is at the top left corner of the grid, such that the pixel [0,0] corresponds to
the highest (most positive) y scaled coordinate and lowest (most negative) x scaled coordinate on the gird.
The scaled coordinate origin is defined by the class attribute origin, and coordinates are shifted to this
origin after computing their values from the 1D grid pixel indexes.
Parameters
----------
grid_pixels_2d_slim: np.ndarray
The slimmed grid of (y,x) coordinates in pixel values which is converted to scaled coordinates.
shape_native
The (y,x) shape of the original 2D array the scaled coordinates were computed on.
pixel_scales
The (y,x) scaled units to pixel units conversion factor of the original 2D array.
origin : (float, flloat)
The (y,x) origin of the grid, which the scaled grid is shifted.
Returns
-------
ndarray
A slimmed grid of 2d scaled coordinates with dimensions (total_pixels, 2).
Examples
--------
grid_pixels_2d_slim = np.array([[0,0], [0,1], [1,0], [1,1])
grid_pixels_2d_slim = grid_scaled_2d_slim_from(grid_pixels_2d_slim=grid_pixels_2d_slim, shape=(2,2),
pixel_scales=(0.5, 0.5), origin=(0.0, 0.0))
"""
grid_scaled_2d_slim = np.zeros((grid_pixels_2d_slim.shape[0], 2))
centres_scaled = geometry_util.central_scaled_coordinate_2d_from(
shape_native=shape_native, pixel_scales=pixel_scales, origin=origin
)
for slim_index in range(grid_scaled_2d_slim.shape[0]):
grid_scaled_2d_slim[slim_index, 0] = (
-(grid_pixels_2d_slim[slim_index, 0] - centres_scaled[0] - 0.5)
* pixel_scales[0]
)
grid_scaled_2d_slim[slim_index, 1] = (
grid_pixels_2d_slim[slim_index, 1] - centres_scaled[1] - 0.5
) * pixel_scales[1]
return grid_scaled_2d_slim
@numba_util.jit()
def grid_pixel_centres_2d_from(
grid_scaled_2d: np.ndarray,
shape_native: Tuple[int, int],
pixel_scales: Union[float, Tuple[float, float]],
origin: Tuple[float, float] = (0.0, 0.0),
) -> np.ndarray:
"""
Convert a native grid of 2D (y,x) scaled coordinates to a native grid of 2D (y,x) pixel values. Pixel coordinates
are returned as integers such that they map directly to the pixel they are contained within.
The input and output grids are both native resolution and therefore have shape (y_pixels, x_pixels, 2).
The pixel coordinate origin is at the top left corner of the grid, such that the pixel [0,0] corresponds to
the highest (most positive) y scaled coordinate and lowest (most negative) x scaled coordinate on the gird.
The scaled coordinate grid is defined by the class attribute origin, and coordinates are shifted to this
origin before computing their 1D grid pixel indexes.
Parameters
----------
grid_scaled_2d: np.ndarray
The native grid of 2D (y,x) coordinates in scaled units which is converted to pixel indexes.
shape_native
The (y,x) shape of the original 2D array the scaled coordinates were computed on.
pixel_scales
The (y,x) scaled units to pixel units conversion factor of the original 2D array.
origin : (float, flloat)
The (y,x) origin of the grid, which the scaled grid is shifted
Returns
-------
ndarray
A native grid of 2D (y,x) pixel indexes with dimensions (y_pixels, x_pixels, 2).
Examples
--------
grid_scaled_2d = np.array([[1.0, 1.0], [2.0, 2.0], [3.0, 3.0], [4.0, 4.0]])
grid_pixel_centres_2d = grid_pixel_centres_2d_from(grid_scaled_2d=grid_scaled_2d, shape=(2,2),
pixel_scales=(0.5, 0.5), origin=(0.0, 0.0))
"""
grid_pixels_2d = np.zeros((grid_scaled_2d.shape[0], grid_scaled_2d.shape[1], 2))
centres_scaled = geometry_util.central_scaled_coordinate_2d_from(
shape_native=shape_native, pixel_scales=pixel_scales, origin=origin
)
for y in range(grid_scaled_2d.shape[0]):
for x in range(grid_scaled_2d.shape[1]):
grid_pixels_2d[y, x, 0] = int(
(-grid_scaled_2d[y, x, 0] / pixel_scales[0]) + centres_scaled[0] + 0.5
)
grid_pixels_2d[y, x, 1] = int(
(grid_scaled_2d[y, x, 1] / pixel_scales[1]) + centres_scaled[1] + 0.5
)
return grid_pixels_2d
@numba_util.jit()
def relocated_grid_via_jit_from(grid, border_grid):
"""
Relocate the coordinates of a grid to its border if they are outside the border, where the border is
defined as all pixels at the edge of the grid's mask (see *mask._border_1d_indexes*).
This is performed as follows:
1: Use the mean value of the grid's y and x coordinates to determine the origin of the grid.
2: Compute the radial distance of every grid coordinate from the origin.
3: For every coordinate, find its nearest pixel in the border.
4: Determine if it is outside the border, by comparing its radial distance from the origin to its paired
border pixel's radial distance.
5: If its radial distance is larger, use the ratio of radial distances to move the coordinate to the
border (if its inside the border, do nothing).
The method can be used on uniform or irregular grids, however for irregular grids the border of the
'image-plane' mask is used to define border pixels.
Parameters
----------
grid : Grid2D
The grid (uniform or irregular) whose pixels are to be relocated to the border edge if outside it.
border_grid : Grid2D
The grid of border (y,x) coordinates.
"""
grid_relocated = | np.zeros(grid.shape) | numpy.zeros |
import numpy as np
import pytest
import theano
import theano.tensor as tt
# Don't import test classes otherwise they get tested as part of the file
from tests import unittest_tools as utt
from tests.gpuarray.config import mode_with_gpu, mode_without_gpu, test_ctx_name
from tests.tensor.test_basic import (
TestAlloc,
TestComparison,
TestJoinAndSplit,
TestReshape,
)
from tests.tensor.utils import rand, safe_make_node
from theano.gpuarray.basic_ops import (
GpuAlloc,
GpuAllocEmpty,
GpuContiguous,
GpuEye,
GpuFromHost,
GpuJoin,
GpuReshape,
GpuSplit,
GpuToGpu,
GpuTri,
HostFromGpu,
gpu_contiguous,
gpu_join,
host_from_gpu,
)
from theano.gpuarray.elemwise import GpuDimShuffle, GpuElemwise
from theano.gpuarray.subtensor import GpuSubtensor
from theano.gpuarray.type import GpuArrayType, get_context, gpuarray_shared_constructor
from theano.tensor import TensorType
from theano.tensor.basic import alloc
pygpu = pytest.importorskip("pygpu")
gpuarray = pygpu.gpuarray
utt.seed_rng()
rng = np.random.RandomState(seed=utt.fetch_seed())
def inplace_func(
inputs,
outputs,
mode=None,
allow_input_downcast=False,
on_unused_input="raise",
name=None,
):
if mode is None:
mode = mode_with_gpu
return theano.function(
inputs,
outputs,
mode=mode,
allow_input_downcast=allow_input_downcast,
accept_inplace=True,
on_unused_input=on_unused_input,
name=name,
)
def fake_shared(value, name=None, strict=False, allow_downcast=None, **kwargs):
from theano.tensor.sharedvar import scalar_constructor, tensor_constructor
for c in (gpuarray_shared_constructor, tensor_constructor, scalar_constructor):
try:
return c(
value, name=name, strict=strict, allow_downcast=allow_downcast, **kwargs
)
except TypeError:
continue
def rand_gpuarray(*shape, **kwargs):
r = rng.rand(*shape) * 2 - 1
dtype = kwargs.pop("dtype", theano.config.floatX)
cls = kwargs.pop("cls", None)
if len(kwargs) != 0:
raise TypeError("Unexpected argument %s", list(kwargs.keys())[0])
return gpuarray.array(r, dtype=dtype, cls=cls, context=get_context(test_ctx_name))
def makeTester(
name,
op,
gpu_op,
cases,
checks=None,
mode_gpu=mode_with_gpu,
mode_nogpu=mode_without_gpu,
skip=False,
eps=1e-10,
):
if checks is None:
checks = {}
_op = op
_gpu_op = gpu_op
_cases = cases
_skip = skip
_checks = checks
class Checker(utt.OptimizationTestMixin):
op = staticmethod(_op)
gpu_op = staticmethod(_gpu_op)
cases = _cases
skip = _skip
checks = _checks
def setup_method(self):
eval(self.__class__.__module__ + "." + self.__class__.__name__)
def test_all(self):
if skip:
pytest.skip(skip)
for testname, inputs in cases.items():
for _ in range(len(inputs)):
if type(inputs[_]) is float:
inputs[_] = np.asarray(inputs[_], dtype=theano.config.floatX)
self.run_case(testname, inputs)
def run_case(self, testname, inputs):
inputs_ref = [theano.shared(inp) for inp in inputs]
inputs_tst = [theano.shared(inp) for inp in inputs]
try:
node_ref = safe_make_node(self.op, *inputs_ref)
node_tst = safe_make_node(self.op, *inputs_tst)
except Exception as exc:
err_msg = (
"Test %s::%s: Error occurred while making " "a node with inputs %s"
) % (self.gpu_op, testname, inputs)
exc.args += (err_msg,)
raise
try:
f_ref = inplace_func([], node_ref.outputs, mode=mode_nogpu)
f_tst = inplace_func([], node_tst.outputs, mode=mode_gpu)
except Exception as exc:
err_msg = (
"Test %s::%s: Error occurred while trying to " "make a Function"
) % (self.gpu_op, testname)
exc.args += (err_msg,)
raise
self.assertFunctionContains1(f_tst, self.gpu_op)
ref_e = None
try:
expecteds = f_ref()
except Exception as exc:
ref_e = exc
try:
variables = f_tst()
except Exception as exc:
if ref_e is None:
err_msg = (
"Test %s::%s: exception when calling the " "Function"
) % (self.gpu_op, testname)
exc.args += (err_msg,)
raise
else:
# if we raised an exception of the same type we're good.
if isinstance(exc, type(ref_e)):
return
else:
err_msg = (
"Test %s::%s: exception raised during test "
"call was not the same as the reference "
"call (got: %s, expected %s)"
% (self.gpu_op, testname, type(exc), type(ref_e))
)
exc.args += (err_msg,)
raise
for i, (variable, expected) in enumerate(zip(variables, expecteds)):
condition = (
variable.dtype != expected.dtype
or variable.shape != expected.shape
or not TensorType.values_eq_approx(variable, expected)
)
assert not condition, (
"Test %s::%s: Output %s gave the wrong "
"value. With inputs %s, expected %s "
"(dtype %s), got %s (dtype %s)."
% (
self.op,
testname,
i,
inputs,
expected,
expected.dtype,
variable,
variable.dtype,
)
)
for description, check in self.checks.items():
assert check(inputs, variables), (
"Test %s::%s: Failed check: %s " "(inputs were %s, ouputs were %s)"
) % (self.op, testname, description, inputs, variables)
Checker.__name__ = name
if hasattr(Checker, "__qualname__"):
Checker.__qualname__ = name
return Checker
def test_transfer_cpu_gpu():
a = tt.fmatrix("a")
g = GpuArrayType(dtype="float32", broadcastable=(False, False))("g")
av = np.asarray(rng.rand(5, 4), dtype="float32")
gv = gpuarray.array(av, context=get_context(test_ctx_name))
f = theano.function([a], GpuFromHost(test_ctx_name)(a))
fv = f(av)
assert GpuArrayType.values_eq(fv, gv)
f = theano.function([g], host_from_gpu(g))
fv = f(gv)
assert np.all(fv == av)
def test_transfer_gpu_gpu():
g = GpuArrayType(
dtype="float32", broadcastable=(False, False), context_name=test_ctx_name
)()
av = np.asarray(rng.rand(5, 4), dtype="float32")
gv = gpuarray.array(av, context=get_context(test_ctx_name))
mode = mode_with_gpu.excluding(
"cut_gpua_host_transfers", "local_cut_gpua_host_gpua"
)
f = theano.function([g], GpuToGpu(test_ctx_name)(g), mode=mode)
topo = f.maker.fgraph.toposort()
assert len(topo) == 1
assert isinstance(topo[0].op, GpuToGpu)
fv = f(gv)
assert GpuArrayType.values_eq(fv, gv)
def test_transfer_strided():
# This is just to ensure that it works in theano
# libgpuarray has a much more comprehensive suit of tests to
# ensure correctness
a = tt.fmatrix("a")
g = GpuArrayType(dtype="float32", broadcastable=(False, False))("g")
av = np.asarray(rng.rand(5, 8), dtype="float32")
gv = gpuarray.array(av, context=get_context(test_ctx_name))
av = av[:, ::2]
gv = gv[:, ::2]
f = theano.function([a], GpuFromHost(test_ctx_name)(a))
fv = f(av)
assert GpuArrayType.values_eq(fv, gv)
f = theano.function([g], host_from_gpu(g))
fv = f(gv)
assert np.all(fv == av)
def gpu_alloc_expected(x, *shp):
g = gpuarray.empty(shp, dtype=x.dtype, context=get_context(test_ctx_name))
g[:] = x
return g
TestGpuAlloc = makeTester(
name="GpuAllocTester",
# The +1 is there to allow the lift to the GPU.
op=lambda *args: alloc(*args) + 1,
gpu_op=GpuAlloc(test_ctx_name),
cases=dict(
correct01=(rand(), np.int32(7)),
# just gives a DeepCopyOp with possibly wrong results on the CPU
# correct01_bcast=(rand(1), np.int32(7)),
correct02=(rand(), np.int32(4), np.int32(7)),
correct12=(rand(7), np.int32(4), np.int32(7)),
correct13=(rand(7), np.int32(2), np.int32(4), np.int32(7)),
correct23=(rand(4, 7), np.int32(2), np.int32(4), np.int32(7)),
bad_shape12=(rand(7), np.int32(7), np.int32(5)),
),
)
class TestGPUAlloc(TestAlloc):
dtype = "float32"
mode = mode_with_gpu
shared = staticmethod(gpuarray_shared_constructor)
allocs = [GpuAlloc(test_ctx_name), GpuAlloc(test_ctx_name), tt.Alloc()]
def test_alloc_empty():
for dt in ["float32", "int8"]:
f = theano.function([], GpuAllocEmpty(dt, context_name=test_ctx_name)(2, 3))
assert len(f.maker.fgraph.apply_nodes) == 1
out = f()
assert out.shape == (2, 3)
assert out.dtype == dt
f = theano.function(
[],
[
GpuAllocEmpty("uint64", test_ctx_name)(3, 2),
GpuAllocEmpty("uint64", test_ctx_name)(3, 2),
],
)
out = f()
assert out[0].shape == (3, 2)
assert out[0].dtype == "uint64"
assert out[1].shape == (3, 2)
assert out[1].dtype == "uint64"
assert (
len(
[
node
for node in f.maker.fgraph.apply_nodes
if isinstance(node.op, GpuAllocEmpty)
]
)
== 1
)
def test_shape():
x = GpuArrayType(dtype="float32", broadcastable=[False, False, False])()
v = gpuarray.zeros((3, 4, 5), dtype="float32", context=get_context(test_ctx_name))
f = theano.function([x], x.shape)
topo = f.maker.fgraph.toposort()
assert np.all(f(v) == (3, 4, 5))
if theano.config.mode != "FAST_COMPILE":
assert len(topo) == 4
assert isinstance(topo[0].op, tt.opt.Shape_i)
assert isinstance(topo[1].op, tt.opt.Shape_i)
assert isinstance(topo[2].op, tt.opt.Shape_i)
assert isinstance(topo[3].op, tt.opt.MakeVector)
mode = mode_with_gpu.excluding("local_shape_to_shape_i")
f = theano.function([x], x.shape, mode=mode)
topo = f.maker.fgraph.toposort()
assert np.all(f(v) == (3, 4, 5))
assert len(topo) == 1
assert isinstance(topo[0].op, tt.Shape)
def test_gpu_contiguous():
a = tt.fmatrix("a")
i = tt.iscalar("i")
a_val = np.asarray(np.random.rand(4, 5), dtype="float32")
# The reshape is needed otherwise we make the subtensor on the CPU
# to transfer less data.
f = theano.function(
[a, i], gpu_contiguous(a.reshape((5, 4))[::i]), mode=mode_with_gpu
)
topo = f.maker.fgraph.toposort()
assert any([isinstance(node.op, GpuSubtensor) for node in topo])
assert any([isinstance(node.op, GpuContiguous) for node in topo])
assert f(a_val, 1).flags.c_contiguous
assert f(a_val, 2).flags.c_contiguous
assert f(a_val, 2).flags.c_contiguous
class TestGPUReshape(TestReshape):
def setup_method(self):
self.shared = gpuarray_shared_constructor
self.op = GpuReshape
self.mode = mode_with_gpu
self.ignore_topo = (
HostFromGpu,
GpuFromHost,
theano.compile.DeepCopyOp,
GpuDimShuffle,
GpuElemwise,
tt.opt.Shape_i,
tt.opt.MakeVector,
)
assert self.op == GpuReshape
class TestGPUComparison(TestComparison):
def setup_method(self):
utt.seed_rng()
self.mode = mode_with_gpu
self.shared = gpuarray_shared_constructor
self.dtypes = ["float64", "float32"]
class TestGPUJoinAndSplit(TestJoinAndSplit):
def setup_method(self):
self.mode = mode_with_gpu.excluding("constant_folding")
self.join_op = GpuJoin()
self.split_op_class = GpuSplit
# Use join instead of MakeVector since there is no MakeVector on GPU
self.make_vector_op = GpuJoin()
# this is to avoid errors with limited devices
self.floatX = "float32"
self.hide_error = theano.config.mode not in ["DebugMode", "DEBUG_MODE"]
def shared(x, **kwargs):
return gpuarray_shared_constructor(x, target=test_ctx_name, **kwargs)
self.shared = shared
def test_gpusplit_opt(self):
# Test that we move the node to the GPU
# Also test float16 computation at the same time.
rng = np.random.RandomState(seed=utt.fetch_seed())
m = self.shared(rng.rand(4, 6).astype("float16"))
o = tt.Split(2)(m, 0, [2, 2])
assert o[0].dtype == "float16"
f = theano.function([], o, mode=self.mode)
assert any(
[
isinstance(node.op, self.split_op_class)
for node in f.maker.fgraph.toposort()
]
)
o1, o2 = f()
assert np.allclose(o1, m.get_value(borrow=True)[:2])
assert np.allclose(o2, m.get_value(borrow=True)[2:])
def test_gpujoin_gpualloc():
a = tt.fmatrix("a")
a_val = np.asarray( | np.random.rand(4, 5) | numpy.random.rand |
# pvtrace is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# pvtrace is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import numpy as np
from external.transformations import translation_matrix, rotation_matrix
import external.transformations as tf
from Trace import Photon
from Geometry import Box, Cylinder, FinitePlane, transform_point, transform_direction, rotation_matrix_from_vector_alignment, norm
from Materials import Spectrum
def random_spherecial_vector():
# This method of calculating isotropic vectors is taken from GNU Scientific Library
LOOP = True
while LOOP:
x = -1. + 2. * np.random.uniform()
y = -1. + 2. * np.random.uniform()
s = x**2 + y**2
if s <= 1.0:
LOOP = False
z = -1. + 2. * s
a = 2 * np.sqrt(1 - s)
x = a * x
y = a * y
return np.array([x,y,z])
class SimpleSource(object):
"""A light source that will generate photons of a single colour, direction and position."""
def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, use_random_polarisation=False):
super(SimpleSource, self).__init__()
self.position = position
self.direction = direction
self.wavelength = wavelength
self.use_random_polarisation = use_random_polarisation
self.throw = 0
self.source_id = "SimpleSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.position = np.array(self.position)
photon.direction = np.array(self.direction)
photon.active = True
photon.wavelength = self.wavelength
# If use_polarisation is set generate a random polarisation vector of the photon
if self.use_random_polarisation:
# Randomise rotation angle around xy-plane, the transform from +z to the direction of the photon
vec = random_spherecial_vector()
vec[2] = 0.
vec = norm(vec)
R = rotation_matrix_from_vector_alignment(self.direction, [0,0,1])
photon.polarisation = transform_direction(vec, R)
else:
photon.polarisation = None
photon.id = self.throw
self.throw = self.throw + 1
return photon
class Laser(object):
"""A light source that will generate photons of a single colour, direction and position."""
def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, polarisation=None):
super(Laser, self).__init__()
self.position = np.array(position)
self.direction = np.array(direction)
self.wavelength = wavelength
assert polarisation != None, "Polarisation of the Laser is not set."
self.polarisation = np.array(polarisation)
self.throw = 0
self.source_id = "LaserSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.position = np.array(self.position)
photon.direction = np.array(self.direction)
photon.active = True
photon.wavelength = self.wavelength
photon.polarisation = self.polarisation
photon.id = self.throw
self.throw = self.throw + 1
return photon
class PlanarSource(object):
"""A box that emits photons from the top surface (normal), sampled from the spectrum."""
def __init__(self, spectrum=None, wavelength=555, direction=(0,0,1), length=0.05, width=0.05):
super(PlanarSource, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.plane = FinitePlane(length=length, width=width)
self.length = length
self.width = width
# direction is the direction that photons are fired out of the plane in the GLOBAL FRAME.
# i.e. this is passed directly to the photon to set is's direction
self.direction = direction
self.throw = 0
self.source_id = "PlanarSource_" + str(id(self))
def translate(self, translation):
self.plane.append_transform(tf.translation_matrix(translation))
def rotate(self, angle, axis):
self.plane.append_transform(tf.rotation_matrix(angle, axis))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.id = self.throw
self.throw = self.throw + 1
# Create a point which is on the surface of the finite plane in it's local frame
x = np.random.uniform(0., self.length)
y = np.random.uniform(0., self.width)
local_point = (x, y, 0.)
# Transform the direciton
photon.position = transform_point(local_point, self.plane.transform)
photon.direction = self.direction
photon.active = True
if self.spectrum != None:
photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform())
else:
photon.wavelength = self.wavelength
return photon
class LensSource(object):
"""
A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize".
The focus line should be perpendicular to the plane normal and aligned with the z-axis.
"""
def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)):
super(LensSource, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.planeorigin = planeorigin
self.planeextent = planeextent
self.linepoint = np.array(linepoint)
self.linedirection = np.array(linedirection)
self.focussize = focussize
self.throw = 0
self.source_id = "LensSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.id = self.throw
self.throw = self.throw + 1
# Position
x = np.random.uniform(self.planeorigin[0],self.planeextent[0])
y = np.random.uniform(self.planeorigin[1],self.planeextent[1])
z = np.random.uniform(self.planeorigin[2],self.planeextent[2])
photon.position = np.array((x,y,z))
# Direction
focuspoint = np.array((0.,0.,0.))
focuspoint[0] = self.linepoint[0] + np.random.uniform(-self.focussize,self.focussize)
focuspoint[1] = self.linepoint[1] + | np.random.uniform(-self.focussize,self.focussize) | numpy.random.uniform |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = | np.linspace(maxima_y[-1], minima_y[-1], 101) | numpy.linspace |
import logging
import george
import numpy as np
from robo.priors.default_priors import DefaultPrior
from robo.models.gaussian_process import GaussianProcess
from robo.models.gaussian_process_mcmc import GaussianProcessMCMC
from robo.maximizers.random_sampling import RandomSampling
from robo.maximizers.scipy_optimizer import SciPyOptimizer
from robo.maximizers.differential_evolution import DifferentialEvolution
from robo.solver.bayesian_optimization import BayesianOptimization
from robo.acquisition_functions.information_gain import InformationGain
from robo.acquisition_functions.ei import EI
from robo.acquisition_functions.marginalization import MarginalizationGPMCMC
from robo.initial_design import init_latin_hypercube_sampling
logger = logging.getLogger(__name__)
def entropy_search(objective_function, lower, upper, num_iterations=30,
maximizer="random", model="gp_mcmc",
n_init=3, output_path=None, rng=None):
"""
Entropy search for global black box optimization problems. This is a reimplemenation of the entropy search
algorithm by Henning and Schuler[1].
[1] Entropy search for information-efficient global optimization.
<NAME> and <NAME>.
JMLR, (1), 2012.
Parameters
----------
objective_function: function
The objective function that is minimized. This function gets a numpy array (D,) as input and returns
the function value (scalar)
lower: np.ndarray (D,)
The lower bound of the search space
upper: np.ndarray (D,)
The upper bound of the search space
num_iterations: int
The number of iterations (initial design + BO)
maximizer: {"random", "scipy", "differential_evolution"}
Defines how the acquisition function is maximized.
model: {"gp", "gp_mcmc"}
The model for the objective function.
n_init: int
Number of points for the initial design. Make sure that it is <= num_iterations.
output_path: string
Specifies the path where the intermediate output after each iteration will be saved.
If None no output will be saved to disk.
rng: numpy.random.RandomState
Random number generator
Returns
-------
dict with all results
"""
assert upper.shape[0] == lower.shape[0], "Dimension miss match"
assert np.all(lower < upper), "Lower bound >= upper bound"
assert n_init <= num_iterations, "Number of initial design point has to be <= than the number of iterations"
if rng is None:
rng = np.random.RandomState(np.random.randint(0, 10000))
cov_amp = 2
n_dims = lower.shape[0]
initial_ls = | np.ones([n_dims]) | numpy.ones |
"""Test the search module"""
from collections.abc import Iterable, Sized
from io import StringIO
from itertools import chain, product
from functools import partial
import pickle
import sys
from types import GeneratorType
import re
import numpy as np
import scipy.sparse as sp
import pytest
from sklearn.utils.fixes import sp_version
from sklearn.utils._testing import assert_raises
from sklearn.utils._testing import assert_warns
from sklearn.utils._testing import assert_warns_message
from sklearn.utils._testing import assert_raise_message
from sklearn.utils._testing import assert_array_equal
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.utils._testing import assert_allclose
from sklearn.utils._testing import assert_almost_equal
from sklearn.utils._testing import ignore_warnings
from sklearn.utils._mocking import CheckingClassifier, MockDataFrame
from scipy.stats import bernoulli, expon, uniform
from sklearn.base import BaseEstimator, ClassifierMixin
from sklearn.base import clone
from sklearn.exceptions import NotFittedError
from sklearn.datasets import make_classification
from sklearn.datasets import make_blobs
from sklearn.datasets import make_multilabel_classification
from sklearn.model_selection import fit_grid_point
from sklearn.model_selection import train_test_split
from sklearn.model_selection import KFold
from sklearn.model_selection import StratifiedKFold
from sklearn.model_selection import StratifiedShuffleSplit
from sklearn.model_selection import LeaveOneGroupOut
from sklearn.model_selection import LeavePGroupsOut
from sklearn.model_selection import GroupKFold
from sklearn.model_selection import GroupShuffleSplit
from sklearn.model_selection import GridSearchCV
from sklearn.model_selection import RandomizedSearchCV
from sklearn.model_selection import ParameterGrid
from sklearn.model_selection import ParameterSampler
from sklearn.model_selection._search import BaseSearchCV
from sklearn.model_selection._validation import FitFailedWarning
from sklearn.svm import LinearSVC, SVC
from sklearn.tree import DecisionTreeRegressor
from sklearn.tree import DecisionTreeClassifier
from sklearn.cluster import KMeans
from sklearn.neighbors import KernelDensity
from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import f1_score
from sklearn.metrics import recall_score
from sklearn.metrics import accuracy_score
from sklearn.metrics import make_scorer
from sklearn.metrics import roc_auc_score
from sklearn.metrics.pairwise import euclidean_distances
from sklearn.impute import SimpleImputer
from sklearn.pipeline import Pipeline
from sklearn.linear_model import Ridge, SGDClassifier, LinearRegression
from sklearn.experimental import enable_hist_gradient_boosting # noqa
from sklearn.ensemble import HistGradientBoostingClassifier
from sklearn.model_selection.tests.common import OneTimeSplitter
# Neither of the following two estimators inherit from BaseEstimator,
# to test hyperparameter search on user-defined classifiers.
class MockClassifier:
"""Dummy classifier to test the parameter search algorithms"""
def __init__(self, foo_param=0):
self.foo_param = foo_param
def fit(self, X, Y):
assert len(X) == len(Y)
self.classes_ = np.unique(Y)
return self
def predict(self, T):
return T.shape[0]
def transform(self, X):
return X + self.foo_param
def inverse_transform(self, X):
return X - self.foo_param
predict_proba = predict
predict_log_proba = predict
decision_function = predict
def score(self, X=None, Y=None):
if self.foo_param > 1:
score = 1.
else:
score = 0.
return score
def get_params(self, deep=False):
return {'foo_param': self.foo_param}
def set_params(self, **params):
self.foo_param = params['foo_param']
return self
class LinearSVCNoScore(LinearSVC):
"""An LinearSVC classifier that has no score method."""
@property
def score(self):
raise AttributeError
X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
y = np.array([1, 1, 2, 2])
def assert_grid_iter_equals_getitem(grid):
assert list(grid) == [grid[i] for i in range(len(grid))]
@pytest.mark.parametrize("klass", [ParameterGrid,
partial(ParameterSampler, n_iter=10)])
@pytest.mark.parametrize(
"input, error_type, error_message",
[(0, TypeError, r'Parameter .* is not a dict or a list \(0\)'),
([{'foo': [0]}, 0], TypeError, r'Parameter .* is not a dict \(0\)'),
({'foo': 0}, TypeError, "Parameter.* value is not iterable .*"
r"\(key='foo', value=0\)")]
)
def test_validate_parameter_input(klass, input, error_type, error_message):
with pytest.raises(error_type, match=error_message):
klass(input)
def test_parameter_grid():
# Test basic properties of ParameterGrid.
params1 = {"foo": [1, 2, 3]}
grid1 = ParameterGrid(params1)
assert isinstance(grid1, Iterable)
assert isinstance(grid1, Sized)
assert len(grid1) == 3
assert_grid_iter_equals_getitem(grid1)
params2 = {"foo": [4, 2],
"bar": ["ham", "spam", "eggs"]}
grid2 = ParameterGrid(params2)
assert len(grid2) == 6
# loop to assert we can iterate over the grid multiple times
for i in range(2):
# tuple + chain transforms {"a": 1, "b": 2} to ("a", 1, "b", 2)
points = set(tuple(chain(*(sorted(p.items())))) for p in grid2)
assert (points ==
set(("bar", x, "foo", y)
for x, y in product(params2["bar"], params2["foo"])))
assert_grid_iter_equals_getitem(grid2)
# Special case: empty grid (useful to get default estimator settings)
empty = ParameterGrid({})
assert len(empty) == 1
assert list(empty) == [{}]
assert_grid_iter_equals_getitem(empty)
assert_raises(IndexError, lambda: empty[1])
has_empty = ParameterGrid([{'C': [1, 10]}, {}, {'C': [.5]}])
assert len(has_empty) == 4
assert list(has_empty) == [{'C': 1}, {'C': 10}, {}, {'C': .5}]
assert_grid_iter_equals_getitem(has_empty)
def test_grid_search():
# Test that the best estimator contains the right value for foo_param
clf = MockClassifier()
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=3, verbose=3)
# make sure it selects the smallest parameter in case of ties
old_stdout = sys.stdout
sys.stdout = StringIO()
grid_search.fit(X, y)
sys.stdout = old_stdout
assert grid_search.best_estimator_.foo_param == 2
assert_array_equal(grid_search.cv_results_["param_foo_param"].data,
[1, 2, 3])
# Smoke test the score etc:
grid_search.score(X, y)
grid_search.predict_proba(X)
grid_search.decision_function(X)
grid_search.transform(X)
# Test exception handling on scoring
grid_search.scoring = 'sklearn'
assert_raises(ValueError, grid_search.fit, X, y)
def test_grid_search_pipeline_steps():
# check that parameters that are estimators are cloned before fitting
pipe = Pipeline([('regressor', LinearRegression())])
param_grid = {'regressor': [LinearRegression(), Ridge()]}
grid_search = GridSearchCV(pipe, param_grid, cv=2)
grid_search.fit(X, y)
regressor_results = grid_search.cv_results_['param_regressor']
assert isinstance(regressor_results[0], LinearRegression)
assert isinstance(regressor_results[1], Ridge)
assert not hasattr(regressor_results[0], 'coef_')
assert not hasattr(regressor_results[1], 'coef_')
assert regressor_results[0] is not grid_search.best_estimator_
assert regressor_results[1] is not grid_search.best_estimator_
# check that we didn't modify the parameter grid that was passed
assert not hasattr(param_grid['regressor'][0], 'coef_')
assert not hasattr(param_grid['regressor'][1], 'coef_')
@pytest.mark.parametrize("SearchCV", [GridSearchCV, RandomizedSearchCV])
def test_SearchCV_with_fit_params(SearchCV):
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
clf = CheckingClassifier(expected_fit_params=['spam', 'eggs'])
searcher = SearchCV(
clf, {'foo_param': [1, 2, 3]}, cv=2, error_score="raise"
)
# The CheckingClassifier generates an assertion error if
# a parameter is missing or has length != len(X).
err_msg = r"Expected fit parameter\(s\) \['eggs'\] not seen."
with pytest.raises(AssertionError, match=err_msg):
searcher.fit(X, y, spam=np.ones(10))
err_msg = "Fit parameter spam has length 1; expected"
with pytest.raises(AssertionError, match=err_msg):
searcher.fit(X, y, spam=np.ones(1), eggs=np.zeros(10))
searcher.fit(X, y, spam=np.ones(10), eggs=np.zeros(10))
@ignore_warnings
def test_grid_search_no_score():
# Test grid-search on classifier that has no score function.
clf = LinearSVC(random_state=0)
X, y = make_blobs(random_state=0, centers=2)
Cs = [.1, 1, 10]
clf_no_score = LinearSVCNoScore(random_state=0)
grid_search = GridSearchCV(clf, {'C': Cs}, scoring='accuracy')
grid_search.fit(X, y)
grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs},
scoring='accuracy')
# smoketest grid search
grid_search_no_score.fit(X, y)
# check that best params are equal
assert grid_search_no_score.best_params_ == grid_search.best_params_
# check that we can call score and that it gives the correct result
assert grid_search.score(X, y) == grid_search_no_score.score(X, y)
# giving no scoring function raises an error
grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs})
assert_raise_message(TypeError, "no scoring", grid_search_no_score.fit,
[[1]])
def test_grid_search_score_method():
X, y = make_classification(n_samples=100, n_classes=2, flip_y=.2,
random_state=0)
clf = LinearSVC(random_state=0)
grid = {'C': [.1]}
search_no_scoring = GridSearchCV(clf, grid, scoring=None).fit(X, y)
search_accuracy = GridSearchCV(clf, grid, scoring='accuracy').fit(X, y)
search_no_score_method_auc = GridSearchCV(LinearSVCNoScore(), grid,
scoring='roc_auc'
).fit(X, y)
search_auc = GridSearchCV(clf, grid, scoring='roc_auc').fit(X, y)
# Check warning only occurs in situation where behavior changed:
# estimator requires score method to compete with scoring parameter
score_no_scoring = search_no_scoring.score(X, y)
score_accuracy = search_accuracy.score(X, y)
score_no_score_auc = search_no_score_method_auc.score(X, y)
score_auc = search_auc.score(X, y)
# ensure the test is sane
assert score_auc < 1.0
assert score_accuracy < 1.0
assert score_auc != score_accuracy
assert_almost_equal(score_accuracy, score_no_scoring)
assert_almost_equal(score_auc, score_no_score_auc)
def test_grid_search_groups():
# Check if ValueError (when groups is None) propagates to GridSearchCV
# And also check if groups is correctly passed to the cv object
rng = np.random.RandomState(0)
X, y = make_classification(n_samples=15, n_classes=2, random_state=0)
groups = rng.randint(0, 3, 15)
clf = LinearSVC(random_state=0)
grid = {'C': [1]}
group_cvs = [LeaveOneGroupOut(), LeavePGroupsOut(2),
GroupKFold(n_splits=3), GroupShuffleSplit()]
for cv in group_cvs:
gs = GridSearchCV(clf, grid, cv=cv)
assert_raise_message(ValueError,
"The 'groups' parameter should not be None.",
gs.fit, X, y)
gs.fit(X, y, groups=groups)
non_group_cvs = [StratifiedKFold(), StratifiedShuffleSplit()]
for cv in non_group_cvs:
gs = GridSearchCV(clf, grid, cv=cv)
# Should not raise an error
gs.fit(X, y)
def test_classes__property():
# Test that classes_ property matches best_estimator_.classes_
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
Cs = [.1, 1, 10]
grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs})
grid_search.fit(X, y)
assert_array_equal(grid_search.best_estimator_.classes_,
grid_search.classes_)
# Test that regressors do not have a classes_ attribute
grid_search = GridSearchCV(Ridge(), {'alpha': [1.0, 2.0]})
grid_search.fit(X, y)
assert not hasattr(grid_search, 'classes_')
# Test that the grid searcher has no classes_ attribute before it's fit
grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs})
assert not hasattr(grid_search, 'classes_')
# Test that the grid searcher has no classes_ attribute without a refit
grid_search = GridSearchCV(LinearSVC(random_state=0),
{'C': Cs}, refit=False)
grid_search.fit(X, y)
assert not hasattr(grid_search, 'classes_')
def test_trivial_cv_results_attr():
# Test search over a "grid" with only one point.
clf = MockClassifier()
grid_search = GridSearchCV(clf, {'foo_param': [1]}, cv=3)
grid_search.fit(X, y)
assert hasattr(grid_search, "cv_results_")
random_search = RandomizedSearchCV(clf, {'foo_param': [0]}, n_iter=1, cv=3)
random_search.fit(X, y)
assert hasattr(grid_search, "cv_results_")
def test_no_refit():
# Test that GSCV can be used for model selection alone without refitting
clf = MockClassifier()
for scoring in [None, ['accuracy', 'precision']]:
grid_search = GridSearchCV(
clf, {'foo_param': [1, 2, 3]}, refit=False, cv=3
)
grid_search.fit(X, y)
assert not hasattr(grid_search, "best_estimator_") and \
hasattr(grid_search, "best_index_") and \
hasattr(grid_search, "best_params_")
# Make sure the functions predict/transform etc raise meaningful
# error messages
for fn_name in ('predict', 'predict_proba', 'predict_log_proba',
'transform', 'inverse_transform'):
assert_raise_message(NotFittedError,
('refit=False. %s is available only after '
'refitting on the best parameters'
% fn_name), getattr(grid_search, fn_name), X)
# Test that an invalid refit param raises appropriate error messages
for refit in ["", 5, True, 'recall', 'accuracy']:
assert_raise_message(ValueError, "For multi-metric scoring, the "
"parameter refit must be set to a scorer key",
GridSearchCV(clf, {}, refit=refit,
scoring={'acc': 'accuracy',
'prec': 'precision'}
).fit,
X, y)
def test_grid_search_error():
# Test that grid search will capture errors on data with different length
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
assert_raises(ValueError, cv.fit, X_[:180], y_)
def test_grid_search_one_grid_point():
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
param_dict = {"C": [1.0], "kernel": ["rbf"], "gamma": [0.1]}
clf = SVC(gamma='auto')
cv = GridSearchCV(clf, param_dict)
cv.fit(X_, y_)
clf = SVC(C=1.0, kernel="rbf", gamma=0.1)
clf.fit(X_, y_)
assert_array_equal(clf.dual_coef_, cv.best_estimator_.dual_coef_)
def test_grid_search_when_param_grid_includes_range():
# Test that the best estimator contains the right value for foo_param
clf = MockClassifier()
grid_search = None
grid_search = GridSearchCV(clf, {'foo_param': range(1, 4)}, cv=3)
grid_search.fit(X, y)
assert grid_search.best_estimator_.foo_param == 2
def test_grid_search_bad_param_grid():
param_dict = {"C": 1}
clf = SVC(gamma='auto')
assert_raise_message(
ValueError,
"Parameter grid for parameter (C) needs to"
" be a list or numpy array, but got (<class 'int'>)."
" Single values need to be wrapped in a list"
" with one element.",
GridSearchCV, clf, param_dict)
param_dict = {"C": []}
clf = SVC()
assert_raise_message(
ValueError,
"Parameter values for parameter (C) need to be a non-empty sequence.",
GridSearchCV, clf, param_dict)
param_dict = {"C": "1,2,3"}
clf = SVC(gamma='auto')
assert_raise_message(
ValueError,
"Parameter grid for parameter (C) needs to"
" be a list or numpy array, but got (<class 'str'>)."
" Single values need to be wrapped in a list"
" with one element.",
GridSearchCV, clf, param_dict)
param_dict = {"C": np.ones((3, 2))}
clf = SVC()
assert_raises(ValueError, GridSearchCV, clf, param_dict)
def test_grid_search_sparse():
# Test that grid search works with both dense and sparse matrices
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(X_[:180], y_[:180])
y_pred = cv.predict(X_[180:])
C = cv.best_estimator_.C
X_ = sp.csr_matrix(X_)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(X_[:180].tocoo(), y_[:180])
y_pred2 = cv.predict(X_[180:])
C2 = cv.best_estimator_.C
assert np.mean(y_pred == y_pred2) >= .9
assert C == C2
def test_grid_search_sparse_scoring():
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1")
cv.fit(X_[:180], y_[:180])
y_pred = cv.predict(X_[180:])
C = cv.best_estimator_.C
X_ = sp.csr_matrix(X_)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1")
cv.fit(X_[:180], y_[:180])
y_pred2 = cv.predict(X_[180:])
C2 = cv.best_estimator_.C
assert_array_equal(y_pred, y_pred2)
assert C == C2
# Smoke test the score
# np.testing.assert_allclose(f1_score(cv.predict(X_[:180]), y[:180]),
# cv.score(X_[:180], y[:180]))
# test loss where greater is worse
def f1_loss(y_true_, y_pred_):
return -f1_score(y_true_, y_pred_)
F1Loss = make_scorer(f1_loss, greater_is_better=False)
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring=F1Loss)
cv.fit(X_[:180], y_[:180])
y_pred3 = cv.predict(X_[180:])
C3 = cv.best_estimator_.C
assert C == C3
assert_array_equal(y_pred, y_pred3)
def test_grid_search_precomputed_kernel():
# Test that grid search works when the input features are given in the
# form of a precomputed kernel matrix
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
# compute the training kernel matrix corresponding to the linear kernel
K_train = np.dot(X_[:180], X_[:180].T)
y_train = y_[:180]
clf = SVC(kernel='precomputed')
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(K_train, y_train)
assert cv.best_score_ >= 0
# compute the test kernel matrix
K_test = np.dot(X_[180:], X_[:180].T)
y_test = y_[180:]
y_pred = cv.predict(K_test)
assert np.mean(y_pred == y_test) >= 0
# test error is raised when the precomputed kernel is not array-like
# or sparse
assert_raises(ValueError, cv.fit, K_train.tolist(), y_train)
def test_grid_search_precomputed_kernel_error_nonsquare():
# Test that grid search returns an error with a non-square precomputed
# training kernel matrix
K_train = np.zeros((10, 20))
y_train = np.ones((10, ))
clf = SVC(kernel='precomputed')
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
assert_raises(ValueError, cv.fit, K_train, y_train)
class BrokenClassifier(BaseEstimator):
"""Broken classifier that cannot be fit twice"""
def __init__(self, parameter=None):
self.parameter = parameter
def fit(self, X, y):
assert not hasattr(self, 'has_been_fit_')
self.has_been_fit_ = True
def predict(self, X):
return np.zeros(X.shape[0])
@ignore_warnings
def test_refit():
# Regression test for bug in refitting
# Simulates re-fitting a broken estimator; this used to break with
# sparse SVMs.
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
clf = GridSearchCV(BrokenClassifier(), [{'parameter': [0, 1]}],
scoring="precision", refit=True)
clf.fit(X, y)
def test_refit_callable():
"""
Test refit=callable, which adds flexibility in identifying the
"best" estimator.
"""
def refit_callable(cv_results):
"""
A dummy function tests `refit=callable` interface.
Return the index of a model that has the least
`mean_test_score`.
"""
# Fit a dummy clf with `refit=True` to get a list of keys in
# clf.cv_results_.
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]},
scoring='precision', refit=True)
clf.fit(X, y)
# Ensure that `best_index_ != 0` for this dummy clf
assert clf.best_index_ != 0
# Assert every key matches those in `cv_results`
for key in clf.cv_results_.keys():
assert key in cv_results
return cv_results['mean_test_score'].argmin()
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]},
scoring='precision', refit=refit_callable)
clf.fit(X, y)
assert clf.best_index_ == 0
# Ensure `best_score_` is disabled when using `refit=callable`
assert not hasattr(clf, 'best_score_')
def test_refit_callable_invalid_type():
"""
Test implementation catches the errors when 'best_index_' returns an
invalid result.
"""
def refit_callable_invalid_type(cv_results):
"""
A dummy function tests when returned 'best_index_' is not integer.
"""
return None
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.1, 1]},
scoring='precision', refit=refit_callable_invalid_type)
with pytest.raises(TypeError,
match='best_index_ returned is not an integer'):
clf.fit(X, y)
@pytest.mark.parametrize('out_bound_value', [-1, 2])
@pytest.mark.parametrize('search_cv', [RandomizedSearchCV, GridSearchCV])
def test_refit_callable_out_bound(out_bound_value, search_cv):
"""
Test implementation catches the errors when 'best_index_' returns an
out of bound result.
"""
def refit_callable_out_bound(cv_results):
"""
A dummy function tests when returned 'best_index_' is out of bounds.
"""
return out_bound_value
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
clf = search_cv(LinearSVC(random_state=42), {'C': [0.1, 1]},
scoring='precision', refit=refit_callable_out_bound)
with pytest.raises(IndexError, match='best_index_ index out of range'):
clf.fit(X, y)
def test_refit_callable_multi_metric():
"""
Test refit=callable in multiple metric evaluation setting
"""
def refit_callable(cv_results):
"""
A dummy function tests `refit=callable` interface.
Return the index of a model that has the least
`mean_test_prec`.
"""
assert 'mean_test_prec' in cv_results
return cv_results['mean_test_prec'].argmin()
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
scoring = {'Accuracy': make_scorer(accuracy_score), 'prec': 'precision'}
clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]},
scoring=scoring, refit=refit_callable)
clf.fit(X, y)
assert clf.best_index_ == 0
# Ensure `best_score_` is disabled when using `refit=callable`
assert not hasattr(clf, 'best_score_')
def test_gridsearch_nd():
# Pass X as list in GridSearchCV
X_4d = np.arange(10 * 5 * 3 * 2).reshape(10, 5, 3, 2)
y_3d = np.arange(10 * 7 * 11).reshape(10, 7, 11)
check_X = lambda x: x.shape[1:] == (5, 3, 2)
check_y = lambda x: x.shape[1:] == (7, 11)
clf = CheckingClassifier(
check_X=check_X, check_y=check_y, methods_to_check=["fit"],
)
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]})
grid_search.fit(X_4d, y_3d).score(X, y)
assert hasattr(grid_search, "cv_results_")
def test_X_as_list():
# Pass X as list in GridSearchCV
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
clf = CheckingClassifier(
check_X=lambda x: isinstance(x, list), methods_to_check=["fit"],
)
cv = KFold(n_splits=3)
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=cv)
grid_search.fit(X.tolist(), y).score(X, y)
assert hasattr(grid_search, "cv_results_")
def test_y_as_list():
# Pass y as list in GridSearchCV
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
clf = CheckingClassifier(
check_y=lambda x: isinstance(x, list), methods_to_check=["fit"],
)
cv = KFold(n_splits=3)
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=cv)
grid_search.fit(X, y.tolist()).score(X, y)
assert hasattr(grid_search, "cv_results_")
@ignore_warnings
def test_pandas_input():
# check cross_val_score doesn't destroy pandas dataframe
types = [(MockDataFrame, MockDataFrame)]
try:
from pandas import Series, DataFrame
types.append((DataFrame, Series))
except ImportError:
pass
X = np.arange(100).reshape(10, 10)
y = | np.array([0] * 5 + [1] * 5) | numpy.array |
from abc import ABCMeta, abstractmethod
import os
from vmaf.tools.misc import make_absolute_path, run_process
from vmaf.tools.stats import ListStats
__copyright__ = "Copyright 2016-2018, Netflix, Inc."
__license__ = "Apache, Version 2.0"
import re
import numpy as np
import ast
from vmaf import ExternalProgramCaller, to_list
from vmaf.config import VmafConfig, VmafExternalConfig
from vmaf.core.executor import Executor
from vmaf.core.result import Result
from vmaf.tools.reader import YuvReader
class FeatureExtractor(Executor):
"""
FeatureExtractor takes in a list of assets, and run feature extraction on
them, and return a list of corresponding results. A FeatureExtractor must
specify a unique type and version combination (by the TYPE and VERSION
attribute), so that the Result generated by it can be identified.
A derived class of FeatureExtractor must:
1) Override TYPE and VERSION
2) Override _generate_result(self, asset), which call a
command-line executable and generate feature scores in a log file.
3) Override _get_feature_scores(self, asset), which read the feature
scores from the log file, and return the scores in a dictionary format.
For an example, follow VmafFeatureExtractor.
"""
__metaclass__ = ABCMeta
@property
@abstractmethod
def ATOM_FEATURES(self):
raise NotImplementedError
def _read_result(self, asset):
result = {}
result.update(self._get_feature_scores(asset))
executor_id = self.executor_id
return Result(asset, executor_id, result)
@classmethod
def get_scores_key(cls, atom_feature):
return "{type}_{atom_feature}_scores".format(
type=cls.TYPE, atom_feature=atom_feature)
@classmethod
def get_score_key(cls, atom_feature):
return "{type}_{atom_feature}_score".format(
type=cls.TYPE, atom_feature=atom_feature)
def _get_feature_scores(self, asset):
# routine to read the feature scores from the log file, and return
# the scores in a dictionary format.
log_file_path = self._get_log_file_path(asset)
atom_feature_scores_dict = {}
atom_feature_idx_dict = {}
for atom_feature in self.ATOM_FEATURES:
atom_feature_scores_dict[atom_feature] = []
atom_feature_idx_dict[atom_feature] = 0
with open(log_file_path, 'rt') as log_file:
for line in log_file.readlines():
for atom_feature in self.ATOM_FEATURES:
re_template = "{af}: ([0-9]+) ([a-zA-Z0-9.-]+)".format(af=atom_feature)
mo = re.match(re_template, line)
if mo:
cur_idx = int(mo.group(1))
assert cur_idx == atom_feature_idx_dict[atom_feature]
# parse value, allowing NaN and inf
val = float(mo.group(2))
if np.isnan(val) or np.isinf(val):
val = None
atom_feature_scores_dict[atom_feature].append(val)
atom_feature_idx_dict[atom_feature] += 1
continue
len_score = len(atom_feature_scores_dict[self.ATOM_FEATURES[0]])
assert len_score != 0
for atom_feature in self.ATOM_FEATURES[1:]:
assert len_score == len(atom_feature_scores_dict[atom_feature]), \
"Feature data possibly corrupt. Run cleanup script and try again."
feature_result = {}
for atom_feature in self.ATOM_FEATURES:
scores_key = self.get_scores_key(atom_feature)
feature_result[scores_key] = atom_feature_scores_dict[atom_feature]
return feature_result
class VmafFeatureExtractor(FeatureExtractor):
TYPE = "VMAF_feature"
# VERSION = '0.1' # vmaf_study; Anush's VIF fix
# VERSION = '0.2' # expose vif_num, vif_den, adm_num, adm_den, anpsnr
# VERSION = '0.2.1' # expose vif num/den of each scale
# VERSION = '0.2.2' # adm abs-->fabs, corrected border handling, uniform reading with option of offset for input YUV, updated VIF corner case
# VERSION = '0.2.2b' # expose adm_den/num_scalex
# VERSION = '0.2.3' # AVX for VMAF convolution; update adm features by folding noise floor into per coef
# VERSION = '0.2.4' # Fix a bug in adm feature passing scale into dwt_quant_step
# VERSION = '0.2.4b' # Modify by adding ADM noise floor outside cube root; add derived feature motion2
VERSION = '0.2.4c' # Modify by moving motion2 to c code
ATOM_FEATURES = ['vif', 'adm', 'ansnr', 'motion', 'motion2',
'vif_num', 'vif_den', 'adm_num', 'adm_den', 'anpsnr',
'vif_num_scale0', 'vif_den_scale0',
'vif_num_scale1', 'vif_den_scale1',
'vif_num_scale2', 'vif_den_scale2',
'vif_num_scale3', 'vif_den_scale3',
'adm_num_scale0', 'adm_den_scale0',
'adm_num_scale1', 'adm_den_scale1',
'adm_num_scale2', 'adm_den_scale2',
'adm_num_scale3', 'adm_den_scale3',
]
DERIVED_ATOM_FEATURES = ['vif_scale0', 'vif_scale1', 'vif_scale2', 'vif_scale3',
'vif2', 'adm2', 'adm3',
'adm_scale0', 'adm_scale1', 'adm_scale2', 'adm_scale3',
]
ADM2_CONSTANT = 0
ADM_SCALE_CONSTANT = 0
def _generate_result(self, asset):
# routine to call the command-line executable and generate feature
# scores in the log file.
quality_width, quality_height = asset.quality_width_height
log_file_path = self._get_log_file_path(asset)
yuv_type=self._get_workfile_yuv_type(asset)
ref_path=asset.ref_workfile_path
dis_path=asset.dis_workfile_path
w=quality_width
h=quality_height
logger = self.logger
ExternalProgramCaller.call_vmaf_feature(yuv_type, ref_path, dis_path, w, h, log_file_path, logger)
@classmethod
def _post_process_result(cls, result):
# override Executor._post_process_result
result = super(VmafFeatureExtractor, cls)._post_process_result(result)
# adm2 =
# (adm_num + ADM2_CONSTANT) / (adm_den + ADM2_CONSTANT)
adm2_scores_key = cls.get_scores_key('adm2')
adm_num_scores_key = cls.get_scores_key('adm_num')
adm_den_scores_key = cls.get_scores_key('adm_den')
result.result_dict[adm2_scores_key] = list(
(np.array(result.result_dict[adm_num_scores_key]) + cls.ADM2_CONSTANT) /
(np.array(result.result_dict[adm_den_scores_key]) + cls.ADM2_CONSTANT)
)
# vif_scalei = vif_num_scalei / vif_den_scalei, i = 0, 1, 2, 3
vif_num_scale0_scores_key = cls.get_scores_key('vif_num_scale0')
vif_den_scale0_scores_key = cls.get_scores_key('vif_den_scale0')
vif_num_scale1_scores_key = cls.get_scores_key('vif_num_scale1')
vif_den_scale1_scores_key = cls.get_scores_key('vif_den_scale1')
vif_num_scale2_scores_key = cls.get_scores_key('vif_num_scale2')
vif_den_scale2_scores_key = cls.get_scores_key('vif_den_scale2')
vif_num_scale3_scores_key = cls.get_scores_key('vif_num_scale3')
vif_den_scale3_scores_key = cls.get_scores_key('vif_den_scale3')
vif_scale0_scores_key = cls.get_scores_key('vif_scale0')
vif_scale1_scores_key = cls.get_scores_key('vif_scale1')
vif_scale2_scores_key = cls.get_scores_key('vif_scale2')
vif_scale3_scores_key = cls.get_scores_key('vif_scale3')
result.result_dict[vif_scale0_scores_key] = list(
(np.array(result.result_dict[vif_num_scale0_scores_key])
/ np.array(result.result_dict[vif_den_scale0_scores_key]))
)
result.result_dict[vif_scale1_scores_key] = list(
(np.array(result.result_dict[vif_num_scale1_scores_key])
/ np.array(result.result_dict[vif_den_scale1_scores_key]))
)
result.result_dict[vif_scale2_scores_key] = list(
(np.array(result.result_dict[vif_num_scale2_scores_key])
/ np.array(result.result_dict[vif_den_scale2_scores_key]))
)
result.result_dict[vif_scale3_scores_key] = list(
(np.array(result.result_dict[vif_num_scale3_scores_key])
/ np.array(result.result_dict[vif_den_scale3_scores_key]))
)
# vif2 =
# ((vif_num_scale0 / vif_den_scale0) + (vif_num_scale1 / vif_den_scale1) +
# (vif_num_scale2 / vif_den_scale2) + (vif_num_scale3 / vif_den_scale3)) / 4.0
vif_scores_key = cls.get_scores_key('vif2')
result.result_dict[vif_scores_key] = list(
(
(np.array(result.result_dict[vif_num_scale0_scores_key])
/ np.array(result.result_dict[vif_den_scale0_scores_key])) +
(np.array(result.result_dict[vif_num_scale1_scores_key])
/ | np.array(result.result_dict[vif_den_scale1_scores_key]) | numpy.array |
from data.data_loader_dad import (
NASA_Anomaly,
WADI
)
from exp.exp_basic import Exp_Basic
from models.model import Informer
from utils.tools import EarlyStopping, adjust_learning_rate
from utils.metrics import metric
from sklearn.metrics import classification_report
import numpy as np
import torch
import torch.nn as nn
from torch import optim
from torch.utils.data import DataLoader
import os
import time
import warnings
warnings.filterwarnings('ignore')
class Exp_Informer_DAD(Exp_Basic):
def __init__(self, args):
super(Exp_Informer_DAD, self).__init__(args)
def _build_model(self):
model_dict = {
'informer':Informer,
}
if self.args.model=='informer':
model = model_dict[self.args.model](
self.args.enc_in,
self.args.dec_in,
self.args.c_out,
self.args.seq_len,
self.args.label_len,
self.args.pred_len,
self.args.factor,
self.args.d_model,
self.args.n_heads,
self.args.e_layers,
self.args.d_layers,
self.args.d_ff,
self.args.dropout,
self.args.attn,
self.args.embed,
self.args.data[:-1],
self.args.activation,
self.device
)
return model.double()
def _get_data(self, flag):
args = self.args
data_dict = {
'SMAP':NASA_Anomaly,
'MSL':NASA_Anomaly,
'WADI':WADI,
}
Data = data_dict[self.args.data]
if flag == 'test':
shuffle_flag = False; drop_last = True; batch_size = args.batch_size
else:
shuffle_flag = True; drop_last = True; batch_size = args.batch_size
data_set = Data(
root_path=args.root_path,
data_path=args.data_path,
flag=flag,
size=[args.seq_len, args.label_len, args.pred_len],
features=args.features,
target=args.target
)
print(flag, len(data_set))
data_loader = DataLoader(
data_set,
batch_size=batch_size,
shuffle=shuffle_flag,
num_workers=args.num_workers,
drop_last=drop_last)
return data_set, data_loader
def _select_optimizer(self):
model_optim = optim.Adam(self.model.parameters(), lr=self.args.learning_rate)
return model_optim
def _select_criterion(self):
criterion = nn.MSELoss()
return criterion
def vali(self, vali_data, vali_loader, criterion):
self.model.eval()
total_loss = []
for i, (batch_x,batch_y,batch_x_mark,batch_y_mark,batch_label) in enumerate(vali_loader):
batch_x = batch_x.double().to(self.device)
batch_y = batch_y.double()
batch_x_mark = batch_x_mark.double().to(self.device)
batch_y_mark = batch_y_mark.double().to(self.device)
# decoder input
dec_inp = torch.zeros_like(batch_y[:,-self.args.pred_len:,:]).double()
dec_inp = torch.cat([batch_y[:,:self.args.label_len,:], dec_inp], dim=1).double().to(self.device)
# encoder - decoder
outputs = self.model(batch_x, batch_x_mark, dec_inp, batch_y_mark)
batch_y = batch_y[:,-self.args.pred_len:,:].to(self.device)
pred = outputs.detach().cpu()
true = batch_y.detach().cpu()
loss = criterion(pred, true)
total_loss.append(loss)
total_loss = | np.average(total_loss) | numpy.average |
"""
YTArray class.
"""
from __future__ import print_function
#-----------------------------------------------------------------------------
# Copyright (c) 2013, yt Development Team.
#
# Distributed under the terms of the Modified BSD License.
#
# The full license is in the file COPYING.txt, distributed with this software.
#-----------------------------------------------------------------------------
import copy
import numpy as np
from distutils.version import LooseVersion
from functools import wraps
from numpy import \
add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, \
floor_divide, negative, power, remainder, mod, absolute, rint, \
sign, conj, exp, exp2, log, log2, log10, expm1, log1p, sqrt, square, \
reciprocal, sin, cos, tan, arcsin, arccos, arctan, arctan2, \
hypot, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad, rad2deg, \
bitwise_and, bitwise_or, bitwise_xor, invert, left_shift, right_shift, \
greater, greater_equal, less, less_equal, not_equal, equal, logical_and, \
logical_or, logical_xor, logical_not, maximum, minimum, fmax, fmin, \
isreal, iscomplex, isfinite, isinf, isnan, signbit, copysign, nextafter, \
modf, ldexp, frexp, fmod, floor, ceil, trunc, fabs, spacing
try:
# numpy 1.13 or newer
from numpy import positive, divmod as divmod_, isnat, heaviside
except ImportError:
positive, divmod_, isnat, heaviside = (None,)*4
from yt.units.unit_object import Unit, UnitParseError
from yt.units.unit_registry import UnitRegistry
from yt.units.dimensions import \
angle, \
current_mks, \
dimensionless, \
em_dimensions
from yt.utilities.exceptions import \
YTUnitOperationError, YTUnitConversionError, \
YTUfuncUnitError, YTIterableUnitCoercionError, \
YTInvalidUnitEquivalence, YTEquivalentDimsError
from yt.utilities.lru_cache import lru_cache
from numbers import Number as numeric_type
from yt.utilities.on_demand_imports import _astropy
from sympy import Rational
from yt.units.unit_lookup_table import \
default_unit_symbol_lut
from yt.units.equivalencies import equivalence_registry
from yt.utilities.logger import ytLogger as mylog
from .pint_conversions import convert_pint_units
NULL_UNIT = Unit()
POWER_SIGN_MAPPING = {multiply: 1, divide: -1}
# redefine this here to avoid a circular import from yt.funcs
def iterable(obj):
try: len(obj)
except: return False
return True
def return_arr(func):
@wraps(func)
def wrapped(*args, **kwargs):
ret, units = func(*args, **kwargs)
if ret.shape == ():
return YTQuantity(ret, units)
else:
# This could be a subclass, so don't call YTArray directly.
return type(args[0])(ret, units)
return wrapped
@lru_cache(maxsize=128, typed=False)
def sqrt_unit(unit):
return unit**0.5
@lru_cache(maxsize=128, typed=False)
def multiply_units(unit1, unit2):
return unit1 * unit2
def preserve_units(unit1, unit2=None):
return unit1
@lru_cache(maxsize=128, typed=False)
def power_unit(unit, power):
return unit**power
@lru_cache(maxsize=128, typed=False)
def square_unit(unit):
return unit*unit
@lru_cache(maxsize=128, typed=False)
def divide_units(unit1, unit2):
return unit1/unit2
@lru_cache(maxsize=128, typed=False)
def reciprocal_unit(unit):
return unit**-1
def passthrough_unit(unit, unit2=None):
return unit
def return_without_unit(unit, unit2=None):
return None
def arctan2_unit(unit1, unit2):
return NULL_UNIT
def comparison_unit(unit1, unit2=None):
return None
def invert_units(unit):
raise TypeError(
"Bit-twiddling operators are not defined for YTArray instances")
def bitop_units(unit1, unit2):
raise TypeError(
"Bit-twiddling operators are not defined for YTArray instances")
def get_inp_u_unary(ufunc, inputs, out_arr=None):
inp = inputs[0]
u = getattr(inp, 'units', None)
if u is None:
u = NULL_UNIT
if u.dimensions is angle and ufunc in trigonometric_operators:
inp = inp.in_units('radian').v
if out_arr is not None:
out_arr = ufunc(inp).view(np.ndarray)
return out_arr, inp, u
def get_inp_u_binary(ufunc, inputs):
inp1 = coerce_iterable_units(inputs[0])
inp2 = coerce_iterable_units(inputs[1])
unit1 = getattr(inp1, 'units', None)
unit2 = getattr(inp2, 'units', None)
ret_class = get_binary_op_return_class(type(inp1), type(inp2))
if unit1 is None:
unit1 = Unit(registry=getattr(unit2, 'registry', None))
if unit2 is None and ufunc is not power:
unit2 = Unit(registry=getattr(unit1, 'registry', None))
elif ufunc is power:
unit2 = inp2
if isinstance(unit2, np.ndarray):
if isinstance(unit2, YTArray):
if unit2.units.is_dimensionless:
pass
else:
raise YTUnitOperationError(ufunc, unit1, unit2)
unit2 = 1.0
return (inp1, inp2), (unit1, unit2), ret_class
def handle_preserve_units(inps, units, ufunc, ret_class):
if units[0] != units[1]:
any_nonzero = [np.any(inps[0]), np.any(inps[1])]
if any_nonzero[0] == np.bool_(False):
units = (units[1], units[1])
elif any_nonzero[1] == np.bool_(False):
units = (units[0], units[0])
else:
if not units[0].same_dimensions_as(units[1]):
raise YTUnitOperationError(ufunc, *units)
inps = (inps[0], ret_class(inps[1]).to(
ret_class(inps[0]).units))
return inps, units
def handle_comparison_units(inps, units, ufunc, ret_class, raise_error=False):
if units[0] != units[1]:
u1d = units[0].is_dimensionless
u2d = units[1].is_dimensionless
any_nonzero = [np.any(inps[0]), np.any(inps[1])]
if any_nonzero[0] == np.bool_(False):
units = (units[1], units[1])
elif any_nonzero[1] == np.bool_(False):
units = (units[0], units[0])
elif not any([u1d, u2d]):
if not units[0].same_dimensions_as(units[1]):
raise YTUnitOperationError(ufunc, *units)
else:
if raise_error:
raise YTUfuncUnitError(ufunc, *units)
inps = (inps[0], ret_class(inps[1]).to(
ret_class(inps[0]).units))
return inps, units
def handle_multiply_divide_units(unit, units, out, out_arr):
if unit.is_dimensionless and unit.base_value != 1.0:
if not units[0].is_dimensionless:
if units[0].dimensions == units[1].dimensions:
out_arr = np.multiply(out_arr.view(np.ndarray),
unit.base_value, out=out)
unit = Unit(registry=unit.registry)
return out, out_arr, unit
def coerce_iterable_units(input_object):
if isinstance(input_object, np.ndarray):
return input_object
if iterable(input_object):
if any([isinstance(o, YTArray) for o in input_object]):
ff = getattr(input_object[0], 'units', NULL_UNIT, )
if any([ff != getattr(_, 'units', NULL_UNIT) for _ in input_object]):
raise YTIterableUnitCoercionError(input_object)
# This will create a copy of the data in the iterable.
return YTArray(input_object)
return input_object
else:
return input_object
def sanitize_units_mul(this_object, other_object):
inp = coerce_iterable_units(this_object)
ret = coerce_iterable_units(other_object)
# If the other object is a YTArray and has the same dimensions as the object
# under consideration, convert so we don't mix units with the same
# dimensions.
if isinstance(ret, YTArray):
if inp.units.same_dimensions_as(ret.units):
ret.in_units(inp.units)
return ret
def sanitize_units_add(this_object, other_object, op_string):
inp = coerce_iterable_units(this_object)
ret = coerce_iterable_units(other_object)
# Make sure the other object is a YTArray before we use the `units`
# attribute.
if isinstance(ret, YTArray):
if not inp.units.same_dimensions_as(ret.units):
# handle special case of adding or subtracting with zero or
# array filled with zero
if not np.any(other_object):
return ret.view(np.ndarray)
elif not np.any(this_object):
return ret
raise YTUnitOperationError(op_string, inp.units, ret.units)
ret = ret.in_units(inp.units)
else:
# If the other object is not a YTArray, then one of the arrays must be
# dimensionless or filled with zeros
if not inp.units.is_dimensionless and np.any(ret):
raise YTUnitOperationError(op_string, inp.units, dimensionless)
return ret
def validate_comparison_units(this, other, op_string):
# Check that other is a YTArray.
if hasattr(other, 'units'):
if this.units.expr is other.units.expr:
if this.units.base_value == other.units.base_value:
return other
if not this.units.same_dimensions_as(other.units):
raise YTUnitOperationError(op_string, this.units, other.units)
return other.in_units(this.units)
return other
@lru_cache(maxsize=128, typed=False)
def _unit_repr_check_same(my_units, other_units):
"""
Takes a Unit object, or string of known unit symbol, and check that it
is compatible with this quantity. Returns Unit object.
"""
# let Unit() handle units arg if it's not already a Unit obj.
if not isinstance(other_units, Unit):
other_units = Unit(other_units, registry=my_units.registry)
equiv_dims = em_dimensions.get(my_units.dimensions, None)
if equiv_dims == other_units.dimensions:
if current_mks in equiv_dims.free_symbols:
base = "SI"
else:
base = "CGS"
raise YTEquivalentDimsError(my_units, other_units, base)
if not my_units.same_dimensions_as(other_units):
raise YTUnitConversionError(
my_units, my_units.dimensions, other_units, other_units.dimensions)
return other_units
unary_operators = (
negative, absolute, rint, sign, conj, exp, exp2, log, log2,
log10, expm1, log1p, sqrt, square, reciprocal, sin, cos, tan, arcsin,
arccos, arctan, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad,
rad2deg, invert, logical_not, isreal, iscomplex, isfinite, isinf, isnan,
signbit, floor, ceil, trunc, modf, frexp, fabs, spacing, positive, isnat,
)
binary_operators = (
add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, power,
remainder, mod, arctan2, hypot, bitwise_and, bitwise_or, bitwise_xor,
left_shift, right_shift, greater, greater_equal, less, less_equal,
not_equal, equal, logical_and, logical_or, logical_xor, maximum, minimum,
fmax, fmin, copysign, nextafter, ldexp, fmod, divmod_, heaviside
)
trigonometric_operators = (
sin, cos, tan,
)
class YTArray(np.ndarray):
"""
An ndarray subclass that attaches a symbolic unit object to the array data.
Parameters
----------
input_array : :obj:`!iterable`
A tuple, list, or array to attach units to
input_units : String unit specification, unit symbol object, or astropy units
The units of the array. Powers must be specified using python
syntax (cm**3, not cm^3).
registry : ~yt.units.unit_registry.UnitRegistry
The registry to create units from. If input_units is already associated
with a unit registry and this is specified, this will be used instead of
the registry associated with the unit object.
dtype : data-type
The dtype of the array data. Defaults to the dtype of the input data,
or, if none is found, uses np.float64
bypass_validation : boolean
If True, all input validation is skipped. Using this option may produce
corrupted, invalid units or array data, but can lead to significant
speedups in the input validation logic adds significant overhead. If set,
input_units *must* be a valid unit object. Defaults to False.
Examples
--------
>>> from yt import YTArray
>>> a = YTArray([1, 2, 3], 'cm')
>>> b = YTArray([4, 5, 6], 'm')
>>> a + b
YTArray([ 401., 502., 603.]) cm
>>> b + a
YTArray([ 4.01, 5.02, 6.03]) m
NumPy ufuncs will pass through units where appropriate.
>>> import numpy as np
>>> a = YTArray(np.arange(8) - 4, 'g/cm**3')
>>> np.abs(a)
YTArray([4, 3, 2, 1, 0, 1, 2, 3]) g/cm**3
and strip them when it would be annoying to deal with them.
>>> np.log10(a)
array([ -inf, 0. , 0.30103 , 0.47712125, 0.60205999,
0.69897 , 0.77815125, 0.84509804])
YTArray is tightly integrated with yt datasets:
>>> import yt
>>> ds = yt.load('IsolatedGalaxy/galaxy0030/galaxy0030')
>>> a = ds.arr(np.ones(5), 'code_length')
>>> a.in_cgs()
YTArray([ 3.08600000e+24, 3.08600000e+24, 3.08600000e+24,
3.08600000e+24, 3.08600000e+24]) cm
This is equivalent to:
>>> b = YTArray(np.ones(5), 'code_length', registry=ds.unit_registry)
>>> np.all(a == b)
True
"""
_ufunc_registry = {
add: preserve_units,
subtract: preserve_units,
multiply: multiply_units,
divide: divide_units,
logaddexp: return_without_unit,
logaddexp2: return_without_unit,
true_divide: divide_units,
floor_divide: divide_units,
negative: passthrough_unit,
power: power_unit,
remainder: preserve_units,
mod: preserve_units,
fmod: preserve_units,
absolute: passthrough_unit,
fabs: passthrough_unit,
rint: return_without_unit,
sign: return_without_unit,
conj: passthrough_unit,
exp: return_without_unit,
exp2: return_without_unit,
log: return_without_unit,
log2: return_without_unit,
log10: return_without_unit,
expm1: return_without_unit,
log1p: return_without_unit,
sqrt: sqrt_unit,
square: square_unit,
reciprocal: reciprocal_unit,
sin: return_without_unit,
cos: return_without_unit,
tan: return_without_unit,
sinh: return_without_unit,
cosh: return_without_unit,
tanh: return_without_unit,
arcsin: return_without_unit,
arccos: return_without_unit,
arctan: return_without_unit,
arctan2: arctan2_unit,
arcsinh: return_without_unit,
arccosh: return_without_unit,
arctanh: return_without_unit,
hypot: preserve_units,
deg2rad: return_without_unit,
rad2deg: return_without_unit,
bitwise_and: bitop_units,
bitwise_or: bitop_units,
bitwise_xor: bitop_units,
invert: invert_units,
left_shift: bitop_units,
right_shift: bitop_units,
greater: comparison_unit,
greater_equal: comparison_unit,
less: comparison_unit,
less_equal: comparison_unit,
not_equal: comparison_unit,
equal: comparison_unit,
logical_and: comparison_unit,
logical_or: comparison_unit,
logical_xor: comparison_unit,
logical_not: return_without_unit,
maximum: preserve_units,
minimum: preserve_units,
fmax: preserve_units,
fmin: preserve_units,
isreal: return_without_unit,
iscomplex: return_without_unit,
isfinite: return_without_unit,
isinf: return_without_unit,
isnan: return_without_unit,
signbit: return_without_unit,
copysign: passthrough_unit,
nextafter: preserve_units,
modf: passthrough_unit,
ldexp: bitop_units,
frexp: return_without_unit,
floor: passthrough_unit,
ceil: passthrough_unit,
trunc: passthrough_unit,
spacing: passthrough_unit,
positive: passthrough_unit,
divmod_: passthrough_unit,
isnat: return_without_unit,
heaviside: preserve_units,
}
__array_priority__ = 2.0
def __new__(cls, input_array, input_units=None, registry=None, dtype=None,
bypass_validation=False):
if dtype is None:
dtype = getattr(input_array, 'dtype', np.float64)
if bypass_validation is True:
obj = np.asarray(input_array, dtype=dtype).view(cls)
obj.units = input_units
if registry is not None:
obj.units.registry = registry
return obj
if input_array is NotImplemented:
return input_array.view(cls)
if registry is None and isinstance(input_units, (str, bytes)):
if input_units.startswith('code_'):
raise UnitParseError(
"Code units used without referring to a dataset. \n"
"Perhaps you meant to do something like this instead: \n"
"ds.arr(%s, \"%s\")" % (input_array, input_units)
)
if isinstance(input_array, YTArray):
ret = input_array.view(cls)
if input_units is None:
if registry is None:
ret.units = input_array.units
else:
units = Unit(str(input_array.units), registry=registry)
ret.units = units
elif isinstance(input_units, Unit):
ret.units = input_units
else:
ret.units = Unit(input_units, registry=registry)
return ret
elif isinstance(input_array, np.ndarray):
pass
elif iterable(input_array) and input_array:
if isinstance(input_array[0], YTArray):
return YTArray(np.array(input_array, dtype=dtype),
input_array[0].units, registry=registry)
# Input array is an already formed ndarray instance
# We first cast to be our class type
obj = np.asarray(input_array, dtype=dtype).view(cls)
# Check units type
if input_units is None:
# Nothing provided. Make dimensionless...
units = Unit()
elif isinstance(input_units, Unit):
if registry and registry is not input_units.registry:
units = Unit(str(input_units), registry=registry)
else:
units = input_units
else:
# units kwarg set, but it's not a Unit object.
# don't handle all the cases here, let the Unit class handle if
# it's a str.
units = Unit(input_units, registry=registry)
# Attach the units
obj.units = units
return obj
def __repr__(self):
"""
"""
return super(YTArray, self).__repr__()+' '+self.units.__repr__()
def __str__(self):
"""
"""
return str(self.view(np.ndarray)) + ' ' + str(self.units)
#
# Start unit conversion methods
#
def convert_to_units(self, units):
"""
Convert the array and units to the given units.
Parameters
----------
units : Unit object or str
The units you want to convert to.
"""
new_units = _unit_repr_check_same(self.units, units)
(conversion_factor, offset) = self.units.get_conversion_factor(new_units)
self.units = new_units
values = self.d
values *= conversion_factor
if offset:
np.subtract(self, offset*self.uq, self)
return self
def convert_to_base(self, unit_system="cgs"):
"""
Convert the array and units to the equivalent base units in
the specified unit system.
Parameters
----------
unit_system : string, optional
The unit system to be used in the conversion. If not specified,
the default base units of cgs are used.
Examples
--------
>>> E = YTQuantity(2.5, "erg/s")
>>> E.convert_to_base(unit_system="galactic")
"""
return self.convert_to_units(self.units.get_base_equivalent(unit_system))
def convert_to_cgs(self):
"""
Convert the array and units to the equivalent cgs units.
"""
return self.convert_to_units(self.units.get_cgs_equivalent())
def convert_to_mks(self):
"""
Convert the array and units to the equivalent mks units.
"""
return self.convert_to_units(self.units.get_mks_equivalent())
def in_units(self, units, equivalence=None, **kwargs):
"""
Creates a copy of this array with the data in the supplied
units, and returns it.
Optionally, an equivalence can be specified to convert to an
equivalent quantity which is not in the same dimensions.
.. note::
All additional keyword arguments are passed to the
equivalency, which should be used if that particular
equivalency requires them.
Parameters
----------
units : Unit object or string
The units you want to get a new quantity in.
equivalence : string, optional
The equivalence you wish to use. To see which
equivalencies are supported for this unitful
quantity, try the :meth:`list_equivalencies`
method. Default: None
Returns
-------
YTArray
"""
if equivalence is None:
new_units = _unit_repr_check_same(self.units, units)
(conversion_factor, offset) = self.units.get_conversion_factor(new_units)
new_array = type(self)(self.ndview * conversion_factor, new_units)
if offset:
np.subtract(new_array, offset*new_array.uq, new_array)
return new_array
else:
return self.to_equivalent(units, equivalence, **kwargs)
def to(self, units, equivalence=None, **kwargs):
"""
An alias for YTArray.in_units().
See the docstrings of that function for details.
"""
return self.in_units(units, equivalence=equivalence, **kwargs)
def to_value(self, units=None, equivalence=None, **kwargs):
"""
Creates a copy of this array with the data in the supplied
units, and returns it without units. Output is therefore a
bare NumPy array.
Optionally, an equivalence can be specified to convert to an
equivalent quantity which is not in the same dimensions.
.. note::
All additional keyword arguments are passed to the
equivalency, which should be used if that particular
equivalency requires them.
Parameters
----------
units : Unit object or string, optional
The units you want to get the bare quantity in. If not
specified, the value will be returned in the current units.
equivalence : string, optional
The equivalence you wish to use. To see which
equivalencies are supported for this unitful
quantity, try the :meth:`list_equivalencies`
method. Default: None
Returns
-------
NumPy array
"""
if units is None:
v = self.value
else:
v = self.in_units(units, equivalence=equivalence, **kwargs).value
if isinstance(self, YTQuantity):
return float(v)
else:
return v
def in_base(self, unit_system="cgs"):
"""
Creates a copy of this array with the data in the specified unit system,
and returns it in that system's base units.
Parameters
----------
unit_system : string, optional
The unit system to be used in the conversion. If not specified,
the default base units of cgs are used.
Examples
--------
>>> E = YTQuantity(2.5, "erg/s")
>>> E_new = E.in_base(unit_system="galactic")
"""
return self.in_units(self.units.get_base_equivalent(unit_system))
def in_cgs(self):
"""
Creates a copy of this array with the data in the equivalent cgs units,
and returns it.
Returns
-------
Quantity object with data converted to cgs units.
"""
return self.in_units(self.units.get_cgs_equivalent())
def in_mks(self):
"""
Creates a copy of this array with the data in the equivalent mks units,
and returns it.
Returns
-------
Quantity object with data converted to mks units.
"""
return self.in_units(self.units.get_mks_equivalent())
def to_equivalent(self, unit, equiv, **kwargs):
"""
Convert a YTArray or YTQuantity to an equivalent, e.g., something that is
related by only a constant factor but not in the same units.
Parameters
----------
unit : string
The unit that you wish to convert to.
equiv : string
The equivalence you wish to use. To see which equivalencies are
supported for this unitful quantity, try the
:meth:`list_equivalencies` method.
Examples
--------
>>> a = yt.YTArray(1.0e7,"K")
>>> a.to_equivalent("keV", "thermal")
"""
conv_unit = Unit(unit, registry=self.units.registry)
if self.units.same_dimensions_as(conv_unit):
return self.in_units(conv_unit)
this_equiv = equivalence_registry[equiv]()
oneway_or_equivalent = (
conv_unit.has_equivalent(equiv) or this_equiv._one_way)
if self.has_equivalent(equiv) and oneway_or_equivalent:
new_arr = this_equiv.convert(
self, conv_unit.dimensions, **kwargs)
if isinstance(new_arr, tuple):
try:
return type(self)(new_arr[0], new_arr[1]).in_units(unit)
except YTUnitConversionError:
raise YTInvalidUnitEquivalence(equiv, self.units, unit)
else:
return new_arr.in_units(unit)
else:
raise YTInvalidUnitEquivalence(equiv, self.units, unit)
def list_equivalencies(self):
"""
Lists the possible equivalencies associated with this YTArray or
YTQuantity.
"""
self.units.list_equivalencies()
def has_equivalent(self, equiv):
"""
Check to see if this YTArray or YTQuantity has an equivalent unit in
*equiv*.
"""
return self.units.has_equivalent(equiv)
def ndarray_view(self):
"""
Returns a view into the array, but as an ndarray rather than ytarray.
Returns
-------
View of this array's data.
"""
return self.view(np.ndarray)
def to_ndarray(self):
"""
Creates a copy of this array with the unit information stripped
"""
return np.array(self)
@classmethod
def from_astropy(cls, arr, unit_registry=None):
"""
Convert an AstroPy "Quantity" to a YTArray or YTQuantity.
Parameters
----------
arr : AstroPy Quantity
The Quantity to convert from.
unit_registry : yt UnitRegistry, optional
A yt unit registry to use in the conversion. If one is not
supplied, the default one will be used.
"""
# Converting from AstroPy Quantity
u = arr.unit
ap_units = []
for base, exponent in zip(u.bases, u.powers):
unit_str = base.to_string()
# we have to do this because AstroPy is silly and defines
# hour as "h"
if unit_str == "h": unit_str = "hr"
ap_units.append("%s**(%s)" % (unit_str, Rational(exponent)))
ap_units = "*".join(ap_units)
if isinstance(arr.value, np.ndarray):
return YTArray(arr.value, ap_units, registry=unit_registry)
else:
return YTQuantity(arr.value, ap_units, registry=unit_registry)
def to_astropy(self, **kwargs):
"""
Creates a new AstroPy quantity with the same unit information.
"""
if _astropy.units is None:
raise ImportError("You don't have AstroPy installed, so you can't convert to " +
"an AstroPy quantity.")
return self.value*_astropy.units.Unit(str(self.units), **kwargs)
@classmethod
def from_pint(cls, arr, unit_registry=None):
"""
Convert a Pint "Quantity" to a YTArray or YTQuantity.
Parameters
----------
arr : Pint Quantity
The Quantity to convert from.
unit_registry : yt UnitRegistry, optional
A yt unit registry to use in the conversion. If one is not
supplied, the default one will be used.
Examples
--------
>>> from pint import UnitRegistry
>>> import numpy as np
>>> ureg = UnitRegistry()
>>> a = np.random.random(10)
>>> b = ureg.Quantity(a, "erg/cm**3")
>>> c = yt.YTArray.from_pint(b)
"""
p_units = []
for base, exponent in arr._units.items():
bs = convert_pint_units(base)
p_units.append("%s**(%s)" % (bs, Rational(exponent)))
p_units = "*".join(p_units)
if isinstance(arr.magnitude, np.ndarray):
return YTArray(arr.magnitude, p_units, registry=unit_registry)
else:
return YTQuantity(arr.magnitude, p_units, registry=unit_registry)
def to_pint(self, unit_registry=None):
"""
Convert a YTArray or YTQuantity to a Pint Quantity.
Parameters
----------
arr : YTArray or YTQuantity
The unitful quantity to convert from.
unit_registry : Pint UnitRegistry, optional
The Pint UnitRegistry to use in the conversion. If one is not
supplied, the default one will be used. NOTE: This is not
the same as a yt UnitRegistry object.
Examples
--------
>>> a = YTQuantity(4.0, "cm**2/s")
>>> b = a.to_pint()
"""
from pint import UnitRegistry
if unit_registry is None:
unit_registry = UnitRegistry()
powers_dict = self.units.expr.as_powers_dict()
units = []
for unit, pow in powers_dict.items():
# we have to do this because Pint doesn't recognize
# "yr" as "year"
if str(unit).endswith("yr") and len(str(unit)) in [2,3]:
unit = str(unit).replace("yr","year")
units.append("%s**(%s)" % (unit, Rational(pow)))
units = "*".join(units)
return unit_registry.Quantity(self.value, units)
#
# End unit conversion methods
#
def write_hdf5(self, filename, dataset_name=None, info=None, group_name=None):
r"""Writes a YTArray to hdf5 file.
Parameters
----------
filename: string
The filename to create and write a dataset to
dataset_name: string
The name of the dataset to create in the file.
info: dictionary
A dictionary of supplementary info to write to append as attributes
to the dataset.
group_name: string
An optional group to write the arrays to. If not specified, the arrays
are datasets at the top level by default.
Examples
--------
>>> a = YTArray([1,2,3], 'cm')
>>> myinfo = {'field':'dinosaurs', 'type':'field_data'}
>>> a.write_hdf5('test_array_data.h5', dataset_name='dinosaurs',
... info=myinfo)
"""
from yt.utilities.on_demand_imports import _h5py as h5py
from yt.extern.six.moves import cPickle as pickle
if info is None:
info = {}
info['units'] = str(self.units)
info['unit_registry'] = np.void(pickle.dumps(self.units.registry.lut))
if dataset_name is None:
dataset_name = 'array_data'
f = h5py.File(filename)
if group_name is not None:
if group_name in f:
g = f[group_name]
else:
g = f.create_group(group_name)
else:
g = f
if dataset_name in g.keys():
d = g[dataset_name]
# Overwrite without deleting if we can get away with it.
if d.shape == self.shape and d.dtype == self.dtype:
d[...] = self
for k in d.attrs.keys():
del d.attrs[k]
else:
del f[dataset_name]
d = g.create_dataset(dataset_name, data=self)
else:
d = g.create_dataset(dataset_name, data=self)
for k, v in info.items():
d.attrs[k] = v
f.close()
@classmethod
def from_hdf5(cls, filename, dataset_name=None, group_name=None):
r"""Attempts read in and convert a dataset in an hdf5 file into a
YTArray.
Parameters
----------
filename: string
The filename to of the hdf5 file.
dataset_name: string
The name of the dataset to read from. If the dataset has a units
attribute, attempt to infer units as well.
group_name: string
An optional group to read the arrays from. If not specified, the
arrays are datasets at the top level by default.
"""
import h5py
from yt.extern.six.moves import cPickle as pickle
if dataset_name is None:
dataset_name = 'array_data'
f = h5py.File(filename)
if group_name is not None:
g = f[group_name]
else:
g = f
dataset = g[dataset_name]
data = dataset[:]
units = dataset.attrs.get('units', '')
if 'unit_registry' in dataset.attrs.keys():
unit_lut = pickle.loads(dataset.attrs['unit_registry'].tostring())
else:
unit_lut = None
f.close()
registry = UnitRegistry(lut=unit_lut, add_default_symbols=False)
return cls(data, units, registry=registry)
#
# Start convenience methods
#
@property
def value(self):
"""Get a copy of the array data as a numpy ndarray"""
return np.array(self)
v = value
@property
def ndview(self):
"""Get a view of the array data."""
return self.ndarray_view()
d = ndview
@property
def unit_quantity(self):
"""Get a YTQuantity with the same unit as this array and a value of
1.0"""
return YTQuantity(1.0, self.units)
uq = unit_quantity
@property
def unit_array(self):
"""Get a YTArray filled with ones with the same unit and shape as this
array"""
return np.ones_like(self)
ua = unit_array
def __getitem__(self, item):
ret = super(YTArray, self).__getitem__(item)
if ret.shape == ():
return YTQuantity(ret, self.units, bypass_validation=True)
else:
if hasattr(self, 'units'):
ret.units = self.units
return ret
#
# Start operation methods
#
if LooseVersion(np.__version__) < LooseVersion('1.13.0'):
def __add__(self, right_object):
"""
Add this ytarray to the object on the right of the `+` operator.
Must check for the correct (same dimension) units.
"""
ro = sanitize_units_add(self, right_object, "addition")
return super(YTArray, self).__add__(ro)
def __radd__(self, left_object):
""" See __add__. """
lo = sanitize_units_add(self, left_object, "addition")
return super(YTArray, self).__radd__(lo)
def __iadd__(self, other):
""" See __add__. """
oth = sanitize_units_add(self, other, "addition")
np.add(self, oth, out=self)
return self
def __sub__(self, right_object):
"""
Subtract the object on the right of the `-` from this ytarray. Must
check for the correct (same dimension) units.
"""
ro = sanitize_units_add(self, right_object, "subtraction")
return super(YTArray, self).__sub__(ro)
def __rsub__(self, left_object):
""" See __sub__. """
lo = sanitize_units_add(self, left_object, "subtraction")
return super(YTArray, self).__rsub__(lo)
def __isub__(self, other):
""" See __sub__. """
oth = sanitize_units_add(self, other, "subtraction")
np.subtract(self, oth, out=self)
return self
def __neg__(self):
""" Negate the data. """
return super(YTArray, self).__neg__()
def __mul__(self, right_object):
"""
Multiply this YTArray by the object on the right of the `*`
operator. The unit objects handle being multiplied.
"""
ro = sanitize_units_mul(self, right_object)
return super(YTArray, self).__mul__(ro)
def __rmul__(self, left_object):
""" See __mul__. """
lo = sanitize_units_mul(self, left_object)
return super(YTArray, self).__rmul__(lo)
def __imul__(self, other):
""" See __mul__. """
oth = sanitize_units_mul(self, other)
np.multiply(self, oth, out=self)
return self
def __div__(self, right_object):
"""
Divide this YTArray by the object on the right of the `/` operator.
"""
ro = sanitize_units_mul(self, right_object)
return super(YTArray, self).__div__(ro)
def __rdiv__(self, left_object):
""" See __div__. """
lo = sanitize_units_mul(self, left_object)
return super(YTArray, self).__rdiv__(lo)
def __idiv__(self, other):
""" See __div__. """
oth = sanitize_units_mul(self, other)
np.divide(self, oth, out=self)
return self
def __truediv__(self, right_object):
ro = sanitize_units_mul(self, right_object)
return super(YTArray, self).__truediv__(ro)
def __rtruediv__(self, left_object):
""" See __div__. """
lo = sanitize_units_mul(self, left_object)
return super(YTArray, self).__rtruediv__(lo)
def __itruediv__(self, other):
""" See __div__. """
oth = sanitize_units_mul(self, other)
np.true_divide(self, oth, out=self)
return self
def __floordiv__(self, right_object):
ro = sanitize_units_mul(self, right_object)
return super(YTArray, self).__floordiv__(ro)
def __rfloordiv__(self, left_object):
""" See __div__. """
lo = sanitize_units_mul(self, left_object)
return super(YTArray, self).__rfloordiv__(lo)
def __ifloordiv__(self, other):
""" See __div__. """
oth = sanitize_units_mul(self, other)
np.floor_divide(self, oth, out=self)
return self
def __or__(self, right_object):
return super(YTArray, self).__or__(right_object)
def __ror__(self, left_object):
return super(YTArray, self).__ror__(left_object)
def __ior__(self, other):
np.bitwise_or(self, other, out=self)
return self
def __xor__(self, right_object):
return super(YTArray, self).__xor__(right_object)
def __rxor__(self, left_object):
return super(YTArray, self).__rxor__(left_object)
def __ixor__(self, other):
np.bitwise_xor(self, other, out=self)
return self
def __and__(self, right_object):
return super(YTArray, self).__and__(right_object)
def __rand__(self, left_object):
return super(YTArray, self).__rand__(left_object)
def __iand__(self, other):
np.bitwise_and(self, other, out=self)
return self
def __pow__(self, power):
"""
Raise this YTArray to some power.
Parameters
----------
power : float or dimensionless YTArray.
The pow value.
"""
if isinstance(power, YTArray):
if not power.units.is_dimensionless:
raise YTUnitOperationError('power', power.unit)
# Work around a sympy issue (I think?)
#
# If I don't do this, super(YTArray, self).__pow__ returns a YTArray
# with a unit attribute set to the sympy expression 1/1 rather than
# a dimensionless Unit object.
if self.units.is_dimensionless and power == -1:
ret = super(YTArray, self).__pow__(power)
return type(self)(ret, input_units='')
return super(YTArray, self).__pow__(power)
def __abs__(self):
""" Return a YTArray with the abs of the data. """
return super(YTArray, self).__abs__()
#
# Start comparison operators.
#
def __lt__(self, other):
""" Test if this is less than the object on the right. """
# converts if possible
oth = validate_comparison_units(self, other, 'less_than')
return super(YTArray, self).__lt__(oth)
def __le__(self, other):
"""Test if this is less than or equal to the object on the right.
"""
oth = validate_comparison_units(self, other, 'less_than or equal')
return super(YTArray, self).__le__(oth)
def __eq__(self, other):
""" Test if this is equal to the object on the right. """
# Check that other is a YTArray.
if other is None:
# self is a YTArray, so it can't be None.
return False
oth = validate_comparison_units(self, other, 'equal')
return super(YTArray, self).__eq__(oth)
def __ne__(self, other):
""" Test if this is not equal to the object on the right. """
# Check that the other is a YTArray.
if other is None:
return True
oth = validate_comparison_units(self, other, 'not equal')
return super(YTArray, self).__ne__(oth)
def __ge__(self, other):
""" Test if this is greater than or equal to other. """
# Check that the other is a YTArray.
oth = validate_comparison_units(
self, other, 'greater than or equal')
return super(YTArray, self).__ge__(oth)
def __gt__(self, other):
""" Test if this is greater than the object on the right. """
# Check that the other is a YTArray.
oth = validate_comparison_units(self, other, 'greater than')
return super(YTArray, self).__gt__(oth)
#
# End comparison operators
#
#
# Begin reduction operators
#
@return_arr
def prod(self, axis=None, dtype=None, out=None):
if axis is not None:
units = self.units**self.shape[axis]
else:
units = self.units**self.size
return super(YTArray, self).prod(axis, dtype, out), units
@return_arr
def mean(self, axis=None, dtype=None, out=None):
return super(YTArray, self).mean(axis, dtype, out), self.units
@return_arr
def sum(self, axis=None, dtype=None, out=None):
return super(YTArray, self).sum(axis, dtype, out), self.units
@return_arr
def std(self, axis=None, dtype=None, out=None, ddof=0):
return super(YTArray, self).std(axis, dtype, out, ddof), self.units
def __array_wrap__(self, out_arr, context=None):
ret = super(YTArray, self).__array_wrap__(out_arr, context)
if isinstance(ret, YTQuantity) and ret.shape != ():
ret = ret.view(YTArray)
if context is None:
if ret.shape == ():
return ret[()]
else:
return ret
ufunc = context[0]
inputs = context[1]
if ufunc in unary_operators:
out_arr, inp, u = get_inp_u_unary(ufunc, inputs, out_arr)
unit = self._ufunc_registry[context[0]](u)
ret_class = type(self)
elif ufunc in binary_operators:
unit_operator = self._ufunc_registry[context[0]]
inps, units, ret_class = get_inp_u_binary(ufunc, inputs)
if unit_operator in (preserve_units, comparison_unit,
arctan2_unit):
inps, units = handle_comparison_units(
inps, units, ufunc, ret_class, raise_error=True)
unit = unit_operator(*units)
if unit_operator in (multiply_units, divide_units):
out_arr, out_arr, unit = handle_multiply_divide_units(
unit, units, out_arr, out_arr)
else:
raise RuntimeError(
"Support for the %s ufunc has not been added "
"to YTArray." % str(context[0]))
if unit is None:
out_arr = np.array(out_arr, copy=False)
return out_arr
out_arr.units = unit
if out_arr.size == 1:
return YTQuantity(np.array(out_arr), unit)
else:
if ret_class is YTQuantity:
# This happens if you do ndarray * YTQuantity. Explicitly
# casting to YTArray avoids creating a YTQuantity with
# size > 1
return YTArray(np.array(out_arr), unit)
return ret_class(np.array(out_arr, copy=False), unit)
else: # numpy version equal to or newer than 1.13
def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
func = getattr(ufunc, method)
if 'out' in kwargs:
out_orig = kwargs.pop('out')
out = np.asarray(out_orig[0])
else:
out = None
if len(inputs) == 1:
_, inp, u = get_inp_u_unary(ufunc, inputs)
out_arr = func(np.asarray(inp), out=out, **kwargs)
if ufunc in (multiply, divide) and method == 'reduce':
power_sign = POWER_SIGN_MAPPING[ufunc]
if 'axis' in kwargs and kwargs['axis'] is not None:
unit = u**(power_sign*inp.shape[kwargs['axis']])
else:
unit = u**(power_sign*inp.size)
else:
unit = self._ufunc_registry[ufunc](u)
ret_class = type(self)
elif len(inputs) == 2:
unit_operator = self._ufunc_registry[ufunc]
inps, units, ret_class = get_inp_u_binary(ufunc, inputs)
if unit_operator in (comparison_unit, arctan2_unit):
inps, units = handle_comparison_units(
inps, units, ufunc, ret_class)
elif unit_operator is preserve_units:
inps, units = handle_preserve_units(
inps, units, ufunc, ret_class)
unit = unit_operator(*units)
out_arr = func(np.asarray(inps[0]), np.asarray(inps[1]),
out=out, **kwargs)
if unit_operator in (multiply_units, divide_units):
out, out_arr, unit = handle_multiply_divide_units(
unit, units, out, out_arr)
else:
raise RuntimeError(
"Support for the %s ufunc with %i inputs has not been"
"added to YTArray." % (str(ufunc), len(inputs)))
if unit is None:
out_arr = np.array(out_arr, copy=False)
elif ufunc in (modf, divmod_):
out_arr = tuple((ret_class(o, unit) for o in out_arr))
elif out_arr.size == 1:
out_arr = YTQuantity(np.asarray(out_arr), unit)
else:
if ret_class is YTQuantity:
# This happens if you do ndarray * YTQuantity. Explicitly
# casting to YTArray avoids creating a YTQuantity with
# size > 1
out_arr = YTArray(np.asarray(out_arr), unit)
else:
out_arr = ret_class(np.asarray(out_arr), unit)
if out is not None:
out_orig[0].flat[:] = out.flat[:]
if isinstance(out_orig[0], YTArray):
out_orig[0].units = unit
return out_arr
def copy(self, order='C'):
return type(self)(np.copy(np.asarray(self)), self.units)
def __array_finalize__(self, obj):
if obj is None and hasattr(self, 'units'):
return
self.units = getattr(obj, 'units', NULL_UNIT)
def __pos__(self):
""" Posify the data. """
# this needs to be defined for all numpy versions, see
# numpy issue #9081
return type(self)(super(YTArray, self).__pos__(), self.units)
@return_arr
def dot(self, b, out=None):
return super(YTArray, self).dot(b), self.units*b.units
def __reduce__(self):
"""Pickle reduction method
See the documentation for the standard library pickle module:
http://docs.python.org/2/library/pickle.html
Unit metadata is encoded in the zeroth element of third element of the
returned tuple, itself a tuple used to restore the state of the ndarray.
This is always defined for numpy arrays.
"""
np_ret = super(YTArray, self).__reduce__()
obj_state = np_ret[2]
unit_state = (((str(self.units), self.units.registry.lut),) + obj_state[:],)
new_ret = np_ret[:2] + unit_state + np_ret[3:]
return new_ret
def __setstate__(self, state):
"""Pickle setstate method
This is called inside pickle.read() and restores the unit data from the
metadata extracted in __reduce__ and then serialized by pickle.
"""
super(YTArray, self).__setstate__(state[1:])
try:
unit, lut = state[0]
except TypeError:
# this case happens when we try to load an old pickle file
# created before we serialized the unit symbol lookup table
# into the pickle file
unit, lut = str(state[0]), default_unit_symbol_lut.copy()
# need to fix up the lut if the pickle was saved prior to PR #1728
# when the pickle format changed
if len(lut['m']) == 2:
lut.update(default_unit_symbol_lut)
for k, v in [(k, v) for k, v in lut.items() if len(v) == 2]:
lut[k] = v + (0.0, r'\rm{' + k.replace('_', '\ ') + '}')
registry = UnitRegistry(lut=lut, add_default_symbols=False)
self.units = Unit(unit, registry=registry)
def __deepcopy__(self, memodict=None):
"""copy.deepcopy implementation
This is necessary for stdlib deepcopy of arrays and quantities.
"""
if memodict is None:
memodict = {}
ret = super(YTArray, self).__deepcopy__(memodict)
return type(self)(ret, copy.deepcopy(self.units))
class YTQuantity(YTArray):
"""
A scalar associated with a unit.
Parameters
----------
input_scalar : an integer or floating point scalar
The scalar to attach units to
input_units : String unit specification, unit symbol object, or astropy units
The units of the quantity. Powers must be specified using python syntax
(cm**3, not cm^3).
registry : A UnitRegistry object
The registry to create units from. If input_units is already associated
with a unit registry and this is specified, this will be used instead of
the registry associated with the unit object.
dtype : data-type
The dtype of the array data.
Examples
--------
>>> from yt import YTQuantity
>>> a = YTQuantity(1, 'cm')
>>> b = YTQuantity(2, 'm')
>>> a + b
201.0 cm
>>> b + a
2.01 m
NumPy ufuncs will pass through units where appropriate.
>>> import numpy as np
>>> a = YTQuantity(12, 'g/cm**3')
>>> np.abs(a)
12 g/cm**3
and strip them when it would be annoying to deal with them.
>>> print(np.log10(a))
1.07918124605
YTQuantity is tightly integrated with yt datasets:
>>> import yt
>>> ds = yt.load('IsolatedGalaxy/galaxy0030/galaxy0030')
>>> a = ds.quan(5, 'code_length')
>>> a.in_cgs()
1.543e+25 cm
This is equivalent to:
>>> b = YTQuantity(5, 'code_length', registry=ds.unit_registry)
>>> np.all(a == b)
True
"""
def __new__(cls, input_scalar, input_units=None, registry=None,
dtype=np.float64, bypass_validation=False):
if not isinstance(input_scalar, (numeric_type, np.number, np.ndarray)):
raise RuntimeError("YTQuantity values must be numeric")
ret = YTArray.__new__(cls, input_scalar, input_units, registry,
dtype=dtype, bypass_validation=bypass_validation)
if ret.size > 1:
raise RuntimeError("YTQuantity instances must be scalars")
return ret
def __repr__(self):
return str(self)
def validate_numpy_wrapper_units(v, arrs):
if not any(isinstance(a, YTArray) for a in arrs):
return v
if not all(isinstance(a, YTArray) for a in arrs):
raise RuntimeError("Not all of your arrays are YTArrays.")
a1 = arrs[0]
if not all(a.units == a1.units for a in arrs[1:]):
raise RuntimeError("Your arrays must have identical units.")
v.units = a1.units
return v
def uconcatenate(arrs, axis=0):
"""Concatenate a sequence of arrays.
This wrapper around numpy.concatenate preserves units. All input arrays must
have the same units. See the documentation of numpy.concatenate for full
details.
Examples
--------
>>> A = yt.YTArray([1, 2, 3], 'cm')
>>> B = yt.YTArray([2, 3, 4], 'cm')
>>> uconcatenate((A, B))
YTArray([ 1., 2., 3., 2., 3., 4.]) cm
"""
v = np.concatenate(arrs, axis=axis)
v = validate_numpy_wrapper_units(v, arrs)
return v
def ucross(arr1, arr2, registry=None, axisa=-1, axisb=-1, axisc=-1, axis=None):
"""Applies the cross product to two YT arrays.
This wrapper around numpy.cross preserves units.
See the documentation of numpy.cross for full
details.
"""
v = np.cross(arr1, arr2, axisa=axisa, axisb=axisb, axisc=axisc, axis=axis)
units = arr1.units * arr2.units
arr = YTArray(v, units, registry=registry)
return arr
def uintersect1d(arr1, arr2, assume_unique=False):
"""Find the sorted unique elements of the two input arrays.
A wrapper around numpy.intersect1d that preserves units. All input arrays
must have the same units. See the documentation of numpy.intersect1d for
full details.
Examples
--------
>>> A = yt.YTArray([1, 2, 3], 'cm')
>>> B = yt.YTArray([2, 3, 4], 'cm')
>>> uintersect1d(A, B)
YTArray([ 2., 3.]) cm
"""
v = np.intersect1d(arr1, arr2, assume_unique=assume_unique)
v = validate_numpy_wrapper_units(v, [arr1, arr2])
return v
def uunion1d(arr1, arr2):
"""Find the union of two arrays.
A wrapper around numpy.intersect1d that preserves units. All input arrays
must have the same units. See the documentation of numpy.intersect1d for
full details.
Examples
--------
>>> A = yt.YTArray([1, 2, 3], 'cm')
>>> B = yt.YTArray([2, 3, 4], 'cm')
>>> uunion1d(A, B)
YTArray([ 1., 2., 3., 4.]) cm
"""
v = | np.union1d(arr1, arr2) | numpy.union1d |
"""
YTArray class.
"""
from __future__ import print_function
#-----------------------------------------------------------------------------
# Copyright (c) 2013, yt Development Team.
#
# Distributed under the terms of the Modified BSD License.
#
# The full license is in the file COPYING.txt, distributed with this software.
#-----------------------------------------------------------------------------
import copy
import numpy as np
from distutils.version import LooseVersion
from functools import wraps
from numpy import \
add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, \
floor_divide, negative, power, remainder, mod, absolute, rint, \
sign, conj, exp, exp2, log, log2, log10, expm1, log1p, sqrt, square, \
reciprocal, sin, cos, tan, arcsin, arccos, arctan, arctan2, \
hypot, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad, rad2deg, \
bitwise_and, bitwise_or, bitwise_xor, invert, left_shift, right_shift, \
greater, greater_equal, less, less_equal, not_equal, equal, logical_and, \
logical_or, logical_xor, logical_not, maximum, minimum, fmax, fmin, \
isreal, iscomplex, isfinite, isinf, isnan, signbit, copysign, nextafter, \
modf, ldexp, frexp, fmod, floor, ceil, trunc, fabs, spacing
try:
# numpy 1.13 or newer
from numpy import positive, divmod as divmod_, isnat, heaviside
except ImportError:
positive, divmod_, isnat, heaviside = (None,)*4
from yt.units.unit_object import Unit, UnitParseError
from yt.units.unit_registry import UnitRegistry
from yt.units.dimensions import \
angle, \
current_mks, \
dimensionless, \
em_dimensions
from yt.utilities.exceptions import \
YTUnitOperationError, YTUnitConversionError, \
YTUfuncUnitError, YTIterableUnitCoercionError, \
YTInvalidUnitEquivalence, YTEquivalentDimsError
from yt.utilities.lru_cache import lru_cache
from numbers import Number as numeric_type
from yt.utilities.on_demand_imports import _astropy
from sympy import Rational
from yt.units.unit_lookup_table import \
default_unit_symbol_lut
from yt.units.equivalencies import equivalence_registry
from yt.utilities.logger import ytLogger as mylog
from .pint_conversions import convert_pint_units
NULL_UNIT = Unit()
POWER_SIGN_MAPPING = {multiply: 1, divide: -1}
# redefine this here to avoid a circular import from yt.funcs
def iterable(obj):
try: len(obj)
except: return False
return True
def return_arr(func):
@wraps(func)
def wrapped(*args, **kwargs):
ret, units = func(*args, **kwargs)
if ret.shape == ():
return YTQuantity(ret, units)
else:
# This could be a subclass, so don't call YTArray directly.
return type(args[0])(ret, units)
return wrapped
@lru_cache(maxsize=128, typed=False)
def sqrt_unit(unit):
return unit**0.5
@lru_cache(maxsize=128, typed=False)
def multiply_units(unit1, unit2):
return unit1 * unit2
def preserve_units(unit1, unit2=None):
return unit1
@lru_cache(maxsize=128, typed=False)
def power_unit(unit, power):
return unit**power
@lru_cache(maxsize=128, typed=False)
def square_unit(unit):
return unit*unit
@lru_cache(maxsize=128, typed=False)
def divide_units(unit1, unit2):
return unit1/unit2
@lru_cache(maxsize=128, typed=False)
def reciprocal_unit(unit):
return unit**-1
def passthrough_unit(unit, unit2=None):
return unit
def return_without_unit(unit, unit2=None):
return None
def arctan2_unit(unit1, unit2):
return NULL_UNIT
def comparison_unit(unit1, unit2=None):
return None
def invert_units(unit):
raise TypeError(
"Bit-twiddling operators are not defined for YTArray instances")
def bitop_units(unit1, unit2):
raise TypeError(
"Bit-twiddling operators are not defined for YTArray instances")
def get_inp_u_unary(ufunc, inputs, out_arr=None):
inp = inputs[0]
u = getattr(inp, 'units', None)
if u is None:
u = NULL_UNIT
if u.dimensions is angle and ufunc in trigonometric_operators:
inp = inp.in_units('radian').v
if out_arr is not None:
out_arr = ufunc(inp).view(np.ndarray)
return out_arr, inp, u
def get_inp_u_binary(ufunc, inputs):
inp1 = coerce_iterable_units(inputs[0])
inp2 = coerce_iterable_units(inputs[1])
unit1 = getattr(inp1, 'units', None)
unit2 = getattr(inp2, 'units', None)
ret_class = get_binary_op_return_class(type(inp1), type(inp2))
if unit1 is None:
unit1 = Unit(registry=getattr(unit2, 'registry', None))
if unit2 is None and ufunc is not power:
unit2 = Unit(registry=getattr(unit1, 'registry', None))
elif ufunc is power:
unit2 = inp2
if isinstance(unit2, np.ndarray):
if isinstance(unit2, YTArray):
if unit2.units.is_dimensionless:
pass
else:
raise YTUnitOperationError(ufunc, unit1, unit2)
unit2 = 1.0
return (inp1, inp2), (unit1, unit2), ret_class
def handle_preserve_units(inps, units, ufunc, ret_class):
if units[0] != units[1]:
any_nonzero = [np.any(inps[0]), np.any(inps[1])]
if any_nonzero[0] == np.bool_(False):
units = (units[1], units[1])
elif any_nonzero[1] == np.bool_(False):
units = (units[0], units[0])
else:
if not units[0].same_dimensions_as(units[1]):
raise YTUnitOperationError(ufunc, *units)
inps = (inps[0], ret_class(inps[1]).to(
ret_class(inps[0]).units))
return inps, units
def handle_comparison_units(inps, units, ufunc, ret_class, raise_error=False):
if units[0] != units[1]:
u1d = units[0].is_dimensionless
u2d = units[1].is_dimensionless
any_nonzero = [np.any(inps[0]), np.any(inps[1])]
if any_nonzero[0] == np.bool_(False):
units = (units[1], units[1])
elif any_nonzero[1] == np.bool_(False):
units = (units[0], units[0])
elif not any([u1d, u2d]):
if not units[0].same_dimensions_as(units[1]):
raise YTUnitOperationError(ufunc, *units)
else:
if raise_error:
raise YTUfuncUnitError(ufunc, *units)
inps = (inps[0], ret_class(inps[1]).to(
ret_class(inps[0]).units))
return inps, units
def handle_multiply_divide_units(unit, units, out, out_arr):
if unit.is_dimensionless and unit.base_value != 1.0:
if not units[0].is_dimensionless:
if units[0].dimensions == units[1].dimensions:
out_arr = np.multiply(out_arr.view(np.ndarray),
unit.base_value, out=out)
unit = Unit(registry=unit.registry)
return out, out_arr, unit
def coerce_iterable_units(input_object):
if isinstance(input_object, np.ndarray):
return input_object
if iterable(input_object):
if any([isinstance(o, YTArray) for o in input_object]):
ff = getattr(input_object[0], 'units', NULL_UNIT, )
if any([ff != getattr(_, 'units', NULL_UNIT) for _ in input_object]):
raise YTIterableUnitCoercionError(input_object)
# This will create a copy of the data in the iterable.
return YTArray(input_object)
return input_object
else:
return input_object
def sanitize_units_mul(this_object, other_object):
inp = coerce_iterable_units(this_object)
ret = coerce_iterable_units(other_object)
# If the other object is a YTArray and has the same dimensions as the object
# under consideration, convert so we don't mix units with the same
# dimensions.
if isinstance(ret, YTArray):
if inp.units.same_dimensions_as(ret.units):
ret.in_units(inp.units)
return ret
def sanitize_units_add(this_object, other_object, op_string):
inp = coerce_iterable_units(this_object)
ret = coerce_iterable_units(other_object)
# Make sure the other object is a YTArray before we use the `units`
# attribute.
if isinstance(ret, YTArray):
if not inp.units.same_dimensions_as(ret.units):
# handle special case of adding or subtracting with zero or
# array filled with zero
if not np.any(other_object):
return ret.view(np.ndarray)
elif not np.any(this_object):
return ret
raise YTUnitOperationError(op_string, inp.units, ret.units)
ret = ret.in_units(inp.units)
else:
# If the other object is not a YTArray, then one of the arrays must be
# dimensionless or filled with zeros
if not inp.units.is_dimensionless and np.any(ret):
raise YTUnitOperationError(op_string, inp.units, dimensionless)
return ret
def validate_comparison_units(this, other, op_string):
# Check that other is a YTArray.
if hasattr(other, 'units'):
if this.units.expr is other.units.expr:
if this.units.base_value == other.units.base_value:
return other
if not this.units.same_dimensions_as(other.units):
raise YTUnitOperationError(op_string, this.units, other.units)
return other.in_units(this.units)
return other
@lru_cache(maxsize=128, typed=False)
def _unit_repr_check_same(my_units, other_units):
"""
Takes a Unit object, or string of known unit symbol, and check that it
is compatible with this quantity. Returns Unit object.
"""
# let Unit() handle units arg if it's not already a Unit obj.
if not isinstance(other_units, Unit):
other_units = Unit(other_units, registry=my_units.registry)
equiv_dims = em_dimensions.get(my_units.dimensions, None)
if equiv_dims == other_units.dimensions:
if current_mks in equiv_dims.free_symbols:
base = "SI"
else:
base = "CGS"
raise YTEquivalentDimsError(my_units, other_units, base)
if not my_units.same_dimensions_as(other_units):
raise YTUnitConversionError(
my_units, my_units.dimensions, other_units, other_units.dimensions)
return other_units
unary_operators = (
negative, absolute, rint, sign, conj, exp, exp2, log, log2,
log10, expm1, log1p, sqrt, square, reciprocal, sin, cos, tan, arcsin,
arccos, arctan, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad,
rad2deg, invert, logical_not, isreal, iscomplex, isfinite, isinf, isnan,
signbit, floor, ceil, trunc, modf, frexp, fabs, spacing, positive, isnat,
)
binary_operators = (
add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, power,
remainder, mod, arctan2, hypot, bitwise_and, bitwise_or, bitwise_xor,
left_shift, right_shift, greater, greater_equal, less, less_equal,
not_equal, equal, logical_and, logical_or, logical_xor, maximum, minimum,
fmax, fmin, copysign, nextafter, ldexp, fmod, divmod_, heaviside
)
trigonometric_operators = (
sin, cos, tan,
)
class YTArray(np.ndarray):
"""
An ndarray subclass that attaches a symbolic unit object to the array data.
Parameters
----------
input_array : :obj:`!iterable`
A tuple, list, or array to attach units to
input_units : String unit specification, unit symbol object, or astropy units
The units of the array. Powers must be specified using python
syntax (cm**3, not cm^3).
registry : ~yt.units.unit_registry.UnitRegistry
The registry to create units from. If input_units is already associated
with a unit registry and this is specified, this will be used instead of
the registry associated with the unit object.
dtype : data-type
The dtype of the array data. Defaults to the dtype of the input data,
or, if none is found, uses np.float64
bypass_validation : boolean
If True, all input validation is skipped. Using this option may produce
corrupted, invalid units or array data, but can lead to significant
speedups in the input validation logic adds significant overhead. If set,
input_units *must* be a valid unit object. Defaults to False.
Examples
--------
>>> from yt import YTArray
>>> a = YTArray([1, 2, 3], 'cm')
>>> b = YTArray([4, 5, 6], 'm')
>>> a + b
YTArray([ 401., 502., 603.]) cm
>>> b + a
YTArray([ 4.01, 5.02, 6.03]) m
NumPy ufuncs will pass through units where appropriate.
>>> import numpy as np
>>> a = YTArray(np.arange(8) - 4, 'g/cm**3')
>>> np.abs(a)
YTArray([4, 3, 2, 1, 0, 1, 2, 3]) g/cm**3
and strip them when it would be annoying to deal with them.
>>> np.log10(a)
array([ -inf, 0. , 0.30103 , 0.47712125, 0.60205999,
0.69897 , 0.77815125, 0.84509804])
YTArray is tightly integrated with yt datasets:
>>> import yt
>>> ds = yt.load('IsolatedGalaxy/galaxy0030/galaxy0030')
>>> a = ds.arr(np.ones(5), 'code_length')
>>> a.in_cgs()
YTArray([ 3.08600000e+24, 3.08600000e+24, 3.08600000e+24,
3.08600000e+24, 3.08600000e+24]) cm
This is equivalent to:
>>> b = YTArray(np.ones(5), 'code_length', registry=ds.unit_registry)
>>> np.all(a == b)
True
"""
_ufunc_registry = {
add: preserve_units,
subtract: preserve_units,
multiply: multiply_units,
divide: divide_units,
logaddexp: return_without_unit,
logaddexp2: return_without_unit,
true_divide: divide_units,
floor_divide: divide_units,
negative: passthrough_unit,
power: power_unit,
remainder: preserve_units,
mod: preserve_units,
fmod: preserve_units,
absolute: passthrough_unit,
fabs: passthrough_unit,
rint: return_without_unit,
sign: return_without_unit,
conj: passthrough_unit,
exp: return_without_unit,
exp2: return_without_unit,
log: return_without_unit,
log2: return_without_unit,
log10: return_without_unit,
expm1: return_without_unit,
log1p: return_without_unit,
sqrt: sqrt_unit,
square: square_unit,
reciprocal: reciprocal_unit,
sin: return_without_unit,
cos: return_without_unit,
tan: return_without_unit,
sinh: return_without_unit,
cosh: return_without_unit,
tanh: return_without_unit,
arcsin: return_without_unit,
arccos: return_without_unit,
arctan: return_without_unit,
arctan2: arctan2_unit,
arcsinh: return_without_unit,
arccosh: return_without_unit,
arctanh: return_without_unit,
hypot: preserve_units,
deg2rad: return_without_unit,
rad2deg: return_without_unit,
bitwise_and: bitop_units,
bitwise_or: bitop_units,
bitwise_xor: bitop_units,
invert: invert_units,
left_shift: bitop_units,
right_shift: bitop_units,
greater: comparison_unit,
greater_equal: comparison_unit,
less: comparison_unit,
less_equal: comparison_unit,
not_equal: comparison_unit,
equal: comparison_unit,
logical_and: comparison_unit,
logical_or: comparison_unit,
logical_xor: comparison_unit,
logical_not: return_without_unit,
maximum: preserve_units,
minimum: preserve_units,
fmax: preserve_units,
fmin: preserve_units,
isreal: return_without_unit,
iscomplex: return_without_unit,
isfinite: return_without_unit,
isinf: return_without_unit,
isnan: return_without_unit,
signbit: return_without_unit,
copysign: passthrough_unit,
nextafter: preserve_units,
modf: passthrough_unit,
ldexp: bitop_units,
frexp: return_without_unit,
floor: passthrough_unit,
ceil: passthrough_unit,
trunc: passthrough_unit,
spacing: passthrough_unit,
positive: passthrough_unit,
divmod_: passthrough_unit,
isnat: return_without_unit,
heaviside: preserve_units,
}
__array_priority__ = 2.0
def __new__(cls, input_array, input_units=None, registry=None, dtype=None,
bypass_validation=False):
if dtype is None:
dtype = getattr(input_array, 'dtype', np.float64)
if bypass_validation is True:
obj = np.asarray(input_array, dtype=dtype).view(cls)
obj.units = input_units
if registry is not None:
obj.units.registry = registry
return obj
if input_array is NotImplemented:
return input_array.view(cls)
if registry is None and isinstance(input_units, (str, bytes)):
if input_units.startswith('code_'):
raise UnitParseError(
"Code units used without referring to a dataset. \n"
"Perhaps you meant to do something like this instead: \n"
"ds.arr(%s, \"%s\")" % (input_array, input_units)
)
if isinstance(input_array, YTArray):
ret = input_array.view(cls)
if input_units is None:
if registry is None:
ret.units = input_array.units
else:
units = Unit(str(input_array.units), registry=registry)
ret.units = units
elif isinstance(input_units, Unit):
ret.units = input_units
else:
ret.units = Unit(input_units, registry=registry)
return ret
elif isinstance(input_array, np.ndarray):
pass
elif iterable(input_array) and input_array:
if isinstance(input_array[0], YTArray):
return YTArray(np.array(input_array, dtype=dtype),
input_array[0].units, registry=registry)
# Input array is an already formed ndarray instance
# We first cast to be our class type
obj = np.asarray(input_array, dtype=dtype).view(cls)
# Check units type
if input_units is None:
# Nothing provided. Make dimensionless...
units = Unit()
elif isinstance(input_units, Unit):
if registry and registry is not input_units.registry:
units = Unit(str(input_units), registry=registry)
else:
units = input_units
else:
# units kwarg set, but it's not a Unit object.
# don't handle all the cases here, let the Unit class handle if
# it's a str.
units = Unit(input_units, registry=registry)
# Attach the units
obj.units = units
return obj
def __repr__(self):
"""
"""
return super(YTArray, self).__repr__()+' '+self.units.__repr__()
def __str__(self):
"""
"""
return str(self.view(np.ndarray)) + ' ' + str(self.units)
#
# Start unit conversion methods
#
def convert_to_units(self, units):
"""
Convert the array and units to the given units.
Parameters
----------
units : Unit object or str
The units you want to convert to.
"""
new_units = _unit_repr_check_same(self.units, units)
(conversion_factor, offset) = self.units.get_conversion_factor(new_units)
self.units = new_units
values = self.d
values *= conversion_factor
if offset:
np.subtract(self, offset*self.uq, self)
return self
def convert_to_base(self, unit_system="cgs"):
"""
Convert the array and units to the equivalent base units in
the specified unit system.
Parameters
----------
unit_system : string, optional
The unit system to be used in the conversion. If not specified,
the default base units of cgs are used.
Examples
--------
>>> E = YTQuantity(2.5, "erg/s")
>>> E.convert_to_base(unit_system="galactic")
"""
return self.convert_to_units(self.units.get_base_equivalent(unit_system))
def convert_to_cgs(self):
"""
Convert the array and units to the equivalent cgs units.
"""
return self.convert_to_units(self.units.get_cgs_equivalent())
def convert_to_mks(self):
"""
Convert the array and units to the equivalent mks units.
"""
return self.convert_to_units(self.units.get_mks_equivalent())
def in_units(self, units, equivalence=None, **kwargs):
"""
Creates a copy of this array with the data in the supplied
units, and returns it.
Optionally, an equivalence can be specified to convert to an
equivalent quantity which is not in the same dimensions.
.. note::
All additional keyword arguments are passed to the
equivalency, which should be used if that particular
equivalency requires them.
Parameters
----------
units : Unit object or string
The units you want to get a new quantity in.
equivalence : string, optional
The equivalence you wish to use. To see which
equivalencies are supported for this unitful
quantity, try the :meth:`list_equivalencies`
method. Default: None
Returns
-------
YTArray
"""
if equivalence is None:
new_units = _unit_repr_check_same(self.units, units)
(conversion_factor, offset) = self.units.get_conversion_factor(new_units)
new_array = type(self)(self.ndview * conversion_factor, new_units)
if offset:
np.subtract(new_array, offset*new_array.uq, new_array)
return new_array
else:
return self.to_equivalent(units, equivalence, **kwargs)
def to(self, units, equivalence=None, **kwargs):
"""
An alias for YTArray.in_units().
See the docstrings of that function for details.
"""
return self.in_units(units, equivalence=equivalence, **kwargs)
def to_value(self, units=None, equivalence=None, **kwargs):
"""
Creates a copy of this array with the data in the supplied
units, and returns it without units. Output is therefore a
bare NumPy array.
Optionally, an equivalence can be specified to convert to an
equivalent quantity which is not in the same dimensions.
.. note::
All additional keyword arguments are passed to the
equivalency, which should be used if that particular
equivalency requires them.
Parameters
----------
units : Unit object or string, optional
The units you want to get the bare quantity in. If not
specified, the value will be returned in the current units.
equivalence : string, optional
The equivalence you wish to use. To see which
equivalencies are supported for this unitful
quantity, try the :meth:`list_equivalencies`
method. Default: None
Returns
-------
NumPy array
"""
if units is None:
v = self.value
else:
v = self.in_units(units, equivalence=equivalence, **kwargs).value
if isinstance(self, YTQuantity):
return float(v)
else:
return v
def in_base(self, unit_system="cgs"):
"""
Creates a copy of this array with the data in the specified unit system,
and returns it in that system's base units.
Parameters
----------
unit_system : string, optional
The unit system to be used in the conversion. If not specified,
the default base units of cgs are used.
Examples
--------
>>> E = YTQuantity(2.5, "erg/s")
>>> E_new = E.in_base(unit_system="galactic")
"""
return self.in_units(self.units.get_base_equivalent(unit_system))
def in_cgs(self):
"""
Creates a copy of this array with the data in the equivalent cgs units,
and returns it.
Returns
-------
Quantity object with data converted to cgs units.
"""
return self.in_units(self.units.get_cgs_equivalent())
def in_mks(self):
"""
Creates a copy of this array with the data in the equivalent mks units,
and returns it.
Returns
-------
Quantity object with data converted to mks units.
"""
return self.in_units(self.units.get_mks_equivalent())
def to_equivalent(self, unit, equiv, **kwargs):
"""
Convert a YTArray or YTQuantity to an equivalent, e.g., something that is
related by only a constant factor but not in the same units.
Parameters
----------
unit : string
The unit that you wish to convert to.
equiv : string
The equivalence you wish to use. To see which equivalencies are
supported for this unitful quantity, try the
:meth:`list_equivalencies` method.
Examples
--------
>>> a = yt.YTArray(1.0e7,"K")
>>> a.to_equivalent("keV", "thermal")
"""
conv_unit = Unit(unit, registry=self.units.registry)
if self.units.same_dimensions_as(conv_unit):
return self.in_units(conv_unit)
this_equiv = equivalence_registry[equiv]()
oneway_or_equivalent = (
conv_unit.has_equivalent(equiv) or this_equiv._one_way)
if self.has_equivalent(equiv) and oneway_or_equivalent:
new_arr = this_equiv.convert(
self, conv_unit.dimensions, **kwargs)
if isinstance(new_arr, tuple):
try:
return type(self)(new_arr[0], new_arr[1]).in_units(unit)
except YTUnitConversionError:
raise YTInvalidUnitEquivalence(equiv, self.units, unit)
else:
return new_arr.in_units(unit)
else:
raise YTInvalidUnitEquivalence(equiv, self.units, unit)
def list_equivalencies(self):
"""
Lists the possible equivalencies associated with this YTArray or
YTQuantity.
"""
self.units.list_equivalencies()
def has_equivalent(self, equiv):
"""
Check to see if this YTArray or YTQuantity has an equivalent unit in
*equiv*.
"""
return self.units.has_equivalent(equiv)
def ndarray_view(self):
"""
Returns a view into the array, but as an ndarray rather than ytarray.
Returns
-------
View of this array's data.
"""
return self.view(np.ndarray)
def to_ndarray(self):
"""
Creates a copy of this array with the unit information stripped
"""
return np.array(self)
@classmethod
def from_astropy(cls, arr, unit_registry=None):
"""
Convert an AstroPy "Quantity" to a YTArray or YTQuantity.
Parameters
----------
arr : AstroPy Quantity
The Quantity to convert from.
unit_registry : yt UnitRegistry, optional
A yt unit registry to use in the conversion. If one is not
supplied, the default one will be used.
"""
# Converting from AstroPy Quantity
u = arr.unit
ap_units = []
for base, exponent in zip(u.bases, u.powers):
unit_str = base.to_string()
# we have to do this because AstroPy is silly and defines
# hour as "h"
if unit_str == "h": unit_str = "hr"
ap_units.append("%s**(%s)" % (unit_str, Rational(exponent)))
ap_units = "*".join(ap_units)
if isinstance(arr.value, np.ndarray):
return YTArray(arr.value, ap_units, registry=unit_registry)
else:
return YTQuantity(arr.value, ap_units, registry=unit_registry)
def to_astropy(self, **kwargs):
"""
Creates a new AstroPy quantity with the same unit information.
"""
if _astropy.units is None:
raise ImportError("You don't have AstroPy installed, so you can't convert to " +
"an AstroPy quantity.")
return self.value*_astropy.units.Unit(str(self.units), **kwargs)
@classmethod
def from_pint(cls, arr, unit_registry=None):
"""
Convert a Pint "Quantity" to a YTArray or YTQuantity.
Parameters
----------
arr : Pint Quantity
The Quantity to convert from.
unit_registry : yt UnitRegistry, optional
A yt unit registry to use in the conversion. If one is not
supplied, the default one will be used.
Examples
--------
>>> from pint import UnitRegistry
>>> import numpy as np
>>> ureg = UnitRegistry()
>>> a = np.random.random(10)
>>> b = ureg.Quantity(a, "erg/cm**3")
>>> c = yt.YTArray.from_pint(b)
"""
p_units = []
for base, exponent in arr._units.items():
bs = convert_pint_units(base)
p_units.append("%s**(%s)" % (bs, Rational(exponent)))
p_units = "*".join(p_units)
if isinstance(arr.magnitude, np.ndarray):
return YTArray(arr.magnitude, p_units, registry=unit_registry)
else:
return YTQuantity(arr.magnitude, p_units, registry=unit_registry)
def to_pint(self, unit_registry=None):
"""
Convert a YTArray or YTQuantity to a Pint Quantity.
Parameters
----------
arr : YTArray or YTQuantity
The unitful quantity to convert from.
unit_registry : Pint UnitRegistry, optional
The Pint UnitRegistry to use in the conversion. If one is not
supplied, the default one will be used. NOTE: This is not
the same as a yt UnitRegistry object.
Examples
--------
>>> a = YTQuantity(4.0, "cm**2/s")
>>> b = a.to_pint()
"""
from pint import UnitRegistry
if unit_registry is None:
unit_registry = UnitRegistry()
powers_dict = self.units.expr.as_powers_dict()
units = []
for unit, pow in powers_dict.items():
# we have to do this because Pint doesn't recognize
# "yr" as "year"
if str(unit).endswith("yr") and len(str(unit)) in [2,3]:
unit = str(unit).replace("yr","year")
units.append("%s**(%s)" % (unit, Rational(pow)))
units = "*".join(units)
return unit_registry.Quantity(self.value, units)
#
# End unit conversion methods
#
def write_hdf5(self, filename, dataset_name=None, info=None, group_name=None):
r"""Writes a YTArray to hdf5 file.
Parameters
----------
filename: string
The filename to create and write a dataset to
dataset_name: string
The name of the dataset to create in the file.
info: dictionary
A dictionary of supplementary info to write to append as attributes
to the dataset.
group_name: string
An optional group to write the arrays to. If not specified, the arrays
are datasets at the top level by default.
Examples
--------
>>> a = YTArray([1,2,3], 'cm')
>>> myinfo = {'field':'dinosaurs', 'type':'field_data'}
>>> a.write_hdf5('test_array_data.h5', dataset_name='dinosaurs',
... info=myinfo)
"""
from yt.utilities.on_demand_imports import _h5py as h5py
from yt.extern.six.moves import cPickle as pickle
if info is None:
info = {}
info['units'] = str(self.units)
info['unit_registry'] = np.void(pickle.dumps(self.units.registry.lut))
if dataset_name is None:
dataset_name = 'array_data'
f = h5py.File(filename)
if group_name is not None:
if group_name in f:
g = f[group_name]
else:
g = f.create_group(group_name)
else:
g = f
if dataset_name in g.keys():
d = g[dataset_name]
# Overwrite without deleting if we can get away with it.
if d.shape == self.shape and d.dtype == self.dtype:
d[...] = self
for k in d.attrs.keys():
del d.attrs[k]
else:
del f[dataset_name]
d = g.create_dataset(dataset_name, data=self)
else:
d = g.create_dataset(dataset_name, data=self)
for k, v in info.items():
d.attrs[k] = v
f.close()
@classmethod
def from_hdf5(cls, filename, dataset_name=None, group_name=None):
r"""Attempts read in and convert a dataset in an hdf5 file into a
YTArray.
Parameters
----------
filename: string
The filename to of the hdf5 file.
dataset_name: string
The name of the dataset to read from. If the dataset has a units
attribute, attempt to infer units as well.
group_name: string
An optional group to read the arrays from. If not specified, the
arrays are datasets at the top level by default.
"""
import h5py
from yt.extern.six.moves import cPickle as pickle
if dataset_name is None:
dataset_name = 'array_data'
f = h5py.File(filename)
if group_name is not None:
g = f[group_name]
else:
g = f
dataset = g[dataset_name]
data = dataset[:]
units = dataset.attrs.get('units', '')
if 'unit_registry' in dataset.attrs.keys():
unit_lut = pickle.loads(dataset.attrs['unit_registry'].tostring())
else:
unit_lut = None
f.close()
registry = UnitRegistry(lut=unit_lut, add_default_symbols=False)
return cls(data, units, registry=registry)
#
# Start convenience methods
#
@property
def value(self):
"""Get a copy of the array data as a numpy ndarray"""
return np.array(self)
v = value
@property
def ndview(self):
"""Get a view of the array data."""
return self.ndarray_view()
d = ndview
@property
def unit_quantity(self):
"""Get a YTQuantity with the same unit as this array and a value of
1.0"""
return YTQuantity(1.0, self.units)
uq = unit_quantity
@property
def unit_array(self):
"""Get a YTArray filled with ones with the same unit and shape as this
array"""
return np.ones_like(self)
ua = unit_array
def __getitem__(self, item):
ret = super(YTArray, self).__getitem__(item)
if ret.shape == ():
return YTQuantity(ret, self.units, bypass_validation=True)
else:
if hasattr(self, 'units'):
ret.units = self.units
return ret
#
# Start operation methods
#
if LooseVersion(np.__version__) < LooseVersion('1.13.0'):
def __add__(self, right_object):
"""
Add this ytarray to the object on the right of the `+` operator.
Must check for the correct (same dimension) units.
"""
ro = sanitize_units_add(self, right_object, "addition")
return super(YTArray, self).__add__(ro)
def __radd__(self, left_object):
""" See __add__. """
lo = sanitize_units_add(self, left_object, "addition")
return super(YTArray, self).__radd__(lo)
def __iadd__(self, other):
""" See __add__. """
oth = sanitize_units_add(self, other, "addition")
np.add(self, oth, out=self)
return self
def __sub__(self, right_object):
"""
Subtract the object on the right of the `-` from this ytarray. Must
check for the correct (same dimension) units.
"""
ro = sanitize_units_add(self, right_object, "subtraction")
return super(YTArray, self).__sub__(ro)
def __rsub__(self, left_object):
""" See __sub__. """
lo = sanitize_units_add(self, left_object, "subtraction")
return super(YTArray, self).__rsub__(lo)
def __isub__(self, other):
""" See __sub__. """
oth = sanitize_units_add(self, other, "subtraction")
np.subtract(self, oth, out=self)
return self
def __neg__(self):
""" Negate the data. """
return super(YTArray, self).__neg__()
def __mul__(self, right_object):
"""
Multiply this YTArray by the object on the right of the `*`
operator. The unit objects handle being multiplied.
"""
ro = sanitize_units_mul(self, right_object)
return super(YTArray, self).__mul__(ro)
def __rmul__(self, left_object):
""" See __mul__. """
lo = sanitize_units_mul(self, left_object)
return super(YTArray, self).__rmul__(lo)
def __imul__(self, other):
""" See __mul__. """
oth = sanitize_units_mul(self, other)
np.multiply(self, oth, out=self)
return self
def __div__(self, right_object):
"""
Divide this YTArray by the object on the right of the `/` operator.
"""
ro = sanitize_units_mul(self, right_object)
return super(YTArray, self).__div__(ro)
def __rdiv__(self, left_object):
""" See __div__. """
lo = sanitize_units_mul(self, left_object)
return super(YTArray, self).__rdiv__(lo)
def __idiv__(self, other):
""" See __div__. """
oth = sanitize_units_mul(self, other)
np.divide(self, oth, out=self)
return self
def __truediv__(self, right_object):
ro = sanitize_units_mul(self, right_object)
return super(YTArray, self).__truediv__(ro)
def __rtruediv__(self, left_object):
""" See __div__. """
lo = sanitize_units_mul(self, left_object)
return super(YTArray, self).__rtruediv__(lo)
def __itruediv__(self, other):
""" See __div__. """
oth = sanitize_units_mul(self, other)
np.true_divide(self, oth, out=self)
return self
def __floordiv__(self, right_object):
ro = sanitize_units_mul(self, right_object)
return super(YTArray, self).__floordiv__(ro)
def __rfloordiv__(self, left_object):
""" See __div__. """
lo = sanitize_units_mul(self, left_object)
return super(YTArray, self).__rfloordiv__(lo)
def __ifloordiv__(self, other):
""" See __div__. """
oth = sanitize_units_mul(self, other)
np.floor_divide(self, oth, out=self)
return self
def __or__(self, right_object):
return super(YTArray, self).__or__(right_object)
def __ror__(self, left_object):
return super(YTArray, self).__ror__(left_object)
def __ior__(self, other):
np.bitwise_or(self, other, out=self)
return self
def __xor__(self, right_object):
return super(YTArray, self).__xor__(right_object)
def __rxor__(self, left_object):
return super(YTArray, self).__rxor__(left_object)
def __ixor__(self, other):
| np.bitwise_xor(self, other, out=self) | numpy.bitwise_xor |
# pvtrace is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# pvtrace is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import numpy as np
from external.transformations import translation_matrix, rotation_matrix
import external.transformations as tf
from Trace import Photon
from Geometry import Box, Cylinder, FinitePlane, transform_point, transform_direction, rotation_matrix_from_vector_alignment, norm
from Materials import Spectrum
def random_spherecial_vector():
# This method of calculating isotropic vectors is taken from GNU Scientific Library
LOOP = True
while LOOP:
x = -1. + 2. * np.random.uniform()
y = -1. + 2. * | np.random.uniform() | numpy.random.uniform |
# pvtrace is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# pvtrace is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import numpy as np
from external.transformations import translation_matrix, rotation_matrix
import external.transformations as tf
from Trace import Photon
from Geometry import Box, Cylinder, FinitePlane, transform_point, transform_direction, rotation_matrix_from_vector_alignment, norm
from Materials import Spectrum
def random_spherecial_vector():
# This method of calculating isotropic vectors is taken from GNU Scientific Library
LOOP = True
while LOOP:
x = -1. + 2. * np.random.uniform()
y = -1. + 2. * np.random.uniform()
s = x**2 + y**2
if s <= 1.0:
LOOP = False
z = -1. + 2. * s
a = 2 * np.sqrt(1 - s)
x = a * x
y = a * y
return np.array([x,y,z])
class SimpleSource(object):
"""A light source that will generate photons of a single colour, direction and position."""
def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, use_random_polarisation=False):
super(SimpleSource, self).__init__()
self.position = position
self.direction = direction
self.wavelength = wavelength
self.use_random_polarisation = use_random_polarisation
self.throw = 0
self.source_id = "SimpleSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.position = np.array(self.position)
photon.direction = np.array(self.direction)
photon.active = True
photon.wavelength = self.wavelength
# If use_polarisation is set generate a random polarisation vector of the photon
if self.use_random_polarisation:
# Randomise rotation angle around xy-plane, the transform from +z to the direction of the photon
vec = random_spherecial_vector()
vec[2] = 0.
vec = norm(vec)
R = rotation_matrix_from_vector_alignment(self.direction, [0,0,1])
photon.polarisation = transform_direction(vec, R)
else:
photon.polarisation = None
photon.id = self.throw
self.throw = self.throw + 1
return photon
class Laser(object):
"""A light source that will generate photons of a single colour, direction and position."""
def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, polarisation=None):
super(Laser, self).__init__()
self.position = np.array(position)
self.direction = | np.array(direction) | numpy.array |
import os
from PIL import Image
import cv2
from os import listdir
from os.path import join
import matplotlib.pyplot as plt
import matplotlib
from matplotlib.colors import LogNorm
from io_utils.io_common import create_folder
from viz_utils.constants import PlotMode, BackgroundType
import pylab
import numpy as np
import cmocean
import shapely
import cartopy.crs as ccrs
import cartopy.feature as cfeature
import cartopy
def select_colormap(field_name):
'''
Based on the name if the field it chooses a colormap from cmocean
Args:
field_name:
Returns:
'''
if np.any([field_name.find(x) != -1 for x in ('ssh', 'srfhgt', 'adt','surf_el')]):
# cmaps_fields.append(cmocean.cm.deep_r)
return cmocean.cm.curl
elif np.any([field_name.find(x) != -1 for x in ('temp', 'sst', 'temperature')]):
return cmocean.cm.thermal
elif np.any([field_name.find(x) != -1 for x in ('vorticity', 'vort')]):
return cmocean.cm.curl
elif np.any([field_name.find(x) != -1 for x in ('salin', 'sss', 'sal')]):
return cmocean.cm.haline
elif field_name.find('error') != -1:
return cmocean.cm.diff
elif field_name.find('binary') != -1:
return cmocean.cm.oxy
elif np.any([field_name.find(x) != -1 for x in ('u_', 'v_', 'u-vel.', 'v-vel.','velocity')]):
return cmocean.cm.speed
class EOAImageVisualizer:
"""This class makes plenty of plots assuming we are plotting Geospatial data (maps).
It is made to read xarrays, numpy arrays, and numpy arrays in dictionaries
vizobj = new EOAImageVisualizer(disp_images=True, output_folder='output',
lats=[lats],lons=[lons])
"""
_COLORS = ['y', 'r', 'c', 'b', 'g', 'w', 'k', 'y', 'r', 'c', 'b', 'g', 'w', 'k']
_figsize = 8
_font_size = 30
_units = ''
_max_imgs_per_row = 4
_mincbar = np.nan # User can set a min and max colorbar values to 'force' same color bar to all plots
_maxcbar = np.nan
_flip_data = True
_eoas_pyutils_path = './eoas_pyutils'# This is the path where the eoas_utils folder is stored with respect to the main project
_contourf = False # When plotting non-regular grids and need precision
_background = BackgroundType.BLUE_MARBLE_LR # Select the background to use
_auto_colormap = True # Selects the colormap based on the name of the field
_show_var_names = False # Includes the name of the field name in the titles
_additional_polygons = [] # MUST BE SHAPELY GEOMETRIES In case we want to include additional polygons in the plots (all of them)
# If you want to add a streamplot of a vector field. It must be a dictionary with keys x,y,u,v
# and optional density, color, cmap, arrowsize, arrowstyle, minlength
_vector_field = None
_norm = None # Use to normalize the colormap. For example with LogNorm
# vizobj = EOAImageVisualizer(disp_images=True, output_folder='output',
# lats=[lats],lons=[lons])
def __init__(self, disp_images=True, output_folder='output',
lats=[-90,90], lons =[-180,180],
projection=ccrs.PlateCarree(), **kwargs):
# All the arguments that are passed to the constructor of the class MUST have its name on it.
self._disp_images = disp_images
self._output_folder = output_folder
self._projection = projection
bbox = self.getExtent(lats, lons)
self._extent = bbox
self._lats = lats
self._lons = lons
self._fig_prop = (bbox[1]-bbox[0])/(bbox[3]-bbox[2])
self._contour_labels = False
for arg_name, arg_value in kwargs.items():
self.__dict__["_" + arg_name] = arg_value
print(self.__dict__["_" + arg_name])
def __getattr__(self, attr):
'''Generic getter for all the properties of the class'''
return self.__dict__["_" + attr]
def __setattr__(self, attr, value):
'''Generic setter for all the properties of the class'''
self.__dict__["_" + attr] = value
def add_colorbar(self, fig, im, ax, show_color_bar, label=""):
# https://matplotlib.org/api/_as_gen/matplotlib.pyplot.colorbar.html
if show_color_bar:
font_size_cbar = self._font_size * .5
# TODO how to make this automatic and works always
cbar = fig.colorbar(im, ax=ax, shrink=.7)
cbar.ax.tick_params(labelsize=font_size_cbar)
if label != "":
cbar.set_label(label, fontsize=font_size_cbar*1.2)
else:
cbar.set_label(self._units, fontsize=font_size_cbar*1.2)
def plot_slice_eoa(self, c_img, ax, cmap='gray', mode=PlotMode.RASTER, mincbar=np.nan, maxcbar=np.nan) -> None:
"""
Plots a 2D img for EOA data.
:param c_img: 2D array
:param ax: geoaxes
:return:
"""
c_ax = ax
if self._flip_data:
origin = 'lower'
else:
origin = 'upper'
if self._background == BackgroundType.CARTO_DEF:
c_ax.stock_img()
else:
if self._background == BackgroundType.BLUE_MARBLE_LR:
img = plt.imread(join(self._eoas_pyutils_path,'viz_utils/imgs/bluemarble.png'))
if self._background == BackgroundType.BLUE_MARBLE_HR:
img = plt.imread(join(self._eoas_pyutils_path,'viz_utils/imgs/bluemarble_5400x2700.jpg'))
if self._background == BackgroundType.TOPO:
img = plt.imread(join(self._eoas_pyutils_path,'viz_utils/imgs/etopo.png'))
if self._background == BackgroundType.BATHYMETRY:
img = plt.imread(join(self._eoas_pyutils_path,'viz_utils/imgs/bathymetry_3600x1800.jpg'))
c_ax.imshow(img, origin='upper', extent=(-180,180,-90,90), transform=ccrs.PlateCarree())
if mode == PlotMode.RASTER or mode == PlotMode.MERGED:
if self._contourf:
im = c_ax.contourf(self._lons, self._lats, c_img, num_colors=255, cmap='inferno', extent=self._extent)
else:
if np.isnan(mincbar):
im = c_ax.imshow(c_img, extent=self._extent, origin=origin, cmap=cmap, transform=self._projection, norm=self._norm)
else:
im = c_ax.imshow(c_img, extent=self._extent, origin=origin, cmap=cmap, vmin=mincbar, vmax=maxcbar, transform=self._projection, norm=self._norm)
if mode == PlotMode.CONTOUR or mode == PlotMode.MERGED:
c_ax.set_extent(self.getExtent(list(self._lats), list(self._lons)))
if mode == PlotMode.CONTOUR:
im = c_ax.contour(c_img, extent=self._extent, transform=self._projection)
if mode == PlotMode.MERGED:
if self._contour_labels:
c_ax.contour(c_img, self._contour_labels, colors='r', extent=self._extent, transform=self._projection)
else:
c_ax.contour(c_img, extent=self._extent, transform=self._projection)
if len(self._additional_polygons) > 0:
pol_lats = []
pol_lons = []
for c_polygon in self._additional_polygons:
if isinstance(c_polygon, shapely.geometry.linestring.LineString):
x,y = c_polygon.xy
elif isinstance(c_polygon, shapely.geometry.polygon.Polygon):
x, y = c_polygon.exterior.xy
pol_lats += y
pol_lons += x
c_ax.plot(x,y, transform=self._projection, c='r')
# Adds a threshold to the plot to see the polygons
c_ax.set_extent(self.getExtent(list(self._lats) + pol_lats, list(self._lons) + pol_lons, 0.5))
if self._vector_field != None:
try:
u = self._vector_field['u']
v = self._vector_field['v']
x = self._vector_field['x']
y = self._vector_field['y']
vec_keys = self._vector_field.keys()
c = 'r'
density = 1
linewidth = 3
vec_cmap = cmocean.cm.solar
if 'color' in vec_keys:
c = self._vector_field['color']
if 'density' in vec_keys:
density = self._vector_field['density']
if 'linewidth' in vec_keys:
linewidth = self._vector_field['linewidth']
if 'cmap' in vec_keys:
vec_cmap = self._vector_field['cmap']
c_ax.set_extent(self.getExtent(list(self._lats), list(self._lons)))
c_ax.streamplot(x, y, u, v, transform=self._projection, density=density, color=c,
cmap=vec_cmap, linewidth=linewidth)
except Exception as e:
print(F"Couldn't add vector field e:{e}")
gl = c_ax.gridlines(draw_labels=True, color='grey', alpha=0.5, linestyle='--')
# gl.xlabel_style = {'size': self._font_size/2, 'color': '#aaaaaa', 'weight':'bold'}
font_coords = {'size': self._font_size*.6}
gl.xlabel_style = font_coords
gl.ylabel_style = font_coords
gl.top_labels = False
gl.right_labels = False
return im
def get_proper_size(self, rows, cols):
"""
Obtains the proper size for a figure.
:param rows: how many rows will the figure have
:param cols: how many colswill the figure have
:param prop: Proportion is the proportion to use w/h
:return:
"""
if rows == 1:
return self._figsize * cols * self._fig_prop, self._figsize
else:
return self._figsize * cols * self._fig_prop, self._figsize * rows
def _close_figure(self):
"""Depending on what is disp_images, the figures are displayed or just closed"""
if self._disp_images:
plt.show()
else:
plt.close()
def getExtent(self, lats, lons, expand_ext=0.0):
'''
Obtains the bbox of the coordinates. If included threshold then increases the bbox in all directions with that thres
Args:
lats:
lons:
inc_threshold:
Returns:
'''
minLat = np.amin(lats) - expand_ext
maxLat = np.amax(lats) + expand_ext
minLon = np.amin(lons) - expand_ext
maxLon = np.amax(lons) + expand_ext
bbox = (minLon, maxLon, minLat, maxLat)
return bbox
def xr_summary(self, ds):
""" Prints a summary of the netcdf (global attributes, variables, etc)
:param ds:
:return:
"""
print("\n========== Global attributes =========")
for name in ds.attrs:
print(F"{name} = {getattr(ds, name)}")
print("\n========== Dimensions =========")
for name in ds.dims:
print(F"{name}: {ds[name].shape}")
print("\n========== Coordinates =========")
for name in ds.coords:
print(F"{name}: {ds[name].shape}")
print("\n========== Variables =========")
for cur_variable_name in ds.variables:
cur_var = ds[cur_variable_name]
print(F"{cur_variable_name}: {cur_var.dims} {cur_var.shape}")
def nc_summary(self, ds):
""" Prints a summary of the netcdf (global attributes, variables, etc)
:param ds:
:return:
"""
print("\n========== Global attributes =========")
for name in ds.ncattrs():
print(F"{name} = {getattr(ds, name)}")
print("\n========== Variables =========")
netCDFvars = ds.variables
for cur_variable_name in netCDFvars.keys():
cur_var = ds.variables[cur_variable_name]
print(F"Dimensions for {cur_variable_name}: {cur_var.dimensions} {cur_var.shape}")
def add_roads(self, ax):
# Names come from: https://www.naturalearthdata.com/features/
# -- Add states
roads = cfeature.NaturalEarthFeature(
category='cultural',
name='roads',
scale='10m',
facecolor='none')
ax.add_feature(roads, edgecolor='black')
return ax
def add_states(self, ax):
# Names come from: https://www.naturalearthdata.com/features/
# -- Add states
states_provinces = cfeature.NaturalEarthFeature(
category='cultural',
name='admin_1_states_provinces_lines',
scale='50m',
facecolor='none')
ax.add_feature(states_provinces, edgecolor='gray')
return ax
def plot_scatter_data(self, lats=None, lons=None, bbox=None, s=1, c='blue', cmap='plasma', title=''):
'''
This function plots points in a map
:param bbox:
:return:
'''
if bbox is None:
bbox = (-180, 180, -90, 90)
if lats is None:
lats = self.lats
if lons is None:
lons = self.lons
fig, ax = plt.subplots(1, 1, figsize=(self._figsize, self._figsize), subplot_kw={'projection': ccrs.PlateCarree()})
ax.set_extent(bbox) # If we do not set this, it will cropp it to the limits of the locations
ax.gridlines()
im = ax.scatter(lons, lats, s=s, c=c, cmap=cmap)
fig.colorbar(im, ax=ax, shrink=0.7)
ax.coastlines()
plt.title(title)
plt.show()
def plot_3d_data_npdict(self, np_variables:list, var_names:list, z_levels= [], title='',
file_name_prefix='', cmap=None, z_names = [],
show_color_bar=True, plot_mode=PlotMode.RASTER, mincbar=np.nan, maxcbar=np.nan):
"""
Plots multiple z_levels for multiple fields.
It uses rows for each depth, and columns for each variable
"""
create_folder(self._output_folder)
orig_cmap = cmap
# If the user do not requires any z-leve, then all are plotted
if len(z_levels) == 0:
z_levels = range(np_variables[var_names[0]].shape[0])
cols = np.min((self._max_imgs_per_row, len(var_names)))
if cols == len(var_names):
rows = len(z_levels)
else:
rows = int(len(z_levels) * np.ceil(len(var_names)/cols))
fig, _axs = plt.subplots(rows, cols,
figsize=self.get_proper_size(rows, cols),
subplot_kw={'projection': self._projection})
for c_zlevel, c_slice in enumerate(z_levels): # Iterates over the z-levels
# Verify the index of the z_levels are the original ones.
if len(z_names) != 0:
c_slice_txt = z_names[c_slice]
else:
c_slice_txt = c_slice
c_mincbar = np.nan
c_maxcbar = np.nan
for idx_var, c_var in enumerate(var_names): # Iterate over the fields
if rows*cols == 1: # Single figure
ax = _axs
else:
ax = _axs.flatten()[c_zlevel*len(var_names) + idx_var]
# Here we chose the min and max colorbars for each field
if not(np.all(np.isnan(mincbar))):
if type(mincbar) is list:
c_mincbar = mincbar[idx_var]
else:
c_mincbar = mincbar
if not(np.all(np.isnan(maxcbar))):
if type(mincbar) is list:
c_maxcbar = maxcbar[idx_var]
else:
c_maxcbar = maxcbar
# By default we select the colorbar from the name of the variable
if self._auto_colormap and orig_cmap is None:
cmap = select_colormap(c_var)
else:
# If there is an array of colormaps we select the one for this field
if type(orig_cmap) is list:
cmap = orig_cmap[idx_var]
else:
# If it is just one cmap, then we use it for all the fields
cmap = orig_cmap
im = self.plot_slice_eoa(np_variables[c_var][c_slice,:,:], ax, cmap=cmap, mode=plot_mode,
mincbar=c_mincbar, maxcbar=c_maxcbar)
if self._show_var_names:
c_title = F'{var_names[idx_var]} {title}'
else:
c_title = F'{title}'
if len(z_levels) > 1:
c_title += F"Z - level: {c_slice_txt}"
ax.set_title(c_title, fontsize=self._font_size)
self.add_colorbar(fig, im, ax, show_color_bar)
plt.tight_layout(pad=.5)
file_name = F'{file_name_prefix}'
pylab.savefig(join(self._output_folder, F'{file_name}.png'), bbox_inches='tight')
self._close_figure()
def plot_2d_data_xr(self, np_variables:list, var_names:list, title='',
file_name_prefix='', cmap='viridis', show_color_bar=True, plot_mode=PlotMode.RASTER, mincbar=np.nan, maxcbar=np.nan):
'''
Wrapper function to receive raw 2D numpy data. It calls the 'main' function for 3D plotting
:param np_variables:
:param var_names:
:param title:
:param file_name_prefix:
:param cmap:
:param flip_data:
:param rot_90:
:param show_color_bar:
:param plot_mode:
:param mincbar:
:param maxcbar:
:return:
'''
npdict_3d = {}
for i, field_name in enumerate(var_names):
npdict_3d[field_name] = np.expand_dims(np_variables[field_name], axis=0)
self.plot_3d_data_npdict(npdict_3d, var_names, z_levels=[0], title=title,
file_name_prefix=file_name_prefix, cmap=cmap, z_names = [],
show_color_bar=show_color_bar, plot_mode=plot_mode, mincbar=mincbar, maxcbar=maxcbar)
def plot_2d_data_np(self, np_variables:list, var_names:list, title='',
file_name_prefix='', cmap=None, flip_data=False,
rot_90=False, show_color_bar=True, plot_mode=PlotMode.RASTER, mincbar=np.nan, maxcbar=np.nan):
'''
Wrapper function to receive raw 2D numpy data. It calls the 'main' function for 3D plotting
:param np_variables: Numpy variables. They can be with shape [fields, x, y] or just a single field with shape [x,y]
:param var_names:
:param title:
:param file_name_prefix:
:param cmap:
:param flip_data:
:param rot_90:
:param show_color_bar:
:param plot_mode:
:param mincbar:
:param maxcbar:
:return:
'''
npdict_3d = {}
for i, field_name in enumerate(var_names):
if len(np_variables.shape) == 3:
c_np_data = np_variables[i, :, :]
else:
c_np_data = np_variables # Single field
if rot_90:
c_np_data = np.rot90(c_np_data)
if flip_data:
c_np_data = np.flip(np.flip(c_np_data), axis=1)
npdict_3d[field_name] = np.expand_dims(c_np_data, axis=0)
self.plot_3d_data_npdict(npdict_3d, var_names, z_levels=[0], title=title,
file_name_prefix=file_name_prefix, cmap=cmap, z_names = [],
show_color_bar=show_color_bar, plot_mode=plot_mode, mincbar=mincbar, maxcbar=maxcbar)
def make_video_from_images(self, input_folder, output_file, fps=24):
files = listdir(input_folder)
files.sort()
print(F"Generating video file: {output_file}")
out_video = -1
for i, file_name in enumerate(files[0:36]):
if i % 10 == 0:
print(F"Adding file # {i}: {file_name}")
c_file = join(input_folder, file_name)
im = Image.open(c_file)
np_im = | np.asarray(im) | numpy.asarray |
import os
import numpy as np
import cv2
import albumentations
from PIL import Image
from torch.utils.data import Dataset
from taming.data.sflckr import SegmentationBase # for examples included in repo
class Examples(SegmentationBase):
def __init__(self, size=256, random_crop=False, interpolation="bicubic"):
super().__init__(data_csv="data/ade20k_examples.txt",
data_root="data/ade20k_images",
segmentation_root="data/ade20k_segmentations",
size=size, random_crop=random_crop,
interpolation=interpolation,
n_labels=151, shift_segmentation=False)
# With semantic map and scene label
class ADE20kBase(Dataset):
def __init__(self, config=None, size=None, random_crop=False, interpolation="bicubic", crop_size=None):
self.split = self.get_split()
self.n_labels = 151 # unknown + 150
self.data_csv = {"train": "data/ade20k_train.txt",
"validation": "data/ade20k_test.txt"}[self.split]
self.data_root = "./data/ade20k_root"
with open(os.path.join(self.data_root, "sceneCategories.txt"), "r") as f:
self.scene_categories = f.read().splitlines()
self.scene_categories = dict(line.split() for line in self.scene_categories)
with open(self.data_csv, "r") as f:
self.image_paths = f.read().splitlines()
self._length = len(self.image_paths)
ss = self.split
if ss=='train':
ss='training'
self.labels = {
"relative_file_path_": [l for l in self.image_paths],
"file_path_": [os.path.join(self.data_root, "images",ss, l)
for l in self.image_paths],
"relative_segmentation_path_": [l.replace(".jpg", ".png")
for l in self.image_paths],
"segmentation_path_": [os.path.join(self.data_root, "annotations",ss,
l.replace(".jpg", ".png"))
for l in self.image_paths],
"scene_category": [self.scene_categories[l.replace(".jpg", "")]
for l in self.image_paths],
}
size = None if size is not None and size<=0 else size
self.size = size
if crop_size is None:
self.crop_size = size if size is not None else None
else:
self.crop_size = crop_size
if self.size is not None:
self.interpolation = interpolation
self.interpolation = {
"nearest": cv2.INTER_NEAREST,
"bilinear": cv2.INTER_LINEAR,
"bicubic": cv2.INTER_CUBIC,
"area": cv2.INTER_AREA,
"lanczos": cv2.INTER_LANCZOS4}[self.interpolation]
self.image_rescaler = albumentations.SmallestMaxSize(max_size=self.size,
interpolation=self.interpolation)
self.segmentation_rescaler = albumentations.SmallestMaxSize(max_size=self.size,
interpolation=cv2.INTER_NEAREST)
if crop_size is not None:
self.center_crop = not random_crop
if self.center_crop:
self.cropper = albumentations.CenterCrop(height=self.crop_size, width=self.crop_size)
else:
self.cropper = albumentations.RandomCrop(height=self.crop_size, width=self.crop_size)
self.preprocessor = self.cropper
def __len__(self):
return self._length
def __getitem__(self, i):
example = dict((k, self.labels[k][i]) for k in self.labels)
image = Image.open(example["file_path_"])
if not image.mode == "RGB":
image = image.convert("RGB")
image = np.array(image).astype(np.uint8)
if self.size is not None:
image = self.image_rescaler(image=image)["image"]
segmentation = Image.open(example["segmentation_path_"])
segmentation = np.array(segmentation).astype(np.uint8)
if self.size is not None:
segmentation = self.segmentation_rescaler(image=segmentation)["image"]
if self.size is not None:
processed = self.preprocessor(image=image, mask=segmentation)
else:
processed = {"image": image, "mask": segmentation}
example["image"] = (processed["image"]/127.5 - 1.0).astype(np.float32)
segmentation = processed["mask"]
onehot = | np.eye(self.n_labels) | numpy.eye |
import copy
import functools
import itertools
import numbers
import warnings
from collections import defaultdict
from datetime import timedelta
from distutils.version import LooseVersion
from typing import (
Any,
Dict,
Hashable,
Mapping,
Optional,
Sequence,
Tuple,
TypeVar,
Union,
)
import numpy as np
import pandas as pd
import xarray as xr # only for Dataset and DataArray
from . import arithmetic, common, dtypes, duck_array_ops, indexing, nputils, ops, utils
from .indexing import (
BasicIndexer,
OuterIndexer,
PandasIndexAdapter,
VectorizedIndexer,
as_indexable,
)
from .npcompat import IS_NEP18_ACTIVE
from .options import _get_keep_attrs
from .pycompat import (
cupy_array_type,
dask_array_type,
integer_types,
is_duck_dask_array,
)
from .utils import (
OrderedSet,
_default,
decode_numpy_dict_values,
drop_dims_from_indexers,
either_dict_or_kwargs,
ensure_us_time_resolution,
infix_dims,
is_duck_array,
)
NON_NUMPY_SUPPORTED_ARRAY_TYPES = (
(
indexing.ExplicitlyIndexed,
pd.Index,
)
+ dask_array_type
+ cupy_array_type
)
# https://github.com/python/mypy/issues/224
BASIC_INDEXING_TYPES = integer_types + (slice,) # type: ignore
VariableType = TypeVar("VariableType", bound="Variable")
"""Type annotation to be used when methods of Variable return self or a copy of self.
When called from an instance of a subclass, e.g. IndexVariable, mypy identifies the
output as an instance of the subclass.
Usage::
class Variable:
def f(self: VariableType, ...) -> VariableType:
...
"""
class MissingDimensionsError(ValueError):
"""Error class used when we can't safely guess a dimension name."""
# inherits from ValueError for backward compatibility
# TODO: move this to an xarray.exceptions module?
def as_variable(obj, name=None) -> "Union[Variable, IndexVariable]":
"""Convert an object into a Variable.
Parameters
----------
obj : object
Object to convert into a Variable.
- If the object is already a Variable, return a shallow copy.
- Otherwise, if the object has 'dims' and 'data' attributes, convert
it into a new Variable.
- If all else fails, attempt to convert the object into a Variable by
unpacking it into the arguments for creating a new Variable.
name : str, optional
If provided:
- `obj` can be a 1D array, which is assumed to label coordinate values
along a dimension of this given name.
- Variables with name matching one of their dimensions are converted
into `IndexVariable` objects.
Returns
-------
var : Variable
The newly created variable.
"""
from .dataarray import DataArray
# TODO: consider extending this method to automatically handle Iris and
if isinstance(obj, DataArray):
# extract the primary Variable from DataArrays
obj = obj.variable
if isinstance(obj, Variable):
obj = obj.copy(deep=False)
elif isinstance(obj, tuple):
try:
obj = Variable(*obj)
except (TypeError, ValueError) as error:
# use .format() instead of % because it handles tuples consistently
raise error.__class__(
"Could not convert tuple of form "
"(dims, data[, attrs, encoding]): "
"{} to Variable.".format(obj)
)
elif utils.is_scalar(obj):
obj = Variable([], obj)
elif isinstance(obj, (pd.Index, IndexVariable)) and obj.name is not None:
obj = Variable(obj.name, obj)
elif isinstance(obj, (set, dict)):
raise TypeError("variable {!r} has invalid type {!r}".format(name, type(obj)))
elif name is not None:
data = as_compatible_data(obj)
if data.ndim != 1:
raise MissingDimensionsError(
"cannot set variable %r with %r-dimensional data "
"without explicit dimension names. Pass a tuple of "
"(dims, data) instead." % (name, data.ndim)
)
obj = Variable(name, data, fastpath=True)
else:
raise TypeError(
"unable to convert object into a variable without an "
"explicit list of dimensions: %r" % obj
)
if name is not None and name in obj.dims:
# convert the Variable into an Index
if obj.ndim != 1:
raise MissingDimensionsError(
"%r has more than 1-dimension and the same name as one of its "
"dimensions %r. xarray disallows such variables because they "
"conflict with the coordinates used to label "
"dimensions." % (name, obj.dims)
)
obj = obj.to_index_variable()
return obj
def _maybe_wrap_data(data):
"""
Put pandas.Index and numpy.ndarray arguments in adapter objects to ensure
they can be indexed properly.
NumpyArrayAdapter, PandasIndexAdapter and LazilyOuterIndexedArray should
all pass through unmodified.
"""
if isinstance(data, pd.Index):
return PandasIndexAdapter(data)
return data
def _possibly_convert_objects(values):
"""Convert arrays of datetime.datetime and datetime.timedelta objects into
datetime64 and timedelta64, according to the pandas convention. Also used for
validating that datetime64 and timedelta64 objects are within the valid date
range for ns precision, as pandas will raise an error if they are not.
"""
return np.asarray(pd.Series(values.ravel())).reshape(values.shape)
def as_compatible_data(data, fastpath=False):
"""Prepare and wrap data to put in a Variable.
- If data does not have the necessary attributes, convert it to ndarray.
- If data has dtype=datetime64, ensure that it has ns precision. If it's a
pandas.Timestamp, convert it to datetime64.
- If data is already a pandas or xarray object (other than an Index), just
use the values.
Finally, wrap it up with an adapter if necessary.
"""
if fastpath and getattr(data, "ndim", 0) > 0:
# can't use fastpath (yet) for scalars
return _maybe_wrap_data(data)
if isinstance(data, Variable):
return data.data
if isinstance(data, NON_NUMPY_SUPPORTED_ARRAY_TYPES):
return _maybe_wrap_data(data)
if isinstance(data, tuple):
data = utils.to_0d_object_array(data)
if isinstance(data, pd.Timestamp):
# TODO: convert, handle datetime objects, too
data = np.datetime64(data.value, "ns")
if isinstance(data, timedelta):
data = np.timedelta64(getattr(data, "value", data), "ns")
# we don't want nested self-described arrays
data = getattr(data, "values", data)
if isinstance(data, np.ma.MaskedArray):
mask = np.ma.getmaskarray(data)
if mask.any():
dtype, fill_value = dtypes.maybe_promote(data.dtype)
data = np.asarray(data, dtype=dtype)
data[mask] = fill_value
else:
data = np.asarray(data)
if not isinstance(data, np.ndarray):
if hasattr(data, "__array_function__"):
if IS_NEP18_ACTIVE:
return data
else:
raise TypeError(
"Got an NumPy-like array type providing the "
"__array_function__ protocol but NEP18 is not enabled. "
"Check that numpy >= v1.16 and that the environment "
'variable "NUMPY_EXPERIMENTAL_ARRAY_FUNCTION" is set to '
'"1"'
)
# validate whether the data is valid data types.
data = np.asarray(data)
if isinstance(data, np.ndarray):
if data.dtype.kind == "O":
data = _possibly_convert_objects(data)
elif data.dtype.kind == "M":
data = _possibly_convert_objects(data)
elif data.dtype.kind == "m":
data = _possibly_convert_objects(data)
return _maybe_wrap_data(data)
def _as_array_or_item(data):
"""Return the given values as a numpy array, or as an individual item if
it's a 0d datetime64 or timedelta64 array.
Importantly, this function does not copy data if it is already an ndarray -
otherwise, it will not be possible to update Variable values in place.
This function mostly exists because 0-dimensional ndarrays with
dtype=datetime64 are broken :(
https://github.com/numpy/numpy/issues/4337
https://github.com/numpy/numpy/issues/7619
TODO: remove this (replace with np.asarray) once these issues are fixed
"""
if isinstance(data, cupy_array_type):
data = data.get()
else:
data = np.asarray(data)
if data.ndim == 0:
if data.dtype.kind == "M":
data = np.datetime64(data, "ns")
elif data.dtype.kind == "m":
data = np.timedelta64(data, "ns")
return data
class Variable(
common.AbstractArray, arithmetic.SupportsArithmetic, utils.NdimSizeLenMixin
):
"""A netcdf-like variable consisting of dimensions, data and attributes
which describe a single Array. A single Variable object is not fully
described outside the context of its parent Dataset (if you want such a
fully described object, use a DataArray instead).
The main functional difference between Variables and numpy arrays is that
numerical operations on Variables implement array broadcasting by dimension
name. For example, adding an Variable with dimensions `('time',)` to
another Variable with dimensions `('space',)` results in a new Variable
with dimensions `('time', 'space')`. Furthermore, numpy reduce operations
like ``mean`` or ``sum`` are overwritten to take a "dimension" argument
instead of an "axis".
Variables are light-weight objects used as the building block for datasets.
They are more primitive objects, so operations with them provide marginally
higher performance than using DataArrays. However, manipulating data in the
form of a Dataset or DataArray should almost always be preferred, because
they can use more complete metadata in context of coordinate labels.
"""
__slots__ = ("_dims", "_data", "_attrs", "_encoding")
def __init__(self, dims, data, attrs=None, encoding=None, fastpath=False):
"""
Parameters
----------
dims : str or sequence of str
Name(s) of the the data dimension(s). Must be either a string (only
for 1D data) or a sequence of strings with length equal to the
number of dimensions.
data : array_like
Data array which supports numpy-like data access.
attrs : dict_like or None, optional
Attributes to assign to the new variable. If None (default), an
empty attribute dictionary is initialized.
encoding : dict_like or None, optional
Dictionary specifying how to encode this array's data into a
serialized format like netCDF4. Currently used keys (for netCDF)
include '_FillValue', 'scale_factor', 'add_offset' and 'dtype'.
Well-behaved code to serialize a Variable should ignore
unrecognized encoding items.
"""
self._data = as_compatible_data(data, fastpath=fastpath)
self._dims = self._parse_dimensions(dims)
self._attrs = None
self._encoding = None
if attrs is not None:
self.attrs = attrs
if encoding is not None:
self.encoding = encoding
@property
def dtype(self):
return self._data.dtype
@property
def shape(self):
return self._data.shape
@property
def nbytes(self):
return self.size * self.dtype.itemsize
@property
def _in_memory(self):
return isinstance(self._data, (np.ndarray, np.number, PandasIndexAdapter)) or (
isinstance(self._data, indexing.MemoryCachedArray)
and isinstance(self._data.array, indexing.NumpyIndexingAdapter)
)
@property
def data(self):
if is_duck_array(self._data):
return self._data
else:
return self.values
@data.setter
def data(self, data):
data = as_compatible_data(data)
if data.shape != self.shape:
raise ValueError(
f"replacement data must match the Variable's shape. "
f"replacement data has shape {data.shape}; Variable has shape {self.shape}"
)
self._data = data
def astype(
self: VariableType,
dtype,
*,
order=None,
casting=None,
subok=None,
copy=None,
keep_attrs=True,
) -> VariableType:
"""
Copy of the Variable object, with data cast to a specified type.
Parameters
----------
dtype : str or dtype
Typecode or data-type to which the array is cast.
order : {'C', 'F', 'A', 'K'}, optional
Controls the memory layout order of the result. ‘C’ means C order,
‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are
Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to
the order the array elements appear in memory as possible.
casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
Controls what kind of data casting may occur.
* 'no' means the data types should not be cast at all.
* 'equiv' means only byte-order changes are allowed.
* 'safe' means only casts which can preserve values are allowed.
* 'same_kind' means only safe casts or casts within a kind,
like float64 to float32, are allowed.
* 'unsafe' means any data conversions may be done.
subok : bool, optional
If True, then sub-classes will be passed-through, otherwise the
returned array will be forced to be a base-class array.
copy : bool, optional
By default, astype always returns a newly allocated array. If this
is set to False and the `dtype` requirement is satisfied, the input
array is returned instead of a copy.
keep_attrs : bool, optional
By default, astype keeps attributes. Set to False to remove
attributes in the returned object.
Returns
-------
out : same as object
New object with data cast to the specified type.
Notes
-----
The ``order``, ``casting``, ``subok`` and ``copy`` arguments are only passed
through to the ``astype`` method of the underlying array when a value
different than ``None`` is supplied.
Make sure to only supply these arguments if the underlying array class
supports them.
See also
--------
numpy.ndarray.astype
dask.array.Array.astype
sparse.COO.astype
"""
from .computation import apply_ufunc
kwargs = dict(order=order, casting=casting, subok=subok, copy=copy)
kwargs = {k: v for k, v in kwargs.items() if v is not None}
return apply_ufunc(
duck_array_ops.astype,
self,
dtype,
kwargs=kwargs,
keep_attrs=keep_attrs,
dask="allowed",
)
def load(self, **kwargs):
"""Manually trigger loading of this variable's data from disk or a
remote source into memory and return this variable.
Normally, it should not be necessary to call this method in user code,
because all xarray functions should either work on deferred data or
load data automatically.
Parameters
----------
**kwargs : dict
Additional keyword arguments passed on to ``dask.array.compute``.
See Also
--------
dask.array.compute
"""
if is_duck_dask_array(self._data):
self._data = as_compatible_data(self._data.compute(**kwargs))
elif not is_duck_array(self._data):
self._data = np.asarray(self._data)
return self
def compute(self, **kwargs):
"""Manually trigger loading of this variable's data from disk or a
remote source into memory and return a new variable. The original is
left unaltered.
Normally, it should not be necessary to call this method in user code,
because all xarray functions should either work on deferred data or
load data automatically.
Parameters
----------
**kwargs : dict
Additional keyword arguments passed on to ``dask.array.compute``.
See Also
--------
dask.array.compute
"""
new = self.copy(deep=False)
return new.load(**kwargs)
def __dask_tokenize__(self):
# Use v.data, instead of v._data, in order to cope with the wrappers
# around NetCDF and the like
from dask.base import normalize_token
return normalize_token((type(self), self._dims, self.data, self._attrs))
def __dask_graph__(self):
if is_duck_dask_array(self._data):
return self._data.__dask_graph__()
else:
return None
def __dask_keys__(self):
return self._data.__dask_keys__()
def __dask_layers__(self):
return self._data.__dask_layers__()
@property
def __dask_optimize__(self):
return self._data.__dask_optimize__
@property
def __dask_scheduler__(self):
return self._data.__dask_scheduler__
def __dask_postcompute__(self):
array_func, array_args = self._data.__dask_postcompute__()
return (
self._dask_finalize,
(array_func, array_args, self._dims, self._attrs, self._encoding),
)
def __dask_postpersist__(self):
array_func, array_args = self._data.__dask_postpersist__()
return (
self._dask_finalize,
(array_func, array_args, self._dims, self._attrs, self._encoding),
)
@staticmethod
def _dask_finalize(results, array_func, array_args, dims, attrs, encoding):
data = array_func(results, *array_args)
return Variable(dims, data, attrs=attrs, encoding=encoding)
@property
def values(self):
"""The variable's data as a numpy.ndarray"""
return _as_array_or_item(self._data)
@values.setter
def values(self, values):
self.data = values
def to_base_variable(self):
"""Return this variable as a base xarray.Variable"""
return Variable(
self.dims, self._data, self._attrs, encoding=self._encoding, fastpath=True
)
to_variable = utils.alias(to_base_variable, "to_variable")
def to_index_variable(self):
"""Return this variable as an xarray.IndexVariable"""
return IndexVariable(
self.dims, self._data, self._attrs, encoding=self._encoding, fastpath=True
)
to_coord = utils.alias(to_index_variable, "to_coord")
def to_index(self):
"""Convert this variable to a pandas.Index"""
return self.to_index_variable().to_index()
def to_dict(self, data=True):
"""Dictionary representation of variable."""
item = {"dims": self.dims, "attrs": decode_numpy_dict_values(self.attrs)}
if data:
item["data"] = ensure_us_time_resolution(self.values).tolist()
else:
item.update({"dtype": str(self.dtype), "shape": self.shape})
return item
@property
def dims(self):
"""Tuple of dimension names with which this variable is associated."""
return self._dims
@dims.setter
def dims(self, value):
self._dims = self._parse_dimensions(value)
def _parse_dimensions(self, dims):
if isinstance(dims, str):
dims = (dims,)
dims = tuple(dims)
if len(dims) != self.ndim:
raise ValueError(
"dimensions %s must have the same length as the "
"number of data dimensions, ndim=%s" % (dims, self.ndim)
)
return dims
def _item_key_to_tuple(self, key):
if utils.is_dict_like(key):
return tuple(key.get(dim, slice(None)) for dim in self.dims)
else:
return key
def _broadcast_indexes(self, key):
"""Prepare an indexing key for an indexing operation.
Parameters
-----------
key: int, slice, array-like, dict or tuple of integer, slice and array-like
Any valid input for indexing.
Returns
-------
dims : tuple
Dimension of the resultant variable.
indexers : IndexingTuple subclass
Tuple of integer, array-like, or slices to use when indexing
self._data. The type of this argument indicates the type of
indexing to perform, either basic, outer or vectorized.
new_order : Optional[Sequence[int]]
Optional reordering to do on the result of indexing. If not None,
the first len(new_order) indexing should be moved to these
positions.
"""
key = self._item_key_to_tuple(key) # key is a tuple
# key is a tuple of full size
key = indexing.expanded_indexer(key, self.ndim)
# Convert a scalar Variable to an integer
key = tuple(
k.data.item() if isinstance(k, Variable) and k.ndim == 0 else k for k in key
)
# Convert a 0d-array to an integer
key = tuple(
k.item() if isinstance(k, np.ndarray) and k.ndim == 0 else k for k in key
)
if all(isinstance(k, BASIC_INDEXING_TYPES) for k in key):
return self._broadcast_indexes_basic(key)
self._validate_indexers(key)
# Detect it can be mapped as an outer indexer
# If all key is unlabeled, or
# key can be mapped as an OuterIndexer.
if all(not isinstance(k, Variable) for k in key):
return self._broadcast_indexes_outer(key)
# If all key is 1-dimensional and there are no duplicate labels,
# key can be mapped as an OuterIndexer.
dims = []
for k, d in zip(key, self.dims):
if isinstance(k, Variable):
if len(k.dims) > 1:
return self._broadcast_indexes_vectorized(key)
dims.append(k.dims[0])
elif not isinstance(k, integer_types):
dims.append(d)
if len(set(dims)) == len(dims):
return self._broadcast_indexes_outer(key)
return self._broadcast_indexes_vectorized(key)
def _broadcast_indexes_basic(self, key):
dims = tuple(
dim for k, dim in zip(key, self.dims) if not isinstance(k, integer_types)
)
return dims, BasicIndexer(key), None
def _validate_indexers(self, key):
""" Make sanity checks """
for dim, k in zip(self.dims, key):
if isinstance(k, BASIC_INDEXING_TYPES):
pass
else:
if not isinstance(k, Variable):
k = np.asarray(k)
if k.ndim > 1:
raise IndexError(
"Unlabeled multi-dimensional array cannot be "
"used for indexing: {}".format(k)
)
if k.dtype.kind == "b":
if self.shape[self.get_axis_num(dim)] != len(k):
raise IndexError(
"Boolean array size {:d} is used to index array "
"with shape {:s}.".format(len(k), str(self.shape))
)
if k.ndim > 1:
raise IndexError(
"{}-dimensional boolean indexing is "
"not supported. ".format(k.ndim)
)
if getattr(k, "dims", (dim,)) != (dim,):
raise IndexError(
"Boolean indexer should be unlabeled or on the "
"same dimension to the indexed array. Indexer is "
"on {:s} but the target dimension is {:s}.".format(
str(k.dims), dim
)
)
def _broadcast_indexes_outer(self, key):
dims = tuple(
k.dims[0] if isinstance(k, Variable) else dim
for k, dim in zip(key, self.dims)
if not isinstance(k, integer_types)
)
new_key = []
for k in key:
if isinstance(k, Variable):
k = k.data
if not isinstance(k, BASIC_INDEXING_TYPES):
k = np.asarray(k)
if k.size == 0:
# Slice by empty list; numpy could not infer the dtype
k = k.astype(int)
elif k.dtype.kind == "b":
(k,) = np.nonzero(k)
new_key.append(k)
return dims, OuterIndexer(tuple(new_key)), None
def _nonzero(self):
""" Equivalent numpy's nonzero but returns a tuple of Varibles. """
# TODO we should replace dask's native nonzero
# after https://github.com/dask/dask/issues/1076 is implemented.
nonzeros = np.nonzero(self.data)
return tuple(Variable((dim), nz) for nz, dim in zip(nonzeros, self.dims))
def _broadcast_indexes_vectorized(self, key):
variables = []
out_dims_set = OrderedSet()
for dim, value in zip(self.dims, key):
if isinstance(value, slice):
out_dims_set.add(dim)
else:
variable = (
value
if isinstance(value, Variable)
else as_variable(value, name=dim)
)
if variable.dtype.kind == "b": # boolean indexing case
(variable,) = variable._nonzero()
variables.append(variable)
out_dims_set.update(variable.dims)
variable_dims = set()
for variable in variables:
variable_dims.update(variable.dims)
slices = []
for i, (dim, value) in enumerate(zip(self.dims, key)):
if isinstance(value, slice):
if dim in variable_dims:
# We only convert slice objects to variables if they share
# a dimension with at least one other variable. Otherwise,
# we can equivalently leave them as slices aknd transpose
# the result. This is significantly faster/more efficient
# for most array backends.
values = np.arange(*value.indices(self.sizes[dim]))
variables.insert(i - len(slices), Variable((dim,), values))
else:
slices.append((i, value))
try:
variables = _broadcast_compat_variables(*variables)
except ValueError:
raise IndexError(f"Dimensions of indexers mismatch: {key}")
out_key = [variable.data for variable in variables]
out_dims = tuple(out_dims_set)
slice_positions = set()
for i, value in slices:
out_key.insert(i, value)
new_position = out_dims.index(self.dims[i])
slice_positions.add(new_position)
if slice_positions:
new_order = [i for i in range(len(out_dims)) if i not in slice_positions]
else:
new_order = None
return out_dims, VectorizedIndexer(tuple(out_key)), new_order
def __getitem__(self: VariableType, key) -> VariableType:
"""Return a new Variable object whose contents are consistent with
getting the provided key from the underlying data.
NB. __getitem__ and __setitem__ implement xarray-style indexing,
where if keys are unlabeled arrays, we index the array orthogonally
with them. If keys are labeled array (such as Variables), they are
broadcasted with our usual scheme and then the array is indexed with
the broadcasted key, like numpy's fancy indexing.
If you really want to do indexing like `x[x > 0]`, manipulate the numpy
array `x.values` directly.
"""
dims, indexer, new_order = self._broadcast_indexes(key)
data = as_indexable(self._data)[indexer]
if new_order:
data = duck_array_ops.moveaxis(data, range(len(new_order)), new_order)
return self._finalize_indexing_result(dims, data)
def _finalize_indexing_result(self: VariableType, dims, data) -> VariableType:
"""Used by IndexVariable to return IndexVariable objects when possible."""
return type(self)(dims, data, self._attrs, self._encoding, fastpath=True)
def _getitem_with_mask(self, key, fill_value=dtypes.NA):
"""Index this Variable with -1 remapped to fill_value."""
# TODO(shoyer): expose this method in public API somewhere (isel?) and
# use it for reindex.
# TODO(shoyer): add a sanity check that all other integers are
# non-negative
# TODO(shoyer): add an optimization, remapping -1 to an adjacent value
# that is actually indexed rather than mapping it to the last value
# along each axis.
if fill_value is dtypes.NA:
fill_value = dtypes.get_fill_value(self.dtype)
dims, indexer, new_order = self._broadcast_indexes(key)
if self.size:
if is_duck_dask_array(self._data):
# dask's indexing is faster this way; also vindex does not
# support negative indices yet:
# https://github.com/dask/dask/pull/2967
actual_indexer = indexing.posify_mask_indexer(indexer)
else:
actual_indexer = indexer
data = as_indexable(self._data)[actual_indexer]
mask = indexing.create_mask(indexer, self.shape, data)
# we need to invert the mask in order to pass data first. This helps
# pint to choose the correct unit
# TODO: revert after https://github.com/hgrecco/pint/issues/1019 is fixed
data = duck_array_ops.where(np.logical_not(mask), data, fill_value)
else:
# array cannot be indexed along dimensions of size 0, so just
# build the mask directly instead.
mask = indexing.create_mask(indexer, self.shape)
data = np.broadcast_to(fill_value, getattr(mask, "shape", ()))
if new_order:
data = duck_array_ops.moveaxis(data, range(len(new_order)), new_order)
return self._finalize_indexing_result(dims, data)
def __setitem__(self, key, value):
"""__setitem__ is overloaded to access the underlying numpy values with
orthogonal indexing.
See __getitem__ for more details.
"""
dims, index_tuple, new_order = self._broadcast_indexes(key)
if not isinstance(value, Variable):
value = as_compatible_data(value)
if value.ndim > len(dims):
raise ValueError(
"shape mismatch: value array of shape %s could not be "
"broadcast to indexing result with %s dimensions"
% (value.shape, len(dims))
)
if value.ndim == 0:
value = Variable((), value)
else:
value = Variable(dims[-value.ndim :], value)
# broadcast to become assignable
value = value.set_dims(dims).data
if new_order:
value = duck_array_ops.asarray(value)
value = value[(len(dims) - value.ndim) * (np.newaxis,) + (Ellipsis,)]
value = duck_array_ops.moveaxis(value, new_order, range(len(new_order)))
indexable = as_indexable(self._data)
indexable[index_tuple] = value
@property
def attrs(self) -> Dict[Hashable, Any]:
"""Dictionary of local attributes on this variable."""
if self._attrs is None:
self._attrs = {}
return self._attrs
@attrs.setter
def attrs(self, value: Mapping[Hashable, Any]) -> None:
self._attrs = dict(value)
@property
def encoding(self):
"""Dictionary of encodings on this variable."""
if self._encoding is None:
self._encoding = {}
return self._encoding
@encoding.setter
def encoding(self, value):
try:
self._encoding = dict(value)
except ValueError:
raise ValueError("encoding must be castable to a dictionary")
def copy(self, deep=True, data=None):
"""Returns a copy of this object.
If `deep=True`, the data array is loaded into memory and copied onto
the new object. Dimensions, attributes and encodings are always copied.
Use `data` to create a new object with the same structure as
original but entirely new data.
Parameters
----------
deep : bool, optional
Whether the data array is loaded into memory and copied onto
the new object. Default is True.
data : array_like, optional
Data to use in the new object. Must have same shape as original.
When `data` is used, `deep` is ignored.
Returns
-------
object : Variable
New object with dimensions, attributes, encodings, and optionally
data copied from original.
Examples
--------
Shallow copy versus deep copy
>>> var = xr.Variable(data=[1, 2, 3], dims="x")
>>> var.copy()
<xarray.Variable (x: 3)>
array([1, 2, 3])
>>> var_0 = var.copy(deep=False)
>>> var_0[0] = 7
>>> var_0
<xarray.Variable (x: 3)>
array([7, 2, 3])
>>> var
<xarray.Variable (x: 3)>
array([7, 2, 3])
Changing the data using the ``data`` argument maintains the
structure of the original object, but with the new data. Original
object is unaffected.
>>> var.copy(data=[0.1, 0.2, 0.3])
<xarray.Variable (x: 3)>
array([0.1, 0.2, 0.3])
>>> var
<xarray.Variable (x: 3)>
array([7, 2, 3])
See Also
--------
pandas.DataFrame.copy
"""
if data is None:
data = self._data
if isinstance(data, indexing.MemoryCachedArray):
# don't share caching between copies
data = indexing.MemoryCachedArray(data.array)
if deep:
data = copy.deepcopy(data)
else:
data = as_compatible_data(data)
if self.shape != data.shape:
raise ValueError(
"Data shape {} must match shape of object {}".format(
data.shape, self.shape
)
)
# note:
# dims is already an immutable tuple
# attributes and encoding will be copied when the new Array is created
return self._replace(data=data)
def _replace(
self, dims=_default, data=_default, attrs=_default, encoding=_default
) -> "Variable":
if dims is _default:
dims = copy.copy(self._dims)
if data is _default:
data = copy.copy(self.data)
if attrs is _default:
attrs = copy.copy(self._attrs)
if encoding is _default:
encoding = copy.copy(self._encoding)
return type(self)(dims, data, attrs, encoding, fastpath=True)
def __copy__(self):
return self.copy(deep=False)
def __deepcopy__(self, memo=None):
# memo does nothing but is required for compatibility with
# copy.deepcopy
return self.copy(deep=True)
# mutable objects should not be hashable
# https://github.com/python/mypy/issues/4266
__hash__ = None # type: ignore
@property
def chunks(self):
"""Block dimensions for this array's data or None if it's not a dask
array.
"""
return getattr(self._data, "chunks", None)
_array_counter = itertools.count()
def chunk(self, chunks={}, name=None, lock=False):
"""Coerce this array's data into a dask arrays with the given chunks.
If this variable is a non-dask array, it will be converted to dask
array. If it's a dask array, it will be rechunked to the given chunk
sizes.
If neither chunks is not provided for one or more dimensions, chunk
sizes along that dimension will not be updated; non-dask arrays will be
converted into dask arrays with a single block.
Parameters
----------
chunks : int, tuple or dict, optional
Chunk sizes along each dimension, e.g., ``5``, ``(5, 5)`` or
``{'x': 5, 'y': 5}``.
name : str, optional
Used to generate the name for this array in the internal dask
graph. Does not need not be unique.
lock : optional
Passed on to :py:func:`dask.array.from_array`, if the array is not
already as dask array.
Returns
-------
chunked : xarray.Variable
"""
import dask
import dask.array as da
if chunks is None:
warnings.warn(
"None value for 'chunks' is deprecated. "
"It will raise an error in the future. Use instead '{}'",
category=FutureWarning,
)
chunks = {}
if utils.is_dict_like(chunks):
chunks = {self.get_axis_num(dim): chunk for dim, chunk in chunks.items()}
data = self._data
if is_duck_dask_array(data):
data = data.rechunk(chunks)
else:
if isinstance(data, indexing.ExplicitlyIndexed):
# Unambiguously handle array storage backends (like NetCDF4 and h5py)
# that can't handle general array indexing. For example, in netCDF4 you
# can do "outer" indexing along two dimensions independent, which works
# differently from how NumPy handles it.
# da.from_array works by using lazy indexing with a tuple of slices.
# Using OuterIndexer is a pragmatic choice: dask does not yet handle
# different indexing types in an explicit way:
# https://github.com/dask/dask/issues/2883
data = indexing.ImplicitToExplicitIndexingAdapter(
data, indexing.OuterIndexer
)
if LooseVersion(dask.__version__) < "2.0.0":
kwargs = {}
else:
# All of our lazily loaded backend array classes should use NumPy
# array operations.
kwargs = {"meta": np.ndarray}
else:
kwargs = {}
if utils.is_dict_like(chunks):
chunks = tuple(chunks.get(n, s) for n, s in enumerate(self.shape))
data = da.from_array(data, chunks, name=name, lock=lock, **kwargs)
return type(self)(self.dims, data, self._attrs, self._encoding, fastpath=True)
def _as_sparse(self, sparse_format=_default, fill_value=dtypes.NA):
"""
use sparse-array as backend.
"""
import sparse
# TODO: what to do if dask-backended?
if fill_value is dtypes.NA:
dtype, fill_value = dtypes.maybe_promote(self.dtype)
else:
dtype = dtypes.result_type(self.dtype, fill_value)
if sparse_format is _default:
sparse_format = "coo"
try:
as_sparse = getattr(sparse, f"as_{sparse_format.lower()}")
except AttributeError:
raise ValueError(f"{sparse_format} is not a valid sparse format")
data = as_sparse(self.data.astype(dtype), fill_value=fill_value)
return self._replace(data=data)
def _to_dense(self):
"""
Change backend from sparse to np.array
"""
if hasattr(self._data, "todense"):
return self._replace(data=self._data.todense())
return self.copy(deep=False)
def isel(
self: VariableType,
indexers: Mapping[Hashable, Any] = None,
missing_dims: str = "raise",
**indexers_kwargs: Any,
) -> VariableType:
"""Return a new array indexed along the specified dimension(s).
Parameters
----------
**indexers : {dim: indexer, ...}
Keyword arguments with names matching dimensions and values given
by integers, slice objects or arrays.
missing_dims : {"raise", "warn", "ignore"}, default: "raise"
What to do if dimensions that should be selected from are not present in the
DataArray:
- "raise": raise an exception
- "warning": raise a warning, and ignore the missing dimensions
- "ignore": ignore the missing dimensions
Returns
-------
obj : Array object
A new Array with the selected data and dimensions. In general,
the new variable's data will be a view of this variable's data,
unless numpy fancy indexing was triggered by using an array
indexer, in which case the data will be a copy.
"""
indexers = either_dict_or_kwargs(indexers, indexers_kwargs, "isel")
indexers = drop_dims_from_indexers(indexers, self.dims, missing_dims)
key = tuple(indexers.get(dim, slice(None)) for dim in self.dims)
return self[key]
def squeeze(self, dim=None):
"""Return a new object with squeezed data.
Parameters
----------
dim : None or str or tuple of str, optional
Selects a subset of the length one dimensions. If a dimension is
selected with length greater than one, an error is raised. If
None, all length one dimensions are squeezed.
Returns
-------
squeezed : same type as caller
This object, but with with all or a subset of the dimensions of
length 1 removed.
See Also
--------
numpy.squeeze
"""
dims = common.get_squeeze_dims(self, dim)
return self.isel({d: 0 for d in dims})
def _shift_one_dim(self, dim, count, fill_value=dtypes.NA):
axis = self.get_axis_num(dim)
if count > 0:
keep = slice(None, -count)
elif count < 0:
keep = slice(-count, None)
else:
keep = slice(None)
trimmed_data = self[(slice(None),) * axis + (keep,)].data
if fill_value is dtypes.NA:
dtype, fill_value = dtypes.maybe_promote(self.dtype)
else:
dtype = self.dtype
width = min(abs(count), self.shape[axis])
dim_pad = (width, 0) if count >= 0 else (0, width)
pads = [(0, 0) if d != dim else dim_pad for d in self.dims]
data = duck_array_ops.pad(
trimmed_data.astype(dtype),
pads,
mode="constant",
constant_values=fill_value,
)
if is_duck_dask_array(data):
# chunked data should come out with the same chunks; this makes
# it feasible to combine shifted and unshifted data
# TODO: remove this once dask.array automatically aligns chunks
data = data.rechunk(self.data.chunks)
return type(self)(self.dims, data, self._attrs, fastpath=True)
def shift(self, shifts=None, fill_value=dtypes.NA, **shifts_kwargs):
"""
Return a new Variable with shifted data.
Parameters
----------
shifts : mapping of the form {dim: offset}
Integer offset to shift along each of the given dimensions.
Positive offsets shift to the right; negative offsets shift to the
left.
fill_value: scalar, optional
Value to use for newly missing values
**shifts_kwargs
The keyword arguments form of ``shifts``.
One of shifts or shifts_kwargs must be provided.
Returns
-------
shifted : Variable
Variable with the same dimensions and attributes but shifted data.
"""
shifts = either_dict_or_kwargs(shifts, shifts_kwargs, "shift")
result = self
for dim, count in shifts.items():
result = result._shift_one_dim(dim, count, fill_value=fill_value)
return result
def _pad_options_dim_to_index(
self,
pad_option: Mapping[Hashable, Union[int, Tuple[int, int]]],
fill_with_shape=False,
):
if fill_with_shape:
return [
(n, n) if d not in pad_option else pad_option[d]
for d, n in zip(self.dims, self.data.shape)
]
return [(0, 0) if d not in pad_option else pad_option[d] for d in self.dims]
def pad(
self,
pad_width: Mapping[Hashable, Union[int, Tuple[int, int]]] = None,
mode: str = "constant",
stat_length: Union[
int, Tuple[int, int], Mapping[Hashable, Tuple[int, int]]
] = None,
constant_values: Union[
int, Tuple[int, int], Mapping[Hashable, Tuple[int, int]]
] = None,
end_values: Union[
int, Tuple[int, int], Mapping[Hashable, Tuple[int, int]]
] = None,
reflect_type: str = None,
**pad_width_kwargs: Any,
):
"""
Return a new Variable with padded data.
Parameters
----------
pad_width : mapping of hashable to tuple of int
Mapping with the form of {dim: (pad_before, pad_after)}
describing the number of values padded along each dimension.
{dim: pad} is a shortcut for pad_before = pad_after = pad
mode : str, default: "constant"
See numpy / Dask docs
stat_length : int, tuple or mapping of hashable to tuple
Used in 'maximum', 'mean', 'median', and 'minimum'. Number of
values at edge of each axis used to calculate the statistic value.
constant_values : scalar, tuple or mapping of hashable to tuple
Used in 'constant'. The values to set the padded values for each
axis.
end_values : scalar, tuple or mapping of hashable to tuple
Used in 'linear_ramp'. The values used for the ending value of the
linear_ramp and that will form the edge of the padded array.
reflect_type : {"even", "odd"}, optional
Used in "reflect", and "symmetric". The "even" style is the
default with an unaltered reflection around the edge value. For
the "odd" style, the extended part of the array is created by
subtracting the reflected values from two times the edge value.
**pad_width_kwargs
One of pad_width or pad_width_kwargs must be provided.
Returns
-------
padded : Variable
Variable with the same dimensions and attributes but padded data.
"""
pad_width = either_dict_or_kwargs(pad_width, pad_width_kwargs, "pad")
# change default behaviour of pad with mode constant
if mode == "constant" and (
constant_values is None or constant_values is dtypes.NA
):
dtype, constant_values = dtypes.maybe_promote(self.dtype)
else:
dtype = self.dtype
# create pad_options_kwargs, numpy requires only relevant kwargs to be nonempty
if isinstance(stat_length, dict):
stat_length = self._pad_options_dim_to_index(
stat_length, fill_with_shape=True
)
if isinstance(constant_values, dict):
constant_values = self._pad_options_dim_to_index(constant_values)
if isinstance(end_values, dict):
end_values = self._pad_options_dim_to_index(end_values)
# workaround for bug in Dask's default value of stat_length https://github.com/dask/dask/issues/5303
if stat_length is None and mode in ["maximum", "mean", "median", "minimum"]:
stat_length = [(n, n) for n in self.data.shape] # type: ignore
# change integer values to a tuple of two of those values and change pad_width to index
for k, v in pad_width.items():
if isinstance(v, numbers.Number):
pad_width[k] = (v, v)
pad_width_by_index = self._pad_options_dim_to_index(pad_width)
# create pad_options_kwargs, numpy/dask requires only relevant kwargs to be nonempty
pad_option_kwargs = {}
if stat_length is not None:
pad_option_kwargs["stat_length"] = stat_length
if constant_values is not None:
pad_option_kwargs["constant_values"] = constant_values
if end_values is not None:
pad_option_kwargs["end_values"] = end_values
if reflect_type is not None:
pad_option_kwargs["reflect_type"] = reflect_type # type: ignore
array = duck_array_ops.pad(
self.data.astype(dtype, copy=False),
pad_width_by_index,
mode=mode,
**pad_option_kwargs,
)
return type(self)(self.dims, array)
def _roll_one_dim(self, dim, count):
axis = self.get_axis_num(dim)
count %= self.shape[axis]
if count != 0:
indices = [slice(-count, None), slice(None, -count)]
else:
indices = [slice(None)]
arrays = [self[(slice(None),) * axis + (idx,)].data for idx in indices]
data = duck_array_ops.concatenate(arrays, axis)
if is_duck_dask_array(data):
# chunked data should come out with the same chunks; this makes
# it feasible to combine shifted and unshifted data
# TODO: remove this once dask.array automatically aligns chunks
data = data.rechunk(self.data.chunks)
return type(self)(self.dims, data, self._attrs, fastpath=True)
def roll(self, shifts=None, **shifts_kwargs):
"""
Return a new Variable with rolld data.
Parameters
----------
shifts : mapping of hashable to int
Integer offset to roll along each of the given dimensions.
Positive offsets roll to the right; negative offsets roll to the
left.
**shifts_kwargs
The keyword arguments form of ``shifts``.
One of shifts or shifts_kwargs must be provided.
Returns
-------
shifted : Variable
Variable with the same dimensions and attributes but rolled data.
"""
shifts = either_dict_or_kwargs(shifts, shifts_kwargs, "roll")
result = self
for dim, count in shifts.items():
result = result._roll_one_dim(dim, count)
return result
def transpose(self, *dims) -> "Variable":
"""Return a new Variable object with transposed dimensions.
Parameters
----------
*dims : str, optional
By default, reverse the dimensions. Otherwise, reorder the
dimensions to this order.
Returns
-------
transposed : Variable
The returned object has transposed data and dimensions with the
same attributes as the original.
Notes
-----
This operation returns a view of this variable's data. It is
lazy for dask-backed Variables but not for numpy-backed Variables.
See Also
--------
numpy.transpose
"""
if len(dims) == 0:
dims = self.dims[::-1]
dims = tuple(infix_dims(dims, self.dims))
axes = self.get_axis_num(dims)
if len(dims) < 2 or dims == self.dims:
# no need to transpose if only one dimension
# or dims are in same order
return self.copy(deep=False)
data = as_indexable(self._data).transpose(axes)
return type(self)(dims, data, self._attrs, self._encoding, fastpath=True)
@property
def T(self) -> "Variable":
return self.transpose()
def set_dims(self, dims, shape=None):
"""Return a new variable with given set of dimensions.
This method might be used to attach new dimension(s) to variable.
When possible, this operation does not copy this variable's data.
Parameters
----------
dims : str or sequence of str or dict
Dimensions to include on the new variable. If a dict, values are
used to provide the sizes of new dimensions; otherwise, new
dimensions are inserted with length 1.
Returns
-------
Variable
"""
if isinstance(dims, str):
dims = [dims]
if shape is None and utils.is_dict_like(dims):
shape = dims.values()
missing_dims = set(self.dims) - set(dims)
if missing_dims:
raise ValueError(
"new dimensions %r must be a superset of "
"existing dimensions %r" % (dims, self.dims)
)
self_dims = set(self.dims)
expanded_dims = tuple(d for d in dims if d not in self_dims) + self.dims
if self.dims == expanded_dims:
# don't use broadcast_to unless necessary so the result remains
# writeable if possible
expanded_data = self.data
elif shape is not None:
dims_map = dict(zip(dims, shape))
tmp_shape = tuple(dims_map[d] for d in expanded_dims)
expanded_data = duck_array_ops.broadcast_to(self.data, tmp_shape)
else:
expanded_data = self.data[(None,) * (len(expanded_dims) - self.ndim)]
expanded_var = Variable(
expanded_dims, expanded_data, self._attrs, self._encoding, fastpath=True
)
return expanded_var.transpose(*dims)
def _stack_once(self, dims, new_dim):
if not set(dims) <= set(self.dims):
raise ValueError("invalid existing dimensions: %s" % dims)
if new_dim in self.dims:
raise ValueError(
"cannot create a new dimension with the same "
"name as an existing dimension"
)
if len(dims) == 0:
# don't stack
return self.copy(deep=False)
other_dims = [d for d in self.dims if d not in dims]
dim_order = other_dims + list(dims)
reordered = self.transpose(*dim_order)
new_shape = reordered.shape[: len(other_dims)] + (-1,)
new_data = reordered.data.reshape(new_shape)
new_dims = reordered.dims[: len(other_dims)] + (new_dim,)
return Variable(new_dims, new_data, self._attrs, self._encoding, fastpath=True)
def stack(self, dimensions=None, **dimensions_kwargs):
"""
Stack any number of existing dimensions into a single new dimension.
New dimensions will be added at the end, and the order of the data
along each new dimension will be in contiguous (C) order.
Parameters
----------
dimensions : mapping of hashable to tuple of hashable
Mapping of form new_name=(dim1, dim2, ...) describing the
names of new dimensions, and the existing dimensions that
they replace.
**dimensions_kwargs
The keyword arguments form of ``dimensions``.
One of dimensions or dimensions_kwargs must be provided.
Returns
-------
stacked : Variable
Variable with the same attributes but stacked data.
See also
--------
Variable.unstack
"""
dimensions = either_dict_or_kwargs(dimensions, dimensions_kwargs, "stack")
result = self
for new_dim, dims in dimensions.items():
result = result._stack_once(dims, new_dim)
return result
def _unstack_once(self, dims, old_dim):
new_dim_names = tuple(dims.keys())
new_dim_sizes = tuple(dims.values())
if old_dim not in self.dims:
raise ValueError("invalid existing dimension: %s" % old_dim)
if set(new_dim_names).intersection(self.dims):
raise ValueError(
"cannot create a new dimension with the same "
"name as an existing dimension"
)
if np.prod(new_dim_sizes) != self.sizes[old_dim]:
raise ValueError(
"the product of the new dimension sizes must "
"equal the size of the old dimension"
)
other_dims = [d for d in self.dims if d != old_dim]
dim_order = other_dims + [old_dim]
reordered = self.transpose(*dim_order)
new_shape = reordered.shape[: len(other_dims)] + new_dim_sizes
new_data = reordered.data.reshape(new_shape)
new_dims = reordered.dims[: len(other_dims)] + new_dim_names
return Variable(new_dims, new_data, self._attrs, self._encoding, fastpath=True)
def unstack(self, dimensions=None, **dimensions_kwargs):
"""
Unstack an existing dimension into multiple new dimensions.
New dimensions will be added at the end, and the order of the data
along each new dimension will be in contiguous (C) order.
Parameters
----------
dimensions : mapping of hashable to mapping of hashable to int
Mapping of the form old_dim={dim1: size1, ...} describing the
names of existing dimensions, and the new dimensions and sizes
that they map to.
**dimensions_kwargs
The keyword arguments form of ``dimensions``.
One of dimensions or dimensions_kwargs must be provided.
Returns
-------
unstacked : Variable
Variable with the same attributes but unstacked data.
See also
--------
Variable.stack
"""
dimensions = either_dict_or_kwargs(dimensions, dimensions_kwargs, "unstack")
result = self
for old_dim, dims in dimensions.items():
result = result._unstack_once(dims, old_dim)
return result
def fillna(self, value):
return ops.fillna(self, value)
def where(self, cond, other=dtypes.NA):
return ops.where_method(self, cond, other)
def reduce(
self,
func,
dim=None,
axis=None,
keep_attrs=None,
keepdims=False,
**kwargs,
):
"""Reduce this array by applying `func` along some dimension(s).
Parameters
----------
func : callable
Function which can be called in the form
`func(x, axis=axis, **kwargs)` to return the result of reducing an
np.ndarray over an integer valued axis.
dim : str or sequence of str, optional
Dimension(s) over which to apply `func`.
axis : int or sequence of int, optional
Axis(es) over which to apply `func`. Only one of the 'dim'
and 'axis' arguments can be supplied. If neither are supplied, then
the reduction is calculated over the flattened array (by calling
`func(x)` without an axis argument).
keep_attrs : bool, optional
If True, the variable's attributes (`attrs`) will be copied from
the original object to the new one. If False (default), the new
object will be returned without attributes.
keepdims : bool, default: False
If True, the dimensions which are reduced are left in the result
as dimensions of size one
**kwargs : dict
Additional keyword arguments passed on to `func`.
Returns
-------
reduced : Array
Array with summarized data and the indicated dimension(s)
removed.
"""
if dim == ...:
dim = None
if dim is not None and axis is not None:
raise ValueError("cannot supply both 'axis' and 'dim' arguments")
if dim is not None:
axis = self.get_axis_num(dim)
with warnings.catch_warnings():
warnings.filterwarnings(
"ignore", r"Mean of empty slice", category=RuntimeWarning
)
if axis is not None:
data = func(self.data, axis=axis, **kwargs)
else:
data = func(self.data, **kwargs)
if getattr(data, "shape", ()) == self.shape:
dims = self.dims
else:
removed_axes = (
range(self.ndim) if axis is None else np.atleast_1d(axis) % self.ndim
)
if keepdims:
# Insert np.newaxis for removed dims
slices = tuple(
np.newaxis if i in removed_axes else slice(None, None)
for i in range(self.ndim)
)
if getattr(data, "shape", None) is None:
# Reduce has produced a scalar value, not an array-like
data = np.asanyarray(data)[slices]
else:
data = data[slices]
dims = self.dims
else:
dims = [
adim for n, adim in enumerate(self.dims) if n not in removed_axes
]
if keep_attrs is None:
keep_attrs = _get_keep_attrs(default=False)
attrs = self._attrs if keep_attrs else None
return Variable(dims, data, attrs=attrs)
@classmethod
def concat(cls, variables, dim="concat_dim", positions=None, shortcut=False):
"""Concatenate variables along a new or existing dimension.
Parameters
----------
variables : iterable of Variable
Arrays to stack together. Each variable is expected to have
matching dimensions and shape except for along the stacked
dimension.
dim : str or DataArray, optional
Name of the dimension to stack along. This can either be a new
dimension name, in which case it is added along axis=0, or an
existing dimension name, in which case the location of the
dimension is unchanged. Where to insert the new dimension is
determined by the first variable.
positions : None or list of array-like, optional
List of integer arrays which specifies the integer positions to
which to assign each dataset along the concatenated dimension.
If not supplied, objects are concatenated in the provided order.
shortcut : bool, optional
This option is used internally to speed-up groupby operations.
If `shortcut` is True, some checks of internal consistency between
arrays to concatenate are skipped.
Returns
-------
stacked : Variable
Concatenated Variable formed by stacking all the supplied variables
along the given dimension.
"""
if not isinstance(dim, str):
(dim,) = dim.dims
# can't do this lazily: we need to loop through variables at least
# twice
variables = list(variables)
first_var = variables[0]
arrays = [v.data for v in variables]
if dim in first_var.dims:
axis = first_var.get_axis_num(dim)
dims = first_var.dims
data = duck_array_ops.concatenate(arrays, axis=axis)
if positions is not None:
# TODO: deprecate this option -- we don't need it for groupby
# any more.
indices = nputils.inverse_permutation(np.concatenate(positions))
data = duck_array_ops.take(data, indices, axis=axis)
else:
axis = 0
dims = (dim,) + first_var.dims
data = duck_array_ops.stack(arrays, axis=axis)
attrs = dict(first_var.attrs)
encoding = dict(first_var.encoding)
if not shortcut:
for var in variables:
if var.dims != first_var.dims:
raise ValueError(
f"Variable has dimensions {list(var.dims)} but first Variable has dimensions {list(first_var.dims)}"
)
return cls(dims, data, attrs, encoding)
def equals(self, other, equiv=duck_array_ops.array_equiv):
"""True if two Variables have the same dimensions and values;
otherwise False.
Variables can still be equal (like pandas objects) if they have NaN
values in the same locations.
This method is necessary because `v1 == v2` for Variables
does element-wise comparisons (like numpy.ndarrays).
"""
other = getattr(other, "variable", other)
try:
return self.dims == other.dims and (
self._data is other._data or equiv(self.data, other.data)
)
except (TypeError, AttributeError):
return False
def broadcast_equals(self, other, equiv=duck_array_ops.array_equiv):
"""True if two Variables have the values after being broadcast against
each other; otherwise False.
Variables can still be equal (like pandas objects) if they have NaN
values in the same locations.
"""
try:
self, other = broadcast_variables(self, other)
except (ValueError, AttributeError):
return False
return self.equals(other, equiv=equiv)
def identical(self, other, equiv=duck_array_ops.array_equiv):
"""Like equals, but also checks attributes."""
try:
return utils.dict_equiv(self.attrs, other.attrs) and self.equals(
other, equiv=equiv
)
except (TypeError, AttributeError):
return False
def no_conflicts(self, other, equiv=duck_array_ops.array_notnull_equiv):
"""True if the intersection of two Variable's non-null data is
equal; otherwise false.
Variables can thus still be equal if there are locations where either,
or both, contain NaN values.
"""
return self.broadcast_equals(other, equiv=equiv)
def quantile(
self, q, dim=None, interpolation="linear", keep_attrs=None, skipna=True
):
"""Compute the qth quantile of the data along the specified dimension.
Returns the qth quantiles(s) of the array elements.
Parameters
----------
q : float or sequence of float
Quantile to compute, which must be between 0 and 1
inclusive.
dim : str or sequence of str, optional
Dimension(s) over which to apply quantile.
interpolation : {"linear", "lower", "higher", "midpoint", "nearest"}, default: "linear"
This optional parameter specifies the interpolation method to
use when the desired quantile lies between two data points
``i < j``:
* linear: ``i + (j - i) * fraction``, where ``fraction`` is
the fractional part of the index surrounded by ``i`` and
``j``.
* lower: ``i``.
* higher: ``j``.
* nearest: ``i`` or ``j``, whichever is nearest.
* midpoint: ``(i + j) / 2``.
keep_attrs : bool, optional
If True, the variable's attributes (`attrs`) will be copied from
the original object to the new one. If False (default), the new
object will be returned without attributes.
Returns
-------
quantiles : Variable
If `q` is a single quantile, then the result
is a scalar. If multiple percentiles are given, first axis of
the result corresponds to the quantile and a quantile dimension
is added to the return array. The other dimensions are the
dimensions that remain after the reduction of the array.
See Also
--------
numpy.nanquantile, pandas.Series.quantile, Dataset.quantile,
DataArray.quantile
"""
from .computation import apply_ufunc
_quantile_func = np.nanquantile if skipna else np.quantile
if keep_attrs is None:
keep_attrs = _get_keep_attrs(default=False)
scalar = utils.is_scalar(q)
q = np.atleast_1d(np.asarray(q, dtype=np.float64))
if dim is None:
dim = self.dims
if utils.is_scalar(dim):
dim = [dim]
def _wrapper(npa, **kwargs):
# move quantile axis to end. required for apply_ufunc
return np.moveaxis(_quantile_func(npa, **kwargs), 0, -1)
axis = np.arange(-1, -1 * len(dim) - 1, -1)
result = apply_ufunc(
_wrapper,
self,
input_core_dims=[dim],
exclude_dims=set(dim),
output_core_dims=[["quantile"]],
output_dtypes=[np.float64],
dask_gufunc_kwargs=dict(output_sizes={"quantile": len(q)}),
dask="parallelized",
kwargs={"q": q, "axis": axis, "interpolation": interpolation},
)
# for backward compatibility
result = result.transpose("quantile", ...)
if scalar:
result = result.squeeze("quantile")
if keep_attrs:
result.attrs = self._attrs
return result
def rank(self, dim, pct=False):
"""Ranks the data.
Equal values are assigned a rank that is the average of the ranks that
would have been otherwise assigned to all of the values within that
set. Ranks begin at 1, not 0. If `pct`, computes percentage ranks.
NaNs in the input array are returned as NaNs.
The `bottleneck` library is required.
Parameters
----------
dim : str
Dimension over which to compute rank.
pct : bool, optional
If True, compute percentage ranks, otherwise compute integer ranks.
Returns
-------
ranked : Variable
See Also
--------
Dataset.rank, DataArray.rank
"""
import bottleneck as bn
data = self.data
if is_duck_dask_array(data):
raise TypeError(
"rank does not work for arrays stored as dask "
"arrays. Load the data via .compute() or .load() "
"prior to calling this method."
)
elif not isinstance(data, np.ndarray):
raise TypeError(
"rank is not implemented for {} objects.".format(type(data))
)
axis = self.get_axis_num(dim)
func = bn.nanrankdata if self.dtype.kind == "f" else bn.rankdata
ranked = func(data, axis=axis)
if pct:
count = np.sum(~np.isnan(data), axis=axis, keepdims=True)
ranked /= count
return Variable(self.dims, ranked)
def rolling_window(
self, dim, window, window_dim, center=False, fill_value=dtypes.NA
):
"""
Make a rolling_window along dim and add a new_dim to the last place.
Parameters
----------
dim : str
Dimension over which to compute rolling_window.
For nd-rolling, should be list of dimensions.
window : int
Window size of the rolling
For nd-rolling, should be list of integers.
window_dim : str
New name of the window dimension.
For nd-rolling, should be list of integers.
center : bool, default: False
If True, pad fill_value for both ends. Otherwise, pad in the head
of the axis.
fill_value
value to be filled.
Returns
-------
Variable that is a view of the original array with a added dimension of
size w.
The return dim: self.dims + (window_dim, )
The return shape: self.shape + (window, )
Examples
--------
>>> v = Variable(("a", "b"), np.arange(8).reshape((2, 4)))
>>> v.rolling_window("b", 3, "window_dim")
<xarray.Variable (a: 2, b: 4, window_dim: 3)>
array([[[nan, nan, 0.],
[nan, 0., 1.],
[ 0., 1., 2.],
[ 1., 2., 3.]],
<BLANKLINE>
[[nan, nan, 4.],
[nan, 4., 5.],
[ 4., 5., 6.],
[ 5., 6., 7.]]])
>>> v.rolling_window("b", 3, "window_dim", center=True)
<xarray.Variable (a: 2, b: 4, window_dim: 3)>
array([[[nan, 0., 1.],
[ 0., 1., 2.],
[ 1., 2., 3.],
[ 2., 3., nan]],
<BLANKLINE>
[[nan, 4., 5.],
[ 4., 5., 6.],
[ 5., 6., 7.],
[ 6., 7., nan]]])
"""
if fill_value is dtypes.NA: # np.nan is passed
dtype, fill_value = dtypes.maybe_promote(self.dtype)
array = self.astype(dtype, copy=False).data
else:
dtype = self.dtype
array = self.data
if isinstance(dim, list):
assert len(dim) == len(window)
assert len(dim) == len(window_dim)
assert len(dim) == len(center)
else:
dim = [dim]
window = [window]
window_dim = [window_dim]
center = [center]
axis = [self.get_axis_num(d) for d in dim]
new_dims = self.dims + tuple(window_dim)
return Variable(
new_dims,
duck_array_ops.rolling_window(
array, axis=axis, window=window, center=center, fill_value=fill_value
),
)
def coarsen(
self, windows, func, boundary="exact", side="left", keep_attrs=None, **kwargs
):
"""
Apply reduction function.
"""
windows = {k: v for k, v in windows.items() if k in self.dims}
if not windows:
return self.copy()
if keep_attrs is None:
keep_attrs = _get_keep_attrs(default=False)
if keep_attrs:
_attrs = self.attrs
else:
_attrs = None
reshaped, axes = self._coarsen_reshape(windows, boundary, side)
if isinstance(func, str):
name = func
func = getattr(duck_array_ops, name, None)
if func is None:
raise NameError(f"{name} is not a valid method.")
return self._replace(data=func(reshaped, axis=axes, **kwargs), attrs=_attrs)
def _coarsen_reshape(self, windows, boundary, side):
"""
Construct a reshaped-array for coarsen
"""
if not utils.is_dict_like(boundary):
boundary = {d: boundary for d in windows.keys()}
if not utils.is_dict_like(side):
side = {d: side for d in windows.keys()}
# remove unrelated dimensions
boundary = {k: v for k, v in boundary.items() if k in windows}
side = {k: v for k, v in side.items() if k in windows}
for d, window in windows.items():
if window <= 0:
raise ValueError(f"window must be > 0. Given {window}")
variable = self
for d, window in windows.items():
# trim or pad the object
size = variable.shape[self._get_axis_num(d)]
n = int(size / window)
if boundary[d] == "exact":
if n * window != size:
raise ValueError(
"Could not coarsen a dimension of size {} with "
"window {}".format(size, window)
)
elif boundary[d] == "trim":
if side[d] == "left":
variable = variable.isel({d: slice(0, window * n)})
else:
excess = size - window * n
variable = variable.isel({d: slice(excess, None)})
elif boundary[d] == "pad": # pad
pad = window * n - size
if pad < 0:
pad += window
if side[d] == "left":
pad_width = {d: (0, pad)}
else:
pad_width = {d: (pad, 0)}
variable = variable.pad(pad_width, mode="constant")
else:
raise TypeError(
"{} is invalid for boundary. Valid option is 'exact', "
"'trim' and 'pad'".format(boundary[d])
)
shape = []
axes = []
axis_count = 0
for i, d in enumerate(variable.dims):
if d in windows:
size = variable.shape[i]
shape.append(int(size / windows[d]))
shape.append(windows[d])
axis_count += 1
axes.append(i + axis_count)
else:
shape.append(variable.shape[i])
return variable.data.reshape(shape), tuple(axes)
def isnull(self, keep_attrs: bool = None):
"""Test each value in the array for whether it is a missing value.
Returns
-------
isnull : Variable
Same type and shape as object, but the dtype of the data is bool.
See Also
--------
pandas.isnull
Examples
--------
>>> var = xr.Variable("x", [1, np.nan, 3])
>>> var
<xarray.Variable (x: 3)>
array([ 1., nan, 3.])
>>> var.isnull()
<xarray.Variable (x: 3)>
array([False, True, False])
"""
from .computation import apply_ufunc
if keep_attrs is None:
keep_attrs = _get_keep_attrs(default=False)
return apply_ufunc(
duck_array_ops.isnull,
self,
dask="allowed",
keep_attrs=keep_attrs,
)
def notnull(self, keep_attrs: bool = None):
"""Test each value in the array for whether it is not a missing value.
Returns
-------
notnull : Variable
Same type and shape as object, but the dtype of the data is bool.
See Also
--------
pandas.notnull
Examples
--------
>>> var = xr.Variable("x", [1, np.nan, 3])
>>> var
<xarray.Variable (x: 3)>
array([ 1., nan, 3.])
>>> var.notnull()
<xarray.Variable (x: 3)>
array([ True, False, True])
"""
from .computation import apply_ufunc
if keep_attrs is None:
keep_attrs = _get_keep_attrs(default=False)
return apply_ufunc(
duck_array_ops.notnull,
self,
dask="allowed",
keep_attrs=keep_attrs,
)
@property
def real(self):
return type(self)(self.dims, self.data.real, self._attrs)
@property
def imag(self):
return type(self)(self.dims, self.data.imag, self._attrs)
def __array_wrap__(self, obj, context=None):
return Variable(self.dims, obj)
@staticmethod
def _unary_op(f):
@functools.wraps(f)
def func(self, *args, **kwargs):
keep_attrs = kwargs.pop("keep_attrs", None)
if keep_attrs is None:
keep_attrs = _get_keep_attrs(default=True)
with np.errstate(all="ignore"):
result = self.__array_wrap__(f(self.data, *args, **kwargs))
if keep_attrs:
result.attrs = self.attrs
return result
return func
@staticmethod
def _binary_op(f, reflexive=False, **ignored_kwargs):
@functools.wraps(f)
def func(self, other):
if isinstance(other, (xr.DataArray, xr.Dataset)):
return NotImplemented
self_data, other_data, dims = _broadcast_compat_data(self, other)
keep_attrs = _get_keep_attrs(default=False)
attrs = self._attrs if keep_attrs else None
with | np.errstate(all="ignore") | numpy.errstate |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = | np.abs(maxima_y[-2] - minima_y[-2]) | numpy.abs |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = | np.linspace(minima_y[-1], max_discard, 101) | numpy.linspace |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * | np.ones_like(max_1_x_time) | numpy.ones_like |
from abc import ABCMeta, abstractmethod
import os
from vmaf.tools.misc import make_absolute_path, run_process
from vmaf.tools.stats import ListStats
__copyright__ = "Copyright 2016-2018, Netflix, Inc."
__license__ = "Apache, Version 2.0"
import re
import numpy as np
import ast
from vmaf import ExternalProgramCaller, to_list
from vmaf.config import VmafConfig, VmafExternalConfig
from vmaf.core.executor import Executor
from vmaf.core.result import Result
from vmaf.tools.reader import YuvReader
class FeatureExtractor(Executor):
"""
FeatureExtractor takes in a list of assets, and run feature extraction on
them, and return a list of corresponding results. A FeatureExtractor must
specify a unique type and version combination (by the TYPE and VERSION
attribute), so that the Result generated by it can be identified.
A derived class of FeatureExtractor must:
1) Override TYPE and VERSION
2) Override _generate_result(self, asset), which call a
command-line executable and generate feature scores in a log file.
3) Override _get_feature_scores(self, asset), which read the feature
scores from the log file, and return the scores in a dictionary format.
For an example, follow VmafFeatureExtractor.
"""
__metaclass__ = ABCMeta
@property
@abstractmethod
def ATOM_FEATURES(self):
raise NotImplementedError
def _read_result(self, asset):
result = {}
result.update(self._get_feature_scores(asset))
executor_id = self.executor_id
return Result(asset, executor_id, result)
@classmethod
def get_scores_key(cls, atom_feature):
return "{type}_{atom_feature}_scores".format(
type=cls.TYPE, atom_feature=atom_feature)
@classmethod
def get_score_key(cls, atom_feature):
return "{type}_{atom_feature}_score".format(
type=cls.TYPE, atom_feature=atom_feature)
def _get_feature_scores(self, asset):
# routine to read the feature scores from the log file, and return
# the scores in a dictionary format.
log_file_path = self._get_log_file_path(asset)
atom_feature_scores_dict = {}
atom_feature_idx_dict = {}
for atom_feature in self.ATOM_FEATURES:
atom_feature_scores_dict[atom_feature] = []
atom_feature_idx_dict[atom_feature] = 0
with open(log_file_path, 'rt') as log_file:
for line in log_file.readlines():
for atom_feature in self.ATOM_FEATURES:
re_template = "{af}: ([0-9]+) ([a-zA-Z0-9.-]+)".format(af=atom_feature)
mo = re.match(re_template, line)
if mo:
cur_idx = int(mo.group(1))
assert cur_idx == atom_feature_idx_dict[atom_feature]
# parse value, allowing NaN and inf
val = float(mo.group(2))
if np.isnan(val) or np.isinf(val):
val = None
atom_feature_scores_dict[atom_feature].append(val)
atom_feature_idx_dict[atom_feature] += 1
continue
len_score = len(atom_feature_scores_dict[self.ATOM_FEATURES[0]])
assert len_score != 0
for atom_feature in self.ATOM_FEATURES[1:]:
assert len_score == len(atom_feature_scores_dict[atom_feature]), \
"Feature data possibly corrupt. Run cleanup script and try again."
feature_result = {}
for atom_feature in self.ATOM_FEATURES:
scores_key = self.get_scores_key(atom_feature)
feature_result[scores_key] = atom_feature_scores_dict[atom_feature]
return feature_result
class VmafFeatureExtractor(FeatureExtractor):
TYPE = "VMAF_feature"
# VERSION = '0.1' # vmaf_study; Anush's VIF fix
# VERSION = '0.2' # expose vif_num, vif_den, adm_num, adm_den, anpsnr
# VERSION = '0.2.1' # expose vif num/den of each scale
# VERSION = '0.2.2' # adm abs-->fabs, corrected border handling, uniform reading with option of offset for input YUV, updated VIF corner case
# VERSION = '0.2.2b' # expose adm_den/num_scalex
# VERSION = '0.2.3' # AVX for VMAF convolution; update adm features by folding noise floor into per coef
# VERSION = '0.2.4' # Fix a bug in adm feature passing scale into dwt_quant_step
# VERSION = '0.2.4b' # Modify by adding ADM noise floor outside cube root; add derived feature motion2
VERSION = '0.2.4c' # Modify by moving motion2 to c code
ATOM_FEATURES = ['vif', 'adm', 'ansnr', 'motion', 'motion2',
'vif_num', 'vif_den', 'adm_num', 'adm_den', 'anpsnr',
'vif_num_scale0', 'vif_den_scale0',
'vif_num_scale1', 'vif_den_scale1',
'vif_num_scale2', 'vif_den_scale2',
'vif_num_scale3', 'vif_den_scale3',
'adm_num_scale0', 'adm_den_scale0',
'adm_num_scale1', 'adm_den_scale1',
'adm_num_scale2', 'adm_den_scale2',
'adm_num_scale3', 'adm_den_scale3',
]
DERIVED_ATOM_FEATURES = ['vif_scale0', 'vif_scale1', 'vif_scale2', 'vif_scale3',
'vif2', 'adm2', 'adm3',
'adm_scale0', 'adm_scale1', 'adm_scale2', 'adm_scale3',
]
ADM2_CONSTANT = 0
ADM_SCALE_CONSTANT = 0
def _generate_result(self, asset):
# routine to call the command-line executable and generate feature
# scores in the log file.
quality_width, quality_height = asset.quality_width_height
log_file_path = self._get_log_file_path(asset)
yuv_type=self._get_workfile_yuv_type(asset)
ref_path=asset.ref_workfile_path
dis_path=asset.dis_workfile_path
w=quality_width
h=quality_height
logger = self.logger
ExternalProgramCaller.call_vmaf_feature(yuv_type, ref_path, dis_path, w, h, log_file_path, logger)
@classmethod
def _post_process_result(cls, result):
# override Executor._post_process_result
result = super(VmafFeatureExtractor, cls)._post_process_result(result)
# adm2 =
# (adm_num + ADM2_CONSTANT) / (adm_den + ADM2_CONSTANT)
adm2_scores_key = cls.get_scores_key('adm2')
adm_num_scores_key = cls.get_scores_key('adm_num')
adm_den_scores_key = cls.get_scores_key('adm_den')
result.result_dict[adm2_scores_key] = list(
(np.array(result.result_dict[adm_num_scores_key]) + cls.ADM2_CONSTANT) /
(np.array(result.result_dict[adm_den_scores_key]) + cls.ADM2_CONSTANT)
)
# vif_scalei = vif_num_scalei / vif_den_scalei, i = 0, 1, 2, 3
vif_num_scale0_scores_key = cls.get_scores_key('vif_num_scale0')
vif_den_scale0_scores_key = cls.get_scores_key('vif_den_scale0')
vif_num_scale1_scores_key = cls.get_scores_key('vif_num_scale1')
vif_den_scale1_scores_key = cls.get_scores_key('vif_den_scale1')
vif_num_scale2_scores_key = cls.get_scores_key('vif_num_scale2')
vif_den_scale2_scores_key = cls.get_scores_key('vif_den_scale2')
vif_num_scale3_scores_key = cls.get_scores_key('vif_num_scale3')
vif_den_scale3_scores_key = cls.get_scores_key('vif_den_scale3')
vif_scale0_scores_key = cls.get_scores_key('vif_scale0')
vif_scale1_scores_key = cls.get_scores_key('vif_scale1')
vif_scale2_scores_key = cls.get_scores_key('vif_scale2')
vif_scale3_scores_key = cls.get_scores_key('vif_scale3')
result.result_dict[vif_scale0_scores_key] = list(
(np.array(result.result_dict[vif_num_scale0_scores_key])
/ np.array(result.result_dict[vif_den_scale0_scores_key]))
)
result.result_dict[vif_scale1_scores_key] = list(
(np.array(result.result_dict[vif_num_scale1_scores_key])
/ np.array(result.result_dict[vif_den_scale1_scores_key]))
)
result.result_dict[vif_scale2_scores_key] = list(
(np.array(result.result_dict[vif_num_scale2_scores_key])
/ np.array(result.result_dict[vif_den_scale2_scores_key]))
)
result.result_dict[vif_scale3_scores_key] = list(
(np.array(result.result_dict[vif_num_scale3_scores_key])
/ np.array(result.result_dict[vif_den_scale3_scores_key]))
)
# vif2 =
# ((vif_num_scale0 / vif_den_scale0) + (vif_num_scale1 / vif_den_scale1) +
# (vif_num_scale2 / vif_den_scale2) + (vif_num_scale3 / vif_den_scale3)) / 4.0
vif_scores_key = cls.get_scores_key('vif2')
result.result_dict[vif_scores_key] = list(
(
(np.array(result.result_dict[vif_num_scale0_scores_key])
/ np.array(result.result_dict[vif_den_scale0_scores_key])) +
(np.array(result.result_dict[vif_num_scale1_scores_key])
/ np.array(result.result_dict[vif_den_scale1_scores_key])) +
(np.array(result.result_dict[vif_num_scale2_scores_key])
/ np.array(result.result_dict[vif_den_scale2_scores_key])) +
(np.array(result.result_dict[vif_num_scale3_scores_key])
/ np.array(result.result_dict[vif_den_scale3_scores_key]))
) / 4.0
)
# adm_scalei = adm_num_scalei / adm_den_scalei, i = 0, 1, 2, 3
adm_num_scale0_scores_key = cls.get_scores_key('adm_num_scale0')
adm_den_scale0_scores_key = cls.get_scores_key('adm_den_scale0')
adm_num_scale1_scores_key = cls.get_scores_key('adm_num_scale1')
adm_den_scale1_scores_key = cls.get_scores_key('adm_den_scale1')
adm_num_scale2_scores_key = cls.get_scores_key('adm_num_scale2')
adm_den_scale2_scores_key = cls.get_scores_key('adm_den_scale2')
adm_num_scale3_scores_key = cls.get_scores_key('adm_num_scale3')
adm_den_scale3_scores_key = cls.get_scores_key('adm_den_scale3')
adm_scale0_scores_key = cls.get_scores_key('adm_scale0')
adm_scale1_scores_key = cls.get_scores_key('adm_scale1')
adm_scale2_scores_key = cls.get_scores_key('adm_scale2')
adm_scale3_scores_key = cls.get_scores_key('adm_scale3')
result.result_dict[adm_scale0_scores_key] = list(
(np.array(result.result_dict[adm_num_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT)
)
result.result_dict[adm_scale1_scores_key] = list(
(np.array(result.result_dict[adm_num_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT)
)
result.result_dict[adm_scale2_scores_key] = list(
(np.array(result.result_dict[adm_num_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT)
)
result.result_dict[adm_scale3_scores_key] = list(
(np.array(result.result_dict[adm_num_scale3_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale3_scores_key]) + cls.ADM_SCALE_CONSTANT)
)
# adm3 = \
# (((adm_num_scale0 + ADM_SCALE_CONSTANT) / (adm_den_scale0 + ADM_SCALE_CONSTANT))
# + ((adm_num_scale1 + ADM_SCALE_CONSTANT) / (adm_den_scale1 + ADM_SCALE_CONSTANT))
# + ((adm_num_scale2 + ADM_SCALE_CONSTANT) / (adm_den_scale2 + ADM_SCALE_CONSTANT))
# + ((adm_num_scale3 + ADM_SCALE_CONSTANT) / (adm_den_scale3 + ADM_SCALE_CONSTANT))) / 4.0
adm3_scores_key = cls.get_scores_key('adm3')
result.result_dict[adm3_scores_key] = list(
(
((np.array(result.result_dict[adm_num_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT)) +
((np.array(result.result_dict[adm_num_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT)) +
((np.array(result.result_dict[adm_num_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT)) +
((np.array(result.result_dict[adm_num_scale3_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ ( | np.array(result.result_dict[adm_den_scale3_scores_key]) | numpy.array |
"""Test the search module"""
from collections.abc import Iterable, Sized
from io import StringIO
from itertools import chain, product
from functools import partial
import pickle
import sys
from types import GeneratorType
import re
import numpy as np
import scipy.sparse as sp
import pytest
from sklearn.utils.fixes import sp_version
from sklearn.utils._testing import assert_raises
from sklearn.utils._testing import assert_warns
from sklearn.utils._testing import assert_warns_message
from sklearn.utils._testing import assert_raise_message
from sklearn.utils._testing import assert_array_equal
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.utils._testing import assert_allclose
from sklearn.utils._testing import assert_almost_equal
from sklearn.utils._testing import ignore_warnings
from sklearn.utils._mocking import CheckingClassifier, MockDataFrame
from scipy.stats import bernoulli, expon, uniform
from sklearn.base import BaseEstimator, ClassifierMixin
from sklearn.base import clone
from sklearn.exceptions import NotFittedError
from sklearn.datasets import make_classification
from sklearn.datasets import make_blobs
from sklearn.datasets import make_multilabel_classification
from sklearn.model_selection import fit_grid_point
from sklearn.model_selection import train_test_split
from sklearn.model_selection import KFold
from sklearn.model_selection import StratifiedKFold
from sklearn.model_selection import StratifiedShuffleSplit
from sklearn.model_selection import LeaveOneGroupOut
from sklearn.model_selection import LeavePGroupsOut
from sklearn.model_selection import GroupKFold
from sklearn.model_selection import GroupShuffleSplit
from sklearn.model_selection import GridSearchCV
from sklearn.model_selection import RandomizedSearchCV
from sklearn.model_selection import ParameterGrid
from sklearn.model_selection import ParameterSampler
from sklearn.model_selection._search import BaseSearchCV
from sklearn.model_selection._validation import FitFailedWarning
from sklearn.svm import LinearSVC, SVC
from sklearn.tree import DecisionTreeRegressor
from sklearn.tree import DecisionTreeClassifier
from sklearn.cluster import KMeans
from sklearn.neighbors import KernelDensity
from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import f1_score
from sklearn.metrics import recall_score
from sklearn.metrics import accuracy_score
from sklearn.metrics import make_scorer
from sklearn.metrics import roc_auc_score
from sklearn.metrics.pairwise import euclidean_distances
from sklearn.impute import SimpleImputer
from sklearn.pipeline import Pipeline
from sklearn.linear_model import Ridge, SGDClassifier, LinearRegression
from sklearn.experimental import enable_hist_gradient_boosting # noqa
from sklearn.ensemble import HistGradientBoostingClassifier
from sklearn.model_selection.tests.common import OneTimeSplitter
# Neither of the following two estimators inherit from BaseEstimator,
# to test hyperparameter search on user-defined classifiers.
class MockClassifier:
"""Dummy classifier to test the parameter search algorithms"""
def __init__(self, foo_param=0):
self.foo_param = foo_param
def fit(self, X, Y):
assert len(X) == len(Y)
self.classes_ = np.unique(Y)
return self
def predict(self, T):
return T.shape[0]
def transform(self, X):
return X + self.foo_param
def inverse_transform(self, X):
return X - self.foo_param
predict_proba = predict
predict_log_proba = predict
decision_function = predict
def score(self, X=None, Y=None):
if self.foo_param > 1:
score = 1.
else:
score = 0.
return score
def get_params(self, deep=False):
return {'foo_param': self.foo_param}
def set_params(self, **params):
self.foo_param = params['foo_param']
return self
class LinearSVCNoScore(LinearSVC):
"""An LinearSVC classifier that has no score method."""
@property
def score(self):
raise AttributeError
X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
y = np.array([1, 1, 2, 2])
def assert_grid_iter_equals_getitem(grid):
assert list(grid) == [grid[i] for i in range(len(grid))]
@pytest.mark.parametrize("klass", [ParameterGrid,
partial(ParameterSampler, n_iter=10)])
@pytest.mark.parametrize(
"input, error_type, error_message",
[(0, TypeError, r'Parameter .* is not a dict or a list \(0\)'),
([{'foo': [0]}, 0], TypeError, r'Parameter .* is not a dict \(0\)'),
({'foo': 0}, TypeError, "Parameter.* value is not iterable .*"
r"\(key='foo', value=0\)")]
)
def test_validate_parameter_input(klass, input, error_type, error_message):
with pytest.raises(error_type, match=error_message):
klass(input)
def test_parameter_grid():
# Test basic properties of ParameterGrid.
params1 = {"foo": [1, 2, 3]}
grid1 = ParameterGrid(params1)
assert isinstance(grid1, Iterable)
assert isinstance(grid1, Sized)
assert len(grid1) == 3
assert_grid_iter_equals_getitem(grid1)
params2 = {"foo": [4, 2],
"bar": ["ham", "spam", "eggs"]}
grid2 = ParameterGrid(params2)
assert len(grid2) == 6
# loop to assert we can iterate over the grid multiple times
for i in range(2):
# tuple + chain transforms {"a": 1, "b": 2} to ("a", 1, "b", 2)
points = set(tuple(chain(*(sorted(p.items())))) for p in grid2)
assert (points ==
set(("bar", x, "foo", y)
for x, y in product(params2["bar"], params2["foo"])))
assert_grid_iter_equals_getitem(grid2)
# Special case: empty grid (useful to get default estimator settings)
empty = ParameterGrid({})
assert len(empty) == 1
assert list(empty) == [{}]
assert_grid_iter_equals_getitem(empty)
assert_raises(IndexError, lambda: empty[1])
has_empty = ParameterGrid([{'C': [1, 10]}, {}, {'C': [.5]}])
assert len(has_empty) == 4
assert list(has_empty) == [{'C': 1}, {'C': 10}, {}, {'C': .5}]
assert_grid_iter_equals_getitem(has_empty)
def test_grid_search():
# Test that the best estimator contains the right value for foo_param
clf = MockClassifier()
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=3, verbose=3)
# make sure it selects the smallest parameter in case of ties
old_stdout = sys.stdout
sys.stdout = StringIO()
grid_search.fit(X, y)
sys.stdout = old_stdout
assert grid_search.best_estimator_.foo_param == 2
assert_array_equal(grid_search.cv_results_["param_foo_param"].data,
[1, 2, 3])
# Smoke test the score etc:
grid_search.score(X, y)
grid_search.predict_proba(X)
grid_search.decision_function(X)
grid_search.transform(X)
# Test exception handling on scoring
grid_search.scoring = 'sklearn'
assert_raises(ValueError, grid_search.fit, X, y)
def test_grid_search_pipeline_steps():
# check that parameters that are estimators are cloned before fitting
pipe = Pipeline([('regressor', LinearRegression())])
param_grid = {'regressor': [LinearRegression(), Ridge()]}
grid_search = GridSearchCV(pipe, param_grid, cv=2)
grid_search.fit(X, y)
regressor_results = grid_search.cv_results_['param_regressor']
assert isinstance(regressor_results[0], LinearRegression)
assert isinstance(regressor_results[1], Ridge)
assert not hasattr(regressor_results[0], 'coef_')
assert not hasattr(regressor_results[1], 'coef_')
assert regressor_results[0] is not grid_search.best_estimator_
assert regressor_results[1] is not grid_search.best_estimator_
# check that we didn't modify the parameter grid that was passed
assert not hasattr(param_grid['regressor'][0], 'coef_')
assert not hasattr(param_grid['regressor'][1], 'coef_')
@pytest.mark.parametrize("SearchCV", [GridSearchCV, RandomizedSearchCV])
def test_SearchCV_with_fit_params(SearchCV):
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
clf = CheckingClassifier(expected_fit_params=['spam', 'eggs'])
searcher = SearchCV(
clf, {'foo_param': [1, 2, 3]}, cv=2, error_score="raise"
)
# The CheckingClassifier generates an assertion error if
# a parameter is missing or has length != len(X).
err_msg = r"Expected fit parameter\(s\) \['eggs'\] not seen."
with pytest.raises(AssertionError, match=err_msg):
searcher.fit(X, y, spam=np.ones(10))
err_msg = "Fit parameter spam has length 1; expected"
with pytest.raises(AssertionError, match=err_msg):
searcher.fit(X, y, spam=np.ones(1), eggs=np.zeros(10))
searcher.fit(X, y, spam=np.ones(10), eggs=np.zeros(10))
@ignore_warnings
def test_grid_search_no_score():
# Test grid-search on classifier that has no score function.
clf = LinearSVC(random_state=0)
X, y = make_blobs(random_state=0, centers=2)
Cs = [.1, 1, 10]
clf_no_score = LinearSVCNoScore(random_state=0)
grid_search = GridSearchCV(clf, {'C': Cs}, scoring='accuracy')
grid_search.fit(X, y)
grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs},
scoring='accuracy')
# smoketest grid search
grid_search_no_score.fit(X, y)
# check that best params are equal
assert grid_search_no_score.best_params_ == grid_search.best_params_
# check that we can call score and that it gives the correct result
assert grid_search.score(X, y) == grid_search_no_score.score(X, y)
# giving no scoring function raises an error
grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs})
assert_raise_message(TypeError, "no scoring", grid_search_no_score.fit,
[[1]])
def test_grid_search_score_method():
X, y = make_classification(n_samples=100, n_classes=2, flip_y=.2,
random_state=0)
clf = LinearSVC(random_state=0)
grid = {'C': [.1]}
search_no_scoring = GridSearchCV(clf, grid, scoring=None).fit(X, y)
search_accuracy = GridSearchCV(clf, grid, scoring='accuracy').fit(X, y)
search_no_score_method_auc = GridSearchCV(LinearSVCNoScore(), grid,
scoring='roc_auc'
).fit(X, y)
search_auc = GridSearchCV(clf, grid, scoring='roc_auc').fit(X, y)
# Check warning only occurs in situation where behavior changed:
# estimator requires score method to compete with scoring parameter
score_no_scoring = search_no_scoring.score(X, y)
score_accuracy = search_accuracy.score(X, y)
score_no_score_auc = search_no_score_method_auc.score(X, y)
score_auc = search_auc.score(X, y)
# ensure the test is sane
assert score_auc < 1.0
assert score_accuracy < 1.0
assert score_auc != score_accuracy
assert_almost_equal(score_accuracy, score_no_scoring)
assert_almost_equal(score_auc, score_no_score_auc)
def test_grid_search_groups():
# Check if ValueError (when groups is None) propagates to GridSearchCV
# And also check if groups is correctly passed to the cv object
rng = np.random.RandomState(0)
X, y = make_classification(n_samples=15, n_classes=2, random_state=0)
groups = rng.randint(0, 3, 15)
clf = LinearSVC(random_state=0)
grid = {'C': [1]}
group_cvs = [LeaveOneGroupOut(), LeavePGroupsOut(2),
GroupKFold(n_splits=3), GroupShuffleSplit()]
for cv in group_cvs:
gs = GridSearchCV(clf, grid, cv=cv)
assert_raise_message(ValueError,
"The 'groups' parameter should not be None.",
gs.fit, X, y)
gs.fit(X, y, groups=groups)
non_group_cvs = [StratifiedKFold(), StratifiedShuffleSplit()]
for cv in non_group_cvs:
gs = GridSearchCV(clf, grid, cv=cv)
# Should not raise an error
gs.fit(X, y)
def test_classes__property():
# Test that classes_ property matches best_estimator_.classes_
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
Cs = [.1, 1, 10]
grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs})
grid_search.fit(X, y)
assert_array_equal(grid_search.best_estimator_.classes_,
grid_search.classes_)
# Test that regressors do not have a classes_ attribute
grid_search = GridSearchCV(Ridge(), {'alpha': [1.0, 2.0]})
grid_search.fit(X, y)
assert not hasattr(grid_search, 'classes_')
# Test that the grid searcher has no classes_ attribute before it's fit
grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs})
assert not hasattr(grid_search, 'classes_')
# Test that the grid searcher has no classes_ attribute without a refit
grid_search = GridSearchCV(LinearSVC(random_state=0),
{'C': Cs}, refit=False)
grid_search.fit(X, y)
assert not hasattr(grid_search, 'classes_')
def test_trivial_cv_results_attr():
# Test search over a "grid" with only one point.
clf = MockClassifier()
grid_search = GridSearchCV(clf, {'foo_param': [1]}, cv=3)
grid_search.fit(X, y)
assert hasattr(grid_search, "cv_results_")
random_search = RandomizedSearchCV(clf, {'foo_param': [0]}, n_iter=1, cv=3)
random_search.fit(X, y)
assert hasattr(grid_search, "cv_results_")
def test_no_refit():
# Test that GSCV can be used for model selection alone without refitting
clf = MockClassifier()
for scoring in [None, ['accuracy', 'precision']]:
grid_search = GridSearchCV(
clf, {'foo_param': [1, 2, 3]}, refit=False, cv=3
)
grid_search.fit(X, y)
assert not hasattr(grid_search, "best_estimator_") and \
hasattr(grid_search, "best_index_") and \
hasattr(grid_search, "best_params_")
# Make sure the functions predict/transform etc raise meaningful
# error messages
for fn_name in ('predict', 'predict_proba', 'predict_log_proba',
'transform', 'inverse_transform'):
assert_raise_message(NotFittedError,
('refit=False. %s is available only after '
'refitting on the best parameters'
% fn_name), getattr(grid_search, fn_name), X)
# Test that an invalid refit param raises appropriate error messages
for refit in ["", 5, True, 'recall', 'accuracy']:
assert_raise_message(ValueError, "For multi-metric scoring, the "
"parameter refit must be set to a scorer key",
GridSearchCV(clf, {}, refit=refit,
scoring={'acc': 'accuracy',
'prec': 'precision'}
).fit,
X, y)
def test_grid_search_error():
# Test that grid search will capture errors on data with different length
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
assert_raises(ValueError, cv.fit, X_[:180], y_)
def test_grid_search_one_grid_point():
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
param_dict = {"C": [1.0], "kernel": ["rbf"], "gamma": [0.1]}
clf = SVC(gamma='auto')
cv = GridSearchCV(clf, param_dict)
cv.fit(X_, y_)
clf = SVC(C=1.0, kernel="rbf", gamma=0.1)
clf.fit(X_, y_)
assert_array_equal(clf.dual_coef_, cv.best_estimator_.dual_coef_)
def test_grid_search_when_param_grid_includes_range():
# Test that the best estimator contains the right value for foo_param
clf = MockClassifier()
grid_search = None
grid_search = GridSearchCV(clf, {'foo_param': range(1, 4)}, cv=3)
grid_search.fit(X, y)
assert grid_search.best_estimator_.foo_param == 2
def test_grid_search_bad_param_grid():
param_dict = {"C": 1}
clf = SVC(gamma='auto')
assert_raise_message(
ValueError,
"Parameter grid for parameter (C) needs to"
" be a list or numpy array, but got (<class 'int'>)."
" Single values need to be wrapped in a list"
" with one element.",
GridSearchCV, clf, param_dict)
param_dict = {"C": []}
clf = SVC()
assert_raise_message(
ValueError,
"Parameter values for parameter (C) need to be a non-empty sequence.",
GridSearchCV, clf, param_dict)
param_dict = {"C": "1,2,3"}
clf = SVC(gamma='auto')
assert_raise_message(
ValueError,
"Parameter grid for parameter (C) needs to"
" be a list or numpy array, but got (<class 'str'>)."
" Single values need to be wrapped in a list"
" with one element.",
GridSearchCV, clf, param_dict)
param_dict = {"C": np.ones((3, 2))}
clf = SVC()
assert_raises(ValueError, GridSearchCV, clf, param_dict)
def test_grid_search_sparse():
# Test that grid search works with both dense and sparse matrices
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(X_[:180], y_[:180])
y_pred = cv.predict(X_[180:])
C = cv.best_estimator_.C
X_ = sp.csr_matrix(X_)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(X_[:180].tocoo(), y_[:180])
y_pred2 = cv.predict(X_[180:])
C2 = cv.best_estimator_.C
assert np.mean(y_pred == y_pred2) >= .9
assert C == C2
def test_grid_search_sparse_scoring():
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1")
cv.fit(X_[:180], y_[:180])
y_pred = cv.predict(X_[180:])
C = cv.best_estimator_.C
X_ = sp.csr_matrix(X_)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1")
cv.fit(X_[:180], y_[:180])
y_pred2 = cv.predict(X_[180:])
C2 = cv.best_estimator_.C
assert_array_equal(y_pred, y_pred2)
assert C == C2
# Smoke test the score
# np.testing.assert_allclose(f1_score(cv.predict(X_[:180]), y[:180]),
# cv.score(X_[:180], y[:180]))
# test loss where greater is worse
def f1_loss(y_true_, y_pred_):
return -f1_score(y_true_, y_pred_)
F1Loss = make_scorer(f1_loss, greater_is_better=False)
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring=F1Loss)
cv.fit(X_[:180], y_[:180])
y_pred3 = cv.predict(X_[180:])
C3 = cv.best_estimator_.C
assert C == C3
assert_array_equal(y_pred, y_pred3)
def test_grid_search_precomputed_kernel():
# Test that grid search works when the input features are given in the
# form of a precomputed kernel matrix
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
# compute the training kernel matrix corresponding to the linear kernel
K_train = np.dot(X_[:180], X_[:180].T)
y_train = y_[:180]
clf = SVC(kernel='precomputed')
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(K_train, y_train)
assert cv.best_score_ >= 0
# compute the test kernel matrix
K_test = np.dot(X_[180:], X_[:180].T)
y_test = y_[180:]
y_pred = cv.predict(K_test)
assert np.mean(y_pred == y_test) >= 0
# test error is raised when the precomputed kernel is not array-like
# or sparse
assert_raises(ValueError, cv.fit, K_train.tolist(), y_train)
def test_grid_search_precomputed_kernel_error_nonsquare():
# Test that grid search returns an error with a non-square precomputed
# training kernel matrix
K_train = np.zeros((10, 20))
y_train = np.ones((10, ))
clf = SVC(kernel='precomputed')
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
assert_raises(ValueError, cv.fit, K_train, y_train)
class BrokenClassifier(BaseEstimator):
"""Broken classifier that cannot be fit twice"""
def __init__(self, parameter=None):
self.parameter = parameter
def fit(self, X, y):
assert not hasattr(self, 'has_been_fit_')
self.has_been_fit_ = True
def predict(self, X):
return np.zeros(X.shape[0])
@ignore_warnings
def test_refit():
# Regression test for bug in refitting
# Simulates re-fitting a broken estimator; this used to break with
# sparse SVMs.
X = | np.arange(100) | numpy.arange |
import argparse
import json
import numpy as np
import pandas as pd
import os
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report,f1_score
from keras.models import Sequential
from keras.layers import Dense, Dropout
from keras import backend as K
from keras.utils.vis_utils import plot_model
from sklearn.externals import joblib
import time
def f1(y_true, y_pred):
def recall(y_true, y_pred):
"""Recall metric.
Only computes a batch-wise average of recall.
Computes the recall, a metric for multi-label classification of
how many relevant items are selected.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
possible_positives = K.sum(K.round(K.clip(y_true, 0, 1)))
recall = true_positives / (possible_positives + K.epsilon())
return recall
def precision(y_true, y_pred):
"""Precision metric.
Only computes a batch-wise average of precision.
Computes the precision, a metric for multi-label classification of
how many selected items are relevant.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
predicted_positives = K.sum(K.round(K.clip(y_pred, 0, 1)))
precision = true_positives / (predicted_positives + K.epsilon())
return precision
precision = precision(y_true, y_pred)
recall = recall(y_true, y_pred)
return 2*((precision*recall)/(precision+recall+K.epsilon()))
def get_embeddings(sentences_list,layer_json):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:return: Dictionary with key each sentence of the sentences_list and as value the embedding
'''
sentences = dict()#dict with key the index of each line of the sentences_list.txt and as value the sentence
embeddings = dict()##dict with key the index of each sentence and as value the its embedding
sentence_emb = dict()#key:sentence,value:its embedding
with open(sentences_list,'r') as file:
for index,line in enumerate(file):
sentences[index] = line.strip()
with open(layer_json, 'r',encoding='utf-8') as f:
for line in f:
embeddings[json.loads(line)['linex_index']] = np.asarray(json.loads(line)['features'])
for key,value in sentences.items():
sentence_emb[value] = embeddings[key]
return sentence_emb
def train_classifier(sentences_list,layer_json,dataset_csv,filename):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:param dataset_csv: the path of the dataset
:param filename: The path of the pickle file that the model will be stored
:return:
'''
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list,layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = np.asarray(previous_emb)
print(previous_emb.shape)
section_emb = np.asarray(section_list)
print(sentence_emb.shape)
length = np.asarray(length)
print(length.shape)
label = np.asarray(label)
print(errors)
features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1)
features = np.column_stack([features, length]) # np.append(features,length,axis=1)
print(features.shape)
X_train, X_val, y_train, y_val = train_test_split(features, label, test_size=0.33, random_state=42)
log = LogisticRegression(random_state=0, solver='newton-cg', max_iter=1000, C=0.1)
log.fit(X_train, y_train)
#save the model
_ = joblib.dump(log, filename, compress=9)
predictions = log.predict(X_val)
print("###########################################")
print("Results using embeddings from the",layer_json,"file")
print(classification_report(y_val, predictions))
print("F1 score using Logistic Regression:",f1_score(y_val, predictions))
print("###########################################")
#train a DNN
f1_results = list()
for i in range(3):
model = Sequential()
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dense(128, activation='relu', trainable=True))
model.add(Dropout(0.30))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.25))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.35))
model.add(Dense(1, activation='sigmoid'))
# compile network
model.compile(loss='binary_crossentropy', optimizer='sgd', metrics=[f1])
# fit network
model.fit(X_train, y_train, epochs=100, batch_size=64)
loss, f_1 = model.evaluate(X_val, y_val, verbose=1)
print('\nTest F1: %f' % (f_1 * 100))
f1_results.append(f_1)
model = None
print("###########################################")
print("Results using embeddings from the", layer_json, "file")
# evaluate
print(np.mean(f1_results))
print("###########################################")
def parameter_tuning_LR(sentences_list,layer_json,dataset_csv):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:param dataset_csv: the path of the dataset
:return:
'''
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list,layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = np.asarray(previous_emb)
print(previous_emb.shape)
section_emb = np.asarray(section_list)
print(sentence_emb.shape)
length = np.asarray(length)
print(length.shape)
label = np.asarray(label)
print(errors)
features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1)
features = np.column_stack([features, length])
print(features.shape)
X_train, X_val, y_train, y_val = train_test_split(features, label, test_size=0.33, random_state=42)
C = [0.1,1,2,5,10]
solver = ['newton-cg','saga','sag']
best_params = dict()
best_score = 0.0
for c in C:
for s in solver:
start = time.time()
log = LogisticRegression(random_state=0, solver=s, max_iter=1000, C=c)
log.fit(X_train, y_train)
predictions = log.predict(X_val)
print("###########################################")
print("LR with C =",c,'and solver = ',s)
print("Results using embeddings from the", layer_json, "file")
print(classification_report(y_val, predictions))
f1 = f1_score(y_val, predictions)
if f1 > best_score:
best_score = f1
best_params['c'] = c
best_params['solver'] = s
print("F1 score using Logistic Regression:",f1)
print("###########################################")
end = time.time()
running_time = end - start
print("Running time:"+str(running_time))
def visualize_DNN(file_to_save):
'''
Save the DNN architecture to a png file. Better use the Visulize_DNN.ipynd
:param file_to_save: the png file that the architecture of the DNN will be saved.
:return: None
'''
model = Sequential()
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dense(128, activation='relu', trainable=True))
model.add(Dropout(0.30))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.25))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.35))
model.add(Dense(1, activation='sigmoid'))
plot_model(model, to_file=file_to_save, show_shapes=True)
def save_model(sentences_list,layer_json,dataset_csv,pkl):
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list, layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append( | np.zeros(768) | numpy.zeros |
import numpy as np
import pytest
import theano
import theano.tensor as tt
# Don't import test classes otherwise they get tested as part of the file
from tests import unittest_tools as utt
from tests.gpuarray.config import mode_with_gpu, mode_without_gpu, test_ctx_name
from tests.tensor.test_basic import (
TestAlloc,
TestComparison,
TestJoinAndSplit,
TestReshape,
)
from tests.tensor.utils import rand, safe_make_node
from theano.gpuarray.basic_ops import (
GpuAlloc,
GpuAllocEmpty,
GpuContiguous,
GpuEye,
GpuFromHost,
GpuJoin,
GpuReshape,
GpuSplit,
GpuToGpu,
GpuTri,
HostFromGpu,
gpu_contiguous,
gpu_join,
host_from_gpu,
)
from theano.gpuarray.elemwise import GpuDimShuffle, GpuElemwise
from theano.gpuarray.subtensor import GpuSubtensor
from theano.gpuarray.type import GpuArrayType, get_context, gpuarray_shared_constructor
from theano.tensor import TensorType
from theano.tensor.basic import alloc
pygpu = pytest.importorskip("pygpu")
gpuarray = pygpu.gpuarray
utt.seed_rng()
rng = np.random.RandomState(seed=utt.fetch_seed())
def inplace_func(
inputs,
outputs,
mode=None,
allow_input_downcast=False,
on_unused_input="raise",
name=None,
):
if mode is None:
mode = mode_with_gpu
return theano.function(
inputs,
outputs,
mode=mode,
allow_input_downcast=allow_input_downcast,
accept_inplace=True,
on_unused_input=on_unused_input,
name=name,
)
def fake_shared(value, name=None, strict=False, allow_downcast=None, **kwargs):
from theano.tensor.sharedvar import scalar_constructor, tensor_constructor
for c in (gpuarray_shared_constructor, tensor_constructor, scalar_constructor):
try:
return c(
value, name=name, strict=strict, allow_downcast=allow_downcast, **kwargs
)
except TypeError:
continue
def rand_gpuarray(*shape, **kwargs):
r = rng.rand(*shape) * 2 - 1
dtype = kwargs.pop("dtype", theano.config.floatX)
cls = kwargs.pop("cls", None)
if len(kwargs) != 0:
raise TypeError("Unexpected argument %s", list(kwargs.keys())[0])
return gpuarray.array(r, dtype=dtype, cls=cls, context=get_context(test_ctx_name))
def makeTester(
name,
op,
gpu_op,
cases,
checks=None,
mode_gpu=mode_with_gpu,
mode_nogpu=mode_without_gpu,
skip=False,
eps=1e-10,
):
if checks is None:
checks = {}
_op = op
_gpu_op = gpu_op
_cases = cases
_skip = skip
_checks = checks
class Checker(utt.OptimizationTestMixin):
op = staticmethod(_op)
gpu_op = staticmethod(_gpu_op)
cases = _cases
skip = _skip
checks = _checks
def setup_method(self):
eval(self.__class__.__module__ + "." + self.__class__.__name__)
def test_all(self):
if skip:
pytest.skip(skip)
for testname, inputs in cases.items():
for _ in range(len(inputs)):
if type(inputs[_]) is float:
inputs[_] = np.asarray(inputs[_], dtype=theano.config.floatX)
self.run_case(testname, inputs)
def run_case(self, testname, inputs):
inputs_ref = [theano.shared(inp) for inp in inputs]
inputs_tst = [theano.shared(inp) for inp in inputs]
try:
node_ref = safe_make_node(self.op, *inputs_ref)
node_tst = safe_make_node(self.op, *inputs_tst)
except Exception as exc:
err_msg = (
"Test %s::%s: Error occurred while making " "a node with inputs %s"
) % (self.gpu_op, testname, inputs)
exc.args += (err_msg,)
raise
try:
f_ref = inplace_func([], node_ref.outputs, mode=mode_nogpu)
f_tst = inplace_func([], node_tst.outputs, mode=mode_gpu)
except Exception as exc:
err_msg = (
"Test %s::%s: Error occurred while trying to " "make a Function"
) % (self.gpu_op, testname)
exc.args += (err_msg,)
raise
self.assertFunctionContains1(f_tst, self.gpu_op)
ref_e = None
try:
expecteds = f_ref()
except Exception as exc:
ref_e = exc
try:
variables = f_tst()
except Exception as exc:
if ref_e is None:
err_msg = (
"Test %s::%s: exception when calling the " "Function"
) % (self.gpu_op, testname)
exc.args += (err_msg,)
raise
else:
# if we raised an exception of the same type we're good.
if isinstance(exc, type(ref_e)):
return
else:
err_msg = (
"Test %s::%s: exception raised during test "
"call was not the same as the reference "
"call (got: %s, expected %s)"
% (self.gpu_op, testname, type(exc), type(ref_e))
)
exc.args += (err_msg,)
raise
for i, (variable, expected) in enumerate(zip(variables, expecteds)):
condition = (
variable.dtype != expected.dtype
or variable.shape != expected.shape
or not TensorType.values_eq_approx(variable, expected)
)
assert not condition, (
"Test %s::%s: Output %s gave the wrong "
"value. With inputs %s, expected %s "
"(dtype %s), got %s (dtype %s)."
% (
self.op,
testname,
i,
inputs,
expected,
expected.dtype,
variable,
variable.dtype,
)
)
for description, check in self.checks.items():
assert check(inputs, variables), (
"Test %s::%s: Failed check: %s " "(inputs were %s, ouputs were %s)"
) % (self.op, testname, description, inputs, variables)
Checker.__name__ = name
if hasattr(Checker, "__qualname__"):
Checker.__qualname__ = name
return Checker
def test_transfer_cpu_gpu():
a = tt.fmatrix("a")
g = GpuArrayType(dtype="float32", broadcastable=(False, False))("g")
av = np.asarray(rng.rand(5, 4), dtype="float32")
gv = gpuarray.array(av, context=get_context(test_ctx_name))
f = theano.function([a], GpuFromHost(test_ctx_name)(a))
fv = f(av)
assert GpuArrayType.values_eq(fv, gv)
f = theano.function([g], host_from_gpu(g))
fv = f(gv)
assert | np.all(fv == av) | numpy.all |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = | np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) | numpy.linspace |
# pylint: disable=protected-access
"""
Test the wrappers for the C API.
"""
import os
from contextlib import contextmanager
import numpy as np
import numpy.testing as npt
import pandas as pd
import pytest
import xarray as xr
from packaging.version import Version
from pygmt import Figure, clib
from pygmt.clib.conversion import dataarray_to_matrix
from pygmt.clib.session import FAMILIES, VIAS
from pygmt.exceptions import (
GMTCLibError,
GMTCLibNoSessionError,
GMTInvalidInput,
GMTVersionError,
)
from pygmt.helpers import GMTTempFile
TEST_DATA_DIR = os.path.join(os.path.dirname(__file__), "data")
with clib.Session() as _lib:
gmt_version = Version(_lib.info["version"])
@contextmanager
def mock(session, func, returns=None, mock_func=None):
"""
Mock a GMT C API function to make it always return a given value.
Used to test that exceptions are raised when API functions fail by
producing a NULL pointer as output or non-zero status codes.
Needed because it's not easy to get some API functions to fail without
inducing a Segmentation Fault (which is a good thing because libgmt usually
only fails with errors).
"""
if mock_func is None:
def mock_api_function(*args): # pylint: disable=unused-argument
"""
A mock GMT API function that always returns a given value.
"""
return returns
mock_func = mock_api_function
get_libgmt_func = session.get_libgmt_func
def mock_get_libgmt_func(name, argtypes=None, restype=None):
"""
Return our mock function.
"""
if name == func:
return mock_func
return get_libgmt_func(name, argtypes, restype)
setattr(session, "get_libgmt_func", mock_get_libgmt_func)
yield
setattr(session, "get_libgmt_func", get_libgmt_func)
def test_getitem():
"""
Test that I can get correct constants from the C lib.
"""
ses = clib.Session()
assert ses["GMT_SESSION_EXTERNAL"] != -99999
assert ses["GMT_MODULE_CMD"] != -99999
assert ses["GMT_PAD_DEFAULT"] != -99999
assert ses["GMT_DOUBLE"] != -99999
with pytest.raises(GMTCLibError):
ses["A_WHOLE_LOT_OF_JUNK"] # pylint: disable=pointless-statement
def test_create_destroy_session():
"""
Test that create and destroy session are called without errors.
"""
# Create two session and make sure they are not pointing to the same memory
session1 = clib.Session()
session1.create(name="test_session1")
assert session1.session_pointer is not None
session2 = clib.Session()
session2.create(name="test_session2")
assert session2.session_pointer is not None
assert session2.session_pointer != session1.session_pointer
session1.destroy()
session2.destroy()
# Create and destroy a session twice
ses = clib.Session()
for __ in range(2):
with pytest.raises(GMTCLibNoSessionError):
ses.session_pointer # pylint: disable=pointless-statement
ses.create("session1")
assert ses.session_pointer is not None
ses.destroy()
with pytest.raises(GMTCLibNoSessionError):
ses.session_pointer # pylint: disable=pointless-statement
def test_create_session_fails():
"""
Check that an exception is raised when failing to create a session.
"""
ses = clib.Session()
with mock(ses, "GMT_Create_Session", returns=None):
with pytest.raises(GMTCLibError):
ses.create("test-session-name")
# Should fail if trying to create a session before destroying the old one.
ses.create("test1")
with pytest.raises(GMTCLibError):
ses.create("test2")
def test_destroy_session_fails():
"""
Fail to destroy session when given bad input.
"""
ses = clib.Session()
with pytest.raises(GMTCLibNoSessionError):
ses.destroy()
ses.create("test-session")
with mock(ses, "GMT_Destroy_Session", returns=1):
with pytest.raises(GMTCLibError):
ses.destroy()
ses.destroy()
def test_call_module():
"""
Run a command to see if call_module works.
"""
data_fname = os.path.join(TEST_DATA_DIR, "points.txt")
out_fname = "test_call_module.txt"
with clib.Session() as lib:
with GMTTempFile() as out_fname:
lib.call_module("info", "{} -C ->{}".format(data_fname, out_fname.name))
assert os.path.exists(out_fname.name)
output = out_fname.read().strip()
assert output == "11.5309 61.7074 -2.9289 7.8648 0.1412 0.9338"
def test_call_module_invalid_arguments():
"""
Fails for invalid module arguments.
"""
with clib.Session() as lib:
with pytest.raises(GMTCLibError):
lib.call_module("info", "bogus-data.bla")
def test_call_module_invalid_name():
"""
Fails when given bad input.
"""
with clib.Session() as lib:
with pytest.raises(GMTCLibError):
lib.call_module("meh", "")
def test_call_module_error_message():
"""
Check is the GMT error message was captured.
"""
with clib.Session() as lib:
try:
lib.call_module("info", "bogus-data.bla")
except GMTCLibError as error:
assert "Module 'info' failed with status code" in str(error)
assert "gmtinfo [ERROR]: Cannot find file bogus-data.bla" in str(error)
def test_method_no_session():
"""
Fails when not in a session.
"""
# Create an instance of Session without "with" so no session is created.
lib = clib.Session()
with pytest.raises(GMTCLibNoSessionError):
lib.call_module("gmtdefaults", "")
with pytest.raises(GMTCLibNoSessionError):
lib.session_pointer # pylint: disable=pointless-statement
def test_parse_constant_single():
"""
Parsing a single family argument correctly.
"""
lib = clib.Session()
for family in FAMILIES:
parsed = lib._parse_constant(family, valid=FAMILIES)
assert parsed == lib[family]
def test_parse_constant_composite():
"""
Parsing a composite constant argument (separated by |) correctly.
"""
lib = clib.Session()
test_cases = ((family, via) for family in FAMILIES for via in VIAS)
for family, via in test_cases:
composite = "|".join([family, via])
expected = lib[family] + lib[via]
parsed = lib._parse_constant(composite, valid=FAMILIES, valid_modifiers=VIAS)
assert parsed == expected
def test_parse_constant_fails():
"""
Check if the function fails when given bad input.
"""
lib = clib.Session()
test_cases = [
"SOME_random_STRING",
"GMT_IS_DATASET|GMT_VIA_MATRIX|GMT_VIA_VECTOR",
"GMT_IS_DATASET|NOT_A_PROPER_VIA",
"NOT_A_PROPER_FAMILY|GMT_VIA_MATRIX",
"NOT_A_PROPER_FAMILY|ALSO_INVALID",
]
for test_case in test_cases:
with pytest.raises(GMTInvalidInput):
lib._parse_constant(test_case, valid=FAMILIES, valid_modifiers=VIAS)
# Should also fail if not given valid modifiers but is using them anyway.
# This should work...
lib._parse_constant(
"GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=VIAS
)
# But this shouldn't.
with pytest.raises(GMTInvalidInput):
lib._parse_constant(
"GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=None
)
def test_create_data_dataset():
"""
Run the function to make sure it doesn't fail badly.
"""
with clib.Session() as lib:
# Dataset from vectors
data_vector = lib.create_data(
family="GMT_IS_DATASET|GMT_VIA_VECTOR",
geometry="GMT_IS_POINT",
mode="GMT_CONTAINER_ONLY",
dim=[10, 20, 1, 0], # columns, rows, layers, dtype
)
# Dataset from matrices
data_matrix = lib.create_data(
family="GMT_IS_DATASET|GMT_VIA_MATRIX",
geometry="GMT_IS_POINT",
mode="GMT_CONTAINER_ONLY",
dim=[10, 20, 1, 0],
)
assert data_vector != data_matrix
def test_create_data_grid_dim():
"""
Create a grid ignoring range and inc.
"""
with clib.Session() as lib:
# Grids from matrices using dim
lib.create_data(
family="GMT_IS_GRID|GMT_VIA_MATRIX",
geometry="GMT_IS_SURFACE",
mode="GMT_CONTAINER_ONLY",
dim=[10, 20, 1, 0],
)
def test_create_data_grid_range():
"""
Create a grid specifying range and inc instead of dim.
"""
with clib.Session() as lib:
# Grids from matrices using range and int
lib.create_data(
family="GMT_IS_GRID|GMT_VIA_MATRIX",
geometry="GMT_IS_SURFACE",
mode="GMT_CONTAINER_ONLY",
ranges=[150.0, 250.0, -20.0, 20.0],
inc=[0.1, 0.2],
)
def test_create_data_fails():
"""
Check that create_data raises exceptions for invalid input and output.
"""
# Passing in invalid mode
with pytest.raises(GMTInvalidInput):
with clib.Session() as lib:
lib.create_data(
family="GMT_IS_DATASET",
geometry="GMT_IS_SURFACE",
mode="Not_a_valid_mode",
dim=[0, 0, 1, 0],
ranges=[150.0, 250.0, -20.0, 20.0],
inc=[0.1, 0.2],
)
# Passing in invalid geometry
with pytest.raises(GMTInvalidInput):
with clib.Session() as lib:
lib.create_data(
family="GMT_IS_GRID",
geometry="Not_a_valid_geometry",
mode="GMT_CONTAINER_ONLY",
dim=[0, 0, 1, 0],
ranges=[150.0, 250.0, -20.0, 20.0],
inc=[0.1, 0.2],
)
# If the data pointer returned is None (NULL pointer)
with pytest.raises(GMTCLibError):
with clib.Session() as lib:
with mock(lib, "GMT_Create_Data", returns=None):
lib.create_data(
family="GMT_IS_DATASET",
geometry="GMT_IS_SURFACE",
mode="GMT_CONTAINER_ONLY",
dim=[11, 10, 2, 0],
)
def test_virtual_file():
"""
Test passing in data via a virtual file with a Dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
shape = (5, 3)
for dtype in dtypes:
with clib.Session() as lib:
family = "GMT_IS_DATASET|GMT_VIA_MATRIX"
geometry = "GMT_IS_POINT"
dataset = lib.create_data(
family=family,
geometry=geometry,
mode="GMT_CONTAINER_ONLY",
dim=[shape[1], shape[0], 1, 0], # columns, rows, layers, dtype
)
data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape)
lib.put_matrix(dataset, matrix=data)
# Add the dataset to a virtual file and pass it along to gmt info
vfargs = (family, geometry, "GMT_IN|GMT_IS_REFERENCE", dataset)
with lib.open_virtual_file(*vfargs) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T]
)
expected = "<matrix memory>: N = {}\t{}\n".format(shape[0], bounds)
assert output == expected
def test_virtual_file_fails():
"""
Check that opening and closing virtual files raises an exception for non-
zero return codes.
"""
vfargs = (
"GMT_IS_DATASET|GMT_VIA_MATRIX",
"GMT_IS_POINT",
"GMT_IN|GMT_IS_REFERENCE",
None,
)
# Mock Open_VirtualFile to test the status check when entering the context.
# If the exception is raised, the code won't get to the closing of the
# virtual file.
with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=1):
with pytest.raises(GMTCLibError):
with lib.open_virtual_file(*vfargs):
print("Should not get to this code")
# Test the status check when closing the virtual file
# Mock the opening to return 0 (success) so that we don't open a file that
# we won't close later.
with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=0), mock(
lib, "GMT_Close_VirtualFile", returns=1
):
with pytest.raises(GMTCLibError):
with lib.open_virtual_file(*vfargs):
pass
print("Shouldn't get to this code either")
def test_virtual_file_bad_direction():
"""
Test passing an invalid direction argument.
"""
with clib.Session() as lib:
vfargs = (
"GMT_IS_DATASET|GMT_VIA_MATRIX",
"GMT_IS_POINT",
"GMT_IS_GRID", # The invalid direction argument
0,
)
with pytest.raises(GMTInvalidInput):
with lib.open_virtual_file(*vfargs):
print("This should have failed")
def test_virtualfile_from_vectors():
"""
Test the automation for transforming vectors to virtual file dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
size = 10
for dtype in dtypes:
x = np.arange(size, dtype=dtype)
y = np.arange(size, size * 2, 1, dtype=dtype)
z = np.arange(size * 2, size * 3, 1, dtype=dtype)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(x, y, z) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(i.min(), i.max()) for i in (x, y, z)]
)
expected = "<vector memory>: N = {}\t{}\n".format(size, bounds)
assert output == expected
@pytest.mark.parametrize("dtype", [str, object])
def test_virtualfile_from_vectors_one_string_or_object_column(dtype):
"""
Test passing in one column with string or object dtype into virtual file
dataset.
"""
size = 5
x = np.arange(size, dtype=np.int32)
y = np.arange(size, size * 2, 1, dtype=np.int32)
strings = np.array(["a", "bc", "defg", "hijklmn", "opqrst"], dtype=dtype)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(x, y, strings) as vfile:
with GMTTempFile() as outfile:
lib.call_module("convert", f"{vfile} ->{outfile.name}")
output = outfile.read(keep_tabs=True)
expected = "".join(f"{i}\t{j}\t{k}\n" for i, j, k in zip(x, y, strings))
assert output == expected
@pytest.mark.parametrize("dtype", [str, object])
def test_virtualfile_from_vectors_two_string_or_object_columns(dtype):
"""
Test passing in two columns of string or object dtype into virtual file
dataset.
"""
size = 5
x = np.arange(size, dtype=np.int32)
y = np.arange(size, size * 2, 1, dtype=np.int32)
strings1 = np.array(["a", "bc", "def", "ghij", "klmno"], dtype=dtype)
strings2 = np.array(["pqrst", "uvwx", "yz!", "@#", "$"], dtype=dtype)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(x, y, strings1, strings2) as vfile:
with GMTTempFile() as outfile:
lib.call_module("convert", f"{vfile} ->{outfile.name}")
output = outfile.read(keep_tabs=True)
expected = "".join(
f"{h}\t{i}\t{j} {k}\n" for h, i, j, k in zip(x, y, strings1, strings2)
)
assert output == expected
def test_virtualfile_from_vectors_transpose():
"""
Test transforming matrix columns to virtual file dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
shape = (7, 5)
for dtype in dtypes:
data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(*data.T) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} -C ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["{:.0f}\t{:.0f}".format(col.min(), col.max()) for col in data.T]
)
expected = "{}\n".format(bounds)
assert output == expected
def test_virtualfile_from_vectors_diff_size():
"""
Test the function fails for arrays of different sizes.
"""
x = np.arange(5)
y = np.arange(6)
with clib.Session() as lib:
with pytest.raises(GMTInvalidInput):
with lib.virtualfile_from_vectors(x, y):
print("This should have failed")
def test_virtualfile_from_matrix():
"""
Test transforming a matrix to virtual file dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
shape = (7, 5)
for dtype in dtypes:
data = | np.arange(shape[0] * shape[1], dtype=dtype) | numpy.arange |
# pvtrace is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# pvtrace is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import numpy as np
from external.transformations import translation_matrix, rotation_matrix
import external.transformations as tf
from Trace import Photon
from Geometry import Box, Cylinder, FinitePlane, transform_point, transform_direction, rotation_matrix_from_vector_alignment, norm
from Materials import Spectrum
def random_spherecial_vector():
# This method of calculating isotropic vectors is taken from GNU Scientific Library
LOOP = True
while LOOP:
x = -1. + 2. * np.random.uniform()
y = -1. + 2. * np.random.uniform()
s = x**2 + y**2
if s <= 1.0:
LOOP = False
z = -1. + 2. * s
a = 2 * np.sqrt(1 - s)
x = a * x
y = a * y
return np.array([x,y,z])
class SimpleSource(object):
"""A light source that will generate photons of a single colour, direction and position."""
def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, use_random_polarisation=False):
super(SimpleSource, self).__init__()
self.position = position
self.direction = direction
self.wavelength = wavelength
self.use_random_polarisation = use_random_polarisation
self.throw = 0
self.source_id = "SimpleSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.position = np.array(self.position)
photon.direction = np.array(self.direction)
photon.active = True
photon.wavelength = self.wavelength
# If use_polarisation is set generate a random polarisation vector of the photon
if self.use_random_polarisation:
# Randomise rotation angle around xy-plane, the transform from +z to the direction of the photon
vec = random_spherecial_vector()
vec[2] = 0.
vec = norm(vec)
R = rotation_matrix_from_vector_alignment(self.direction, [0,0,1])
photon.polarisation = transform_direction(vec, R)
else:
photon.polarisation = None
photon.id = self.throw
self.throw = self.throw + 1
return photon
class Laser(object):
"""A light source that will generate photons of a single colour, direction and position."""
def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, polarisation=None):
super(Laser, self).__init__()
self.position = np.array(position)
self.direction = np.array(direction)
self.wavelength = wavelength
assert polarisation != None, "Polarisation of the Laser is not set."
self.polarisation = np.array(polarisation)
self.throw = 0
self.source_id = "LaserSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.position = np.array(self.position)
photon.direction = np.array(self.direction)
photon.active = True
photon.wavelength = self.wavelength
photon.polarisation = self.polarisation
photon.id = self.throw
self.throw = self.throw + 1
return photon
class PlanarSource(object):
"""A box that emits photons from the top surface (normal), sampled from the spectrum."""
def __init__(self, spectrum=None, wavelength=555, direction=(0,0,1), length=0.05, width=0.05):
super(PlanarSource, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.plane = FinitePlane(length=length, width=width)
self.length = length
self.width = width
# direction is the direction that photons are fired out of the plane in the GLOBAL FRAME.
# i.e. this is passed directly to the photon to set is's direction
self.direction = direction
self.throw = 0
self.source_id = "PlanarSource_" + str(id(self))
def translate(self, translation):
self.plane.append_transform(tf.translation_matrix(translation))
def rotate(self, angle, axis):
self.plane.append_transform(tf.rotation_matrix(angle, axis))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.id = self.throw
self.throw = self.throw + 1
# Create a point which is on the surface of the finite plane in it's local frame
x = np.random.uniform(0., self.length)
y = np.random.uniform(0., self.width)
local_point = (x, y, 0.)
# Transform the direciton
photon.position = transform_point(local_point, self.plane.transform)
photon.direction = self.direction
photon.active = True
if self.spectrum != None:
photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform())
else:
photon.wavelength = self.wavelength
return photon
class LensSource(object):
"""
A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize".
The focus line should be perpendicular to the plane normal and aligned with the z-axis.
"""
def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)):
super(LensSource, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.planeorigin = planeorigin
self.planeextent = planeextent
self.linepoint = np.array(linepoint)
self.linedirection = np.array(linedirection)
self.focussize = focussize
self.throw = 0
self.source_id = "LensSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.id = self.throw
self.throw = self.throw + 1
# Position
x = np.random.uniform(self.planeorigin[0],self.planeextent[0])
y = np.random.uniform(self.planeorigin[1],self.planeextent[1])
z = np.random.uniform(self.planeorigin[2],self.planeextent[2])
photon.position = np.array((x,y,z))
# Direction
focuspoint = np.array((0.,0.,0.))
focuspoint[0] = self.linepoint[0] + np.random.uniform(-self.focussize,self.focussize)
focuspoint[1] = self.linepoint[1] + np.random.uniform(-self.focussize,self.focussize)
focuspoint[2] = photon.position[2]
direction = focuspoint - photon.position
modulus = (direction[0]**2+direction[1]**2+direction[2]**2)**0.5
photon.direction = direction/modulus
# Wavelength
if self.spectrum != None:
photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform())
else:
photon.wavelength = self.wavelength
return photon
class LensSourceAngle(object):
"""
A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize".
The focus line should be perpendicular to the plane normal and aligned with the z-axis.
For this lense an additional z-boost is added (Angle of incidence in z-direction).
"""
def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), angle = 0, focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)):
super(LensSourceAngle, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.planeorigin = planeorigin
self.planeextent = planeextent
self.linepoint = np.array(linepoint)
self.linedirection = np.array(linedirection)
self.focussize = focussize
self.angle = angle
self.throw = 0
self.source_id = "LensSourceAngle_" + str(id(self))
def photon(self):
photon = Photon()
photon.id = self.throw
self.throw = self.throw + 1
# Position
x = np.random.uniform(self.planeorigin[0],self.planeextent[0])
y = np.random.uniform(self.planeorigin[1],self.planeextent[1])
boost = y*np.tan(self.angle)
z = np.random.uniform(self.planeorigin[2],self.planeextent[2]) - boost
photon.position = np.array((x,y,z))
# Direction
focuspoint = np.array((0.,0.,0.))
focuspoint[0] = self.linepoint[0] + np.random.uniform(-self.focussize,self.focussize)
focuspoint[1] = self.linepoint[1] + np.random.uniform(-self.focussize,self.focussize)
focuspoint[2] = photon.position[2] + boost
direction = focuspoint - photon.position
modulus = (direction[0]**2+direction[1]**2+direction[2]**2)**0.5
photon.direction = direction/modulus
# Wavelength
if self.spectrum != None:
photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform())
else:
photon.wavelength = self.wavelength
return photon
class CylindricalSource(object):
"""
A source for photons emitted in a random direction and position inside a cylinder(radius, length)
"""
def __init__(self, spectrum = None, wavelength = 555, radius = 1, length = 10):
super(CylindricalSource, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.shape = Cylinder(radius = radius, length = length)
self.radius = radius
self.length = length
self.throw = 0
self.source_id = "CylindricalSource_" + str(id(self))
def translate(self, translation):
self.shape.append_transform(tf.translation_matrix(translation))
def rotate(self, angle, axis):
self.shape.append_transform(tf.rotation_matrix(angle, axis))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.id = self.throw
self.throw = self.throw + 1
# Position of emission
phi = np.random.uniform(0., 2*np.pi)
r = np.random.uniform(0.,self.radius)
x = r*np.cos(phi)
y = r*np.sin(phi)
z = np.random.uniform(0.,self.length)
local_center = (x,y,z)
photon.position = transform_point(local_center, self.shape.transform)
# Direction of emission (no need to transform if meant to be isotropic)
phi = np.random.uniform(0.,2*np.pi)
theta = np.random.uniform(0.,np.pi)
x = np.cos(phi)*np.sin(theta)
y = np.sin(phi)*np.sin(theta)
z = np.cos(theta)
local_direction = (x,y,z)
photon.direction = local_direction
# Set wavelength of photon
if self.spectrum != None:
photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform())
else:
photon.wavelength = self.wavelength
# Further initialisation
photon.active = True
return photon
class PointSource(object):
"""
A point source that emits randomly in solid angle specified by phimin, ..., thetamax
"""
def __init__(self, spectrum = None, wavelength = 555, center = (0.,0.,0.), phimin = 0, phimax = 2*np.pi, thetamin = 0, thetamax = np.pi):
super(PointSource, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.center = center
self.phimin = phimin
self.phimax = phimax
self.thetamin = thetamin
self.thetamax = thetamax
self.throw = 0
self.source_id = "PointSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.id = self.throw
self.throw = self.throw + 1
phi = np.random.uniform(self.phimin, self.phimax)
theta = np.random.uniform(self.thetamin, self.thetamax)
x = np.cos(phi)*np.sin(theta)
y = np.sin(phi)*np.sin(theta)
z = | np.cos(theta) | numpy.cos |
import inspect
import numpy as np
from pandas._libs import reduction as libreduction
from pandas.util._decorators import cache_readonly
from pandas.core.dtypes.common import (
is_dict_like,
is_extension_array_dtype,
is_list_like,
is_sequence,
)
from pandas.core.dtypes.generic import ABCSeries
def frame_apply(
obj,
func,
axis=0,
raw=False,
result_type=None,
ignore_failures=False,
args=None,
kwds=None,
):
""" construct and return a row or column based frame apply object """
axis = obj._get_axis_number(axis)
if axis == 0:
klass = FrameRowApply
elif axis == 1:
klass = FrameColumnApply
return klass(
obj,
func,
raw=raw,
result_type=result_type,
ignore_failures=ignore_failures,
args=args,
kwds=kwds,
)
class FrameApply:
def __init__(self, obj, func, raw, result_type, ignore_failures, args, kwds):
self.obj = obj
self.raw = raw
self.ignore_failures = ignore_failures
self.args = args or ()
self.kwds = kwds or {}
if result_type not in [None, "reduce", "broadcast", "expand"]:
raise ValueError(
"invalid value for result_type, must be one "
"of {None, 'reduce', 'broadcast', 'expand'}"
)
self.result_type = result_type
# curry if needed
if (kwds or args) and not isinstance(func, (np.ufunc, str)):
def f(x):
return func(x, *args, **kwds)
else:
f = func
self.f = f
# results
self.result = None
self.res_index = None
self.res_columns = None
@property
def columns(self):
return self.obj.columns
@property
def index(self):
return self.obj.index
@cache_readonly
def values(self):
return self.obj.values
@cache_readonly
def dtypes(self):
return self.obj.dtypes
@property
def agg_axis(self):
return self.obj._get_agg_axis(self.axis)
def get_result(self):
""" compute the results """
# dispatch to agg
if is_list_like(self.f) or is_dict_like(self.f):
return self.obj.aggregate(self.f, axis=self.axis, *self.args, **self.kwds)
# all empty
if len(self.columns) == 0 and len(self.index) == 0:
return self.apply_empty_result()
# string dispatch
if isinstance(self.f, str):
# Support for `frame.transform('method')`
# Some methods (shift, etc.) require the axis argument, others
# don't, so inspect and insert if necessary.
func = getattr(self.obj, self.f)
sig = inspect.getfullargspec(func)
if "axis" in sig.args:
self.kwds["axis"] = self.axis
return func(*self.args, **self.kwds)
# ufunc
elif isinstance(self.f, np.ufunc):
with np.errstate(all="ignore"):
results = self.obj._data.apply("apply", func=self.f)
return self.obj._constructor(
data=results, index=self.index, columns=self.columns, copy=False
)
# broadcasting
if self.result_type == "broadcast":
return self.apply_broadcast()
# one axis empty
elif not all(self.obj.shape):
return self.apply_empty_result()
# raw
elif self.raw and not self.obj._is_mixed_type:
return self.apply_raw()
return self.apply_standard()
def apply_empty_result(self):
"""
we have an empty result; at least 1 axis is 0
we will try to apply the function to an empty
series in order to see if this is a reduction function
"""
# we are not asked to reduce or infer reduction
# so just return a copy of the existing object
if self.result_type not in ["reduce", None]:
return self.obj.copy()
# we may need to infer
should_reduce = self.result_type == "reduce"
from pandas import Series
if not should_reduce:
try:
r = self.f(Series([]))
except Exception:
pass
else:
should_reduce = not isinstance(r, Series)
if should_reduce:
if len(self.agg_axis):
r = self.f(Series([]))
else:
r = np.nan
return self.obj._constructor_sliced(r, index=self.agg_axis)
else:
return self.obj.copy()
def apply_raw(self):
""" apply to the values as a numpy array """
try:
result = libreduction.compute_reduction(self.values, self.f, axis=self.axis)
except ValueError as err:
if "Function does not reduce" not in str(err):
# catch only ValueError raised intentionally in libreduction
raise
result = np.apply_along_axis(self.f, self.axis, self.values)
# TODO: mixed type case
if result.ndim == 2:
return self.obj._constructor(result, index=self.index, columns=self.columns)
else:
return self.obj._constructor_sliced(result, index=self.agg_axis)
def apply_broadcast(self, target):
result_values = np.empty_like(target.values)
# axis which we want to compare compliance
result_compare = target.shape[0]
for i, col in enumerate(target.columns):
res = self.f(target[col])
ares = | np.asarray(res) | numpy.asarray |
import hashlib
from io import BytesIO
import logging
import os
from typing import Any, cast, Dict, List, Optional, Sequence, Type, TYPE_CHECKING, Union
from pkg_resources import parse_version
import wandb
from wandb import util
from ._private import MEDIA_TMP
from .base_types.media import BatchableMedia, Media
from .helper_types.bounding_boxes_2d import BoundingBoxes2D
from .helper_types.classes import Classes
from .helper_types.image_mask import ImageMask
if TYPE_CHECKING: # pragma: no cover
import matplotlib # type: ignore
import numpy as np # type: ignore
import PIL # type: ignore
import torch # type: ignore
from wandb.apis.public import Artifact as PublicArtifact
from ..wandb_artifacts import Artifact as LocalArtifact
from ..wandb_run import Run as LocalRun
ImageDataType = Union[
"matplotlib.artist.Artist", "PIL.Image", "TorchTensorType", "np.ndarray"
]
ImageDataOrPathType = Union[str, "Image", ImageDataType]
TorchTensorType = Union["torch.Tensor", "torch.Variable"]
def _server_accepts_image_filenames() -> bool:
# Newer versions of wandb accept large image filenames arrays
# but older versions would have issues with this.
max_cli_version = util._get_max_cli_version()
if max_cli_version is None:
return False
return parse_version("0.12.10") <= parse_version(max_cli_version)
class Image(BatchableMedia):
"""Format images for logging to W&B.
Arguments:
data_or_path: (numpy array, string, io) Accepts numpy array of
image data, or a PIL image. The class attempts to infer
the data format and converts it.
mode: (string) The PIL mode for an image. Most common are "L", "RGB",
"RGBA". Full explanation at https://pillow.readthedocs.io/en/4.2.x/handbook/concepts.html#concept-modes.
caption: (string) Label for display of image.
Examples:
### Create a wandb.Image from a numpy array
<!--yeadoc-test:log-image-numpy->
```python
import numpy as np
import wandb
wandb.init()
examples = []
for i in range(3):
pixels = np.random.randint(low=0, high=256, size=(100, 100, 3))
image = wandb.Image(pixels, caption=f"random field {i}")
examples.append(image)
wandb.log({"examples": examples})
```
### Create a wandb.Image from a PILImage
<!--yeadoc-test:log-image-pil->
```python
import numpy as np
from PIL import Image as PILImage
import wandb
wandb.init()
examples = []
for i in range(3):
pixels = np.random.randint(low=0, high=256, size=(100, 100, 3), dtype=np.uint8)
pil_image = PILImage.fromarray(pixels, mode="RGB")
image = wandb.Image(pil_image, caption=f"random field {i}")
examples.append(image)
wandb.log({"examples": examples})
```
"""
MAX_ITEMS = 108
# PIL limit
MAX_DIMENSION = 65500
_log_type = "image-file"
format: Optional[str]
_grouping: Optional[int]
_caption: Optional[str]
_width: Optional[int]
_height: Optional[int]
_image: Optional["PIL.Image"]
_classes: Optional["Classes"]
_boxes: Optional[Dict[str, "BoundingBoxes2D"]]
_masks: Optional[Dict[str, "ImageMask"]]
def __init__(
self,
data_or_path: "ImageDataOrPathType",
mode: Optional[str] = None,
caption: Optional[str] = None,
grouping: Optional[int] = None,
classes: Optional[Union["Classes", Sequence[dict]]] = None,
boxes: Optional[Union[Dict[str, "BoundingBoxes2D"], Dict[str, dict]]] = None,
masks: Optional[Union[Dict[str, "ImageMask"], Dict[str, dict]]] = None,
) -> None:
super(Image, self).__init__()
# TODO: We should remove grouping, it's a terrible name and I don't
# think anyone uses it.
self._grouping = None
self._caption = None
self._width = None
self._height = None
self._image = None
self._classes = None
self._boxes = None
self._masks = None
# Allows the user to pass an Image object as the first parameter and have a perfect copy,
# only overriding additional metdata passed in. If this pattern is compelling, we can generalize.
if isinstance(data_or_path, Image):
self._initialize_from_wbimage(data_or_path)
elif isinstance(data_or_path, str):
self._initialize_from_path(data_or_path)
else:
self._initialize_from_data(data_or_path, mode)
self._set_initialization_meta(grouping, caption, classes, boxes, masks)
def _set_initialization_meta(
self,
grouping: Optional[int] = None,
caption: Optional[str] = None,
classes: Optional[Union["Classes", Sequence[dict]]] = None,
boxes: Optional[Union[Dict[str, "BoundingBoxes2D"], Dict[str, dict]]] = None,
masks: Optional[Union[Dict[str, "ImageMask"], Dict[str, dict]]] = None,
) -> None:
if grouping is not None:
self._grouping = grouping
if caption is not None:
self._caption = caption
total_classes = {}
if boxes:
if not isinstance(boxes, dict):
raise ValueError('Images "boxes" argument must be a dictionary')
boxes_final: Dict[str, BoundingBoxes2D] = {}
for key in boxes:
box_item = boxes[key]
if isinstance(box_item, BoundingBoxes2D):
boxes_final[key] = box_item
elif isinstance(box_item, dict):
# TODO: Consider injecting top-level classes if user-provided is empty
boxes_final[key] = BoundingBoxes2D(box_item, key)
total_classes.update(boxes_final[key]._class_labels)
self._boxes = boxes_final
if masks:
if not isinstance(masks, dict):
raise ValueError('Images "masks" argument must be a dictionary')
masks_final: Dict[str, ImageMask] = {}
for key in masks:
mask_item = masks[key]
if isinstance(mask_item, ImageMask):
masks_final[key] = mask_item
elif isinstance(mask_item, dict):
# TODO: Consider injecting top-level classes if user-provided is empty
masks_final[key] = ImageMask(mask_item, key)
if hasattr(masks_final[key], "_val"):
total_classes.update(masks_final[key]._val["class_labels"])
self._masks = masks_final
if classes is not None:
if isinstance(classes, Classes):
total_classes.update(
{val["id"]: val["name"] for val in classes._class_set}
)
else:
total_classes.update({val["id"]: val["name"] for val in classes})
if len(total_classes.keys()) > 0:
self._classes = Classes(
[
{"id": key, "name": total_classes[key]}
for key in total_classes.keys()
]
)
self._width, self._height = self.image.size # type: ignore
self._free_ram()
def _initialize_from_wbimage(self, wbimage: "Image") -> None:
self._grouping = wbimage._grouping
self._caption = wbimage._caption
self._width = wbimage._width
self._height = wbimage._height
self._image = wbimage._image
self._classes = wbimage._classes
self._path = wbimage._path
self._is_tmp = wbimage._is_tmp
self._extension = wbimage._extension
self._sha256 = wbimage._sha256
self._size = wbimage._size
self.format = wbimage.format
self._artifact_source = wbimage._artifact_source
self._artifact_target = wbimage._artifact_target
# We do not want to implicitly copy boxes or masks, just the image-related data.
# self._boxes = wbimage._boxes
# self._masks = wbimage._masks
def _initialize_from_path(self, path: str) -> None:
pil_image = util.get_module(
"PIL.Image",
required='wandb.Image needs the PIL package. To get it, run "pip install pillow".',
)
self._set_file(path, is_tmp=False)
self._image = pil_image.open(path)
self._image.load()
ext = os.path.splitext(path)[1][1:]
self.format = ext
def _initialize_from_data(self, data: "ImageDataType", mode: str = None,) -> None:
pil_image = util.get_module(
"PIL.Image",
required='wandb.Image needs the PIL package. To get it, run "pip install pillow".',
)
if util.is_matplotlib_typename(util.get_full_typename(data)):
buf = BytesIO()
util.ensure_matplotlib_figure(data).savefig(buf)
self._image = pil_image.open(buf)
elif isinstance(data, pil_image.Image):
self._image = data
elif util.is_pytorch_tensor_typename(util.get_full_typename(data)):
vis_util = util.get_module(
"torchvision.utils", "torchvision is required to render images"
)
if hasattr(data, "requires_grad") and data.requires_grad:
data = data.detach()
data = vis_util.make_grid(data, normalize=True)
self._image = pil_image.fromarray(
data.mul(255).clamp(0, 255).byte().permute(1, 2, 0).cpu().numpy()
)
else:
if hasattr(data, "numpy"): # TF data eager tensors
data = data.numpy()
if data.ndim > 2:
data = data.squeeze() # get rid of trivial dimensions as a convenience
self._image = pil_image.fromarray(
self.to_uint8(data), mode=mode or self.guess_mode(data)
)
tmp_path = os.path.join(MEDIA_TMP.name, str(util.generate_id()) + ".png")
self.format = "png"
self._image.save(tmp_path, transparency=None)
self._set_file(tmp_path, is_tmp=True)
@classmethod
def from_json(
cls: Type["Image"], json_obj: dict, source_artifact: "PublicArtifact"
) -> "Image":
classes = None
if json_obj.get("classes") is not None:
classes = source_artifact.get(json_obj["classes"]["path"])
masks = json_obj.get("masks")
_masks: Optional[Dict[str, ImageMask]] = None
if masks:
_masks = {}
for key in masks:
_masks[key] = ImageMask.from_json(masks[key], source_artifact)
_masks[key]._set_artifact_source(source_artifact)
_masks[key]._key = key
boxes = json_obj.get("boxes")
_boxes: Optional[Dict[str, BoundingBoxes2D]] = None
if boxes:
_boxes = {}
for key in boxes:
_boxes[key] = BoundingBoxes2D.from_json(boxes[key], source_artifact)
_boxes[key]._key = key
return cls(
source_artifact.get_path(json_obj["path"]).download(),
caption=json_obj.get("caption"),
grouping=json_obj.get("grouping"),
classes=classes,
boxes=_boxes,
masks=_masks,
)
@classmethod
def get_media_subdir(cls: Type["Image"]) -> str:
return os.path.join("media", "images")
def bind_to_run(
self,
run: "LocalRun",
key: Union[int, str],
step: Union[int, str],
id_: Optional[Union[int, str]] = None,
ignore_copy_err: Optional[bool] = None,
) -> None:
super().bind_to_run(run, key, step, id_, ignore_copy_err=ignore_copy_err)
if self._boxes is not None:
for i, k in enumerate(self._boxes):
id_ = "{}{}".format(id_, i) if id_ is not None else None
self._boxes[k].bind_to_run(
run, key, step, id_, ignore_copy_err=ignore_copy_err
)
if self._masks is not None:
for i, k in enumerate(self._masks):
id_ = "{}{}".format(id_, i) if id_ is not None else None
self._masks[k].bind_to_run(
run, key, step, id_, ignore_copy_err=ignore_copy_err
)
def to_json(self, run_or_artifact: Union["LocalRun", "LocalArtifact"]) -> dict:
json_dict = super(Image, self).to_json(run_or_artifact)
json_dict["_type"] = Image._log_type
json_dict["format"] = self.format
if self._width is not None:
json_dict["width"] = self._width
if self._height is not None:
json_dict["height"] = self._height
if self._grouping:
json_dict["grouping"] = self._grouping
if self._caption:
json_dict["caption"] = self._caption
if isinstance(run_or_artifact, wandb.wandb_sdk.wandb_artifacts.Artifact):
artifact = run_or_artifact
if (
self._masks is not None or self._boxes is not None
) and self._classes is None:
raise ValueError(
"classes must be passed to wandb.Image which have masks or bounding boxes when adding to artifacts"
)
if self._classes is not None:
class_id = hashlib.md5(
str(self._classes._class_set).encode("utf-8")
).hexdigest()
class_name = os.path.join("media", "classes", class_id + "_cls",)
classes_entry = artifact.add(self._classes, class_name)
json_dict["classes"] = {
"type": "classes-file",
"path": classes_entry.path,
"digest": classes_entry.digest,
}
elif not isinstance(run_or_artifact, wandb.wandb_sdk.wandb_run.Run):
raise ValueError("to_json accepts wandb_run.Run or wandb_artifact.Artifact")
if self._boxes:
json_dict["boxes"] = {
k: box.to_json(run_or_artifact) for (k, box) in self._boxes.items()
}
if self._masks:
json_dict["masks"] = {
k: mask.to_json(run_or_artifact) for (k, mask) in self._masks.items()
}
return json_dict
def guess_mode(self, data: "np.ndarray") -> str:
"""
Guess what type of image the np.array is representing
"""
# TODO: do we want to support dimensions being at the beginning of the array?
if data.ndim == 2:
return "L"
elif data.shape[-1] == 3:
return "RGB"
elif data.shape[-1] == 4:
return "RGBA"
else:
raise ValueError(
"Un-supported shape for image conversion %s" % list(data.shape)
)
@classmethod
def to_uint8(cls, data: "np.ndarray") -> "np.ndarray":
"""
Converts floating point image on the range [0,1] and integer images
on the range [0,255] to uint8, clipping if necessary.
"""
np = util.get_module(
"numpy",
required="wandb.Image requires numpy if not supplying PIL Images: pip install numpy",
)
# I think it's better to check the image range vs the data type, since many
# image libraries will return floats between 0 and 255
# some images have range -1...1 or 0-1
dmin = np.min(data)
if dmin < 0:
data = (data - np.min(data)) / | np.ptp(data) | numpy.ptp |
from __future__ import print_function
import numpy as np
import matplotlib.pyplot as plt
class TwoLayerNet(object):
"""
A two-layer fully-connected neural network. The net has an input dimension
of N, a hidden layer dimension of H, and performs classification over C
classes.
We train the network with a softmax loss function and L2 regularization on
the weight matrices. The network uses a ReLU nonlinearity after the first
fully connected layer.
In other words, the network has the following architecture:
input - fully connected layer - ReLU - fully connected layer - softmax
The outputs of the second fully-connected layer are the scores for each
class.
"""
def __init__(self, input_size, hidden_size, output_size, std=1e-4):
"""
Initialize the model. Weights are initialized to small random values
and biases are initialized to zero. Weights and biases are stored in
the variable self.params, which is a dictionary with the following keys
W1: First layer weights; has shape (D, H)
b1: First layer biases; has shape (H,)
W2: Second layer weights; has shape (H, C)
b2: Second layer biases; has shape (C,)
Inputs:
- input_size: The dimension D of the input data.
- hidden_size: The number of neurons H in the hidden layer.
- output_size: The number of classes C.
"""
self.params = {}
self.params['W1'] = std * np.random.randn(input_size, hidden_size)
self.params['b1'] = np.zeros(hidden_size)
self.params['W2'] = std * | np.random.randn(hidden_size, output_size) | numpy.random.randn |
try:
import importlib.resources as pkg_resources
except ImportError:
# Try backported to PY<37 `importlib_resources`.
import importlib_resources as pkg_resources
from . import images
from gym import Env, spaces
from time import time
import numpy as np
from copy import copy
import colorsys
import pygame
from pygame.transform import scale
class MinesweeperEnv(Env):
def __init__(self, grid_shape=(10, 15), bombs_density=0.1, n_bombs=None, impact_size=3, max_time=999, chicken=False):
self.grid_shape = grid_shape
self.grid_size = np.prod(grid_shape)
self.n_bombs = max(1, int(bombs_density * self.grid_size)) if n_bombs is None else n_bombs
self.n_bombs = min(self.grid_size - 1, self.n_bombs)
self.flaged_bombs = 0
self.flaged_empty = 0
self.max_time = max_time
if impact_size % 2 == 0:
raise ValueError('Impact_size must be an odd number !')
self.impact_size = impact_size
# Define constants
self.HIDDEN = 0
self.REVEAL = 1
self.FLAG = 2
self.BOMB = self.impact_size ** 2
# Setting up gym Env conventions
nvec_observation = (self.BOMB + 2) * np.ones(self.grid_shape)
self.observation_space = spaces.MultiDiscrete(nvec_observation)
nvec_action = np.array(self.grid_shape + (2,))
self.action_space = spaces.MultiDiscrete(nvec_action)
# Initalize state
self.state = np.zeros(self.grid_shape + (2,), dtype=np.uint8)
## Setup bombs places
idx = np.indices(self.grid_shape).reshape(2, -1)
bombs_ids = np.random.choice(range(self.grid_size), size=self.n_bombs, replace=False)
self.bombs_positions = idx[0][bombs_ids], idx[1][bombs_ids]
## Place numbers
self.semi_impact_size = (self.impact_size-1)//2
bomb_impact = np.ones((self.impact_size, self.impact_size), dtype=np.uint8)
for bombs_id in bombs_ids:
bomb_x, bomb_y = idx[0][bombs_id], idx[1][bombs_id]
x_min, x_max, dx_min, dx_max = self.clip_index(bomb_x, 0)
y_min, y_max, dy_min, dy_max = self.clip_index(bomb_y, 1)
bomb_region = self.state[x_min:x_max, y_min:y_max, 0]
bomb_region += bomb_impact[dx_min:dx_max, dy_min:dy_max]
## Place bombs
self.state[self.bombs_positions + (0,)] = self.BOMB
self.start_time = time()
self.time_left = int(time() - self.start_time)
# Setup rendering
self.pygame_is_init = False
self.chicken = chicken
self.done = False
self.score = 0
def get_observation(self):
observation = copy(self.state[:, :, 1])
revealed = observation == 1
flaged = observation == 2
observation += self.impact_size ** 2 + 1
observation[revealed] = copy(self.state[:, :, 0][revealed])
observation[flaged] -= 1
return observation
def reveal_around(self, coords, reward, done, without_loss=False):
if not done:
x_min, x_max, _, _ = self.clip_index(coords[0], 0)
y_min, y_max, _, _ = self.clip_index(coords[1], 1)
region = self.state[x_min:x_max, y_min:y_max, :]
unseen_around = np.sum(region[..., 1] == 0)
if unseen_around == 0:
if not without_loss:
reward -= 0.001
return
flags_around = np.sum(region[..., 1] == 2)
if flags_around == self.state[coords + (0,)]:
unrevealed_zeros_around = np.logical_and(region[..., 0] == 0, region[..., 1] == self.HIDDEN)
if np.any(unrevealed_zeros_around):
zeros_coords = np.argwhere(unrevealed_zeros_around)
for zero in zeros_coords:
coord = (x_min + zero[0], y_min + zero[1])
self.state[coord + (1,)] = 1
self.reveal_around(coord, reward, done, without_loss=True)
self.state[x_min:x_max, y_min:y_max, 1][self.state[x_min:x_max, y_min:y_max, 1] != self.FLAG] = 1
unflagged_bombs_around = np.logical_and(region[..., 0] == self.BOMB, region[..., 1] != self.FLAG)
if np.any(unflagged_bombs_around):
self.done = True
reward, done = -1, True
else:
if not without_loss:
reward -= 0.001
def clip_index(self, x, axis):
max_idx = self.grid_shape[axis]
x_min, x_max = max(0, x-self.semi_impact_size), min(max_idx, x + self.semi_impact_size + 1)
dx_min, dx_max = x_min - (x - self.semi_impact_size), x_max - (x + self.semi_impact_size + 1) + self.impact_size
return x_min, x_max, dx_min, dx_max
def step(self, action):
coords = action[:2]
action_type = action[2] + 1 # 0 -> 1 = reveal; 1 -> 2 = toggle_flag
case_state = self.state[coords + (1,)]
case_content = self.state[coords + (0,)]
NO_BOMBS_AROUND = 0
reward, done = 0, False
self.time_left = self.max_time - time() + self.start_time
if self.time_left <= 0:
score = -(self.n_bombs - self.flaged_bombs + self.flaged_empty)/self.n_bombs
reward, done = score, True
return self.get_observation(), reward, done, {'passed':False}
if action_type == self.REVEAL:
if case_state == self.HIDDEN:
self.state[coords + (1,)] = action_type
if case_content == self.BOMB:
if self.pygame_is_init: self.done = True
reward, done = -1, True
return self.get_observation(), reward, done, {'passed':False}
elif case_content == NO_BOMBS_AROUND:
self.reveal_around(coords, reward, done)
elif case_state == self.REVEAL:
self.reveal_around(coords, reward, done)
reward -= 0.01
else:
reward -= 0.001
self.score += reward
return self.get_observation(), reward, done, {'passed':True}
elif action_type == self.FLAG:
if case_state == self.REVEAL:
reward -= 0.001
else:
flaging = 1
if case_state == self.FLAG:
flaging = -1
self.state[coords + (1,)] = self.HIDDEN
else:
self.state[coords + (1,)] = self.FLAG
if case_content == self.BOMB:
self.flaged_bombs += flaging
else:
self.flaged_empty += flaging
if self.flaged_bombs == self.n_bombs and self.flaged_empty == 0:
reward, done = 2 + self.time_left/self.max_time, True
if np.any(np.logical_and(self.state[..., 0]==9, self.state[..., 1]==1)) or self.done:
reward, done = -1 + self.time_left/self.max_time + (self.flaged_bombs - self.flaged_empty)/self.n_bombs, True
self.score += reward
return self.get_observation(), reward, done, {'passed':False}
def reset(self):
self.__init__(self.grid_shape, n_bombs=self.n_bombs, impact_size=self.impact_size, max_time=self.max_time, chicken=self.chicken)
return self.get_observation()
def render(self):
if not self.pygame_is_init:
self._init_pygame()
self.pygame_is_init = True
for event in pygame.event.get():
if event.type == pygame.QUIT: # pylint: disable=E1101
pygame.quit() # pylint: disable=E1101
# Plot background
pygame.draw.rect(self.window, (60, 56, 53), (0, 0, self.height, self.width))
# Plot grid
for index, state in | np.ndenumerate(self.state[..., 1]) | numpy.ndenumerate |
# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Defines coordinate frames and ties them to data axes.
"""
from __future__ import absolute_import, division, unicode_literals, print_function
import numpy as np
from astropy import units as u
from astropy import utils as astutil
from astropy import coordinates as coord
from astropy.extern import six
from . import utils as gwutils
__all__ = ['Frame2D', 'CelestialFrame', 'SpectralFrame', 'CompositeFrame',
'CoordinateFrame']
STANDARD_REFERENCE_FRAMES = [frame.upper() for frame in coord.builtin_frames.__all__]
STANDARD_REFERENCE_POSITION = ["GEOCENTER", "BARYCENTER", "HELIOCENTER",
"TOPOCENTER", "LSR", "LSRK", "LSRD",
"GALACTIC_CENTER", "LOCAL_GROUP_CENTER"]
class CoordinateFrame(object):
"""
Base class for CoordinateFrames.
Parameters
----------
naxes : int
Number of axes.
axes_type : str
One of ["SPATIAL", "SPECTRAL", "TIME"]
axes_order : tuple of int
A dimension in the input data that corresponds to this axis.
reference_frame : astropy.coordinates.builtin_frames
Reference frame (usually used with output_frame to convert to world coordinate objects).
reference_position : str
Reference position - one of `STANDARD_REFERENCE_POSITION`
unit : list of astropy.units.Unit
Unit for each axis.
axes_names : list
Names of the axes in this frame.
name : str
Name of this frame.
"""
def __init__(self, naxes, axes_type, axes_order, reference_frame=None,
reference_position=None, unit=None, axes_names=None,
name=None):
self._naxes = naxes
self._axes_order = tuple(axes_order)
if isinstance(axes_type, six.string_types):
self._axes_type = (axes_type,)
else:
self._axes_type = tuple(axes_type)
self._reference_frame = reference_frame
if unit is not None:
if astutil.isiterable(unit):
unit = tuple(unit)
else:
unit = (unit,)
if len(unit) != naxes:
raise ValueError("Number of units does not match number of axes.")
else:
self._unit = tuple([u.Unit(au) for au in unit])
if axes_names is not None:
if isinstance(axes_names, six.string_types):
axes_names = (axes_names,)
else:
axes_names = tuple(axes_names)
if len(axes_names) != naxes:
raise ValueError("Number of axes names does not match number of axes.")
else:
axes_names = tuple([""] * naxes)
self._axes_names = axes_names
if name is None:
self._name = self.__class__.__name__
else:
self._name = name
if reference_position is not None:
self._reference_position = reference_position
else:
self._reference_position = None
super(CoordinateFrame, self).__init__()
def __repr__(self):
fmt = '<{0}(name="{1}", unit={2}, axes_names={3}, axes_order={4}'.format(
self.__class__.__name__, self.name,
self.unit, self.axes_names, self.axes_order)
if self.reference_position is not None:
fmt += ', reference_position="{0}"'.format(self.reference_position)
if self.reference_frame is not None:
fmt += ", reference_frame={0}".format(self.reference_frame)
fmt += ")>"
return fmt
def __str__(self):
if self._name is not None:
return self._name
else:
return self.__class__.__name__
@property
def name(self):
""" A custom name of this frame."""
return self._name
@name.setter
def name(self, val):
""" A custom name of this frame."""
self._name = val
@property
def naxes(self):
""" The number of axes intheis frame."""
return self._naxes
@property
def unit(self):
"""The unit of this frame."""
return self._unit
@property
def axes_names(self):
""" Names of axes in the frame."""
return self._axes_names
@property
def axes_order(self):
""" A tuple of indices which map inputs to axes."""
return self._axes_order
@property
def reference_frame(self):
return self._reference_frame
@property
def reference_position(self):
try:
return self._reference_position
except AttributeError:
return None
def input_axes(self, start_frame=None):
"""
Computes which axes in `start_frame` contribute to each axis in the current frame.
Parameters
----------
start_frame : ~gwcs.coordinate_frames.CoordinateFrame
A frame in the WCS pipeline
The transform between start_frame and the current frame is used to compute the
mapping inputs: outputs.
"""
sep = self._separable(start_frame)
inputs = []
for ax in self.axes_order:
inputs.append(list(sep[ax].nonzero()[0]))
return inputs
@property
def axes_type(self):
""" Type of this frame : 'SPATIAL', 'SPECTRAL', 'TIME'. """
return self._axes_type
def coordinates(self, *args):
""" Create world coordinates object"""
raise NotImplementedError("Subclasses may implement this")
class CelestialFrame(CoordinateFrame):
"""
Celestial Frame Representation
Parameters
----------
axes_order : tuple of int
A dimension in the input data that corresponds to this axis.
reference_frame : astropy.coordinates.builtin_frames
A reference frame.
reference_position : str
Reference position.
unit : str or units.Unit instance or iterable of those
Units on axes.
axes_names : list
Names of the axes in this frame.
name : str
Name of this frame.
"""
def __init__(self, axes_order=None, reference_frame=None,
unit=None, axes_names=None,
name=None):
naxes = 2
if reference_frame is not None:
if reference_frame.name.upper() in STANDARD_REFERENCE_FRAMES:
_axes_names = list(reference_frame.representation_component_names.values())
if 'distance' in _axes_names:
_axes_names.remove('distance')
if axes_names is None:
axes_names = _axes_names
naxes = len(_axes_names)
_unit = list(reference_frame.representation_component_units.values())
if unit is None and _unit:
unit = _unit
if axes_order is None:
axes_order = tuple(range(naxes))
if unit is None:
unit = tuple([u.degree] * naxes)
axes_type = ['SPATIAL'] * naxes
super(CelestialFrame, self).__init__(naxes=naxes, axes_type=axes_type,
axes_order=axes_order,
reference_frame=reference_frame,
unit=unit,
axes_names=axes_names,
name=name)
def coordinates(self, *args):
"""
Create a SkyCoord object.
Parameters
----------
args : float
inputs to wcs.input_frame
"""
# Reorder axes if necesary.
try:
return coord.SkyCoord(*args, unit=self.unit, frame=self._reference_frame)
except:
raise
class SpectralFrame(CoordinateFrame):
"""
Represents Spectral Frame
Parameters
----------
axes_order : tuple or int
A dimension in the input data that corresponds to this axis.
reference_frame : astropy.coordinates.builtin_frames
Reference frame (usually used with output_frame to convert to world coordinate objects).
unit : str or units.Unit instance
Spectral unit.
axes_names : str
Spectral axis name.
name : str
Name for this frame.
"""
def __init__(self, axes_order=(0,), reference_frame=None, unit=None,
axes_names=None, name=None, reference_position=None):
super(SpectralFrame, self).__init__(naxes=1, axes_type="SPECTRAL", axes_order=axes_order,
axes_names=axes_names, reference_frame=reference_frame,
unit=unit, name=name,
reference_position=reference_position)
def coordinates(self, *args):
if | np.isscalar(args) | numpy.isscalar |
"""
Random Variables.
This module implements random variables. Random variables are the main in- and outputs
of probabilistic numerical methods.
"""
from typing import Any, Callable, Dict, Generic, Optional, Tuple, TypeVar, Union
import numpy as np
from probnum import utils as _utils
from probnum.type import (
ArrayLikeGetitemArgType,
DTypeArgType,
FloatArgType,
RandomStateArgType,
RandomStateType,
ShapeArgType,
ShapeType,
)
try:
# functools.cached_property is only available in Python >=3.8
from functools import cached_property
except ImportError:
from cached_property import cached_property
_ValueType = TypeVar("ValueType")
class RandomVariable(Generic[_ValueType]):
"""
Random variables are the main objects used by probabilistic numerical methods.
Every probabilistic numerical method takes a random variable encoding the prior
distribution as input and outputs a random variable whose distribution encodes the
uncertainty arising from finite computation. The generic signature of a
probabilistic numerical method is:
``output_rv = probnum_method(input_rv, method_params)``
In practice, most random variables used by methods in ProbNum have Dirac or Gaussian
measure.
Instances of :class:`RandomVariable` can be added, multiplied, etc. with arrays and
linear operators. This may change their ``distribution`` and not necessarily all
previously available methods are retained.
The internals of :class:`RandomVariable` objects are assumed to be constant over
their whole lifecycle. This is due to the caches used to make certain computations
more efficient. As a consequence, altering the internal state of a
:class:`RandomVariable` (e.g. its mean, cov, sampling function, etc.) will result in
undefined behavior. In particular, this should be kept in mind when subclassing
:class:`RandomVariable` or any of its descendants.
Parameters
----------
shape :
Shape of realizations of this random variable.
dtype :
Data type of realizations of this random variable. If ``object`` will be
converted to ``numpy.dtype``.
as_value_type :
Function which can be used to transform user-supplied arguments, interpreted as
realizations of this random variable, to an easy-to-process, normalized format.
Will be called internally to transform the argument of functions like
``in_support``, ``cdf`` and ``logcdf``, ``pmf`` and ``logpmf`` (in
:class:`DiscreteRandomVariable`), ``pdf`` and ``logpdf`` (in
:class:`ContinuousRandomVariable`), and potentially by similar functions in
subclasses.
For instance, this method is useful if (``log``)``cdf`` and (``log``)``pdf``
both only work on :class:`np.float_` arguments, but we still want the user to be
able to pass Python :class:`float`. Then ``as_value_type`` should be set to
something like ``lambda x: np.float64(x)``.
See Also
--------
asrandvar : Transform into a :class:`RandomVariable`.
Examples
--------
"""
# pylint: disable=too-many-instance-attributes,too-many-public-methods
def __init__(
self,
shape: ShapeArgType,
dtype: DTypeArgType,
random_state: RandomStateArgType = None,
parameters: Optional[Dict[str, Any]] = None,
sample: Optional[Callable[[ShapeType], _ValueType]] = None,
in_support: Optional[Callable[[_ValueType], bool]] = None,
cdf: Optional[Callable[[_ValueType], np.float_]] = None,
logcdf: Optional[Callable[[_ValueType], np.float_]] = None,
quantile: Optional[Callable[[FloatArgType], _ValueType]] = None,
mode: Optional[Callable[[], _ValueType]] = None,
median: Optional[Callable[[], _ValueType]] = None,
mean: Optional[Callable[[], _ValueType]] = None,
cov: Optional[Callable[[], _ValueType]] = None,
var: Optional[Callable[[], _ValueType]] = None,
std: Optional[Callable[[], _ValueType]] = None,
entropy: Optional[Callable[[], np.float_]] = None,
as_value_type: Optional[Callable[[Any], _ValueType]] = None,
):
# pylint: disable=too-many-arguments,too-many-locals
"""Create a new random variable."""
self.__shape = _utils.as_shape(shape)
# Data Types
self.__dtype = np.dtype(dtype)
self.__median_dtype = RandomVariable.infer_median_dtype(self.__dtype)
self.__moment_dtype = RandomVariable.infer_moment_dtype(self.__dtype)
self._random_state = _utils.as_random_state(random_state)
# Probability distribution of the random variable
self.__parameters = parameters.copy() if parameters is not None else {}
self.__sample = sample
self.__in_support = in_support
self.__cdf = cdf
self.__logcdf = logcdf
self.__quantile = quantile
# Properties of the random variable
self.__mode = mode
self.__median = median
self.__mean = mean
self.__cov = cov
self.__var = var
self.__std = std
self.__entropy = entropy
# Utilities
self.__as_value_type = as_value_type
def __repr__(self) -> str:
return f"<{self.shape} {self.__class__.__name__} with dtype={self.dtype}>"
@property
def shape(self) -> ShapeType:
"""Shape of realizations of the random variable."""
return self.__shape
@cached_property
def ndim(self) -> int:
return len(self.__shape)
@cached_property
def size(self) -> int:
return int(np.prod(self.__shape))
@property
def dtype(self) -> np.dtype:
"""Data type of (elements of) a realization of this random variable."""
return self.__dtype
@property
def median_dtype(self) -> np.dtype:
"""The dtype of the :attr:`median`. It will be set to the dtype arising from
the multiplication of values with dtypes :attr:`dtype` and :class:`np.float_`.
This is motivated by the fact that, even for discrete random variables, e.g.
integer-valued random variables, the :attr:`median` might lie in between two
values in which case these values are averaged. For example, a uniform random
variable on :math:`\\{ 1, 2, 3, 4 \\}` will have a median of :math:`2.5`.
"""
return self.__median_dtype
@property
def moment_dtype(self) -> np.dtype:
"""The dtype of any (function of a) moment of the random variable, e.g. its
:attr:`mean`, :attr:`cov`, :attr:`var`, or :attr:`std`. It will be set to the
dtype arising from the multiplication of values with dtypes :attr:`dtype`
and :class:`np.float_`. This is motivated by the mathematical definition of a
moment as a sum or an integral over products of probabilities and values of the
random variable, which are represented as using the dtypes :class:`np.float_`
and :attr:`dtype`, respectively.
"""
return self.__moment_dtype
@property
def random_state(self) -> RandomStateType:
"""Random state of the random variable.
This attribute defines the RandomState object to use for drawing
realizations from this random variable.
If None (or np.random), the global np.random state is used.
If integer, it is used to seed the local :class:`~numpy.random.RandomState`
instance.
"""
return self._random_state
@random_state.setter
def random_state(self, seed: RandomStateArgType):
"""Get or set the RandomState object of the underlying distribution.
This can be either None or an existing RandomState object.
If None (or np.random), use the RandomState singleton used by np.random.
If already a RandomState instance, use it.
If an int, use a new RandomState instance seeded with seed.
"""
self._random_state = _utils.as_random_state(seed)
@property
def parameters(self) -> Dict[str, Any]:
"""
Parameters of the probability distribution.
The parameters of the distribution such as mean, variance, et cetera stored in a
``dict``.
"""
return self.__parameters.copy()
@cached_property
def mode(self) -> _ValueType:
"""
Mode of the random variable.
Returns
-------
mode : float
The mode of the random variable.
"""
if self.__mode is None:
raise NotImplementedError
mode = self.__mode()
RandomVariable._check_property_value(
"mode",
mode,
shape=self.__shape,
dtype=self.__dtype,
)
# Make immutable
if isinstance(mode, np.ndarray):
mode.setflags(write=False)
return mode
@cached_property
def median(self) -> _ValueType:
"""
Median of the random variable.
To learn about the dtype of the median, see :attr:`median_dtype`.
Returns
-------
median : float
The median of the distribution.
"""
if self.__shape != ():
raise NotImplementedError(
"The median is only defined for scalar random variables."
)
median = self.__median()
RandomVariable._check_property_value(
"median",
median,
shape=self.__shape,
dtype=self.__median_dtype,
)
# Make immutable
if isinstance(median, np.ndarray):
median.setflags(write=False)
return median
@cached_property
def mean(self) -> _ValueType:
"""
Mean :math:`\\mathbb{E}(X)` of the distribution.
To learn about the dtype of the mean, see :attr:`moment_dtype`.
Returns
-------
mean : array-like
The mean of the distribution.
"""
if self.__mean is None:
raise NotImplementedError
mean = self.__mean()
RandomVariable._check_property_value(
"mean",
mean,
shape=self.__shape,
dtype=self.__moment_dtype,
)
# Make immutable
if isinstance(mean, np.ndarray):
mean.setflags(write=False)
return mean
@cached_property
def cov(self) -> _ValueType:
"""
Covariance :math:`\\operatorname{Cov}(X) = \\mathbb{E}((X-\\mathbb{E}(X))(X-\\mathbb{E}(X))^\\top)`
of the random variable.
To learn about the dtype of the covariance, see :attr:`moment_dtype`.
Returns
-------
cov : array-like
The kernels of the random variable.
""" # pylint: disable=line-too-long
if self.__cov is None:
raise NotImplementedError
cov = self.__cov()
RandomVariable._check_property_value(
"covariance",
cov,
shape=(self.size, self.size) if self.ndim > 0 else (),
dtype=self.__moment_dtype,
)
# Make immutable
if isinstance(cov, np.ndarray):
cov.setflags(write=False)
return cov
@cached_property
def var(self) -> _ValueType:
"""
Variance :math:`\\operatorname{Var}(X) = \\mathbb{E}((X-\\mathbb{E}(X))^2)` of
the distribution.
To learn about the dtype of the variance, see :attr:`moment_dtype`.
Returns
-------
var : array-like
The variance of the distribution.
"""
if self.__var is None:
try:
var = | np.diag(self.cov) | numpy.diag |
import numpy as np
from stumpff import C, S
from CelestialBody import BODIES
from numerical import newton, laguerre
from lagrange import calc_f, calc_fd, calc_g, calc_gd
def kepler_chi(chi, alpha, r0, vr0, mu, dt):
''' Kepler's Equation of the universal anomaly, modified
for use in numerical solvers. '''
z = alpha*chi**2
return (r0*vr0/np.sqrt(mu))*chi**2*C(z) + \
(1 - alpha*r0)*chi**3*S(z) + \
r0*chi - np.sqrt(mu)*dt
def dkepler_dchi(chi, alpha, r0, vr0, mu, dt):
''' Derivative of Kepler's Equation of the universal anomaly,
modified for use in numerical solvers. '''
z = alpha*chi**2
return (r0*vr0/np.sqrt(mu))*chi*(1 - alpha*chi**2*S(z)) + \
(1 - alpha*r0)*chi**2*C(z) + r0
def d2kepler_dchi2(chi, alpha, r0, vr0, mu, dt):
''' Second derivative of Kepler's Equation of the universal
anomaly, modified for use in numerical solvers. '''
z = alpha*chi**2
S_ = S(z)
return (r0*vr0/np.sqrt(mu))*(1 - 3*z*S_ + z*(C(z) - 3*S_)) + \
chi*(1 - z*S_)*(1 - alpha*r0)
def solve_kepler_chi(r_0, v_0, dt, body=BODIES['Earth'], method='laguerre', tol=1e-7, max_iters=100):
''' Solve Kepler's Equation of the universal anomaly chi using the specified
numerical method. Applies Algorithm 3.4 from Orbital Mechanics for Engineering
Students, 4 ed, Curtis.
:param r_0: `iterable` (km) initial position 3-vector
:param v_0: `iterable` (km/s) initial velocity 3-vector
:param dt: `float` (s) time after initial state to solve for r, v as 3-vectors
:param body: `CelestialBody` (--) the celestial body to use for orbital parameters
:param method: `str` (--) which numerical method to use to solve Kepler's Equation
:param tol: `float` (--) decimal tolerance for numerical method (default 1e-7 is IEEE 745 single precision)
:param max_iters: `int` (--) maximum number of iterations in numerical method before breaking
:return: (km) final position 3-vector, (km/s) final velocity 3-vector
'''
VALID_METHODS = ('laguerre', 'newton')
mu = body.mu # (km**3/s**2) gravitational parameter of the specified primary body
r0 = np.linalg.norm(r_0) # (km) initial position magnitude
v0 = np.linalg.norm(v_0) # (km/s) initial velocity magnitude
vr0 = np.dot(v_0, r_0)/r0 # (km/s) initial radial velocity magnitude
alpha = 2/r0 - v0**2/mu # (1/km) inverse of semi-major axis
chi0 = np.sqrt(mu)*np.abs(alpha)*dt
if method not in VALID_METHODS:
print(f'Method \'{method}\' is not valid, must be one of {VALID_METHODS}.\nDefaulting to laguerre method.')
chi, _, _ = laguerre(chi0, kepler_chi, dkepler_dchi, d2kepler_dchi2, alpha, r0, vr0, mu, dt)
elif method == 'newton':
chi, _, _ = newton(chi0, kepler_chi, dkepler_dchi, alpha, r0, vr0, mu, dt)
else: # method == 'laguerre'
chi, _, _ = laguerre(chi0, kepler_chi, dkepler_dchi, d2kepler_dchi2, alpha, r0, vr0, mu, dt)
f = calc_f(chi, r0, alpha)
g = calc_g(dt, mu, chi, alpha)
r_1 = f*r_0 + g*v_0
r1 = np.linalg.norm(r_1)
fd = calc_fd(mu, r1, r0, alpha, chi)
gd = calc_gd(chi, r1, alpha)
v_1 = fd*r_0 + gd*v_0
return r_1, v_1
def solve_kepler_E(e, Me, tol=1e-7, max_iters=100):
''' Solve Kepler's Equation in the form containing Eccentric Anomaly (E),
eccentricity (e), and Mean Anomaly of Ellipse (Me). Uses Algorithm 3.1 from Orbital
Mechanics for Engineering Students, 4 ed, Curtis. '''
# TODO: have this function make use of one of the numerical methods in numerical.py
def f(E, e, Me):
return E - e* | np.sin(E) | numpy.sin |
# coding: utf-8
# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Test the Logarithmic Units and Quantities
"""
from __future__ import (absolute_import, unicode_literals, division,
print_function)
from ...extern import six
from ...extern.six.moves import zip
import pickle
import itertools
import pytest
import numpy as np
from numpy.testing.utils import assert_allclose
from ...tests.helper import assert_quantity_allclose
from ... import units as u, constants as c
lu_units = [u.dex, u.mag, u.decibel]
lu_subclasses = [u.DexUnit, u.MagUnit, u.DecibelUnit]
lq_subclasses = [u.Dex, u.Magnitude, u.Decibel]
pu_sample = (u.dimensionless_unscaled, u.m, u.g/u.s**2, u.Jy)
class TestLogUnitCreation(object):
def test_logarithmic_units(self):
"""Check logarithmic units are set up correctly."""
assert u.dB.to(u.dex) == 0.1
assert u.dex.to(u.mag) == -2.5
assert u.mag.to(u.dB) == -4
@pytest.mark.parametrize('lu_unit, lu_cls', zip(lu_units, lu_subclasses))
def test_callable_units(self, lu_unit, lu_cls):
assert isinstance(lu_unit, u.UnitBase)
assert callable(lu_unit)
assert lu_unit._function_unit_class is lu_cls
@pytest.mark.parametrize('lu_unit', lu_units)
def test_equality_to_normal_unit_for_dimensionless(self, lu_unit):
lu = lu_unit()
assert lu == lu._default_function_unit # eg, MagUnit() == u.mag
assert lu._default_function_unit == lu # and u.mag == MagUnit()
@pytest.mark.parametrize('lu_unit, physical_unit',
itertools.product(lu_units, pu_sample))
def test_call_units(self, lu_unit, physical_unit):
"""Create a LogUnit subclass using the callable unit and physical unit,
and do basic check that output is right."""
lu1 = lu_unit(physical_unit)
assert lu1.physical_unit == physical_unit
assert lu1.function_unit == lu1._default_function_unit
def test_call_invalid_unit(self):
with pytest.raises(TypeError):
u.mag([])
with pytest.raises(ValueError):
u.mag(u.mag())
@pytest.mark.parametrize('lu_cls, physical_unit', itertools.product(
lu_subclasses + [u.LogUnit], pu_sample))
def test_subclass_creation(self, lu_cls, physical_unit):
"""Create a LogUnit subclass object for given physical unit,
and do basic check that output is right."""
lu1 = lu_cls(physical_unit)
assert lu1.physical_unit == physical_unit
assert lu1.function_unit == lu1._default_function_unit
lu2 = lu_cls(physical_unit,
function_unit=2*lu1._default_function_unit)
assert lu2.physical_unit == physical_unit
assert lu2.function_unit == u.Unit(2*lu2._default_function_unit)
with pytest.raises(ValueError):
lu_cls(physical_unit, u.m)
def test_predefined_magnitudes():
assert_quantity_allclose((-21.1*u.STmag).physical,
1.*u.erg/u.cm**2/u.s/u.AA)
assert_quantity_allclose((-48.6*u.ABmag).physical,
1.*u.erg/u.cm**2/u.s/u.Hz)
assert_quantity_allclose((0*u.M_bol).physical, c.L_bol0)
assert_quantity_allclose((0*u.m_bol).physical,
c.L_bol0/(4.*np.pi*(10.*c.pc)**2))
def test_predefined_reinitialisation():
assert u.mag('ST') == u.STmag
assert u.mag('AB') == u.ABmag
assert u.mag('Bol') == u.M_bol
assert u.mag('bol') == u.m_bol
def test_predefined_string_roundtrip():
"""Ensure roundtripping; see #5015"""
with u.magnitude_zero_points.enable():
assert u.Unit(u.STmag.to_string()) == u.STmag
assert u.Unit(u.ABmag.to_string()) == u.ABmag
assert u.Unit(u.M_bol.to_string()) == u.M_bol
assert u.Unit(u.m_bol.to_string()) == u.m_bol
def test_inequality():
"""Check __ne__ works (regresssion for #5342)."""
lu1 = u.mag(u.Jy)
lu2 = u.dex(u.Jy)
lu3 = u.mag(u.Jy**2)
lu4 = lu3 - lu1
assert lu1 != lu2
assert lu1 != lu3
assert lu1 == lu4
class TestLogUnitStrings(object):
def test_str(self):
"""Do some spot checks that str, repr, etc. work as expected."""
lu1 = u.mag(u.Jy)
assert str(lu1) == 'mag(Jy)'
assert repr(lu1) == 'Unit("mag(Jy)")'
assert lu1.to_string('generic') == 'mag(Jy)'
with pytest.raises(ValueError):
lu1.to_string('fits')
lu2 = u.dex()
assert str(lu2) == 'dex'
assert repr(lu2) == 'Unit("dex(1)")'
assert lu2.to_string() == 'dex(1)'
lu3 = u.MagUnit(u.Jy, function_unit=2*u.mag)
assert str(lu3) == '2 mag(Jy)'
assert repr(lu3) == 'MagUnit("Jy", unit="2 mag")'
assert lu3.to_string() == '2 mag(Jy)'
lu4 = u.mag(u.ct)
assert lu4.to_string('generic') == 'mag(ct)'
assert lu4.to_string('latex') == ('$\\mathrm{mag}$$\\mathrm{\\left( '
'\\mathrm{ct} \\right)}$')
assert lu4._repr_latex_() == lu4.to_string('latex')
class TestLogUnitConversion(object):
@pytest.mark.parametrize('lu_unit, physical_unit',
itertools.product(lu_units, pu_sample))
def test_physical_unit_conversion(self, lu_unit, physical_unit):
"""Check various LogUnit subclasses are equivalent and convertible
to their non-log counterparts."""
lu1 = lu_unit(physical_unit)
assert lu1.is_equivalent(physical_unit)
assert lu1.to(physical_unit, 0.) == 1.
assert physical_unit.is_equivalent(lu1)
assert physical_unit.to(lu1, 1.) == 0.
pu = u.Unit(8.*physical_unit)
assert lu1.is_equivalent(physical_unit)
assert lu1.to(pu, 0.) == 0.125
assert pu.is_equivalent(lu1)
assert_allclose(pu.to(lu1, 0.125), 0., atol=1.e-15)
# Check we round-trip.
value = np.linspace(0., 10., 6)
assert_allclose(pu.to(lu1, lu1.to(pu, value)), value, atol=1.e-15)
# And that we're not just returning True all the time.
pu2 = u.g
assert not lu1.is_equivalent(pu2)
with pytest.raises(u.UnitsError):
lu1.to(pu2)
assert not pu2.is_equivalent(lu1)
with pytest.raises(u.UnitsError):
pu2.to(lu1)
@pytest.mark.parametrize('lu_unit', lu_units)
def test_container_unit_conversion(self, lu_unit):
"""Check that conversion to logarithmic units (u.mag, u.dB, u.dex)
is only possible when the physical unit is dimensionless."""
values = np.linspace(0., 10., 6)
lu1 = lu_unit(u.dimensionless_unscaled)
assert lu1.is_equivalent(lu1.function_unit)
assert_allclose(lu1.to(lu1.function_unit, values), values)
lu2 = lu_unit(u.Jy)
assert not lu2.is_equivalent(lu2.function_unit)
with pytest.raises(u.UnitsError):
lu2.to(lu2.function_unit, values)
@pytest.mark.parametrize(
'flu_unit, tlu_unit, physical_unit',
itertools.product(lu_units, lu_units, pu_sample))
def test_subclass_conversion(self, flu_unit, tlu_unit, physical_unit):
"""Check various LogUnit subclasses are equivalent and convertible
to each other if they correspond to equivalent physical units."""
values = np.linspace(0., 10., 6)
flu = flu_unit(physical_unit)
tlu = tlu_unit(physical_unit)
assert flu.is_equivalent(tlu)
assert_allclose(flu.to(tlu), flu.function_unit.to(tlu.function_unit))
assert_allclose(flu.to(tlu, values),
values * flu.function_unit.to(tlu.function_unit))
tlu2 = tlu_unit(u.Unit(100.*physical_unit))
assert flu.is_equivalent(tlu2)
# Check that we round-trip.
assert_allclose(flu.to(tlu2, tlu2.to(flu, values)), values, atol=1.e-15)
tlu3 = tlu_unit(physical_unit.to_system(u.si)[0])
assert flu.is_equivalent(tlu3)
assert_allclose(flu.to(tlu3, tlu3.to(flu, values)), values, atol=1.e-15)
tlu4 = tlu_unit(u.g)
assert not flu.is_equivalent(tlu4)
with pytest.raises(u.UnitsError):
flu.to(tlu4, values)
def test_unit_decomposition(self):
lu = u.mag(u.Jy)
assert lu.decompose() == u.mag(u.Jy.decompose())
assert lu.decompose().physical_unit.bases == [u.kg, u.s]
assert lu.si == u.mag(u.Jy.si)
assert lu.si.physical_unit.bases == [u.kg, u.s]
assert lu.cgs == u.mag(u.Jy.cgs)
assert lu.cgs.physical_unit.bases == [u.g, u.s]
def test_unit_multiple_possible_equivalencies(self):
lu = u.mag(u.Jy)
assert lu.is_equivalent(pu_sample)
class TestLogUnitArithmetic(object):
def test_multiplication_division(self):
"""Check that multiplication/division with other units is only
possible when the physical unit is dimensionless, and that this
turns the unit into a normal one."""
lu1 = u.mag(u.Jy)
with pytest.raises(u.UnitsError):
lu1 * u.m
with pytest.raises(u.UnitsError):
u.m * lu1
with pytest.raises(u.UnitsError):
lu1 / lu1
for unit in (u.dimensionless_unscaled, u.m, u.mag, u.dex):
with pytest.raises(u.UnitsError):
lu1 / unit
lu2 = u.mag(u.dimensionless_unscaled)
with pytest.raises(u.UnitsError):
lu2 * lu1
with pytest.raises(u.UnitsError):
lu2 / lu1
# But dimensionless_unscaled can be cancelled.
assert lu2 / lu2 == u.dimensionless_unscaled
# With dimensionless, normal units are OK, but we return a plain unit.
tf = lu2 * u.m
tr = u.m * lu2
for t in (tf, tr):
assert not isinstance(t, type(lu2))
assert t == lu2.function_unit * u.m
with u.set_enabled_equivalencies(u.logarithmic()):
with pytest.raises(u.UnitsError):
t.to(lu2.physical_unit)
# Now we essentially have a LogUnit with a prefactor of 100,
# so should be equivalent again.
t = tf / u.cm
with u.set_enabled_equivalencies(u.logarithmic()):
assert t.is_equivalent(lu2.function_unit)
assert_allclose(t.to(u.dimensionless_unscaled, np.arange(3.)/100.),
lu2.to(lu2.physical_unit, np.arange(3.)))
# If we effectively remove lu1, a normal unit should be returned.
t2 = tf / lu2
assert not isinstance(t2, type(lu2))
assert t2 == u.m
t3 = tf / lu2.function_unit
assert not isinstance(t3, type(lu2))
assert t3 == u.m
# For completeness, also ensure non-sensical operations fail
with pytest.raises(TypeError):
lu1 * object()
with pytest.raises(TypeError):
slice(None) * lu1
with pytest.raises(TypeError):
lu1 / []
with pytest.raises(TypeError):
1 / lu1
@pytest.mark.parametrize('power', (2, 0.5, 1, 0))
def test_raise_to_power(self, power):
"""Check that raising LogUnits to some power is only possible when the
physical unit is dimensionless, and that conversion is turned off when
the resulting logarithmic unit (such as mag**2) is incompatible."""
lu1 = u.mag(u.Jy)
if power == 0:
assert lu1 ** power == u.dimensionless_unscaled
elif power == 1:
assert lu1 ** power == lu1
else:
with pytest.raises(u.UnitsError):
lu1 ** power
# With dimensionless, though, it works, but returns a normal unit.
lu2 = u.mag(u.dimensionless_unscaled)
t = lu2**power
if power == 0:
assert t == u.dimensionless_unscaled
elif power == 1:
assert t == lu2
else:
assert not isinstance(t, type(lu2))
assert t == lu2.function_unit**power
# also check we roundtrip
t2 = t**(1./power)
assert t2 == lu2.function_unit
with u.set_enabled_equivalencies(u.logarithmic()):
assert_allclose(t2.to(u.dimensionless_unscaled, np.arange(3.)),
lu2.to(lu2.physical_unit, np.arange(3.)))
@pytest.mark.parametrize('other', pu_sample)
def test_addition_subtraction_to_normal_units_fails(self, other):
lu1 = u.mag(u.Jy)
with pytest.raises(u.UnitsError):
lu1 + other
with pytest.raises(u.UnitsError):
lu1 - other
with pytest.raises(u.UnitsError):
other - lu1
def test_addition_subtraction_to_non_units_fails(self):
lu1 = u.mag(u.Jy)
with pytest.raises(TypeError):
lu1 + 1.
with pytest.raises(TypeError):
lu1 - [1., 2., 3.]
@pytest.mark.parametrize(
'other', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m),
u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag)))
def test_addition_subtraction(self, other):
"""Check physical units are changed appropriately"""
lu1 = u.mag(u.Jy)
other_pu = getattr(other, 'physical_unit', u.dimensionless_unscaled)
lu_sf = lu1 + other
assert lu_sf.is_equivalent(lu1.physical_unit * other_pu)
lu_sr = other + lu1
assert lu_sr.is_equivalent(lu1.physical_unit * other_pu)
lu_df = lu1 - other
assert lu_df.is_equivalent(lu1.physical_unit / other_pu)
lu_dr = other - lu1
assert lu_dr.is_equivalent(other_pu / lu1.physical_unit)
def test_complicated_addition_subtraction(self):
"""for fun, a more complicated example of addition and subtraction"""
dm0 = u.Unit('DM', 1./(4.*np.pi*(10.*u.pc)**2))
lu_dm = u.mag(dm0)
lu_absST = u.STmag - lu_dm
assert lu_absST.is_equivalent(u.erg/u.s/u.AA)
def test_neg_pos(self):
lu1 = u.mag(u.Jy)
neg_lu = -lu1
assert neg_lu != lu1
assert neg_lu.physical_unit == u.Jy**-1
assert -neg_lu == lu1
pos_lu = +lu1
assert pos_lu is not lu1
assert pos_lu == lu1
def test_pickle():
lu1 = u.dex(u.cm/u.s**2)
s = pickle.dumps(lu1)
lu2 = pickle.loads(s)
assert lu1 == lu2
def test_hashable():
lu1 = u.dB(u.mW)
lu2 = u.dB(u.m)
lu3 = u.dB(u.mW)
assert hash(lu1) != hash(lu2)
assert hash(lu1) == hash(lu3)
luset = {lu1, lu2, lu3}
assert len(luset) == 2
class TestLogQuantityCreation(object):
@pytest.mark.parametrize('lq, lu', zip(lq_subclasses + [u.LogQuantity],
lu_subclasses + [u.LogUnit]))
def test_logarithmic_quantities(self, lq, lu):
"""Check logarithmic quantities are all set up correctly"""
assert lq._unit_class == lu
assert type(lu()._quantity_class(1.)) is lq
@pytest.mark.parametrize('lq_cls, physical_unit',
itertools.product(lq_subclasses, pu_sample))
def test_subclass_creation(self, lq_cls, physical_unit):
"""Create LogQuantity subclass objects for some physical units,
and basic check on transformations"""
value = np.arange(1., 10.)
log_q = lq_cls(value * physical_unit)
assert log_q.unit.physical_unit == physical_unit
assert log_q.unit.function_unit == log_q.unit._default_function_unit
assert_allclose(log_q.physical.value, value)
with pytest.raises(ValueError):
lq_cls(value, physical_unit)
@pytest.mark.parametrize(
'unit', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m),
u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag),
u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag)))
def test_different_units(self, unit):
q = u.Magnitude(1.23, unit)
assert q.unit.function_unit == getattr(unit, 'function_unit', unit)
assert q.unit.physical_unit is getattr(unit, 'physical_unit',
u.dimensionless_unscaled)
@pytest.mark.parametrize('value, unit', (
(1.*u.mag(u.Jy), None),
(1.*u.dex(u.Jy), None),
(1.*u.mag(u.W/u.m**2/u.Hz), u.mag(u.Jy)),
(1.*u.dex(u.W/u.m**2/u.Hz), u.mag(u.Jy))))
def test_function_values(self, value, unit):
lq = u.Magnitude(value, unit)
assert lq == value
assert lq.unit.function_unit == u.mag
assert lq.unit.physical_unit == getattr(unit, 'physical_unit',
value.unit.physical_unit)
@pytest.mark.parametrize(
'unit', (u.mag(), u.mag(u.Jy), u.mag(u.m), u.MagUnit('', 2.*u.mag),
u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag)))
def test_indirect_creation(self, unit):
q1 = 2.5 * unit
assert isinstance(q1, u.Magnitude)
assert q1.value == 2.5
assert q1.unit == unit
pv = 100. * unit.physical_unit
q2 = unit * pv
assert q2.unit == unit
assert q2.unit.physical_unit == pv.unit
assert q2.to_value(unit.physical_unit) == 100.
assert (q2._function_view / u.mag).to_value(1) == -5.
q3 = unit / 0.4
assert q3 == q1
def test_from_view(self):
# Cannot view a physical quantity as a function quantity, since the
# values would change.
q = [100., 1000.] * u.cm/u.s**2
with pytest.raises(TypeError):
q.view(u.Dex)
# But fine if we have the right magnitude.
q = [2., 3.] * u.dex
lq = q.view(u.Dex)
assert isinstance(lq, u.Dex)
assert lq.unit.physical_unit == u.dimensionless_unscaled
assert np.all(q == lq)
def test_using_quantity_class(self):
"""Check that we can use Quantity if we have subok=True"""
# following issue #5851
lu = u.dex(u.AA)
with pytest.raises(u.UnitTypeError):
u.Quantity(1., lu)
q = u.Quantity(1., lu, subok=True)
assert type(q) is lu._quantity_class
def test_conversion_to_and_from_physical_quantities():
"""Ensures we can convert from regular quantities."""
mst = [10., 12., 14.] * u.STmag
flux_lambda = mst.physical
mst_roundtrip = flux_lambda.to(u.STmag)
# check we return a logquantity; see #5178.
assert isinstance(mst_roundtrip, u.Magnitude)
assert mst_roundtrip.unit == mst.unit
assert_allclose(mst_roundtrip.value, mst.value)
wave = [4956.8, 4959.55, 4962.3] * u.AA
flux_nu = mst.to(u.Jy, equivalencies=u.spectral_density(wave))
mst_roundtrip2 = flux_nu.to(u.STmag, u.spectral_density(wave))
assert isinstance(mst_roundtrip2, u.Magnitude)
assert mst_roundtrip2.unit == mst.unit
assert_allclose(mst_roundtrip2.value, mst.value)
def test_quantity_decomposition():
lq = 10.*u.mag(u.Jy)
assert lq.decompose() == lq
assert lq.decompose().unit.physical_unit.bases == [u.kg, u.s]
assert lq.si == lq
assert lq.si.unit.physical_unit.bases == [u.kg, u.s]
assert lq.cgs == lq
assert lq.cgs.unit.physical_unit.bases == [u.g, u.s]
class TestLogQuantityViews(object):
def setup(self):
self.lq = u.Magnitude(np.arange(10.) * u.Jy)
self.lq2 = u.Magnitude(np.arange(5.))
def test_value_view(self):
lq_value = self.lq.value
assert type(lq_value) is np.ndarray
lq_value[2] = -1.
assert np.all(self.lq.value == lq_value)
def test_function_view(self):
lq_fv = self.lq._function_view
assert type(lq_fv) is u.Quantity
assert lq_fv.unit is self.lq.unit.function_unit
lq_fv[3] = -2. * lq_fv.unit
assert np.all(self.lq.value == lq_fv.value)
def test_quantity_view(self):
# Cannot view as Quantity, since the unit cannot be represented.
with pytest.raises(TypeError):
self.lq.view(u.Quantity)
# But a dimensionless one is fine.
q2 = self.lq2.view(u.Quantity)
assert q2.unit is u.mag
assert np.all(q2.value == self.lq2.value)
lq3 = q2.view(u.Magnitude)
assert type(lq3.unit) is u.MagUnit
assert lq3.unit.physical_unit == u.dimensionless_unscaled
assert np.all(lq3 == self.lq2)
class TestLogQuantitySlicing(object):
def test_item_get_and_set(self):
lq1 = u.Magnitude(np.arange(1., 11.)*u.Jy)
assert lq1[9] == u.Magnitude(10.*u.Jy)
lq1[2] = 100.*u.Jy
assert lq1[2] == u.Magnitude(100.*u.Jy)
with pytest.raises(u.UnitsError):
lq1[2] = 100.*u.m
with pytest.raises(u.UnitsError):
lq1[2] = 100.*u.mag
with pytest.raises(u.UnitsError):
lq1[2] = u.Magnitude(100.*u.m)
assert lq1[2] == u.Magnitude(100.*u.Jy)
def test_slice_get_and_set(self):
lq1 = u.Magnitude(np.arange(1., 10.)*u.Jy)
lq1[2:4] = 100.*u.Jy
assert np.all(lq1[2:4] == u.Magnitude(100.*u.Jy))
with pytest.raises(u.UnitsError):
lq1[2:4] = 100.*u.m
with pytest.raises(u.UnitsError):
lq1[2:4] = 100.*u.mag
with pytest.raises(u.UnitsError):
lq1[2:4] = u.Magnitude(100.*u.m)
assert np.all(lq1[2] == u.Magnitude(100.*u.Jy))
class TestLogQuantityArithmetic(object):
def test_multiplication_division(self):
"""Check that multiplication/division with other quantities is only
possible when the physical unit is dimensionless, and that this turns
the result into a normal quantity."""
lq = u.Magnitude(np.arange(1., 11.)*u.Jy)
with pytest.raises(u.UnitsError):
lq * (1.*u.m)
with pytest.raises(u.UnitsError):
(1.*u.m) * lq
with pytest.raises(u.UnitsError):
lq / lq
for unit in (u.m, u.mag, u.dex):
with pytest.raises(u.UnitsError):
lq / unit
lq2 = u.Magnitude(np.arange(1, 11.))
with pytest.raises(u.UnitsError):
lq2 * lq
with pytest.raises(u.UnitsError):
lq2 / lq
with pytest.raises(u.UnitsError):
lq / lq2
# but dimensionless_unscaled can be cancelled
r = lq2 / u.Magnitude(2.)
assert r.unit == u.dimensionless_unscaled
assert | np.all(r.value == lq2.value/2.) | numpy.all |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
min_1_y_time = minima_x[-1] * np.ones_like(min_1_y)
dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101)
dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Characteristic Wave Effects Example')
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10))
plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10))
plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4,
label=textwrap.fill('Coughlin maximum', 14))
plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4,
label=textwrap.fill('Coughlin minimum', 14))
plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4,
label=textwrap.fill('Average maximum', 14))
plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4,
label=textwrap.fill('Average minimum', 14))
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14))
plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14))
plt.plot(max_2_x_time, max_2_x, 'k-')
plt.plot(max_2_x_time_side, max_2_x, 'k-')
plt.plot(min_2_x_time, min_2_x, 'k-')
plt.plot(min_2_x_time_side, min_2_x, 'k-')
plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--')
plt.text(5.16 * np.pi, 0.85, r'$2a_2$')
plt.plot(max_2_y_time, max_2_y, 'k-')
plt.plot(max_2_y_time, max_2_y_side, 'k-')
plt.plot(min_2_y_time, min_2_y, 'k-')
plt.plot(min_2_y_time, min_2_y_side, 'k-')
plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--')
plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$')
plt.plot(max_1_x_time, max_1_x, 'k-')
plt.plot(max_1_x_time_side, max_1_x, 'k-')
plt.plot(min_1_x_time, min_1_x, 'k-')
plt.plot(min_1_x_time_side, min_1_x, 'k-')
plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--')
plt.text(5.42 * np.pi, -0.1, r'$2a_1$')
plt.plot(max_1_y_time, max_1_y, 'k-')
plt.plot(max_1_y_time, max_1_y_side, 'k-')
plt.plot(min_1_y_time, min_1_y, 'k-')
plt.plot(min_1_y_time, min_1_y_side, 'k-')
plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--')
plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$')
plt.xlim(3.9 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_characteristic_wave.png')
plt.show()
# plot 6
t = np.linspace(5, 95, 100)
signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200)
util_nn = emd_utils.Utility(time=t, time_series=signal_orig)
maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()]
minima = signal_orig[util_nn.min_bool_func_1st_order_fd()]
cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima)
cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima)
time = np.linspace(0, 5 * np.pi, 1001)
lsq_signal = np.cos(time) + np.cos(5 * time)
knots = np.linspace(0, 5 * np.pi, 101)
time_extended = time_extension(time)
time_series_extended = np.zeros_like(time_extended) / 0
time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal
neural_network_m = 200
neural_network_k = 100
# forward ->
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))]
P[-1, col] = 1 # for additive constant
t = lsq_signal[-neural_network_m:]
# test - top
seed_weights = np.ones(neural_network_k) / neural_network_k
weights = 0 * seed_weights.copy()
train_input = P[:-1, :]
lr = 0.01
for iterations in range(1000):
output = np.matmul(weights, train_input)
error = (t - output)
gradients = error * (- train_input)
# guess average gradients
average_gradients = np.mean(gradients, axis=1)
# steepest descent
max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients)))
adjustment = - lr * average_gradients
# adjustment = - lr * max_gradient_vector
weights += adjustment
# test - bottom
weights_right = np.hstack((weights, 0))
max_count_right = 0
min_count_right = 0
i_right = 0
while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1):
time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \
sum(weights_right * np.hstack((time_series_extended[
int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right):
int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1)))
i_right += 1
if i_right > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_right += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_right += 1
# backward <-
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)]
P[-1, col] = 1 # for additive constant
t = lsq_signal[:neural_network_m]
vx = cvx.Variable(int(neural_network_k + 1))
objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary
prob = cvx.Problem(objective)
result = prob.solve(verbose=True, solver=cvx.ECOS)
weights_left = np.array(vx.value)
max_count_left = 0
min_count_left = 0
i_left = 0
while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1):
time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \
2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left):
int(len(lsq_signal) - 1 - i_left + neural_network_k)],
1))) + 1
i_left += 1
if i_left > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_left += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_left += 1
lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal)
utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended)
maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()]
maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()]
maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()]
minima_time = time[lsq_utils.min_bool_func_1st_order_fd()]
minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Single Neuron Neural Network Example')
plt.plot(time, lsq_signal, zorder=2, label='Signal')
plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12))
plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima')
plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima')
plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3,
label=textwrap.fill('Extrapolated maxima', 12))
plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4,
label=textwrap.fill('Extrapolated minima', 12))
plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k',
label=textwrap.fill('Neural network inputs', 13))
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k')
plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k')
plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed',
label=textwrap.fill('Neural network targets', 13))
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray')
plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray',
linestyle='dashed')
plt.xlim(3.4 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/neural_network.png')
plt.show()
# plot 6a
np.random.seed(0)
time = np.linspace(0, 5 * np.pi, 1001)
knots_51 = np.linspace(0, 5 * np.pi, 51)
time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time)
noise = np.random.normal(0, 1, len(time_series))
time_series += noise
advemdpy = EMD(time=time, time_series=time_series)
imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_31 = np.linspace(0, 5 * np.pi, 31)
imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_11 = np.linspace(0, 5 * np.pi, 11)
imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1,
edge_effect='symmetric_anchor', verbose=False)[:3]
fig, axs = plt.subplots(3, 1)
plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40))
plt.subplots_adjust(hspace=0.1)
axs[0].plot(time, time_series, label='Time series')
axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21))
print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}')
for knot in knots_51:
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[0].set_xticklabels(['', '', '', '', '', ''])
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[1].plot(time, time_series, label='Time series')
axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19))
axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19))
print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}')
for knot in knots_31:
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[1].set_xticklabels(['', '', '', '', '', ''])
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[1].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[1].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
axs[2].plot(time, time_series, label='Time series')
axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots')
axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots')
axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots')
print(f'DFA fluctuation with 11 knots: {np.round(np.var(time_series - imfs_51[3, :]), 3)}')
for knot in knots_11:
axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[2].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[2].set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$', r'$5\pi$'])
box_2 = axs[2].get_position()
axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height])
axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[2].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[2].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
plt.savefig('jss_figures/DFA_different_trends.png')
plt.show()
# plot 6b
fig, axs = plt.subplots(3, 1)
plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences Zoomed Region', 40))
plt.subplots_adjust(hspace=0.1)
axs[0].plot(time, time_series, label='Time series')
axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21))
for knot in knots_51:
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[0].set_xticklabels(['', '', '', '', '', ''])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[0].set_ylim(-5.5, 5.5)
axs[0].set_xlim(0.95 * np.pi, 1.55 * np.pi)
axs[1].plot(time, time_series, label='Time series')
axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19))
axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19))
for knot in knots_31:
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[1].set_xticklabels(['', '', '', '', '', ''])
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[1].set_ylim(-5.5, 5.5)
axs[1].set_xlim(0.95 * np.pi, 1.55 * np.pi)
axs[2].plot(time, time_series, label='Time series')
axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots')
axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots')
axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots')
for knot in knots_11:
axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[2].plot(knot * np.ones(101), | np.linspace(-5, 5, 101) | numpy.linspace |
import numpy as np
from stumpff import C, S
from CelestialBody import BODIES
from numerical import newton, laguerre
from lagrange import calc_f, calc_fd, calc_g, calc_gd
def kepler_chi(chi, alpha, r0, vr0, mu, dt):
''' Kepler's Equation of the universal anomaly, modified
for use in numerical solvers. '''
z = alpha*chi**2
return (r0*vr0/np.sqrt(mu))*chi**2*C(z) + \
(1 - alpha*r0)*chi**3*S(z) + \
r0*chi - np.sqrt(mu)*dt
def dkepler_dchi(chi, alpha, r0, vr0, mu, dt):
''' Derivative of Kepler's Equation of the universal anomaly,
modified for use in numerical solvers. '''
z = alpha*chi**2
return (r0*vr0/np.sqrt(mu))*chi*(1 - alpha*chi**2*S(z)) + \
(1 - alpha*r0)*chi**2*C(z) + r0
def d2kepler_dchi2(chi, alpha, r0, vr0, mu, dt):
''' Second derivative of Kepler's Equation of the universal
anomaly, modified for use in numerical solvers. '''
z = alpha*chi**2
S_ = S(z)
return (r0*vr0/np.sqrt(mu))*(1 - 3*z*S_ + z*(C(z) - 3*S_)) + \
chi*(1 - z*S_)*(1 - alpha*r0)
def solve_kepler_chi(r_0, v_0, dt, body=BODIES['Earth'], method='laguerre', tol=1e-7, max_iters=100):
''' Solve Kepler's Equation of the universal anomaly chi using the specified
numerical method. Applies Algorithm 3.4 from Orbital Mechanics for Engineering
Students, 4 ed, Curtis.
:param r_0: `iterable` (km) initial position 3-vector
:param v_0: `iterable` (km/s) initial velocity 3-vector
:param dt: `float` (s) time after initial state to solve for r, v as 3-vectors
:param body: `CelestialBody` (--) the celestial body to use for orbital parameters
:param method: `str` (--) which numerical method to use to solve Kepler's Equation
:param tol: `float` (--) decimal tolerance for numerical method (default 1e-7 is IEEE 745 single precision)
:param max_iters: `int` (--) maximum number of iterations in numerical method before breaking
:return: (km) final position 3-vector, (km/s) final velocity 3-vector
'''
VALID_METHODS = ('laguerre', 'newton')
mu = body.mu # (km**3/s**2) gravitational parameter of the specified primary body
r0 = np.linalg.norm(r_0) # (km) initial position magnitude
v0 = np.linalg.norm(v_0) # (km/s) initial velocity magnitude
vr0 = np.dot(v_0, r_0)/r0 # (km/s) initial radial velocity magnitude
alpha = 2/r0 - v0**2/mu # (1/km) inverse of semi-major axis
chi0 = np.sqrt(mu)*np.abs(alpha)*dt
if method not in VALID_METHODS:
print(f'Method \'{method}\' is not valid, must be one of {VALID_METHODS}.\nDefaulting to laguerre method.')
chi, _, _ = laguerre(chi0, kepler_chi, dkepler_dchi, d2kepler_dchi2, alpha, r0, vr0, mu, dt)
elif method == 'newton':
chi, _, _ = newton(chi0, kepler_chi, dkepler_dchi, alpha, r0, vr0, mu, dt)
else: # method == 'laguerre'
chi, _, _ = laguerre(chi0, kepler_chi, dkepler_dchi, d2kepler_dchi2, alpha, r0, vr0, mu, dt)
f = calc_f(chi, r0, alpha)
g = calc_g(dt, mu, chi, alpha)
r_1 = f*r_0 + g*v_0
r1 = np.linalg.norm(r_1)
fd = calc_fd(mu, r1, r0, alpha, chi)
gd = calc_gd(chi, r1, alpha)
v_1 = fd*r_0 + gd*v_0
return r_1, v_1
def solve_kepler_E(e, Me, tol=1e-7, max_iters=100):
''' Solve Kepler's Equation in the form containing Eccentric Anomaly (E),
eccentricity (e), and Mean Anomaly of Ellipse (Me). Uses Algorithm 3.1 from Orbital
Mechanics for Engineering Students, 4 ed, Curtis. '''
# TODO: have this function make use of one of the numerical methods in numerical.py
def f(E, e, Me):
return E - e*np.sin(E) - Me
def fp(E, e):
return 1 - e*np.cos(E)
E = Me + e/2 if Me < np.pi else Me - e/2
ratio = f(E, e, Me)/fp(E, e)
iters = 0
while abs(ratio) > tol and iters < max_iters:
E -= ratio
ratio = f(E, e, Me)/fp(E, e)
iters += 1
E -= ratio
converged = np.abs(ratio) <= tol
return E, iters, converged
def test():
''' Test the functionality of solve_kepler_chi
and solve_kepler_laguerre using Problem 3.20 from
Orbital Mechanics for Engineering Students, 4 ed, Curtis.
'''
# given starting information
Earth = BODIES['Earth'] # `CelestialBody` (--) Earth and all the Earth things
r_0 = np.array([20000, -105000, -19000]) # (km) initial position vector
v_0 = np.array([0.9, -3.4, -1.5]) # (km/s) initial velocity vector
dt = 2*60*60 # (s) time of interest after initial time
# given correct answer from textbook
correct_r_1 = | np.array([26338, -128750, -29656]) | numpy.array |
# pvtrace is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# pvtrace is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import numpy as np
from external.transformations import translation_matrix, rotation_matrix
import external.transformations as tf
from Trace import Photon
from Geometry import Box, Cylinder, FinitePlane, transform_point, transform_direction, rotation_matrix_from_vector_alignment, norm
from Materials import Spectrum
def random_spherecial_vector():
# This method of calculating isotropic vectors is taken from GNU Scientific Library
LOOP = True
while LOOP:
x = -1. + 2. * np.random.uniform()
y = -1. + 2. * np.random.uniform()
s = x**2 + y**2
if s <= 1.0:
LOOP = False
z = -1. + 2. * s
a = 2 * np.sqrt(1 - s)
x = a * x
y = a * y
return np.array([x,y,z])
class SimpleSource(object):
"""A light source that will generate photons of a single colour, direction and position."""
def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, use_random_polarisation=False):
super(SimpleSource, self).__init__()
self.position = position
self.direction = direction
self.wavelength = wavelength
self.use_random_polarisation = use_random_polarisation
self.throw = 0
self.source_id = "SimpleSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.position = np.array(self.position)
photon.direction = np.array(self.direction)
photon.active = True
photon.wavelength = self.wavelength
# If use_polarisation is set generate a random polarisation vector of the photon
if self.use_random_polarisation:
# Randomise rotation angle around xy-plane, the transform from +z to the direction of the photon
vec = random_spherecial_vector()
vec[2] = 0.
vec = norm(vec)
R = rotation_matrix_from_vector_alignment(self.direction, [0,0,1])
photon.polarisation = transform_direction(vec, R)
else:
photon.polarisation = None
photon.id = self.throw
self.throw = self.throw + 1
return photon
class Laser(object):
"""A light source that will generate photons of a single colour, direction and position."""
def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, polarisation=None):
super(Laser, self).__init__()
self.position = np.array(position)
self.direction = np.array(direction)
self.wavelength = wavelength
assert polarisation != None, "Polarisation of the Laser is not set."
self.polarisation = np.array(polarisation)
self.throw = 0
self.source_id = "LaserSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.position = np.array(self.position)
photon.direction = np.array(self.direction)
photon.active = True
photon.wavelength = self.wavelength
photon.polarisation = self.polarisation
photon.id = self.throw
self.throw = self.throw + 1
return photon
class PlanarSource(object):
"""A box that emits photons from the top surface (normal), sampled from the spectrum."""
def __init__(self, spectrum=None, wavelength=555, direction=(0,0,1), length=0.05, width=0.05):
super(PlanarSource, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.plane = FinitePlane(length=length, width=width)
self.length = length
self.width = width
# direction is the direction that photons are fired out of the plane in the GLOBAL FRAME.
# i.e. this is passed directly to the photon to set is's direction
self.direction = direction
self.throw = 0
self.source_id = "PlanarSource_" + str(id(self))
def translate(self, translation):
self.plane.append_transform(tf.translation_matrix(translation))
def rotate(self, angle, axis):
self.plane.append_transform(tf.rotation_matrix(angle, axis))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.id = self.throw
self.throw = self.throw + 1
# Create a point which is on the surface of the finite plane in it's local frame
x = np.random.uniform(0., self.length)
y = np.random.uniform(0., self.width)
local_point = (x, y, 0.)
# Transform the direciton
photon.position = transform_point(local_point, self.plane.transform)
photon.direction = self.direction
photon.active = True
if self.spectrum != None:
photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform())
else:
photon.wavelength = self.wavelength
return photon
class LensSource(object):
"""
A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize".
The focus line should be perpendicular to the plane normal and aligned with the z-axis.
"""
def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)):
super(LensSource, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.planeorigin = planeorigin
self.planeextent = planeextent
self.linepoint = np.array(linepoint)
self.linedirection = np.array(linedirection)
self.focussize = focussize
self.throw = 0
self.source_id = "LensSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.id = self.throw
self.throw = self.throw + 1
# Position
x = np.random.uniform(self.planeorigin[0],self.planeextent[0])
y = np.random.uniform(self.planeorigin[1],self.planeextent[1])
z = np.random.uniform(self.planeorigin[2],self.planeextent[2])
photon.position = np.array((x,y,z))
# Direction
focuspoint = np.array((0.,0.,0.))
focuspoint[0] = self.linepoint[0] + np.random.uniform(-self.focussize,self.focussize)
focuspoint[1] = self.linepoint[1] + np.random.uniform(-self.focussize,self.focussize)
focuspoint[2] = photon.position[2]
direction = focuspoint - photon.position
modulus = (direction[0]**2+direction[1]**2+direction[2]**2)**0.5
photon.direction = direction/modulus
# Wavelength
if self.spectrum != None:
photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform())
else:
photon.wavelength = self.wavelength
return photon
class LensSourceAngle(object):
"""
A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize".
The focus line should be perpendicular to the plane normal and aligned with the z-axis.
For this lense an additional z-boost is added (Angle of incidence in z-direction).
"""
def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), angle = 0, focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)):
super(LensSourceAngle, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.planeorigin = planeorigin
self.planeextent = planeextent
self.linepoint = np.array(linepoint)
self.linedirection = np.array(linedirection)
self.focussize = focussize
self.angle = angle
self.throw = 0
self.source_id = "LensSourceAngle_" + str(id(self))
def photon(self):
photon = Photon()
photon.id = self.throw
self.throw = self.throw + 1
# Position
x = np.random.uniform(self.planeorigin[0],self.planeextent[0])
y = np.random.uniform(self.planeorigin[1],self.planeextent[1])
boost = y*np.tan(self.angle)
z = np.random.uniform(self.planeorigin[2],self.planeextent[2]) - boost
photon.position = np.array((x,y,z))
# Direction
focuspoint = np.array((0.,0.,0.))
focuspoint[0] = self.linepoint[0] + np.random.uniform(-self.focussize,self.focussize)
focuspoint[1] = self.linepoint[1] + np.random.uniform(-self.focussize,self.focussize)
focuspoint[2] = photon.position[2] + boost
direction = focuspoint - photon.position
modulus = (direction[0]**2+direction[1]**2+direction[2]**2)**0.5
photon.direction = direction/modulus
# Wavelength
if self.spectrum != None:
photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform())
else:
photon.wavelength = self.wavelength
return photon
class CylindricalSource(object):
"""
A source for photons emitted in a random direction and position inside a cylinder(radius, length)
"""
def __init__(self, spectrum = None, wavelength = 555, radius = 1, length = 10):
super(CylindricalSource, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.shape = Cylinder(radius = radius, length = length)
self.radius = radius
self.length = length
self.throw = 0
self.source_id = "CylindricalSource_" + str(id(self))
def translate(self, translation):
self.shape.append_transform(tf.translation_matrix(translation))
def rotate(self, angle, axis):
self.shape.append_transform(tf.rotation_matrix(angle, axis))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.id = self.throw
self.throw = self.throw + 1
# Position of emission
phi = np.random.uniform(0., 2*np.pi)
r = np.random.uniform(0.,self.radius)
x = r*np.cos(phi)
y = r*np.sin(phi)
z = np.random.uniform(0.,self.length)
local_center = (x,y,z)
photon.position = transform_point(local_center, self.shape.transform)
# Direction of emission (no need to transform if meant to be isotropic)
phi = np.random.uniform(0.,2*np.pi)
theta = np.random.uniform(0.,np.pi)
x = | np.cos(phi) | numpy.cos |
from abc import ABCMeta, abstractmethod
import os
from vmaf.tools.misc import make_absolute_path, run_process
from vmaf.tools.stats import ListStats
__copyright__ = "Copyright 2016-2018, Netflix, Inc."
__license__ = "Apache, Version 2.0"
import re
import numpy as np
import ast
from vmaf import ExternalProgramCaller, to_list
from vmaf.config import VmafConfig, VmafExternalConfig
from vmaf.core.executor import Executor
from vmaf.core.result import Result
from vmaf.tools.reader import YuvReader
class FeatureExtractor(Executor):
"""
FeatureExtractor takes in a list of assets, and run feature extraction on
them, and return a list of corresponding results. A FeatureExtractor must
specify a unique type and version combination (by the TYPE and VERSION
attribute), so that the Result generated by it can be identified.
A derived class of FeatureExtractor must:
1) Override TYPE and VERSION
2) Override _generate_result(self, asset), which call a
command-line executable and generate feature scores in a log file.
3) Override _get_feature_scores(self, asset), which read the feature
scores from the log file, and return the scores in a dictionary format.
For an example, follow VmafFeatureExtractor.
"""
__metaclass__ = ABCMeta
@property
@abstractmethod
def ATOM_FEATURES(self):
raise NotImplementedError
def _read_result(self, asset):
result = {}
result.update(self._get_feature_scores(asset))
executor_id = self.executor_id
return Result(asset, executor_id, result)
@classmethod
def get_scores_key(cls, atom_feature):
return "{type}_{atom_feature}_scores".format(
type=cls.TYPE, atom_feature=atom_feature)
@classmethod
def get_score_key(cls, atom_feature):
return "{type}_{atom_feature}_score".format(
type=cls.TYPE, atom_feature=atom_feature)
def _get_feature_scores(self, asset):
# routine to read the feature scores from the log file, and return
# the scores in a dictionary format.
log_file_path = self._get_log_file_path(asset)
atom_feature_scores_dict = {}
atom_feature_idx_dict = {}
for atom_feature in self.ATOM_FEATURES:
atom_feature_scores_dict[atom_feature] = []
atom_feature_idx_dict[atom_feature] = 0
with open(log_file_path, 'rt') as log_file:
for line in log_file.readlines():
for atom_feature in self.ATOM_FEATURES:
re_template = "{af}: ([0-9]+) ([a-zA-Z0-9.-]+)".format(af=atom_feature)
mo = re.match(re_template, line)
if mo:
cur_idx = int(mo.group(1))
assert cur_idx == atom_feature_idx_dict[atom_feature]
# parse value, allowing NaN and inf
val = float(mo.group(2))
if np.isnan(val) or np.isinf(val):
val = None
atom_feature_scores_dict[atom_feature].append(val)
atom_feature_idx_dict[atom_feature] += 1
continue
len_score = len(atom_feature_scores_dict[self.ATOM_FEATURES[0]])
assert len_score != 0
for atom_feature in self.ATOM_FEATURES[1:]:
assert len_score == len(atom_feature_scores_dict[atom_feature]), \
"Feature data possibly corrupt. Run cleanup script and try again."
feature_result = {}
for atom_feature in self.ATOM_FEATURES:
scores_key = self.get_scores_key(atom_feature)
feature_result[scores_key] = atom_feature_scores_dict[atom_feature]
return feature_result
class VmafFeatureExtractor(FeatureExtractor):
TYPE = "VMAF_feature"
# VERSION = '0.1' # vmaf_study; Anush's VIF fix
# VERSION = '0.2' # expose vif_num, vif_den, adm_num, adm_den, anpsnr
# VERSION = '0.2.1' # expose vif num/den of each scale
# VERSION = '0.2.2' # adm abs-->fabs, corrected border handling, uniform reading with option of offset for input YUV, updated VIF corner case
# VERSION = '0.2.2b' # expose adm_den/num_scalex
# VERSION = '0.2.3' # AVX for VMAF convolution; update adm features by folding noise floor into per coef
# VERSION = '0.2.4' # Fix a bug in adm feature passing scale into dwt_quant_step
# VERSION = '0.2.4b' # Modify by adding ADM noise floor outside cube root; add derived feature motion2
VERSION = '0.2.4c' # Modify by moving motion2 to c code
ATOM_FEATURES = ['vif', 'adm', 'ansnr', 'motion', 'motion2',
'vif_num', 'vif_den', 'adm_num', 'adm_den', 'anpsnr',
'vif_num_scale0', 'vif_den_scale0',
'vif_num_scale1', 'vif_den_scale1',
'vif_num_scale2', 'vif_den_scale2',
'vif_num_scale3', 'vif_den_scale3',
'adm_num_scale0', 'adm_den_scale0',
'adm_num_scale1', 'adm_den_scale1',
'adm_num_scale2', 'adm_den_scale2',
'adm_num_scale3', 'adm_den_scale3',
]
DERIVED_ATOM_FEATURES = ['vif_scale0', 'vif_scale1', 'vif_scale2', 'vif_scale3',
'vif2', 'adm2', 'adm3',
'adm_scale0', 'adm_scale1', 'adm_scale2', 'adm_scale3',
]
ADM2_CONSTANT = 0
ADM_SCALE_CONSTANT = 0
def _generate_result(self, asset):
# routine to call the command-line executable and generate feature
# scores in the log file.
quality_width, quality_height = asset.quality_width_height
log_file_path = self._get_log_file_path(asset)
yuv_type=self._get_workfile_yuv_type(asset)
ref_path=asset.ref_workfile_path
dis_path=asset.dis_workfile_path
w=quality_width
h=quality_height
logger = self.logger
ExternalProgramCaller.call_vmaf_feature(yuv_type, ref_path, dis_path, w, h, log_file_path, logger)
@classmethod
def _post_process_result(cls, result):
# override Executor._post_process_result
result = super(VmafFeatureExtractor, cls)._post_process_result(result)
# adm2 =
# (adm_num + ADM2_CONSTANT) / (adm_den + ADM2_CONSTANT)
adm2_scores_key = cls.get_scores_key('adm2')
adm_num_scores_key = cls.get_scores_key('adm_num')
adm_den_scores_key = cls.get_scores_key('adm_den')
result.result_dict[adm2_scores_key] = list(
(np.array(result.result_dict[adm_num_scores_key]) + cls.ADM2_CONSTANT) /
(np.array(result.result_dict[adm_den_scores_key]) + cls.ADM2_CONSTANT)
)
# vif_scalei = vif_num_scalei / vif_den_scalei, i = 0, 1, 2, 3
vif_num_scale0_scores_key = cls.get_scores_key('vif_num_scale0')
vif_den_scale0_scores_key = cls.get_scores_key('vif_den_scale0')
vif_num_scale1_scores_key = cls.get_scores_key('vif_num_scale1')
vif_den_scale1_scores_key = cls.get_scores_key('vif_den_scale1')
vif_num_scale2_scores_key = cls.get_scores_key('vif_num_scale2')
vif_den_scale2_scores_key = cls.get_scores_key('vif_den_scale2')
vif_num_scale3_scores_key = cls.get_scores_key('vif_num_scale3')
vif_den_scale3_scores_key = cls.get_scores_key('vif_den_scale3')
vif_scale0_scores_key = cls.get_scores_key('vif_scale0')
vif_scale1_scores_key = cls.get_scores_key('vif_scale1')
vif_scale2_scores_key = cls.get_scores_key('vif_scale2')
vif_scale3_scores_key = cls.get_scores_key('vif_scale3')
result.result_dict[vif_scale0_scores_key] = list(
(np.array(result.result_dict[vif_num_scale0_scores_key])
/ np.array(result.result_dict[vif_den_scale0_scores_key]))
)
result.result_dict[vif_scale1_scores_key] = list(
(np.array(result.result_dict[vif_num_scale1_scores_key])
/ np.array(result.result_dict[vif_den_scale1_scores_key]))
)
result.result_dict[vif_scale2_scores_key] = list(
(np.array(result.result_dict[vif_num_scale2_scores_key])
/ np.array(result.result_dict[vif_den_scale2_scores_key]))
)
result.result_dict[vif_scale3_scores_key] = list(
(np.array(result.result_dict[vif_num_scale3_scores_key])
/ np.array(result.result_dict[vif_den_scale3_scores_key]))
)
# vif2 =
# ((vif_num_scale0 / vif_den_scale0) + (vif_num_scale1 / vif_den_scale1) +
# (vif_num_scale2 / vif_den_scale2) + (vif_num_scale3 / vif_den_scale3)) / 4.0
vif_scores_key = cls.get_scores_key('vif2')
result.result_dict[vif_scores_key] = list(
(
(np.array(result.result_dict[vif_num_scale0_scores_key])
/ np.array(result.result_dict[vif_den_scale0_scores_key])) +
(np.array(result.result_dict[vif_num_scale1_scores_key])
/ np.array(result.result_dict[vif_den_scale1_scores_key])) +
(np.array(result.result_dict[vif_num_scale2_scores_key])
/ np.array(result.result_dict[vif_den_scale2_scores_key])) +
(np.array(result.result_dict[vif_num_scale3_scores_key])
/ np.array(result.result_dict[vif_den_scale3_scores_key]))
) / 4.0
)
# adm_scalei = adm_num_scalei / adm_den_scalei, i = 0, 1, 2, 3
adm_num_scale0_scores_key = cls.get_scores_key('adm_num_scale0')
adm_den_scale0_scores_key = cls.get_scores_key('adm_den_scale0')
adm_num_scale1_scores_key = cls.get_scores_key('adm_num_scale1')
adm_den_scale1_scores_key = cls.get_scores_key('adm_den_scale1')
adm_num_scale2_scores_key = cls.get_scores_key('adm_num_scale2')
adm_den_scale2_scores_key = cls.get_scores_key('adm_den_scale2')
adm_num_scale3_scores_key = cls.get_scores_key('adm_num_scale3')
adm_den_scale3_scores_key = cls.get_scores_key('adm_den_scale3')
adm_scale0_scores_key = cls.get_scores_key('adm_scale0')
adm_scale1_scores_key = cls.get_scores_key('adm_scale1')
adm_scale2_scores_key = cls.get_scores_key('adm_scale2')
adm_scale3_scores_key = cls.get_scores_key('adm_scale3')
result.result_dict[adm_scale0_scores_key] = list(
(np.array(result.result_dict[adm_num_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT)
)
result.result_dict[adm_scale1_scores_key] = list(
(np.array(result.result_dict[adm_num_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT)
)
result.result_dict[adm_scale2_scores_key] = list(
(np.array(result.result_dict[adm_num_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT)
)
result.result_dict[adm_scale3_scores_key] = list(
(np.array(result.result_dict[adm_num_scale3_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale3_scores_key]) + cls.ADM_SCALE_CONSTANT)
)
# adm3 = \
# (((adm_num_scale0 + ADM_SCALE_CONSTANT) / (adm_den_scale0 + ADM_SCALE_CONSTANT))
# + ((adm_num_scale1 + ADM_SCALE_CONSTANT) / (adm_den_scale1 + ADM_SCALE_CONSTANT))
# + ((adm_num_scale2 + ADM_SCALE_CONSTANT) / (adm_den_scale2 + ADM_SCALE_CONSTANT))
# + ((adm_num_scale3 + ADM_SCALE_CONSTANT) / (adm_den_scale3 + ADM_SCALE_CONSTANT))) / 4.0
adm3_scores_key = cls.get_scores_key('adm3')
result.result_dict[adm3_scores_key] = list(
(
((np.array(result.result_dict[adm_num_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ ( | np.array(result.result_dict[adm_den_scale0_scores_key]) | numpy.array |
# coding: utf-8
# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Test the Logarithmic Units and Quantities
"""
from __future__ import (absolute_import, unicode_literals, division,
print_function)
from ...extern import six
from ...extern.six.moves import zip
import pickle
import itertools
import pytest
import numpy as np
from numpy.testing.utils import assert_allclose
from ...tests.helper import assert_quantity_allclose
from ... import units as u, constants as c
lu_units = [u.dex, u.mag, u.decibel]
lu_subclasses = [u.DexUnit, u.MagUnit, u.DecibelUnit]
lq_subclasses = [u.Dex, u.Magnitude, u.Decibel]
pu_sample = (u.dimensionless_unscaled, u.m, u.g/u.s**2, u.Jy)
class TestLogUnitCreation(object):
def test_logarithmic_units(self):
"""Check logarithmic units are set up correctly."""
assert u.dB.to(u.dex) == 0.1
assert u.dex.to(u.mag) == -2.5
assert u.mag.to(u.dB) == -4
@pytest.mark.parametrize('lu_unit, lu_cls', zip(lu_units, lu_subclasses))
def test_callable_units(self, lu_unit, lu_cls):
assert isinstance(lu_unit, u.UnitBase)
assert callable(lu_unit)
assert lu_unit._function_unit_class is lu_cls
@pytest.mark.parametrize('lu_unit', lu_units)
def test_equality_to_normal_unit_for_dimensionless(self, lu_unit):
lu = lu_unit()
assert lu == lu._default_function_unit # eg, MagUnit() == u.mag
assert lu._default_function_unit == lu # and u.mag == MagUnit()
@pytest.mark.parametrize('lu_unit, physical_unit',
itertools.product(lu_units, pu_sample))
def test_call_units(self, lu_unit, physical_unit):
"""Create a LogUnit subclass using the callable unit and physical unit,
and do basic check that output is right."""
lu1 = lu_unit(physical_unit)
assert lu1.physical_unit == physical_unit
assert lu1.function_unit == lu1._default_function_unit
def test_call_invalid_unit(self):
with pytest.raises(TypeError):
u.mag([])
with pytest.raises(ValueError):
u.mag(u.mag())
@pytest.mark.parametrize('lu_cls, physical_unit', itertools.product(
lu_subclasses + [u.LogUnit], pu_sample))
def test_subclass_creation(self, lu_cls, physical_unit):
"""Create a LogUnit subclass object for given physical unit,
and do basic check that output is right."""
lu1 = lu_cls(physical_unit)
assert lu1.physical_unit == physical_unit
assert lu1.function_unit == lu1._default_function_unit
lu2 = lu_cls(physical_unit,
function_unit=2*lu1._default_function_unit)
assert lu2.physical_unit == physical_unit
assert lu2.function_unit == u.Unit(2*lu2._default_function_unit)
with pytest.raises(ValueError):
lu_cls(physical_unit, u.m)
def test_predefined_magnitudes():
assert_quantity_allclose((-21.1*u.STmag).physical,
1.*u.erg/u.cm**2/u.s/u.AA)
assert_quantity_allclose((-48.6*u.ABmag).physical,
1.*u.erg/u.cm**2/u.s/u.Hz)
assert_quantity_allclose((0*u.M_bol).physical, c.L_bol0)
assert_quantity_allclose((0*u.m_bol).physical,
c.L_bol0/(4.*np.pi*(10.*c.pc)**2))
def test_predefined_reinitialisation():
assert u.mag('ST') == u.STmag
assert u.mag('AB') == u.ABmag
assert u.mag('Bol') == u.M_bol
assert u.mag('bol') == u.m_bol
def test_predefined_string_roundtrip():
"""Ensure roundtripping; see #5015"""
with u.magnitude_zero_points.enable():
assert u.Unit(u.STmag.to_string()) == u.STmag
assert u.Unit(u.ABmag.to_string()) == u.ABmag
assert u.Unit(u.M_bol.to_string()) == u.M_bol
assert u.Unit(u.m_bol.to_string()) == u.m_bol
def test_inequality():
"""Check __ne__ works (regresssion for #5342)."""
lu1 = u.mag(u.Jy)
lu2 = u.dex(u.Jy)
lu3 = u.mag(u.Jy**2)
lu4 = lu3 - lu1
assert lu1 != lu2
assert lu1 != lu3
assert lu1 == lu4
class TestLogUnitStrings(object):
def test_str(self):
"""Do some spot checks that str, repr, etc. work as expected."""
lu1 = u.mag(u.Jy)
assert str(lu1) == 'mag(Jy)'
assert repr(lu1) == 'Unit("mag(Jy)")'
assert lu1.to_string('generic') == 'mag(Jy)'
with pytest.raises(ValueError):
lu1.to_string('fits')
lu2 = u.dex()
assert str(lu2) == 'dex'
assert repr(lu2) == 'Unit("dex(1)")'
assert lu2.to_string() == 'dex(1)'
lu3 = u.MagUnit(u.Jy, function_unit=2*u.mag)
assert str(lu3) == '2 mag(Jy)'
assert repr(lu3) == 'MagUnit("Jy", unit="2 mag")'
assert lu3.to_string() == '2 mag(Jy)'
lu4 = u.mag(u.ct)
assert lu4.to_string('generic') == 'mag(ct)'
assert lu4.to_string('latex') == ('$\\mathrm{mag}$$\\mathrm{\\left( '
'\\mathrm{ct} \\right)}$')
assert lu4._repr_latex_() == lu4.to_string('latex')
class TestLogUnitConversion(object):
@pytest.mark.parametrize('lu_unit, physical_unit',
itertools.product(lu_units, pu_sample))
def test_physical_unit_conversion(self, lu_unit, physical_unit):
"""Check various LogUnit subclasses are equivalent and convertible
to their non-log counterparts."""
lu1 = lu_unit(physical_unit)
assert lu1.is_equivalent(physical_unit)
assert lu1.to(physical_unit, 0.) == 1.
assert physical_unit.is_equivalent(lu1)
assert physical_unit.to(lu1, 1.) == 0.
pu = u.Unit(8.*physical_unit)
assert lu1.is_equivalent(physical_unit)
assert lu1.to(pu, 0.) == 0.125
assert pu.is_equivalent(lu1)
assert_allclose(pu.to(lu1, 0.125), 0., atol=1.e-15)
# Check we round-trip.
value = np.linspace(0., 10., 6)
assert_allclose(pu.to(lu1, lu1.to(pu, value)), value, atol=1.e-15)
# And that we're not just returning True all the time.
pu2 = u.g
assert not lu1.is_equivalent(pu2)
with pytest.raises(u.UnitsError):
lu1.to(pu2)
assert not pu2.is_equivalent(lu1)
with pytest.raises(u.UnitsError):
pu2.to(lu1)
@pytest.mark.parametrize('lu_unit', lu_units)
def test_container_unit_conversion(self, lu_unit):
"""Check that conversion to logarithmic units (u.mag, u.dB, u.dex)
is only possible when the physical unit is dimensionless."""
values = np.linspace(0., 10., 6)
lu1 = lu_unit(u.dimensionless_unscaled)
assert lu1.is_equivalent(lu1.function_unit)
assert_allclose(lu1.to(lu1.function_unit, values), values)
lu2 = lu_unit(u.Jy)
assert not lu2.is_equivalent(lu2.function_unit)
with pytest.raises(u.UnitsError):
lu2.to(lu2.function_unit, values)
@pytest.mark.parametrize(
'flu_unit, tlu_unit, physical_unit',
itertools.product(lu_units, lu_units, pu_sample))
def test_subclass_conversion(self, flu_unit, tlu_unit, physical_unit):
"""Check various LogUnit subclasses are equivalent and convertible
to each other if they correspond to equivalent physical units."""
values = np.linspace(0., 10., 6)
flu = flu_unit(physical_unit)
tlu = tlu_unit(physical_unit)
assert flu.is_equivalent(tlu)
assert_allclose(flu.to(tlu), flu.function_unit.to(tlu.function_unit))
assert_allclose(flu.to(tlu, values),
values * flu.function_unit.to(tlu.function_unit))
tlu2 = tlu_unit(u.Unit(100.*physical_unit))
assert flu.is_equivalent(tlu2)
# Check that we round-trip.
assert_allclose(flu.to(tlu2, tlu2.to(flu, values)), values, atol=1.e-15)
tlu3 = tlu_unit(physical_unit.to_system(u.si)[0])
assert flu.is_equivalent(tlu3)
assert_allclose(flu.to(tlu3, tlu3.to(flu, values)), values, atol=1.e-15)
tlu4 = tlu_unit(u.g)
assert not flu.is_equivalent(tlu4)
with pytest.raises(u.UnitsError):
flu.to(tlu4, values)
def test_unit_decomposition(self):
lu = u.mag(u.Jy)
assert lu.decompose() == u.mag(u.Jy.decompose())
assert lu.decompose().physical_unit.bases == [u.kg, u.s]
assert lu.si == u.mag(u.Jy.si)
assert lu.si.physical_unit.bases == [u.kg, u.s]
assert lu.cgs == u.mag(u.Jy.cgs)
assert lu.cgs.physical_unit.bases == [u.g, u.s]
def test_unit_multiple_possible_equivalencies(self):
lu = u.mag(u.Jy)
assert lu.is_equivalent(pu_sample)
class TestLogUnitArithmetic(object):
def test_multiplication_division(self):
"""Check that multiplication/division with other units is only
possible when the physical unit is dimensionless, and that this
turns the unit into a normal one."""
lu1 = u.mag(u.Jy)
with pytest.raises(u.UnitsError):
lu1 * u.m
with pytest.raises(u.UnitsError):
u.m * lu1
with pytest.raises(u.UnitsError):
lu1 / lu1
for unit in (u.dimensionless_unscaled, u.m, u.mag, u.dex):
with pytest.raises(u.UnitsError):
lu1 / unit
lu2 = u.mag(u.dimensionless_unscaled)
with pytest.raises(u.UnitsError):
lu2 * lu1
with pytest.raises(u.UnitsError):
lu2 / lu1
# But dimensionless_unscaled can be cancelled.
assert lu2 / lu2 == u.dimensionless_unscaled
# With dimensionless, normal units are OK, but we return a plain unit.
tf = lu2 * u.m
tr = u.m * lu2
for t in (tf, tr):
assert not isinstance(t, type(lu2))
assert t == lu2.function_unit * u.m
with u.set_enabled_equivalencies(u.logarithmic()):
with pytest.raises(u.UnitsError):
t.to(lu2.physical_unit)
# Now we essentially have a LogUnit with a prefactor of 100,
# so should be equivalent again.
t = tf / u.cm
with u.set_enabled_equivalencies(u.logarithmic()):
assert t.is_equivalent(lu2.function_unit)
assert_allclose(t.to(u.dimensionless_unscaled, np.arange(3.)/100.),
lu2.to(lu2.physical_unit, np.arange(3.)))
# If we effectively remove lu1, a normal unit should be returned.
t2 = tf / lu2
assert not isinstance(t2, type(lu2))
assert t2 == u.m
t3 = tf / lu2.function_unit
assert not isinstance(t3, type(lu2))
assert t3 == u.m
# For completeness, also ensure non-sensical operations fail
with pytest.raises(TypeError):
lu1 * object()
with pytest.raises(TypeError):
slice(None) * lu1
with pytest.raises(TypeError):
lu1 / []
with pytest.raises(TypeError):
1 / lu1
@pytest.mark.parametrize('power', (2, 0.5, 1, 0))
def test_raise_to_power(self, power):
"""Check that raising LogUnits to some power is only possible when the
physical unit is dimensionless, and that conversion is turned off when
the resulting logarithmic unit (such as mag**2) is incompatible."""
lu1 = u.mag(u.Jy)
if power == 0:
assert lu1 ** power == u.dimensionless_unscaled
elif power == 1:
assert lu1 ** power == lu1
else:
with pytest.raises(u.UnitsError):
lu1 ** power
# With dimensionless, though, it works, but returns a normal unit.
lu2 = u.mag(u.dimensionless_unscaled)
t = lu2**power
if power == 0:
assert t == u.dimensionless_unscaled
elif power == 1:
assert t == lu2
else:
assert not isinstance(t, type(lu2))
assert t == lu2.function_unit**power
# also check we roundtrip
t2 = t**(1./power)
assert t2 == lu2.function_unit
with u.set_enabled_equivalencies(u.logarithmic()):
assert_allclose(t2.to(u.dimensionless_unscaled, np.arange(3.)),
lu2.to(lu2.physical_unit, np.arange(3.)))
@pytest.mark.parametrize('other', pu_sample)
def test_addition_subtraction_to_normal_units_fails(self, other):
lu1 = u.mag(u.Jy)
with pytest.raises(u.UnitsError):
lu1 + other
with pytest.raises(u.UnitsError):
lu1 - other
with pytest.raises(u.UnitsError):
other - lu1
def test_addition_subtraction_to_non_units_fails(self):
lu1 = u.mag(u.Jy)
with pytest.raises(TypeError):
lu1 + 1.
with pytest.raises(TypeError):
lu1 - [1., 2., 3.]
@pytest.mark.parametrize(
'other', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m),
u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag)))
def test_addition_subtraction(self, other):
"""Check physical units are changed appropriately"""
lu1 = u.mag(u.Jy)
other_pu = getattr(other, 'physical_unit', u.dimensionless_unscaled)
lu_sf = lu1 + other
assert lu_sf.is_equivalent(lu1.physical_unit * other_pu)
lu_sr = other + lu1
assert lu_sr.is_equivalent(lu1.physical_unit * other_pu)
lu_df = lu1 - other
assert lu_df.is_equivalent(lu1.physical_unit / other_pu)
lu_dr = other - lu1
assert lu_dr.is_equivalent(other_pu / lu1.physical_unit)
def test_complicated_addition_subtraction(self):
"""for fun, a more complicated example of addition and subtraction"""
dm0 = u.Unit('DM', 1./(4.*np.pi*(10.*u.pc)**2))
lu_dm = u.mag(dm0)
lu_absST = u.STmag - lu_dm
assert lu_absST.is_equivalent(u.erg/u.s/u.AA)
def test_neg_pos(self):
lu1 = u.mag(u.Jy)
neg_lu = -lu1
assert neg_lu != lu1
assert neg_lu.physical_unit == u.Jy**-1
assert -neg_lu == lu1
pos_lu = +lu1
assert pos_lu is not lu1
assert pos_lu == lu1
def test_pickle():
lu1 = u.dex(u.cm/u.s**2)
s = pickle.dumps(lu1)
lu2 = pickle.loads(s)
assert lu1 == lu2
def test_hashable():
lu1 = u.dB(u.mW)
lu2 = u.dB(u.m)
lu3 = u.dB(u.mW)
assert hash(lu1) != hash(lu2)
assert hash(lu1) == hash(lu3)
luset = {lu1, lu2, lu3}
assert len(luset) == 2
class TestLogQuantityCreation(object):
@pytest.mark.parametrize('lq, lu', zip(lq_subclasses + [u.LogQuantity],
lu_subclasses + [u.LogUnit]))
def test_logarithmic_quantities(self, lq, lu):
"""Check logarithmic quantities are all set up correctly"""
assert lq._unit_class == lu
assert type(lu()._quantity_class(1.)) is lq
@pytest.mark.parametrize('lq_cls, physical_unit',
itertools.product(lq_subclasses, pu_sample))
def test_subclass_creation(self, lq_cls, physical_unit):
"""Create LogQuantity subclass objects for some physical units,
and basic check on transformations"""
value = np.arange(1., 10.)
log_q = lq_cls(value * physical_unit)
assert log_q.unit.physical_unit == physical_unit
assert log_q.unit.function_unit == log_q.unit._default_function_unit
assert_allclose(log_q.physical.value, value)
with pytest.raises(ValueError):
lq_cls(value, physical_unit)
@pytest.mark.parametrize(
'unit', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m),
u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag),
u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag)))
def test_different_units(self, unit):
q = u.Magnitude(1.23, unit)
assert q.unit.function_unit == getattr(unit, 'function_unit', unit)
assert q.unit.physical_unit is getattr(unit, 'physical_unit',
u.dimensionless_unscaled)
@pytest.mark.parametrize('value, unit', (
(1.*u.mag(u.Jy), None),
(1.*u.dex(u.Jy), None),
(1.*u.mag(u.W/u.m**2/u.Hz), u.mag(u.Jy)),
(1.*u.dex(u.W/u.m**2/u.Hz), u.mag(u.Jy))))
def test_function_values(self, value, unit):
lq = u.Magnitude(value, unit)
assert lq == value
assert lq.unit.function_unit == u.mag
assert lq.unit.physical_unit == getattr(unit, 'physical_unit',
value.unit.physical_unit)
@pytest.mark.parametrize(
'unit', (u.mag(), u.mag(u.Jy), u.mag(u.m), u.MagUnit('', 2.*u.mag),
u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag)))
def test_indirect_creation(self, unit):
q1 = 2.5 * unit
assert isinstance(q1, u.Magnitude)
assert q1.value == 2.5
assert q1.unit == unit
pv = 100. * unit.physical_unit
q2 = unit * pv
assert q2.unit == unit
assert q2.unit.physical_unit == pv.unit
assert q2.to_value(unit.physical_unit) == 100.
assert (q2._function_view / u.mag).to_value(1) == -5.
q3 = unit / 0.4
assert q3 == q1
def test_from_view(self):
# Cannot view a physical quantity as a function quantity, since the
# values would change.
q = [100., 1000.] * u.cm/u.s**2
with pytest.raises(TypeError):
q.view(u.Dex)
# But fine if we have the right magnitude.
q = [2., 3.] * u.dex
lq = q.view(u.Dex)
assert isinstance(lq, u.Dex)
assert lq.unit.physical_unit == u.dimensionless_unscaled
assert np.all(q == lq)
def test_using_quantity_class(self):
"""Check that we can use Quantity if we have subok=True"""
# following issue #5851
lu = u.dex(u.AA)
with pytest.raises(u.UnitTypeError):
u.Quantity(1., lu)
q = u.Quantity(1., lu, subok=True)
assert type(q) is lu._quantity_class
def test_conversion_to_and_from_physical_quantities():
"""Ensures we can convert from regular quantities."""
mst = [10., 12., 14.] * u.STmag
flux_lambda = mst.physical
mst_roundtrip = flux_lambda.to(u.STmag)
# check we return a logquantity; see #5178.
assert isinstance(mst_roundtrip, u.Magnitude)
assert mst_roundtrip.unit == mst.unit
assert_allclose(mst_roundtrip.value, mst.value)
wave = [4956.8, 4959.55, 4962.3] * u.AA
flux_nu = mst.to(u.Jy, equivalencies=u.spectral_density(wave))
mst_roundtrip2 = flux_nu.to(u.STmag, u.spectral_density(wave))
assert isinstance(mst_roundtrip2, u.Magnitude)
assert mst_roundtrip2.unit == mst.unit
assert_allclose(mst_roundtrip2.value, mst.value)
def test_quantity_decomposition():
lq = 10.*u.mag(u.Jy)
assert lq.decompose() == lq
assert lq.decompose().unit.physical_unit.bases == [u.kg, u.s]
assert lq.si == lq
assert lq.si.unit.physical_unit.bases == [u.kg, u.s]
assert lq.cgs == lq
assert lq.cgs.unit.physical_unit.bases == [u.g, u.s]
class TestLogQuantityViews(object):
def setup(self):
self.lq = u.Magnitude(np.arange(10.) * u.Jy)
self.lq2 = u.Magnitude(np.arange(5.))
def test_value_view(self):
lq_value = self.lq.value
assert type(lq_value) is np.ndarray
lq_value[2] = -1.
assert np.all(self.lq.value == lq_value)
def test_function_view(self):
lq_fv = self.lq._function_view
assert type(lq_fv) is u.Quantity
assert lq_fv.unit is self.lq.unit.function_unit
lq_fv[3] = -2. * lq_fv.unit
assert np.all(self.lq.value == lq_fv.value)
def test_quantity_view(self):
# Cannot view as Quantity, since the unit cannot be represented.
with pytest.raises(TypeError):
self.lq.view(u.Quantity)
# But a dimensionless one is fine.
q2 = self.lq2.view(u.Quantity)
assert q2.unit is u.mag
assert np.all(q2.value == self.lq2.value)
lq3 = q2.view(u.Magnitude)
assert type(lq3.unit) is u.MagUnit
assert lq3.unit.physical_unit == u.dimensionless_unscaled
assert np.all(lq3 == self.lq2)
class TestLogQuantitySlicing(object):
def test_item_get_and_set(self):
lq1 = u.Magnitude(np.arange(1., 11.)*u.Jy)
assert lq1[9] == u.Magnitude(10.*u.Jy)
lq1[2] = 100.*u.Jy
assert lq1[2] == u.Magnitude(100.*u.Jy)
with pytest.raises(u.UnitsError):
lq1[2] = 100.*u.m
with pytest.raises(u.UnitsError):
lq1[2] = 100.*u.mag
with pytest.raises(u.UnitsError):
lq1[2] = u.Magnitude(100.*u.m)
assert lq1[2] == u.Magnitude(100.*u.Jy)
def test_slice_get_and_set(self):
lq1 = u.Magnitude(np.arange(1., 10.)*u.Jy)
lq1[2:4] = 100.*u.Jy
assert np.all(lq1[2:4] == u.Magnitude(100.*u.Jy))
with pytest.raises(u.UnitsError):
lq1[2:4] = 100.*u.m
with pytest.raises(u.UnitsError):
lq1[2:4] = 100.*u.mag
with pytest.raises(u.UnitsError):
lq1[2:4] = u.Magnitude(100.*u.m)
assert np.all(lq1[2] == u.Magnitude(100.*u.Jy))
class TestLogQuantityArithmetic(object):
def test_multiplication_division(self):
"""Check that multiplication/division with other quantities is only
possible when the physical unit is dimensionless, and that this turns
the result into a normal quantity."""
lq = u.Magnitude(np.arange(1., 11.)*u.Jy)
with pytest.raises(u.UnitsError):
lq * (1.*u.m)
with pytest.raises(u.UnitsError):
(1.*u.m) * lq
with pytest.raises(u.UnitsError):
lq / lq
for unit in (u.m, u.mag, u.dex):
with pytest.raises(u.UnitsError):
lq / unit
lq2 = u.Magnitude(np.arange(1, 11.))
with pytest.raises(u.UnitsError):
lq2 * lq
with pytest.raises(u.UnitsError):
lq2 / lq
with pytest.raises(u.UnitsError):
lq / lq2
# but dimensionless_unscaled can be cancelled
r = lq2 / u.Magnitude(2.)
assert r.unit == u.dimensionless_unscaled
assert np.all(r.value == lq2.value/2.)
# with dimensionless, normal units OK, but return normal quantities
tf = lq2 * u.m
tr = u.m * lq2
for t in (tf, tr):
assert not isinstance(t, type(lq2))
assert t.unit == lq2.unit.function_unit * u.m
with u.set_enabled_equivalencies(u.logarithmic()):
with pytest.raises(u.UnitsError):
t.to(lq2.unit.physical_unit)
t = tf / (50.*u.cm)
# now we essentially have the same quantity but with a prefactor of 2
assert t.unit.is_equivalent(lq2.unit.function_unit)
assert_allclose(t.to(lq2.unit.function_unit), lq2._function_view*2)
@pytest.mark.parametrize('power', (2, 0.5, 1, 0))
def test_raise_to_power(self, power):
"""Check that raising LogQuantities to some power is only possible when
the physical unit is dimensionless, and that conversion is turned off
when the resulting logarithmic unit (say, mag**2) is incompatible."""
lq = u.Magnitude(np.arange(1., 4.)*u.Jy)
if power == 0:
assert np.all(lq ** power == 1.)
elif power == 1:
assert np.all(lq ** power == lq)
else:
with pytest.raises(u.UnitsError):
lq ** power
# with dimensionless, it works, but falls back to normal quantity
# (except for power=1)
lq2 = u.Magnitude(np.arange(10.))
t = lq2**power
if power == 0:
assert t.unit is u.dimensionless_unscaled
assert np.all(t.value == 1.)
elif power == 1:
assert np.all(t == lq2)
else:
assert not isinstance(t, type(lq2))
assert t.unit == lq2.unit.function_unit ** power
with u.set_enabled_equivalencies(u.logarithmic()):
with pytest.raises(u.UnitsError):
t.to(u.dimensionless_unscaled)
def test_error_on_lq_as_power(self):
lq = u.Magnitude(np.arange(1., 4.)*u.Jy)
with pytest.raises(TypeError):
lq ** lq
@pytest.mark.parametrize('other', pu_sample)
def test_addition_subtraction_to_normal_units_fails(self, other):
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
q = 1.23 * other
with pytest.raises(u.UnitsError):
lq + q
with pytest.raises(u.UnitsError):
lq - q
with pytest.raises(u.UnitsError):
q - lq
@pytest.mark.parametrize(
'other', (1.23 * u.mag, 2.34 * u.mag(),
u.Magnitude(3.45 * u.Jy), u.Magnitude(4.56 * u.m),
5.67 * u.Unit(2*u.mag), u.Magnitude(6.78, 2.*u.mag)))
def test_addition_subtraction(self, other):
"""Check that addition/subtraction with quantities with magnitude or
MagUnit units works, and that it changes the physical units
appropriately."""
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
other_physical = other.to(getattr(other.unit, 'physical_unit',
u.dimensionless_unscaled),
equivalencies=u.logarithmic())
lq_sf = lq + other
assert_allclose(lq_sf.physical, lq.physical * other_physical)
lq_sr = other + lq
assert_allclose(lq_sr.physical, lq.physical * other_physical)
lq_df = lq - other
assert_allclose(lq_df.physical, lq.physical / other_physical)
lq_dr = other - lq
assert_allclose(lq_dr.physical, other_physical / lq.physical)
@pytest.mark.parametrize('other', pu_sample)
def test_inplace_addition_subtraction_unit_checks(self, other):
lu1 = u.mag(u.Jy)
lq1 = u.Magnitude(np.arange(1., 10.), lu1)
with pytest.raises(u.UnitsError):
lq1 += other
assert np.all(lq1.value == np.arange(1., 10.))
assert lq1.unit == lu1
with pytest.raises(u.UnitsError):
lq1 -= other
assert np.all(lq1.value == np.arange(1., 10.))
assert lq1.unit == lu1
@pytest.mark.parametrize(
'other', (1.23 * u.mag, 2.34 * u.mag(),
u.Magnitude(3.45 * u.Jy), u.Magnitude(4.56 * u.m),
5.67 * u.Unit(2*u.mag), u.Magnitude(6.78, 2.*u.mag)))
def test_inplace_addition_subtraction(self, other):
"""Check that inplace addition/subtraction with quantities with
magnitude or MagUnit units works, and that it changes the physical
units appropriately."""
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
other_physical = other.to(getattr(other.unit, 'physical_unit',
u.dimensionless_unscaled),
equivalencies=u.logarithmic())
lq_sf = lq.copy()
lq_sf += other
assert_allclose(lq_sf.physical, lq.physical * other_physical)
lq_df = lq.copy()
lq_df -= other
assert_allclose(lq_df.physical, lq.physical / other_physical)
def test_complicated_addition_subtraction(self):
"""For fun, a more complicated example of addition and subtraction."""
dm0 = u.Unit('DM', 1./(4.*np.pi*(10.*u.pc)**2))
DMmag = u.mag(dm0)
m_st = 10. * u.STmag
dm = 5. * DMmag
M_st = m_st - dm
assert M_st.unit.is_equivalent(u.erg/u.s/u.AA)
assert np.abs(M_st.physical /
(m_st.physical*4.*np.pi*(100.*u.pc)**2) - 1.) < 1.e-15
class TestLogQuantityComparisons(object):
def test_comparison_to_non_quantities_fails(self):
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
# On python2, ordering operations always succeed, given essentially
# meaningless results.
if not six.PY2:
with pytest.raises(TypeError):
lq > 'a'
assert not (lq == 'a')
assert lq != 'a'
def test_comparison(self):
lq1 = u.Magnitude(np.arange(1., 4.)*u.Jy)
lq2 = u.Magnitude(2.*u.Jy)
assert np.all((lq1 > lq2) == np.array([True, False, False]))
assert np.all((lq1 == lq2) == np.array([False, True, False]))
lq3 = u.Dex(2.*u.Jy)
assert np.all((lq1 > lq3) == np.array([True, False, False]))
assert np.all((lq1 == lq3) == np.array([False, True, False]))
lq4 = u.Magnitude(2.*u.m)
assert not (lq1 == lq4)
assert lq1 != lq4
with pytest.raises(u.UnitsError):
lq1 < lq4
q5 = 1.5 * u.Jy
assert np.all((lq1 > q5) == np.array([True, False, False]))
assert np.all((q5 < lq1) == np.array([True, False, False]))
with pytest.raises(u.UnitsError):
lq1 >= 2.*u.m
with pytest.raises(u.UnitsError):
lq1 <= lq1.value * u.mag
# For physically dimensionless, we can compare with the function unit.
lq6 = u.Magnitude(np.arange(1., 4.))
fv6 = lq6.value * u.mag
assert np.all(lq6 == fv6)
# but not some arbitrary unit, of course.
with pytest.raises(u.UnitsError):
lq6 < 2.*u.m
class TestLogQuantityMethods(object):
def setup(self):
self.mJy = np.arange(1., 5.).reshape(2, 2) * u.mag(u.Jy)
self.m1 = | np.arange(1., 5.5, 0.5) | numpy.arange |
'''
<NAME>
set up :2020-1-9
intergrate img and label into one file
-- fiducial1024_v1
'''
import argparse
import sys, os
import pickle
import random
import collections
import json
import numpy as np
import scipy.io as io
import scipy.misc as m
import matplotlib.pyplot as plt
import glob
import math
import time
import threading
import multiprocessing as mp
from multiprocessing import Pool
import re
import cv2
# sys.path.append('/lustre/home/gwxie/hope/project/dewarp/datasets/') # /lustre/home/gwxie/program/project/unwarp/perturbed_imgaes/GAN
import utils
def getDatasets(dir):
return os.listdir(dir)
class perturbed(utils.BasePerturbed):
def __init__(self, path, bg_path, save_path, save_suffix):
self.path = path
self.bg_path = bg_path
self.save_path = save_path
self.save_suffix = save_suffix
def save_img(self, m, n, fold_curve='fold', repeat_time=4, fiducial_points = 16, relativeShift_position='relativeShift_v2'):
origin_img = cv2.imread(self.path, flags=cv2.IMREAD_COLOR)
save_img_shape = [512*2, 480*2] # 320
# reduce_value = np.random.choice([2**4, 2**5, 2**6, 2**7, 2**8], p=[0.01, 0.1, 0.4, 0.39, 0.1])
reduce_value = | np.random.choice([2*2, 4*2, 8*2, 16*2, 24*2, 32*2, 40*2, 48*2], p=[0.02, 0.18, 0.2, 0.3, 0.1, 0.1, 0.08, 0.02]) | numpy.random.choice |
import time
import h5py
import hdbscan
import numpy as np
import torch
from sklearn.cluster import MeanShift
from pytorch3dunet.datasets.hdf5 import SliceBuilder
from pytorch3dunet.unet3d.utils import get_logger
from pytorch3dunet.unet3d.utils import unpad
logger = get_logger('UNet3DPredictor')
class _AbstractPredictor:
def __init__(self, model, loader, output_file, config, **kwargs):
self.model = model
self.loader = loader
self.output_file = output_file
self.config = config
self.predictor_config = kwargs
@staticmethod
def _volume_shape(dataset):
# TODO: support multiple internal datasets
raw = dataset.raws[0]
if raw.ndim == 3:
return raw.shape
else:
return raw.shape[1:]
@staticmethod
def _get_output_dataset_names(number_of_datasets, prefix='predictions'):
if number_of_datasets == 1:
return [prefix]
else:
return [f'{prefix}{i}' for i in range(number_of_datasets)]
def predict(self):
raise NotImplementedError
class StandardPredictor(_AbstractPredictor):
"""
Applies the model on the given dataset and saves the result in the `output_file` in the H5 format.
Predictions from the network are kept in memory. If the results from the network don't fit in into RAM
use `LazyPredictor` instead.
The output dataset names inside the H5 is given by `des_dataset_name` config argument. If the argument is
not present in the config 'predictions{n}' is used as a default dataset name, where `n` denotes the number
of the output head from the network.
Args:
model (Unet3D): trained 3D UNet model used for prediction
data_loader (torch.utils.data.DataLoader): input data loader
output_file (str): path to the output H5 file
config (dict): global config dict
"""
def __init__(self, model, loader, output_file, config, **kwargs):
super().__init__(model, loader, output_file, config, **kwargs)
def predict(self):
out_channels = self.config['model'].get('out_channels')
if out_channels is None:
out_channels = self.config['model']['dt_out_channels']
prediction_channel = self.config.get('prediction_channel', None)
if prediction_channel is not None:
logger.info(f"Using only channel '{prediction_channel}' from the network output")
device = self.config['device']
output_heads = self.config['model'].get('output_heads', 1)
logger.info(f'Running prediction on {len(self.loader)} batches...')
# dimensionality of the the output predictions
volume_shape = self._volume_shape(self.loader.dataset)
if prediction_channel is None:
prediction_maps_shape = (out_channels,) + volume_shape
else:
# single channel prediction map
prediction_maps_shape = (1,) + volume_shape
logger.info(f'The shape of the output prediction maps (CDHW): {prediction_maps_shape}')
avoid_block_artifacts = self.predictor_config.get('avoid_block_artifacts', True)
logger.info(f'Avoid block artifacts: {avoid_block_artifacts}')
# create destination H5 file
h5_output_file = h5py.File(self.output_file, 'w')
# allocate prediction and normalization arrays
logger.info('Allocating prediction and normalization arrays...')
prediction_maps, normalization_masks = self._allocate_prediction_maps(prediction_maps_shape,
output_heads, h5_output_file)
# Sets the module in evaluation mode explicitly (necessary for batchnorm/dropout layers if present)
self.model.eval()
# Set the `testing=true` flag otherwise the final Softmax/Sigmoid won't be applied!
self.model.testing = True
# Run predictions on the entire input dataset
with torch.no_grad():
for batch, indices in self.loader:
# send batch to device
batch = batch.to(device)
# forward pass
predictions = self.model(batch)
# wrap predictions into a list if there is only one output head from the network
if output_heads == 1:
predictions = [predictions]
# for each output head
for prediction, prediction_map, normalization_mask in zip(predictions, prediction_maps,
normalization_masks):
# convert to numpy array
prediction = prediction.cpu().numpy()
# for each batch sample
for pred, index in zip(prediction, indices):
# save patch index: (C,D,H,W)
if prediction_channel is None:
channel_slice = slice(0, out_channels)
else:
channel_slice = slice(0, 1)
index = (channel_slice,) + index
if prediction_channel is not None:
# use only the 'prediction_channel'
logger.info(f"Using channel '{prediction_channel}'...")
pred = np.expand_dims(pred[prediction_channel], axis=0)
logger.info(f'Saving predictions for slice:{index}...')
if avoid_block_artifacts:
# unpad in order to avoid block artifacts in the output probability maps
u_prediction, u_index = unpad(pred, index, volume_shape)
# accumulate probabilities into the output prediction array
prediction_map[u_index] += u_prediction
# count voxel visits for normalization
normalization_mask[u_index] += 1
else:
# accumulate probabilities into the output prediction array
prediction_map[index] += pred
# count voxel visits for normalization
normalization_mask[index] += 1
# save results to
self._save_results(prediction_maps, normalization_masks, output_heads, h5_output_file, self.loader.dataset)
# close the output H5 file
h5_output_file.close()
def _allocate_prediction_maps(self, output_shape, output_heads, output_file):
# initialize the output prediction arrays
prediction_maps = [np.zeros(output_shape, dtype='float32') for _ in range(output_heads)]
# initialize normalization mask in order to average out probabilities of overlapping patches
normalization_masks = [ | np.zeros(output_shape, dtype='uint8') | numpy.zeros |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + | np.sin(5 * knot_demonstrate_time) | numpy.sin |
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import os
import matplotlib.pyplot as plt
import CurveFit
import shutil
#find all DIRECTORIES containing non-hidden files ending in FILENAME
def getDataDirectories(DIRECTORY, FILENAME="valLoss.txt"):
directories=[]
for directory in os.scandir(DIRECTORY):
for item in os.scandir(directory):
if item.name.endswith(FILENAME) and not item.name.startswith("."):
directories.append(directory.path)
return directories
#get all non-hidden data files in DIRECTORY with extension EXT
def getDataFiles(DIRECTORY, EXT='txt'):
datafiles=[]
for item in os.scandir(DIRECTORY):
if item.name.endswith("."+EXT) and not item.name.startswith("."):
datafiles.append(item.path)
return datafiles
#checking if loss ever doesn't decrease for numEpochs epochs in a row.
def stopsDecreasing(loss, epoch, numEpochs):
minLoss=np.inf
epochMin=0
for i in range(0,loss.size):
if loss[i] < minLoss:
minLoss=loss[i]
epochMin=epoch[i]
elif (epoch[i]-epochMin) >= numEpochs:
return i, minLoss
return i, minLoss
#dirpath is where the accuracy and loss files are stored. want to move the files into the same format expected by grabNNData.
def createFolders(SEARCHDIR, SAVEDIR):
for item in os.scandir(SEARCHDIR):
name=str(item.name)
files=name.split('-')
SAVEFULLDIR=SAVEDIR+str(files[0])
if not os.path.exists(SAVEFULLDIR):
try:
os.makedirs(SAVEFULLDIR)
except FileExistsError:
#directory already exists--must have been created between the if statement & our attempt at making directory
pass
shutil.move(item.path, SAVEFULLDIR+"/"+str(files[1]))
#a function to read in information (e.g. accuracy, loss) stored at FILENAME
def grabNNData(FILENAME, header='infer', sep=' '):
data = pd.read_csv(FILENAME, sep, header=header)
if ('epochs' in data.columns) and ('trainLoss' in data.columns) and ('valLoss' in data.columns) and ('valAcc' in data.columns) and ('batch_size' in data.columns) and ('learning_rate' in data.columns):
sortedData=data.sort_values(by="epochs", axis=0, ascending=True)
epoch=np.array(sortedData['epochs'])
trainLoss=np.array(sortedData['trainLoss'])
valLoss=np.array(sortedData['valLoss'])
valAcc=np.array(sortedData['valAcc'])
batch_size=np.array(sortedData['batch_size'])
learning_rate=np.array(sortedData['learning_rate'])
convKers=np.array(sortedData['convKernels'])
return(epoch, trainLoss, valLoss, valAcc, batch_size, learning_rate, convKers)
elif ('epochs' in data.columns) and ('trainLoss' in data.columns) and ('valLoss' in data.columns) and ('valAcc' in data.columns):
sortedData=data.sort_values(by="epochs", axis=0, ascending=True)
epoch= | np.array(sortedData['epochs']) | numpy.array |
"""Test the search module"""
from collections.abc import Iterable, Sized
from io import StringIO
from itertools import chain, product
from functools import partial
import pickle
import sys
from types import GeneratorType
import re
import numpy as np
import scipy.sparse as sp
import pytest
from sklearn.utils.fixes import sp_version
from sklearn.utils._testing import assert_raises
from sklearn.utils._testing import assert_warns
from sklearn.utils._testing import assert_warns_message
from sklearn.utils._testing import assert_raise_message
from sklearn.utils._testing import assert_array_equal
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.utils._testing import assert_allclose
from sklearn.utils._testing import assert_almost_equal
from sklearn.utils._testing import ignore_warnings
from sklearn.utils._mocking import CheckingClassifier, MockDataFrame
from scipy.stats import bernoulli, expon, uniform
from sklearn.base import BaseEstimator, ClassifierMixin
from sklearn.base import clone
from sklearn.exceptions import NotFittedError
from sklearn.datasets import make_classification
from sklearn.datasets import make_blobs
from sklearn.datasets import make_multilabel_classification
from sklearn.model_selection import fit_grid_point
from sklearn.model_selection import train_test_split
from sklearn.model_selection import KFold
from sklearn.model_selection import StratifiedKFold
from sklearn.model_selection import StratifiedShuffleSplit
from sklearn.model_selection import LeaveOneGroupOut
from sklearn.model_selection import LeavePGroupsOut
from sklearn.model_selection import GroupKFold
from sklearn.model_selection import GroupShuffleSplit
from sklearn.model_selection import GridSearchCV
from sklearn.model_selection import RandomizedSearchCV
from sklearn.model_selection import ParameterGrid
from sklearn.model_selection import ParameterSampler
from sklearn.model_selection._search import BaseSearchCV
from sklearn.model_selection._validation import FitFailedWarning
from sklearn.svm import LinearSVC, SVC
from sklearn.tree import DecisionTreeRegressor
from sklearn.tree import DecisionTreeClassifier
from sklearn.cluster import KMeans
from sklearn.neighbors import KernelDensity
from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import f1_score
from sklearn.metrics import recall_score
from sklearn.metrics import accuracy_score
from sklearn.metrics import make_scorer
from sklearn.metrics import roc_auc_score
from sklearn.metrics.pairwise import euclidean_distances
from sklearn.impute import SimpleImputer
from sklearn.pipeline import Pipeline
from sklearn.linear_model import Ridge, SGDClassifier, LinearRegression
from sklearn.experimental import enable_hist_gradient_boosting # noqa
from sklearn.ensemble import HistGradientBoostingClassifier
from sklearn.model_selection.tests.common import OneTimeSplitter
# Neither of the following two estimators inherit from BaseEstimator,
# to test hyperparameter search on user-defined classifiers.
class MockClassifier:
"""Dummy classifier to test the parameter search algorithms"""
def __init__(self, foo_param=0):
self.foo_param = foo_param
def fit(self, X, Y):
assert len(X) == len(Y)
self.classes_ = np.unique(Y)
return self
def predict(self, T):
return T.shape[0]
def transform(self, X):
return X + self.foo_param
def inverse_transform(self, X):
return X - self.foo_param
predict_proba = predict
predict_log_proba = predict
decision_function = predict
def score(self, X=None, Y=None):
if self.foo_param > 1:
score = 1.
else:
score = 0.
return score
def get_params(self, deep=False):
return {'foo_param': self.foo_param}
def set_params(self, **params):
self.foo_param = params['foo_param']
return self
class LinearSVCNoScore(LinearSVC):
"""An LinearSVC classifier that has no score method."""
@property
def score(self):
raise AttributeError
X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
y = np.array([1, 1, 2, 2])
def assert_grid_iter_equals_getitem(grid):
assert list(grid) == [grid[i] for i in range(len(grid))]
@pytest.mark.parametrize("klass", [ParameterGrid,
partial(ParameterSampler, n_iter=10)])
@pytest.mark.parametrize(
"input, error_type, error_message",
[(0, TypeError, r'Parameter .* is not a dict or a list \(0\)'),
([{'foo': [0]}, 0], TypeError, r'Parameter .* is not a dict \(0\)'),
({'foo': 0}, TypeError, "Parameter.* value is not iterable .*"
r"\(key='foo', value=0\)")]
)
def test_validate_parameter_input(klass, input, error_type, error_message):
with pytest.raises(error_type, match=error_message):
klass(input)
def test_parameter_grid():
# Test basic properties of ParameterGrid.
params1 = {"foo": [1, 2, 3]}
grid1 = ParameterGrid(params1)
assert isinstance(grid1, Iterable)
assert isinstance(grid1, Sized)
assert len(grid1) == 3
assert_grid_iter_equals_getitem(grid1)
params2 = {"foo": [4, 2],
"bar": ["ham", "spam", "eggs"]}
grid2 = ParameterGrid(params2)
assert len(grid2) == 6
# loop to assert we can iterate over the grid multiple times
for i in range(2):
# tuple + chain transforms {"a": 1, "b": 2} to ("a", 1, "b", 2)
points = set(tuple(chain(*(sorted(p.items())))) for p in grid2)
assert (points ==
set(("bar", x, "foo", y)
for x, y in product(params2["bar"], params2["foo"])))
assert_grid_iter_equals_getitem(grid2)
# Special case: empty grid (useful to get default estimator settings)
empty = ParameterGrid({})
assert len(empty) == 1
assert list(empty) == [{}]
assert_grid_iter_equals_getitem(empty)
assert_raises(IndexError, lambda: empty[1])
has_empty = ParameterGrid([{'C': [1, 10]}, {}, {'C': [.5]}])
assert len(has_empty) == 4
assert list(has_empty) == [{'C': 1}, {'C': 10}, {}, {'C': .5}]
assert_grid_iter_equals_getitem(has_empty)
def test_grid_search():
# Test that the best estimator contains the right value for foo_param
clf = MockClassifier()
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=3, verbose=3)
# make sure it selects the smallest parameter in case of ties
old_stdout = sys.stdout
sys.stdout = StringIO()
grid_search.fit(X, y)
sys.stdout = old_stdout
assert grid_search.best_estimator_.foo_param == 2
assert_array_equal(grid_search.cv_results_["param_foo_param"].data,
[1, 2, 3])
# Smoke test the score etc:
grid_search.score(X, y)
grid_search.predict_proba(X)
grid_search.decision_function(X)
grid_search.transform(X)
# Test exception handling on scoring
grid_search.scoring = 'sklearn'
assert_raises(ValueError, grid_search.fit, X, y)
def test_grid_search_pipeline_steps():
# check that parameters that are estimators are cloned before fitting
pipe = Pipeline([('regressor', LinearRegression())])
param_grid = {'regressor': [LinearRegression(), Ridge()]}
grid_search = GridSearchCV(pipe, param_grid, cv=2)
grid_search.fit(X, y)
regressor_results = grid_search.cv_results_['param_regressor']
assert isinstance(regressor_results[0], LinearRegression)
assert isinstance(regressor_results[1], Ridge)
assert not hasattr(regressor_results[0], 'coef_')
assert not hasattr(regressor_results[1], 'coef_')
assert regressor_results[0] is not grid_search.best_estimator_
assert regressor_results[1] is not grid_search.best_estimator_
# check that we didn't modify the parameter grid that was passed
assert not hasattr(param_grid['regressor'][0], 'coef_')
assert not hasattr(param_grid['regressor'][1], 'coef_')
@pytest.mark.parametrize("SearchCV", [GridSearchCV, RandomizedSearchCV])
def test_SearchCV_with_fit_params(SearchCV):
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
clf = CheckingClassifier(expected_fit_params=['spam', 'eggs'])
searcher = SearchCV(
clf, {'foo_param': [1, 2, 3]}, cv=2, error_score="raise"
)
# The CheckingClassifier generates an assertion error if
# a parameter is missing or has length != len(X).
err_msg = r"Expected fit parameter\(s\) \['eggs'\] not seen."
with pytest.raises(AssertionError, match=err_msg):
searcher.fit(X, y, spam=np.ones(10))
err_msg = "Fit parameter spam has length 1; expected"
with pytest.raises(AssertionError, match=err_msg):
searcher.fit(X, y, spam=np.ones(1), eggs=np.zeros(10))
searcher.fit(X, y, spam=np.ones(10), eggs=np.zeros(10))
@ignore_warnings
def test_grid_search_no_score():
# Test grid-search on classifier that has no score function.
clf = LinearSVC(random_state=0)
X, y = make_blobs(random_state=0, centers=2)
Cs = [.1, 1, 10]
clf_no_score = LinearSVCNoScore(random_state=0)
grid_search = GridSearchCV(clf, {'C': Cs}, scoring='accuracy')
grid_search.fit(X, y)
grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs},
scoring='accuracy')
# smoketest grid search
grid_search_no_score.fit(X, y)
# check that best params are equal
assert grid_search_no_score.best_params_ == grid_search.best_params_
# check that we can call score and that it gives the correct result
assert grid_search.score(X, y) == grid_search_no_score.score(X, y)
# giving no scoring function raises an error
grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs})
assert_raise_message(TypeError, "no scoring", grid_search_no_score.fit,
[[1]])
def test_grid_search_score_method():
X, y = make_classification(n_samples=100, n_classes=2, flip_y=.2,
random_state=0)
clf = LinearSVC(random_state=0)
grid = {'C': [.1]}
search_no_scoring = GridSearchCV(clf, grid, scoring=None).fit(X, y)
search_accuracy = GridSearchCV(clf, grid, scoring='accuracy').fit(X, y)
search_no_score_method_auc = GridSearchCV(LinearSVCNoScore(), grid,
scoring='roc_auc'
).fit(X, y)
search_auc = GridSearchCV(clf, grid, scoring='roc_auc').fit(X, y)
# Check warning only occurs in situation where behavior changed:
# estimator requires score method to compete with scoring parameter
score_no_scoring = search_no_scoring.score(X, y)
score_accuracy = search_accuracy.score(X, y)
score_no_score_auc = search_no_score_method_auc.score(X, y)
score_auc = search_auc.score(X, y)
# ensure the test is sane
assert score_auc < 1.0
assert score_accuracy < 1.0
assert score_auc != score_accuracy
assert_almost_equal(score_accuracy, score_no_scoring)
assert_almost_equal(score_auc, score_no_score_auc)
def test_grid_search_groups():
# Check if ValueError (when groups is None) propagates to GridSearchCV
# And also check if groups is correctly passed to the cv object
rng = np.random.RandomState(0)
X, y = make_classification(n_samples=15, n_classes=2, random_state=0)
groups = rng.randint(0, 3, 15)
clf = LinearSVC(random_state=0)
grid = {'C': [1]}
group_cvs = [LeaveOneGroupOut(), LeavePGroupsOut(2),
GroupKFold(n_splits=3), GroupShuffleSplit()]
for cv in group_cvs:
gs = GridSearchCV(clf, grid, cv=cv)
assert_raise_message(ValueError,
"The 'groups' parameter should not be None.",
gs.fit, X, y)
gs.fit(X, y, groups=groups)
non_group_cvs = [StratifiedKFold(), StratifiedShuffleSplit()]
for cv in non_group_cvs:
gs = GridSearchCV(clf, grid, cv=cv)
# Should not raise an error
gs.fit(X, y)
def test_classes__property():
# Test that classes_ property matches best_estimator_.classes_
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
Cs = [.1, 1, 10]
grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs})
grid_search.fit(X, y)
assert_array_equal(grid_search.best_estimator_.classes_,
grid_search.classes_)
# Test that regressors do not have a classes_ attribute
grid_search = GridSearchCV(Ridge(), {'alpha': [1.0, 2.0]})
grid_search.fit(X, y)
assert not hasattr(grid_search, 'classes_')
# Test that the grid searcher has no classes_ attribute before it's fit
grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs})
assert not hasattr(grid_search, 'classes_')
# Test that the grid searcher has no classes_ attribute without a refit
grid_search = GridSearchCV(LinearSVC(random_state=0),
{'C': Cs}, refit=False)
grid_search.fit(X, y)
assert not hasattr(grid_search, 'classes_')
def test_trivial_cv_results_attr():
# Test search over a "grid" with only one point.
clf = MockClassifier()
grid_search = GridSearchCV(clf, {'foo_param': [1]}, cv=3)
grid_search.fit(X, y)
assert hasattr(grid_search, "cv_results_")
random_search = RandomizedSearchCV(clf, {'foo_param': [0]}, n_iter=1, cv=3)
random_search.fit(X, y)
assert hasattr(grid_search, "cv_results_")
def test_no_refit():
# Test that GSCV can be used for model selection alone without refitting
clf = MockClassifier()
for scoring in [None, ['accuracy', 'precision']]:
grid_search = GridSearchCV(
clf, {'foo_param': [1, 2, 3]}, refit=False, cv=3
)
grid_search.fit(X, y)
assert not hasattr(grid_search, "best_estimator_") and \
hasattr(grid_search, "best_index_") and \
hasattr(grid_search, "best_params_")
# Make sure the functions predict/transform etc raise meaningful
# error messages
for fn_name in ('predict', 'predict_proba', 'predict_log_proba',
'transform', 'inverse_transform'):
assert_raise_message(NotFittedError,
('refit=False. %s is available only after '
'refitting on the best parameters'
% fn_name), getattr(grid_search, fn_name), X)
# Test that an invalid refit param raises appropriate error messages
for refit in ["", 5, True, 'recall', 'accuracy']:
assert_raise_message(ValueError, "For multi-metric scoring, the "
"parameter refit must be set to a scorer key",
GridSearchCV(clf, {}, refit=refit,
scoring={'acc': 'accuracy',
'prec': 'precision'}
).fit,
X, y)
def test_grid_search_error():
# Test that grid search will capture errors on data with different length
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
assert_raises(ValueError, cv.fit, X_[:180], y_)
def test_grid_search_one_grid_point():
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
param_dict = {"C": [1.0], "kernel": ["rbf"], "gamma": [0.1]}
clf = SVC(gamma='auto')
cv = GridSearchCV(clf, param_dict)
cv.fit(X_, y_)
clf = SVC(C=1.0, kernel="rbf", gamma=0.1)
clf.fit(X_, y_)
assert_array_equal(clf.dual_coef_, cv.best_estimator_.dual_coef_)
def test_grid_search_when_param_grid_includes_range():
# Test that the best estimator contains the right value for foo_param
clf = MockClassifier()
grid_search = None
grid_search = GridSearchCV(clf, {'foo_param': range(1, 4)}, cv=3)
grid_search.fit(X, y)
assert grid_search.best_estimator_.foo_param == 2
def test_grid_search_bad_param_grid():
param_dict = {"C": 1}
clf = SVC(gamma='auto')
assert_raise_message(
ValueError,
"Parameter grid for parameter (C) needs to"
" be a list or numpy array, but got (<class 'int'>)."
" Single values need to be wrapped in a list"
" with one element.",
GridSearchCV, clf, param_dict)
param_dict = {"C": []}
clf = SVC()
assert_raise_message(
ValueError,
"Parameter values for parameter (C) need to be a non-empty sequence.",
GridSearchCV, clf, param_dict)
param_dict = {"C": "1,2,3"}
clf = SVC(gamma='auto')
assert_raise_message(
ValueError,
"Parameter grid for parameter (C) needs to"
" be a list or numpy array, but got (<class 'str'>)."
" Single values need to be wrapped in a list"
" with one element.",
GridSearchCV, clf, param_dict)
param_dict = {"C": np.ones((3, 2))}
clf = SVC()
assert_raises(ValueError, GridSearchCV, clf, param_dict)
def test_grid_search_sparse():
# Test that grid search works with both dense and sparse matrices
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(X_[:180], y_[:180])
y_pred = cv.predict(X_[180:])
C = cv.best_estimator_.C
X_ = sp.csr_matrix(X_)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(X_[:180].tocoo(), y_[:180])
y_pred2 = cv.predict(X_[180:])
C2 = cv.best_estimator_.C
assert np.mean(y_pred == y_pred2) >= .9
assert C == C2
def test_grid_search_sparse_scoring():
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1")
cv.fit(X_[:180], y_[:180])
y_pred = cv.predict(X_[180:])
C = cv.best_estimator_.C
X_ = sp.csr_matrix(X_)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1")
cv.fit(X_[:180], y_[:180])
y_pred2 = cv.predict(X_[180:])
C2 = cv.best_estimator_.C
assert_array_equal(y_pred, y_pred2)
assert C == C2
# Smoke test the score
# np.testing.assert_allclose(f1_score(cv.predict(X_[:180]), y[:180]),
# cv.score(X_[:180], y[:180]))
# test loss where greater is worse
def f1_loss(y_true_, y_pred_):
return -f1_score(y_true_, y_pred_)
F1Loss = make_scorer(f1_loss, greater_is_better=False)
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring=F1Loss)
cv.fit(X_[:180], y_[:180])
y_pred3 = cv.predict(X_[180:])
C3 = cv.best_estimator_.C
assert C == C3
assert_array_equal(y_pred, y_pred3)
def test_grid_search_precomputed_kernel():
# Test that grid search works when the input features are given in the
# form of a precomputed kernel matrix
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
# compute the training kernel matrix corresponding to the linear kernel
K_train = np.dot(X_[:180], X_[:180].T)
y_train = y_[:180]
clf = SVC(kernel='precomputed')
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(K_train, y_train)
assert cv.best_score_ >= 0
# compute the test kernel matrix
K_test = np.dot(X_[180:], X_[:180].T)
y_test = y_[180:]
y_pred = cv.predict(K_test)
assert np.mean(y_pred == y_test) >= 0
# test error is raised when the precomputed kernel is not array-like
# or sparse
assert_raises(ValueError, cv.fit, K_train.tolist(), y_train)
def test_grid_search_precomputed_kernel_error_nonsquare():
# Test that grid search returns an error with a non-square precomputed
# training kernel matrix
K_train = np.zeros((10, 20))
y_train = np.ones((10, ))
clf = SVC(kernel='precomputed')
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
assert_raises(ValueError, cv.fit, K_train, y_train)
class BrokenClassifier(BaseEstimator):
"""Broken classifier that cannot be fit twice"""
def __init__(self, parameter=None):
self.parameter = parameter
def fit(self, X, y):
assert not hasattr(self, 'has_been_fit_')
self.has_been_fit_ = True
def predict(self, X):
return np.zeros(X.shape[0])
@ignore_warnings
def test_refit():
# Regression test for bug in refitting
# Simulates re-fitting a broken estimator; this used to break with
# sparse SVMs.
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
clf = GridSearchCV(BrokenClassifier(), [{'parameter': [0, 1]}],
scoring="precision", refit=True)
clf.fit(X, y)
def test_refit_callable():
"""
Test refit=callable, which adds flexibility in identifying the
"best" estimator.
"""
def refit_callable(cv_results):
"""
A dummy function tests `refit=callable` interface.
Return the index of a model that has the least
`mean_test_score`.
"""
# Fit a dummy clf with `refit=True` to get a list of keys in
# clf.cv_results_.
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]},
scoring='precision', refit=True)
clf.fit(X, y)
# Ensure that `best_index_ != 0` for this dummy clf
assert clf.best_index_ != 0
# Assert every key matches those in `cv_results`
for key in clf.cv_results_.keys():
assert key in cv_results
return cv_results['mean_test_score'].argmin()
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]},
scoring='precision', refit=refit_callable)
clf.fit(X, y)
assert clf.best_index_ == 0
# Ensure `best_score_` is disabled when using `refit=callable`
assert not hasattr(clf, 'best_score_')
def test_refit_callable_invalid_type():
"""
Test implementation catches the errors when 'best_index_' returns an
invalid result.
"""
def refit_callable_invalid_type(cv_results):
"""
A dummy function tests when returned 'best_index_' is not integer.
"""
return None
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.1, 1]},
scoring='precision', refit=refit_callable_invalid_type)
with pytest.raises(TypeError,
match='best_index_ returned is not an integer'):
clf.fit(X, y)
@pytest.mark.parametrize('out_bound_value', [-1, 2])
@pytest.mark.parametrize('search_cv', [RandomizedSearchCV, GridSearchCV])
def test_refit_callable_out_bound(out_bound_value, search_cv):
"""
Test implementation catches the errors when 'best_index_' returns an
out of bound result.
"""
def refit_callable_out_bound(cv_results):
"""
A dummy function tests when returned 'best_index_' is out of bounds.
"""
return out_bound_value
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
clf = search_cv(LinearSVC(random_state=42), {'C': [0.1, 1]},
scoring='precision', refit=refit_callable_out_bound)
with pytest.raises(IndexError, match='best_index_ index out of range'):
clf.fit(X, y)
def test_refit_callable_multi_metric():
"""
Test refit=callable in multiple metric evaluation setting
"""
def refit_callable(cv_results):
"""
A dummy function tests `refit=callable` interface.
Return the index of a model that has the least
`mean_test_prec`.
"""
assert 'mean_test_prec' in cv_results
return cv_results['mean_test_prec'].argmin()
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
scoring = {'Accuracy': make_scorer(accuracy_score), 'prec': 'precision'}
clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]},
scoring=scoring, refit=refit_callable)
clf.fit(X, y)
assert clf.best_index_ == 0
# Ensure `best_score_` is disabled when using `refit=callable`
assert not hasattr(clf, 'best_score_')
def test_gridsearch_nd():
# Pass X as list in GridSearchCV
X_4d = np.arange(10 * 5 * 3 * 2).reshape(10, 5, 3, 2)
y_3d = | np.arange(10 * 7 * 11) | numpy.arange |
try:
import importlib.resources as pkg_resources
except ImportError:
# Try backported to PY<37 `importlib_resources`.
import importlib_resources as pkg_resources
from . import images
from gym import Env, spaces
from time import time
import numpy as np
from copy import copy
import colorsys
import pygame
from pygame.transform import scale
class MinesweeperEnv(Env):
def __init__(self, grid_shape=(10, 15), bombs_density=0.1, n_bombs=None, impact_size=3, max_time=999, chicken=False):
self.grid_shape = grid_shape
self.grid_size = np.prod(grid_shape)
self.n_bombs = max(1, int(bombs_density * self.grid_size)) if n_bombs is None else n_bombs
self.n_bombs = min(self.grid_size - 1, self.n_bombs)
self.flaged_bombs = 0
self.flaged_empty = 0
self.max_time = max_time
if impact_size % 2 == 0:
raise ValueError('Impact_size must be an odd number !')
self.impact_size = impact_size
# Define constants
self.HIDDEN = 0
self.REVEAL = 1
self.FLAG = 2
self.BOMB = self.impact_size ** 2
# Setting up gym Env conventions
nvec_observation = (self.BOMB + 2) * np.ones(self.grid_shape)
self.observation_space = spaces.MultiDiscrete(nvec_observation)
nvec_action = np.array(self.grid_shape + (2,))
self.action_space = spaces.MultiDiscrete(nvec_action)
# Initalize state
self.state = np.zeros(self.grid_shape + (2,), dtype=np.uint8)
## Setup bombs places
idx = np.indices(self.grid_shape).reshape(2, -1)
bombs_ids = np.random.choice(range(self.grid_size), size=self.n_bombs, replace=False)
self.bombs_positions = idx[0][bombs_ids], idx[1][bombs_ids]
## Place numbers
self.semi_impact_size = (self.impact_size-1)//2
bomb_impact = np.ones((self.impact_size, self.impact_size), dtype=np.uint8)
for bombs_id in bombs_ids:
bomb_x, bomb_y = idx[0][bombs_id], idx[1][bombs_id]
x_min, x_max, dx_min, dx_max = self.clip_index(bomb_x, 0)
y_min, y_max, dy_min, dy_max = self.clip_index(bomb_y, 1)
bomb_region = self.state[x_min:x_max, y_min:y_max, 0]
bomb_region += bomb_impact[dx_min:dx_max, dy_min:dy_max]
## Place bombs
self.state[self.bombs_positions + (0,)] = self.BOMB
self.start_time = time()
self.time_left = int(time() - self.start_time)
# Setup rendering
self.pygame_is_init = False
self.chicken = chicken
self.done = False
self.score = 0
def get_observation(self):
observation = copy(self.state[:, :, 1])
revealed = observation == 1
flaged = observation == 2
observation += self.impact_size ** 2 + 1
observation[revealed] = copy(self.state[:, :, 0][revealed])
observation[flaged] -= 1
return observation
def reveal_around(self, coords, reward, done, without_loss=False):
if not done:
x_min, x_max, _, _ = self.clip_index(coords[0], 0)
y_min, y_max, _, _ = self.clip_index(coords[1], 1)
region = self.state[x_min:x_max, y_min:y_max, :]
unseen_around = np.sum(region[..., 1] == 0)
if unseen_around == 0:
if not without_loss:
reward -= 0.001
return
flags_around = np.sum(region[..., 1] == 2)
if flags_around == self.state[coords + (0,)]:
unrevealed_zeros_around = | np.logical_and(region[..., 0] == 0, region[..., 1] == self.HIDDEN) | numpy.logical_and |
import argparse
import json
import numpy as np
import pandas as pd
import os
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report,f1_score
from keras.models import Sequential
from keras.layers import Dense, Dropout
from keras import backend as K
from keras.utils.vis_utils import plot_model
from sklearn.externals import joblib
import time
def f1(y_true, y_pred):
def recall(y_true, y_pred):
"""Recall metric.
Only computes a batch-wise average of recall.
Computes the recall, a metric for multi-label classification of
how many relevant items are selected.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
possible_positives = K.sum(K.round(K.clip(y_true, 0, 1)))
recall = true_positives / (possible_positives + K.epsilon())
return recall
def precision(y_true, y_pred):
"""Precision metric.
Only computes a batch-wise average of precision.
Computes the precision, a metric for multi-label classification of
how many selected items are relevant.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
predicted_positives = K.sum(K.round(K.clip(y_pred, 0, 1)))
precision = true_positives / (predicted_positives + K.epsilon())
return precision
precision = precision(y_true, y_pred)
recall = recall(y_true, y_pred)
return 2*((precision*recall)/(precision+recall+K.epsilon()))
def get_embeddings(sentences_list,layer_json):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:return: Dictionary with key each sentence of the sentences_list and as value the embedding
'''
sentences = dict()#dict with key the index of each line of the sentences_list.txt and as value the sentence
embeddings = dict()##dict with key the index of each sentence and as value the its embedding
sentence_emb = dict()#key:sentence,value:its embedding
with open(sentences_list,'r') as file:
for index,line in enumerate(file):
sentences[index] = line.strip()
with open(layer_json, 'r',encoding='utf-8') as f:
for line in f:
embeddings[json.loads(line)['linex_index']] = np.asarray(json.loads(line)['features'])
for key,value in sentences.items():
sentence_emb[value] = embeddings[key]
return sentence_emb
def train_classifier(sentences_list,layer_json,dataset_csv,filename):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:param dataset_csv: the path of the dataset
:param filename: The path of the pickle file that the model will be stored
:return:
'''
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list,layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = np.asarray(previous_emb)
print(previous_emb.shape)
section_emb = np.asarray(section_list)
print(sentence_emb.shape)
length = np.asarray(length)
print(length.shape)
label = np.asarray(label)
print(errors)
features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1)
features = np.column_stack([features, length]) # np.append(features,length,axis=1)
print(features.shape)
X_train, X_val, y_train, y_val = train_test_split(features, label, test_size=0.33, random_state=42)
log = LogisticRegression(random_state=0, solver='newton-cg', max_iter=1000, C=0.1)
log.fit(X_train, y_train)
#save the model
_ = joblib.dump(log, filename, compress=9)
predictions = log.predict(X_val)
print("###########################################")
print("Results using embeddings from the",layer_json,"file")
print(classification_report(y_val, predictions))
print("F1 score using Logistic Regression:",f1_score(y_val, predictions))
print("###########################################")
#train a DNN
f1_results = list()
for i in range(3):
model = Sequential()
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dense(128, activation='relu', trainable=True))
model.add(Dropout(0.30))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.25))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.35))
model.add(Dense(1, activation='sigmoid'))
# compile network
model.compile(loss='binary_crossentropy', optimizer='sgd', metrics=[f1])
# fit network
model.fit(X_train, y_train, epochs=100, batch_size=64)
loss, f_1 = model.evaluate(X_val, y_val, verbose=1)
print('\nTest F1: %f' % (f_1 * 100))
f1_results.append(f_1)
model = None
print("###########################################")
print("Results using embeddings from the", layer_json, "file")
# evaluate
print(np.mean(f1_results))
print("###########################################")
def parameter_tuning_LR(sentences_list,layer_json,dataset_csv):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:param dataset_csv: the path of the dataset
:return:
'''
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list,layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = np.asarray(previous_emb)
print(previous_emb.shape)
section_emb = np.asarray(section_list)
print(sentence_emb.shape)
length = np.asarray(length)
print(length.shape)
label = np.asarray(label)
print(errors)
features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1)
features = np.column_stack([features, length])
print(features.shape)
X_train, X_val, y_train, y_val = train_test_split(features, label, test_size=0.33, random_state=42)
C = [0.1,1,2,5,10]
solver = ['newton-cg','saga','sag']
best_params = dict()
best_score = 0.0
for c in C:
for s in solver:
start = time.time()
log = LogisticRegression(random_state=0, solver=s, max_iter=1000, C=c)
log.fit(X_train, y_train)
predictions = log.predict(X_val)
print("###########################################")
print("LR with C =",c,'and solver = ',s)
print("Results using embeddings from the", layer_json, "file")
print(classification_report(y_val, predictions))
f1 = f1_score(y_val, predictions)
if f1 > best_score:
best_score = f1
best_params['c'] = c
best_params['solver'] = s
print("F1 score using Logistic Regression:",f1)
print("###########################################")
end = time.time()
running_time = end - start
print("Running time:"+str(running_time))
def visualize_DNN(file_to_save):
'''
Save the DNN architecture to a png file. Better use the Visulize_DNN.ipynd
:param file_to_save: the png file that the architecture of the DNN will be saved.
:return: None
'''
model = Sequential()
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dense(128, activation='relu', trainable=True))
model.add(Dropout(0.30))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.25))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.35))
model.add(Dense(1, activation='sigmoid'))
plot_model(model, to_file=file_to_save, show_shapes=True)
def save_model(sentences_list,layer_json,dataset_csv,pkl):
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list, layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append( | np.zeros(768) | numpy.zeros |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
min_1_y_time = minima_x[-1] * np.ones_like(min_1_y)
dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101)
dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Characteristic Wave Effects Example')
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10))
plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10))
plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4,
label=textwrap.fill('Coughlin maximum', 14))
plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4,
label=textwrap.fill('Coughlin minimum', 14))
plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4,
label=textwrap.fill('Average maximum', 14))
plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4,
label=textwrap.fill('Average minimum', 14))
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14))
plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14))
plt.plot(max_2_x_time, max_2_x, 'k-')
plt.plot(max_2_x_time_side, max_2_x, 'k-')
plt.plot(min_2_x_time, min_2_x, 'k-')
plt.plot(min_2_x_time_side, min_2_x, 'k-')
plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--')
plt.text(5.16 * np.pi, 0.85, r'$2a_2$')
plt.plot(max_2_y_time, max_2_y, 'k-')
plt.plot(max_2_y_time, max_2_y_side, 'k-')
plt.plot(min_2_y_time, min_2_y, 'k-')
plt.plot(min_2_y_time, min_2_y_side, 'k-')
plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--')
plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$')
plt.plot(max_1_x_time, max_1_x, 'k-')
plt.plot(max_1_x_time_side, max_1_x, 'k-')
plt.plot(min_1_x_time, min_1_x, 'k-')
plt.plot(min_1_x_time_side, min_1_x, 'k-')
plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--')
plt.text(5.42 * np.pi, -0.1, r'$2a_1$')
plt.plot(max_1_y_time, max_1_y, 'k-')
plt.plot(max_1_y_time, max_1_y_side, 'k-')
plt.plot(min_1_y_time, min_1_y, 'k-')
plt.plot(min_1_y_time, min_1_y_side, 'k-')
plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--')
plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$')
plt.xlim(3.9 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_characteristic_wave.png')
plt.show()
# plot 6
t = np.linspace(5, 95, 100)
signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200)
util_nn = emd_utils.Utility(time=t, time_series=signal_orig)
maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()]
minima = signal_orig[util_nn.min_bool_func_1st_order_fd()]
cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima)
cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima)
time = np.linspace(0, 5 * np.pi, 1001)
lsq_signal = np.cos(time) + np.cos(5 * time)
knots = np.linspace(0, 5 * np.pi, 101)
time_extended = time_extension(time)
time_series_extended = np.zeros_like(time_extended) / 0
time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal
neural_network_m = 200
neural_network_k = 100
# forward ->
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))]
P[-1, col] = 1 # for additive constant
t = lsq_signal[-neural_network_m:]
# test - top
seed_weights = np.ones(neural_network_k) / neural_network_k
weights = 0 * seed_weights.copy()
train_input = P[:-1, :]
lr = 0.01
for iterations in range(1000):
output = np.matmul(weights, train_input)
error = (t - output)
gradients = error * (- train_input)
# guess average gradients
average_gradients = np.mean(gradients, axis=1)
# steepest descent
max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients)))
adjustment = - lr * average_gradients
# adjustment = - lr * max_gradient_vector
weights += adjustment
# test - bottom
weights_right = np.hstack((weights, 0))
max_count_right = 0
min_count_right = 0
i_right = 0
while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1):
time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \
sum(weights_right * np.hstack((time_series_extended[
int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right):
int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1)))
i_right += 1
if i_right > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_right += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_right += 1
# backward <-
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)]
P[-1, col] = 1 # for additive constant
t = lsq_signal[:neural_network_m]
vx = cvx.Variable(int(neural_network_k + 1))
objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary
prob = cvx.Problem(objective)
result = prob.solve(verbose=True, solver=cvx.ECOS)
weights_left = np.array(vx.value)
max_count_left = 0
min_count_left = 0
i_left = 0
while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1):
time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \
2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left):
int(len(lsq_signal) - 1 - i_left + neural_network_k)],
1))) + 1
i_left += 1
if i_left > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_left += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_left += 1
lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal)
utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended)
maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()]
maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()]
maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()]
minima_time = time[lsq_utils.min_bool_func_1st_order_fd()]
minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Single Neuron Neural Network Example')
plt.plot(time, lsq_signal, zorder=2, label='Signal')
plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12))
plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima')
plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima')
plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3,
label=textwrap.fill('Extrapolated maxima', 12))
plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4,
label=textwrap.fill('Extrapolated minima', 12))
plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k',
label=textwrap.fill('Neural network inputs', 13))
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k')
plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k')
plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed',
label=textwrap.fill('Neural network targets', 13))
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray')
plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray',
linestyle='dashed')
plt.xlim(3.4 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/neural_network.png')
plt.show()
# plot 6a
np.random.seed(0)
time = np.linspace(0, 5 * np.pi, 1001)
knots_51 = np.linspace(0, 5 * np.pi, 51)
time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time)
noise = np.random.normal(0, 1, len(time_series))
time_series += noise
advemdpy = EMD(time=time, time_series=time_series)
imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_31 = np.linspace(0, 5 * np.pi, 31)
imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_11 = np.linspace(0, 5 * np.pi, 11)
imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1,
edge_effect='symmetric_anchor', verbose=False)[:3]
fig, axs = plt.subplots(3, 1)
plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40))
plt.subplots_adjust(hspace=0.1)
axs[0].plot(time, time_series, label='Time series')
axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21))
print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}')
for knot in knots_51:
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[0].set_xticklabels(['', '', '', '', '', ''])
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[1].plot(time, time_series, label='Time series')
axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19))
axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19))
print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}')
for knot in knots_31:
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[1].set_xticklabels(['', '', '', '', '', ''])
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[1].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[1].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
axs[2].plot(time, time_series, label='Time series')
axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots')
axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots')
axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots')
print(f'DFA fluctuation with 11 knots: {np.round(np.var(time_series - imfs_51[3, :]), 3)}')
for knot in knots_11:
axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[2].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[2].set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$', r'$5\pi$'])
box_2 = axs[2].get_position()
axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height])
axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[2].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[2].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
plt.savefig('jss_figures/DFA_different_trends.png')
plt.show()
# plot 6b
fig, axs = plt.subplots(3, 1)
plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences Zoomed Region', 40))
plt.subplots_adjust(hspace=0.1)
axs[0].plot(time, time_series, label='Time series')
axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21))
for knot in knots_51:
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[0].plot(knot * | np.ones(101) | numpy.ones |
from os import listdir
from os.path import isfile, join
from path import Path
import numpy as np
import cv2
# Dataset path
target_path = Path('target/')
annotation_images_path = Path('dataset/ade20k/annotations/training/').abspath()
dataset = [ f for f in listdir(annotation_images_path) if isfile(join(annotation_images_path,f))]
images = np.empty(len(dataset), dtype = object)
count = 1
# Iterate all Training Images
for n in range(0, len(dataset)):
# Read image
images[n] = cv2.imread(join(annotation_images_path,dataset[n]))
# Convert it to array
array = np.asarray(images[n],dtype=np.int8)
# Conditions when the value equal less than 1, change it to 255.
# If it is >= 1, increment it by -1
arr = | np.where(array < 1, 255, array -1) | numpy.where |
import numpy as np
from albumentations import (Compose, HorizontalFlip, VerticalFlip, Rotate, RandomRotate90,
ShiftScaleRotate, ElasticTransform,
GridDistortion, RandomSizedCrop, RandomCrop, CenterCrop,
RandomBrightnessContrast, HueSaturationValue, IAASharpen,
RandomGamma, RandomBrightness, RandomBrightnessContrast,
GaussianBlur,CLAHE,
Cutout, CoarseDropout, GaussNoise, ChannelShuffle, ToGray, OpticalDistortion,
Normalize, OneOf, NoOp)
from albumentations.pytorch import ToTensorV2 as ToTensor
from get_config import get_config
config = get_config()
MEAN = np.array([0.485, 0.456, 0.406])
STD = | np.array([0.229, 0.224, 0.225]) | numpy.array |
'''
<NAME>
set up :2020-1-9
intergrate img and label into one file
-- fiducial1024_v1
'''
import argparse
import sys, os
import pickle
import random
import collections
import json
import numpy as np
import scipy.io as io
import scipy.misc as m
import matplotlib.pyplot as plt
import glob
import math
import time
import threading
import multiprocessing as mp
from multiprocessing import Pool
import re
import cv2
# sys.path.append('/lustre/home/gwxie/hope/project/dewarp/datasets/') # /lustre/home/gwxie/program/project/unwarp/perturbed_imgaes/GAN
import utils
def getDatasets(dir):
return os.listdir(dir)
class perturbed(utils.BasePerturbed):
def __init__(self, path, bg_path, save_path, save_suffix):
self.path = path
self.bg_path = bg_path
self.save_path = save_path
self.save_suffix = save_suffix
def save_img(self, m, n, fold_curve='fold', repeat_time=4, fiducial_points = 16, relativeShift_position='relativeShift_v2'):
origin_img = cv2.imread(self.path, flags=cv2.IMREAD_COLOR)
save_img_shape = [512*2, 480*2] # 320
# reduce_value = np.random.choice([2**4, 2**5, 2**6, 2**7, 2**8], p=[0.01, 0.1, 0.4, 0.39, 0.1])
reduce_value = np.random.choice([2*2, 4*2, 8*2, 16*2, 24*2, 32*2, 40*2, 48*2], p=[0.02, 0.18, 0.2, 0.3, 0.1, 0.1, 0.08, 0.02])
# reduce_value = np.random.choice([8*2, 16*2, 24*2, 32*2, 40*2, 48*2], p=[0.01, 0.02, 0.2, 0.4, 0.19, 0.18])
# reduce_value = np.random.choice([16, 24, 32, 40, 48, 64], p=[0.01, 0.1, 0.2, 0.4, 0.2, 0.09])
base_img_shrink = save_img_shape[0] - reduce_value
# enlarge_img_shrink = [1024, 768]
# enlarge_img_shrink = [896, 672] # 420
enlarge_img_shrink = [512*4, 480*4] # 420
# enlarge_img_shrink = [896*2, 768*2] # 420
# enlarge_img_shrink = [896, 768] # 420
# enlarge_img_shrink = [768, 576] # 420
# enlarge_img_shrink = [640, 480] # 420
''''''
im_lr = origin_img.shape[0]
im_ud = origin_img.shape[1]
reduce_value_v2 = np.random.choice([2*2, 4*2, 8*2, 16*2, 24*2, 28*2, 32*2, 48*2], p=[0.02, 0.18, 0.2, 0.2, 0.1, 0.1, 0.1, 0.1])
# reduce_value_v2 = np.random.choice([16, 24, 28, 32, 48, 64], p=[0.01, 0.1, 0.2, 0.3, 0.25, 0.14])
if im_lr > im_ud:
im_ud = min(int(im_ud / im_lr * base_img_shrink), save_img_shape[1] - reduce_value_v2)
im_lr = save_img_shape[0] - reduce_value
else:
base_img_shrink = save_img_shape[1] - reduce_value
im_lr = min(int(im_lr / im_ud * base_img_shrink), save_img_shape[0] - reduce_value_v2)
im_ud = base_img_shrink
if round(im_lr / im_ud, 2) < 0.5 or round(im_ud / im_lr, 2) < 0.5:
repeat_time = min(repeat_time, 8)
edge_padding = 3
im_lr -= im_lr % (fiducial_points-1) - (2*edge_padding) # im_lr % (fiducial_points-1) - 1
im_ud -= im_ud % (fiducial_points-1) - (2*edge_padding) # im_ud % (fiducial_points-1) - 1
im_hight = np.linspace(edge_padding, im_lr - edge_padding, fiducial_points, dtype=np.int64)
im_wide = np.linspace(edge_padding, im_ud - edge_padding, fiducial_points, dtype=np.int64)
# im_lr -= im_lr % (fiducial_points-1) - (1+2*edge_padding) # im_lr % (fiducial_points-1) - 1
# im_ud -= im_ud % (fiducial_points-1) - (1+2*edge_padding) # im_ud % (fiducial_points-1) - 1
# im_hight = np.linspace(edge_padding, im_lr - (1+edge_padding), fiducial_points, dtype=np.int64)
# im_wide = np.linspace(edge_padding, im_ud - (1+edge_padding), fiducial_points, dtype=np.int64)
im_x, im_y = np.meshgrid(im_hight, im_wide)
segment_x = (im_lr) // (fiducial_points-1)
segment_y = (im_ud) // (fiducial_points-1)
# plt.plot(im_x, im_y,
# color='limegreen',
# marker='.',
# linestyle='')
# plt.grid(True)
# plt.show()
self.origin_img = cv2.resize(origin_img, (im_ud, im_lr), interpolation=cv2.INTER_CUBIC)
perturbed_bg_ = getDatasets(self.bg_path)
perturbed_bg_img_ = self.bg_path+random.choice(perturbed_bg_)
perturbed_bg_img = cv2.imread(perturbed_bg_img_, flags=cv2.IMREAD_COLOR)
mesh_shape = self.origin_img.shape[:2]
self.synthesis_perturbed_img = np.full((enlarge_img_shrink[0], enlarge_img_shrink[1], 3), 256, dtype=np.float32)#np.zeros_like(perturbed_bg_img)
# self.synthesis_perturbed_img = np.full((enlarge_img_shrink[0], enlarge_img_shrink[1], 3), 0, dtype=np.int16)#np.zeros_like(perturbed_bg_img)
self.new_shape = self.synthesis_perturbed_img.shape[:2]
perturbed_bg_img = cv2.resize(perturbed_bg_img, (save_img_shape[1], save_img_shape[0]), cv2.INPAINT_TELEA)
origin_pixel_position = np.argwhere(np.zeros(mesh_shape, dtype=np.uint32) == 0).reshape(mesh_shape[0], mesh_shape[1], 2)
pixel_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape(self.new_shape[0], self.new_shape[1], 2)
self.perturbed_xy_ = np.zeros((self.new_shape[0], self.new_shape[1], 2))
# self.perturbed_xy_ = pixel_position.copy().astype(np.float32)
# fiducial_points_grid = origin_pixel_position[im_x, im_y]
self.synthesis_perturbed_label = np.zeros((self.new_shape[0], self.new_shape[1], 2))
x_min, y_min, x_max, y_max = self.adjust_position_v2(0, 0, mesh_shape[0], mesh_shape[1], save_img_shape)
origin_pixel_position += [x_min, y_min]
x_min, y_min, x_max, y_max = self.adjust_position(0, 0, mesh_shape[0], mesh_shape[1])
x_shift = random.randint(-enlarge_img_shrink[0]//16, enlarge_img_shrink[0]//16)
y_shift = random.randint(-enlarge_img_shrink[1]//16, enlarge_img_shrink[1]//16)
x_min += x_shift
x_max += x_shift
y_min += y_shift
y_max += y_shift
'''im_x,y'''
im_x += x_min
im_y += y_min
self.synthesis_perturbed_img[x_min:x_max, y_min:y_max] = self.origin_img
self.synthesis_perturbed_label[x_min:x_max, y_min:y_max] = origin_pixel_position
synthesis_perturbed_img_map = self.synthesis_perturbed_img.copy()
synthesis_perturbed_label_map = self.synthesis_perturbed_label.copy()
foreORbackground_label = np.full((mesh_shape), 1, dtype=np.int16)
foreORbackground_label_map = np.full((self.new_shape), 0, dtype=np.int16)
foreORbackground_label_map[x_min:x_max, y_min:y_max] = foreORbackground_label
# synthesis_perturbed_img_map = self.pad(self.synthesis_perturbed_img.copy(), x_min, y_min, x_max, y_max)
# synthesis_perturbed_label_map = self.pad(synthesis_perturbed_label_map, x_min, y_min, x_max, y_max)
'''*****************************************************************'''
is_normalizationFun_mixture = self.is_perform(0.2, 0.8)
# if not is_normalizationFun_mixture:
normalizationFun_0_1 = False
# normalizationFun_0_1 = self.is_perform(0.5, 0.5)
if fold_curve == 'fold':
fold_curve_random = True
# is_normalizationFun_mixture = False
normalizationFun_0_1 = self.is_perform(0.2, 0.8)
if is_normalizationFun_mixture:
alpha_perturbed = random.randint(80, 120) / 100
else:
if normalizationFun_0_1 and repeat_time < 8:
alpha_perturbed = random.randint(50, 70) / 100
else:
alpha_perturbed = random.randint(70, 130) / 100
else:
fold_curve_random = self.is_perform(0.1, 0.9) # False # self.is_perform(0.01, 0.99)
alpha_perturbed = random.randint(80, 160) / 100
# is_normalizationFun_mixture = False # self.is_perform(0.01, 0.99)
synthesis_perturbed_img = np.full_like(self.synthesis_perturbed_img, 256)
# synthesis_perturbed_img = np.full_like(self.synthesis_perturbed_img, 0, dtype=np.int16)
synthesis_perturbed_label = np.zeros_like(self.synthesis_perturbed_label)
alpha_perturbed_change = self.is_perform(0.5, 0.5)
p_pp_choice = self.is_perform(0.8, 0.2) if fold_curve == 'fold' else self.is_perform(0.1, 0.9)
for repeat_i in range(repeat_time):
if alpha_perturbed_change:
if fold_curve == 'fold':
if is_normalizationFun_mixture:
alpha_perturbed = random.randint(80, 120) / 100
else:
if normalizationFun_0_1 and repeat_time < 8:
alpha_perturbed = random.randint(50, 70) / 100
else:
alpha_perturbed = random.randint(70, 130) / 100
else:
alpha_perturbed = random.randint(80, 160) / 100
''''''
linspace_x = [0, (self.new_shape[0] - im_lr) // 2 - 1,
self.new_shape[0] - (self.new_shape[0] - im_lr) // 2 - 1, self.new_shape[0] - 1]
linspace_y = [0, (self.new_shape[1] - im_ud) // 2 - 1,
self.new_shape[1] - (self.new_shape[1] - im_ud) // 2 - 1, self.new_shape[1] - 1]
linspace_x_seq = [1, 2, 3]
linspace_y_seq = [1, 2, 3]
r_x = random.choice(linspace_x_seq)
r_y = random.choice(linspace_y_seq)
perturbed_p = np.array(
[random.randint(linspace_x[r_x-1] * 10, linspace_x[r_x] * 10),
random.randint(linspace_y[r_y-1] * 10, linspace_y[r_y] * 10)])/10
if ((r_x == 1 or r_x == 3) and (r_y == 1 or r_y == 3)) and p_pp_choice:
linspace_x_seq.remove(r_x)
linspace_y_seq.remove(r_y)
r_x = random.choice(linspace_x_seq)
r_y = random.choice(linspace_y_seq)
perturbed_pp = np.array(
[random.randint(linspace_x[r_x-1] * 10, linspace_x[r_x] * 10),
random.randint(linspace_y[r_y-1] * 10, linspace_y[r_y] * 10)])/10
# perturbed_p, perturbed_pp = np.array(
# [random.randint(0, self.new_shape[0] * 10) / 10,
# random.randint(0, self.new_shape[1] * 10) / 10]) \
# , np.array([random.randint(0, self.new_shape[0] * 10) / 10,
# random.randint(0, self.new_shape[1] * 10) / 10])
# perturbed_p, perturbed_pp = np.array(
# [random.randint((self.new_shape[0]-im_lr)//2*10, (self.new_shape[0]-(self.new_shape[0]-im_lr)//2) * 10) / 10,
# random.randint((self.new_shape[1]-im_ud)//2*10, (self.new_shape[1]-(self.new_shape[1]-im_ud)//2) * 10) / 10]) \
# , np.array([random.randint((self.new_shape[0]-im_lr)//2*10, (self.new_shape[0]-(self.new_shape[0]-im_lr)//2) * 10) / 10,
# random.randint((self.new_shape[1]-im_ud)//2*10, (self.new_shape[1]-(self.new_shape[1]-im_ud)//2) * 10) / 10])
''''''
perturbed_vp = perturbed_pp - perturbed_p
perturbed_vp_norm = np.linalg.norm(perturbed_vp)
perturbed_distance_vertex_and_line = np.dot((perturbed_p - pixel_position), perturbed_vp) / perturbed_vp_norm
''''''
# perturbed_v = np.array([random.randint(-3000, 3000) / 100, random.randint(-3000, 3000) / 100])
# perturbed_v = np.array([random.randint(-4000, 4000) / 100, random.randint(-4000, 4000) / 100])
if fold_curve == 'fold' and self.is_perform(0.6, 0.4): # self.is_perform(0.3, 0.7):
# perturbed_v = np.array([random.randint(-9000, 9000) / 100, random.randint(-9000, 9000) / 100])
perturbed_v = np.array([random.randint(-10000, 10000) / 100, random.randint(-10000, 10000) / 100])
# perturbed_v = np.array([random.randint(-11000, 11000) / 100, random.randint(-11000, 11000) / 100])
else:
# perturbed_v = np.array([random.randint(-9000, 9000) / 100, random.randint(-9000, 9000) / 100])
# perturbed_v = np.array([random.randint(-16000, 16000) / 100, random.randint(-16000, 16000) / 100])
perturbed_v = np.array([random.randint(-8000, 8000) / 100, random.randint(-8000, 8000) / 100])
# perturbed_v = np.array([random.randint(-3500, 3500) / 100, random.randint(-3500, 3500) / 100])
# perturbed_v = np.array([random.randint(-600, 600) / 10, random.randint(-600, 600) / 10])
''''''
if fold_curve == 'fold':
if is_normalizationFun_mixture:
if self.is_perform(0.5, 0.5):
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
else:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), random.randint(1, 2))
else:
if normalizationFun_0_1:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), 2)
else:
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
else:
if is_normalizationFun_mixture:
if self.is_perform(0.5, 0.5):
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
else:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), random.randint(1, 2))
else:
if normalizationFun_0_1:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), 2)
else:
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
''''''
if fold_curve_random:
# omega_perturbed = (alpha_perturbed+0.2) / (perturbed_d + alpha_perturbed)
# omega_perturbed = alpha_perturbed**perturbed_d
omega_perturbed = alpha_perturbed / (perturbed_d + alpha_perturbed)
else:
omega_perturbed = 1 - perturbed_d ** alpha_perturbed
'''shadow'''
if self.is_perform(0.6, 0.4):
synthesis_perturbed_img_map[x_min:x_max, y_min:y_max] = np.minimum(np.maximum(synthesis_perturbed_img_map[x_min:x_max, y_min:y_max] - np.int16(np.round(omega_perturbed[x_min:x_max, y_min:y_max].repeat(3).reshape(x_max-x_min, y_max-y_min, 3) * abs(np.linalg.norm(perturbed_v//2))*np.array([0.4-random.random()*0.1, 0.4-random.random()*0.1, 0.4-random.random()*0.1]))), 0), 255)
''''''
if relativeShift_position in ['position', 'relativeShift_v2']:
self.perturbed_xy_ += np.array([omega_perturbed * perturbed_v[0], omega_perturbed * perturbed_v[1]]).transpose(1, 2, 0)
else:
print('relativeShift_position error')
exit()
'''
flat_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape(
self.new_shape[0] * self.new_shape[1], 2)
vtx, wts = self.interp_weights(self.perturbed_xy_.reshape(self.new_shape[0] * self.new_shape[1], 2), flat_position)
wts_sum = np.abs(wts).sum(-1)
# flat_img.reshape(flat_shape[0] * flat_shape[1], 3)[:] = interpolate(pixel, vtx, wts)
wts = wts[wts_sum <= 1, :]
vtx = vtx[wts_sum <= 1, :]
synthesis_perturbed_img.reshape(self.new_shape[0] * self.new_shape[1], 3)[wts_sum <= 1,
:] = self.interpolate(synthesis_perturbed_img_map.reshape(self.new_shape[0] * self.new_shape[1], 3), vtx, wts)
synthesis_perturbed_label.reshape(self.new_shape[0] * self.new_shape[1], 2)[wts_sum <= 1,
:] = self.interpolate(synthesis_perturbed_label_map.reshape(self.new_shape[0] * self.new_shape[1], 2), vtx, wts)
foreORbackground_label = np.zeros(self.new_shape)
foreORbackground_label.reshape(self.new_shape[0] * self.new_shape[1], 1)[wts_sum <= 1, :] = self.interpolate(foreORbackground_label_map.reshape(self.new_shape[0] * self.new_shape[1], 1), vtx, wts)
foreORbackground_label[foreORbackground_label < 0.99] = 0
foreORbackground_label[foreORbackground_label >= 0.99] = 1
# synthesis_perturbed_img = np.around(synthesis_perturbed_img).astype(np.uint8)
synthesis_perturbed_label[:, :, 0] *= foreORbackground_label
synthesis_perturbed_label[:, :, 1] *= foreORbackground_label
synthesis_perturbed_img[:, :, 0] *= foreORbackground_label
synthesis_perturbed_img[:, :, 1] *= foreORbackground_label
synthesis_perturbed_img[:, :, 2] *= foreORbackground_label
self.synthesis_perturbed_img = synthesis_perturbed_img
self.synthesis_perturbed_label = synthesis_perturbed_label
'''
'''perspective'''
perspective_shreshold = random.randint(26, 36)*10 # 280
x_min_per, y_min_per, x_max_per, y_max_per = self.adjust_position(perspective_shreshold, perspective_shreshold, self.new_shape[0]-perspective_shreshold, self.new_shape[1]-perspective_shreshold)
pts1 = np.float32([[x_min_per, y_min_per], [x_max_per, y_min_per], [x_min_per, y_max_per], [x_max_per, y_max_per]])
e_1_ = x_max_per - x_min_per
e_2_ = y_max_per - y_min_per
e_3_ = e_2_
e_4_ = e_1_
perspective_shreshold_h = e_1_*0.02
perspective_shreshold_w = e_2_*0.02
a_min_, a_max_ = 70, 110
# if self.is_perform(1, 0):
if fold_curve == 'curve' and self.is_perform(0.5, 0.5):
if self.is_perform(0.5, 0.5):
while True:
pts2 = np.around(
np.float32([[x_min_per - (random.random()) * perspective_shreshold, y_min_per + (random.random()) * perspective_shreshold],
[x_max_per - (random.random()) * perspective_shreshold, y_min_per - (random.random()) * perspective_shreshold],
[x_min_per + (random.random()) * perspective_shreshold, y_max_per + (random.random()) * perspective_shreshold],
[x_max_per + (random.random()) * perspective_shreshold, y_max_per - (random.random()) * perspective_shreshold]])) # right
e_1 = np.linalg.norm(pts2[0]-pts2[1])
e_2 = np.linalg.norm(pts2[0]-pts2[2])
e_3 = np.linalg.norm(pts2[1]-pts2[3])
e_4 = np.linalg.norm(pts2[2]-pts2[3])
if e_1_+perspective_shreshold_h > e_1 and e_2_+perspective_shreshold_w > e_2 and e_3_+perspective_shreshold_w > e_3 and e_4_+perspective_shreshold_h > e_4 and \
e_1_ - perspective_shreshold_h < e_1 and e_2_ - perspective_shreshold_w < e_2 and e_3_ - perspective_shreshold_w < e_3 and e_4_ - perspective_shreshold_h < e_4 and \
abs(e_1-e_4) < perspective_shreshold_h and abs(e_2-e_3) < perspective_shreshold_w:
a0_, a1_, a2_, a3_ = self.get_angle_4(pts2)
if (a0_ > a_min_ and a0_ < a_max_) or (a1_ > a_min_ and a1_ < a_max_) or (a2_ > a_min_ and a2_ < a_max_) or (a3_ > a_min_ and a3_ < a_max_):
break
else:
while True:
pts2 = np.around(
np.float32([[x_min_per + (random.random()) * perspective_shreshold, y_min_per - (random.random()) * perspective_shreshold],
[x_max_per + (random.random()) * perspective_shreshold, y_min_per + (random.random()) * perspective_shreshold],
[x_min_per - (random.random()) * perspective_shreshold, y_max_per - (random.random()) * perspective_shreshold],
[x_max_per - (random.random()) * perspective_shreshold, y_max_per + (random.random()) * perspective_shreshold]]))
e_1 = np.linalg.norm(pts2[0]-pts2[1])
e_2 = np.linalg.norm(pts2[0]-pts2[2])
e_3 = np.linalg.norm(pts2[1]-pts2[3])
e_4 = np.linalg.norm(pts2[2]-pts2[3])
if e_1_+perspective_shreshold_h > e_1 and e_2_+perspective_shreshold_w > e_2 and e_3_+perspective_shreshold_w > e_3 and e_4_+perspective_shreshold_h > e_4 and \
e_1_ - perspective_shreshold_h < e_1 and e_2_ - perspective_shreshold_w < e_2 and e_3_ - perspective_shreshold_w < e_3 and e_4_ - perspective_shreshold_h < e_4 and \
abs(e_1-e_4) < perspective_shreshold_h and abs(e_2-e_3) < perspective_shreshold_w:
a0_, a1_, a2_, a3_ = self.get_angle_4(pts2)
if (a0_ > a_min_ and a0_ < a_max_) or (a1_ > a_min_ and a1_ < a_max_) or (a2_ > a_min_ and a2_ < a_max_) or (a3_ > a_min_ and a3_ < a_max_):
break
else:
while True:
pts2 = np.around(np.float32([[x_min_per+(random.random()-0.5)*perspective_shreshold, y_min_per+(random.random()-0.5)*perspective_shreshold],
[x_max_per+(random.random()-0.5)*perspective_shreshold, y_min_per+(random.random()-0.5)*perspective_shreshold],
[x_min_per+(random.random()-0.5)*perspective_shreshold, y_max_per+(random.random()-0.5)*perspective_shreshold],
[x_max_per+(random.random()-0.5)*perspective_shreshold, y_max_per+(random.random()-0.5)*perspective_shreshold]]))
e_1 = np.linalg.norm(pts2[0]-pts2[1])
e_2 = np.linalg.norm(pts2[0]-pts2[2])
e_3 = np.linalg.norm(pts2[1]-pts2[3])
e_4 = | np.linalg.norm(pts2[2]-pts2[3]) | numpy.linalg.norm |
# pylint: disable=protected-access
"""
Test the wrappers for the C API.
"""
import os
from contextlib import contextmanager
import numpy as np
import numpy.testing as npt
import pandas as pd
import pytest
import xarray as xr
from packaging.version import Version
from pygmt import Figure, clib
from pygmt.clib.conversion import dataarray_to_matrix
from pygmt.clib.session import FAMILIES, VIAS
from pygmt.exceptions import (
GMTCLibError,
GMTCLibNoSessionError,
GMTInvalidInput,
GMTVersionError,
)
from pygmt.helpers import GMTTempFile
TEST_DATA_DIR = os.path.join(os.path.dirname(__file__), "data")
with clib.Session() as _lib:
gmt_version = Version(_lib.info["version"])
@contextmanager
def mock(session, func, returns=None, mock_func=None):
"""
Mock a GMT C API function to make it always return a given value.
Used to test that exceptions are raised when API functions fail by
producing a NULL pointer as output or non-zero status codes.
Needed because it's not easy to get some API functions to fail without
inducing a Segmentation Fault (which is a good thing because libgmt usually
only fails with errors).
"""
if mock_func is None:
def mock_api_function(*args): # pylint: disable=unused-argument
"""
A mock GMT API function that always returns a given value.
"""
return returns
mock_func = mock_api_function
get_libgmt_func = session.get_libgmt_func
def mock_get_libgmt_func(name, argtypes=None, restype=None):
"""
Return our mock function.
"""
if name == func:
return mock_func
return get_libgmt_func(name, argtypes, restype)
setattr(session, "get_libgmt_func", mock_get_libgmt_func)
yield
setattr(session, "get_libgmt_func", get_libgmt_func)
def test_getitem():
"""
Test that I can get correct constants from the C lib.
"""
ses = clib.Session()
assert ses["GMT_SESSION_EXTERNAL"] != -99999
assert ses["GMT_MODULE_CMD"] != -99999
assert ses["GMT_PAD_DEFAULT"] != -99999
assert ses["GMT_DOUBLE"] != -99999
with pytest.raises(GMTCLibError):
ses["A_WHOLE_LOT_OF_JUNK"] # pylint: disable=pointless-statement
def test_create_destroy_session():
"""
Test that create and destroy session are called without errors.
"""
# Create two session and make sure they are not pointing to the same memory
session1 = clib.Session()
session1.create(name="test_session1")
assert session1.session_pointer is not None
session2 = clib.Session()
session2.create(name="test_session2")
assert session2.session_pointer is not None
assert session2.session_pointer != session1.session_pointer
session1.destroy()
session2.destroy()
# Create and destroy a session twice
ses = clib.Session()
for __ in range(2):
with pytest.raises(GMTCLibNoSessionError):
ses.session_pointer # pylint: disable=pointless-statement
ses.create("session1")
assert ses.session_pointer is not None
ses.destroy()
with pytest.raises(GMTCLibNoSessionError):
ses.session_pointer # pylint: disable=pointless-statement
def test_create_session_fails():
"""
Check that an exception is raised when failing to create a session.
"""
ses = clib.Session()
with mock(ses, "GMT_Create_Session", returns=None):
with pytest.raises(GMTCLibError):
ses.create("test-session-name")
# Should fail if trying to create a session before destroying the old one.
ses.create("test1")
with pytest.raises(GMTCLibError):
ses.create("test2")
def test_destroy_session_fails():
"""
Fail to destroy session when given bad input.
"""
ses = clib.Session()
with pytest.raises(GMTCLibNoSessionError):
ses.destroy()
ses.create("test-session")
with mock(ses, "GMT_Destroy_Session", returns=1):
with pytest.raises(GMTCLibError):
ses.destroy()
ses.destroy()
def test_call_module():
"""
Run a command to see if call_module works.
"""
data_fname = os.path.join(TEST_DATA_DIR, "points.txt")
out_fname = "test_call_module.txt"
with clib.Session() as lib:
with GMTTempFile() as out_fname:
lib.call_module("info", "{} -C ->{}".format(data_fname, out_fname.name))
assert os.path.exists(out_fname.name)
output = out_fname.read().strip()
assert output == "11.5309 61.7074 -2.9289 7.8648 0.1412 0.9338"
def test_call_module_invalid_arguments():
"""
Fails for invalid module arguments.
"""
with clib.Session() as lib:
with pytest.raises(GMTCLibError):
lib.call_module("info", "bogus-data.bla")
def test_call_module_invalid_name():
"""
Fails when given bad input.
"""
with clib.Session() as lib:
with pytest.raises(GMTCLibError):
lib.call_module("meh", "")
def test_call_module_error_message():
"""
Check is the GMT error message was captured.
"""
with clib.Session() as lib:
try:
lib.call_module("info", "bogus-data.bla")
except GMTCLibError as error:
assert "Module 'info' failed with status code" in str(error)
assert "gmtinfo [ERROR]: Cannot find file bogus-data.bla" in str(error)
def test_method_no_session():
"""
Fails when not in a session.
"""
# Create an instance of Session without "with" so no session is created.
lib = clib.Session()
with pytest.raises(GMTCLibNoSessionError):
lib.call_module("gmtdefaults", "")
with pytest.raises(GMTCLibNoSessionError):
lib.session_pointer # pylint: disable=pointless-statement
def test_parse_constant_single():
"""
Parsing a single family argument correctly.
"""
lib = clib.Session()
for family in FAMILIES:
parsed = lib._parse_constant(family, valid=FAMILIES)
assert parsed == lib[family]
def test_parse_constant_composite():
"""
Parsing a composite constant argument (separated by |) correctly.
"""
lib = clib.Session()
test_cases = ((family, via) for family in FAMILIES for via in VIAS)
for family, via in test_cases:
composite = "|".join([family, via])
expected = lib[family] + lib[via]
parsed = lib._parse_constant(composite, valid=FAMILIES, valid_modifiers=VIAS)
assert parsed == expected
def test_parse_constant_fails():
"""
Check if the function fails when given bad input.
"""
lib = clib.Session()
test_cases = [
"SOME_random_STRING",
"GMT_IS_DATASET|GMT_VIA_MATRIX|GMT_VIA_VECTOR",
"GMT_IS_DATASET|NOT_A_PROPER_VIA",
"NOT_A_PROPER_FAMILY|GMT_VIA_MATRIX",
"NOT_A_PROPER_FAMILY|ALSO_INVALID",
]
for test_case in test_cases:
with pytest.raises(GMTInvalidInput):
lib._parse_constant(test_case, valid=FAMILIES, valid_modifiers=VIAS)
# Should also fail if not given valid modifiers but is using them anyway.
# This should work...
lib._parse_constant(
"GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=VIAS
)
# But this shouldn't.
with pytest.raises(GMTInvalidInput):
lib._parse_constant(
"GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=None
)
def test_create_data_dataset():
"""
Run the function to make sure it doesn't fail badly.
"""
with clib.Session() as lib:
# Dataset from vectors
data_vector = lib.create_data(
family="GMT_IS_DATASET|GMT_VIA_VECTOR",
geometry="GMT_IS_POINT",
mode="GMT_CONTAINER_ONLY",
dim=[10, 20, 1, 0], # columns, rows, layers, dtype
)
# Dataset from matrices
data_matrix = lib.create_data(
family="GMT_IS_DATASET|GMT_VIA_MATRIX",
geometry="GMT_IS_POINT",
mode="GMT_CONTAINER_ONLY",
dim=[10, 20, 1, 0],
)
assert data_vector != data_matrix
def test_create_data_grid_dim():
"""
Create a grid ignoring range and inc.
"""
with clib.Session() as lib:
# Grids from matrices using dim
lib.create_data(
family="GMT_IS_GRID|GMT_VIA_MATRIX",
geometry="GMT_IS_SURFACE",
mode="GMT_CONTAINER_ONLY",
dim=[10, 20, 1, 0],
)
def test_create_data_grid_range():
"""
Create a grid specifying range and inc instead of dim.
"""
with clib.Session() as lib:
# Grids from matrices using range and int
lib.create_data(
family="GMT_IS_GRID|GMT_VIA_MATRIX",
geometry="GMT_IS_SURFACE",
mode="GMT_CONTAINER_ONLY",
ranges=[150.0, 250.0, -20.0, 20.0],
inc=[0.1, 0.2],
)
def test_create_data_fails():
"""
Check that create_data raises exceptions for invalid input and output.
"""
# Passing in invalid mode
with pytest.raises(GMTInvalidInput):
with clib.Session() as lib:
lib.create_data(
family="GMT_IS_DATASET",
geometry="GMT_IS_SURFACE",
mode="Not_a_valid_mode",
dim=[0, 0, 1, 0],
ranges=[150.0, 250.0, -20.0, 20.0],
inc=[0.1, 0.2],
)
# Passing in invalid geometry
with pytest.raises(GMTInvalidInput):
with clib.Session() as lib:
lib.create_data(
family="GMT_IS_GRID",
geometry="Not_a_valid_geometry",
mode="GMT_CONTAINER_ONLY",
dim=[0, 0, 1, 0],
ranges=[150.0, 250.0, -20.0, 20.0],
inc=[0.1, 0.2],
)
# If the data pointer returned is None (NULL pointer)
with pytest.raises(GMTCLibError):
with clib.Session() as lib:
with mock(lib, "GMT_Create_Data", returns=None):
lib.create_data(
family="GMT_IS_DATASET",
geometry="GMT_IS_SURFACE",
mode="GMT_CONTAINER_ONLY",
dim=[11, 10, 2, 0],
)
def test_virtual_file():
"""
Test passing in data via a virtual file with a Dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
shape = (5, 3)
for dtype in dtypes:
with clib.Session() as lib:
family = "GMT_IS_DATASET|GMT_VIA_MATRIX"
geometry = "GMT_IS_POINT"
dataset = lib.create_data(
family=family,
geometry=geometry,
mode="GMT_CONTAINER_ONLY",
dim=[shape[1], shape[0], 1, 0], # columns, rows, layers, dtype
)
data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape)
lib.put_matrix(dataset, matrix=data)
# Add the dataset to a virtual file and pass it along to gmt info
vfargs = (family, geometry, "GMT_IN|GMT_IS_REFERENCE", dataset)
with lib.open_virtual_file(*vfargs) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T]
)
expected = "<matrix memory>: N = {}\t{}\n".format(shape[0], bounds)
assert output == expected
def test_virtual_file_fails():
"""
Check that opening and closing virtual files raises an exception for non-
zero return codes.
"""
vfargs = (
"GMT_IS_DATASET|GMT_VIA_MATRIX",
"GMT_IS_POINT",
"GMT_IN|GMT_IS_REFERENCE",
None,
)
# Mock Open_VirtualFile to test the status check when entering the context.
# If the exception is raised, the code won't get to the closing of the
# virtual file.
with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=1):
with pytest.raises(GMTCLibError):
with lib.open_virtual_file(*vfargs):
print("Should not get to this code")
# Test the status check when closing the virtual file
# Mock the opening to return 0 (success) so that we don't open a file that
# we won't close later.
with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=0), mock(
lib, "GMT_Close_VirtualFile", returns=1
):
with pytest.raises(GMTCLibError):
with lib.open_virtual_file(*vfargs):
pass
print("Shouldn't get to this code either")
def test_virtual_file_bad_direction():
"""
Test passing an invalid direction argument.
"""
with clib.Session() as lib:
vfargs = (
"GMT_IS_DATASET|GMT_VIA_MATRIX",
"GMT_IS_POINT",
"GMT_IS_GRID", # The invalid direction argument
0,
)
with pytest.raises(GMTInvalidInput):
with lib.open_virtual_file(*vfargs):
print("This should have failed")
def test_virtualfile_from_vectors():
"""
Test the automation for transforming vectors to virtual file dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
size = 10
for dtype in dtypes:
x = np.arange(size, dtype=dtype)
y = np.arange(size, size * 2, 1, dtype=dtype)
z = np.arange(size * 2, size * 3, 1, dtype=dtype)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(x, y, z) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(i.min(), i.max()) for i in (x, y, z)]
)
expected = "<vector memory>: N = {}\t{}\n".format(size, bounds)
assert output == expected
@pytest.mark.parametrize("dtype", [str, object])
def test_virtualfile_from_vectors_one_string_or_object_column(dtype):
"""
Test passing in one column with string or object dtype into virtual file
dataset.
"""
size = 5
x = np.arange(size, dtype=np.int32)
y = np.arange(size, size * 2, 1, dtype=np.int32)
strings = np.array(["a", "bc", "defg", "hijklmn", "opqrst"], dtype=dtype)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(x, y, strings) as vfile:
with GMTTempFile() as outfile:
lib.call_module("convert", f"{vfile} ->{outfile.name}")
output = outfile.read(keep_tabs=True)
expected = "".join(f"{i}\t{j}\t{k}\n" for i, j, k in zip(x, y, strings))
assert output == expected
@pytest.mark.parametrize("dtype", [str, object])
def test_virtualfile_from_vectors_two_string_or_object_columns(dtype):
"""
Test passing in two columns of string or object dtype into virtual file
dataset.
"""
size = 5
x = np.arange(size, dtype=np.int32)
y = np.arange(size, size * 2, 1, dtype=np.int32)
strings1 = np.array(["a", "bc", "def", "ghij", "klmno"], dtype=dtype)
strings2 = np.array(["pqrst", "uvwx", "yz!", "@#", "$"], dtype=dtype)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(x, y, strings1, strings2) as vfile:
with GMTTempFile() as outfile:
lib.call_module("convert", f"{vfile} ->{outfile.name}")
output = outfile.read(keep_tabs=True)
expected = "".join(
f"{h}\t{i}\t{j} {k}\n" for h, i, j, k in zip(x, y, strings1, strings2)
)
assert output == expected
def test_virtualfile_from_vectors_transpose():
"""
Test transforming matrix columns to virtual file dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
shape = (7, 5)
for dtype in dtypes:
data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(*data.T) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} -C ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["{:.0f}\t{:.0f}".format(col.min(), col.max()) for col in data.T]
)
expected = "{}\n".format(bounds)
assert output == expected
def test_virtualfile_from_vectors_diff_size():
"""
Test the function fails for arrays of different sizes.
"""
x = np.arange(5)
y = np.arange(6)
with clib.Session() as lib:
with pytest.raises(GMTInvalidInput):
with lib.virtualfile_from_vectors(x, y):
print("This should have failed")
def test_virtualfile_from_matrix():
"""
Test transforming a matrix to virtual file dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
shape = (7, 5)
for dtype in dtypes:
data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape)
with clib.Session() as lib:
with lib.virtualfile_from_matrix(data) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T]
)
expected = "<matrix memory>: N = {}\t{}\n".format(shape[0], bounds)
assert output == expected
def test_virtualfile_from_matrix_slice():
"""
Test transforming a slice of a larger array to virtual file dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
shape = (10, 6)
for dtype in dtypes:
full_data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape)
rows = 5
cols = 3
data = full_data[:rows, :cols]
with clib.Session() as lib:
with lib.virtualfile_from_matrix(data) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T]
)
expected = "<matrix memory>: N = {}\t{}\n".format(rows, bounds)
assert output == expected
def test_virtualfile_from_vectors_pandas():
"""
Pass vectors to a dataset using pandas Series.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
size = 13
for dtype in dtypes:
data = pd.DataFrame(
data=dict(
x=np.arange(size, dtype=dtype),
y=np.arange(size, size * 2, 1, dtype=dtype),
z=np.arange(size * 2, size * 3, 1, dtype=dtype),
)
)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(data.x, data.y, data.z) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
[
"<{:.0f}/{:.0f}>".format(i.min(), i.max())
for i in (data.x, data.y, data.z)
]
)
expected = "<vector memory>: N = {}\t{}\n".format(size, bounds)
assert output == expected
def test_virtualfile_from_vectors_arraylike():
"""
Pass array-like vectors to a dataset.
"""
size = 13
x = list(range(0, size, 1))
y = tuple(range(size, size * 2, 1))
z = range(size * 2, size * 3, 1)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(x, y, z) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(min(i), max(i)) for i in (x, y, z)]
)
expected = "<vector memory>: N = {}\t{}\n".format(size, bounds)
assert output == expected
def test_extract_region_fails():
"""
Check that extract region fails if nothing has been plotted.
"""
Figure()
with pytest.raises(GMTCLibError):
with clib.Session() as lib:
lib.extract_region()
def test_extract_region_two_figures():
"""
Extract region should handle multiple figures existing at the same time.
"""
# Make two figures before calling extract_region to make sure that it's
# getting from the current figure, not the last figure.
fig1 = Figure()
region1 = np.array([0, 10, -20, -10])
fig1.coast(region=region1, projection="M6i", frame=True, land="black")
fig2 = Figure()
fig2.basemap(region="US.HI+r5", projection="M6i", frame=True)
# Activate the first figure and extract the region from it
# Use in a different session to avoid any memory problems.
with clib.Session() as lib:
lib.call_module("figure", "{} -".format(fig1._name))
with clib.Session() as lib:
wesn1 = lib.extract_region()
npt.assert_allclose(wesn1, region1)
# Now try it with the second one
with clib.Session() as lib:
lib.call_module("figure", "{} -".format(fig2._name))
with clib.Session() as lib:
wesn2 = lib.extract_region()
npt.assert_allclose(wesn2, np.array([-165.0, -150.0, 15.0, 25.0]))
def test_write_data_fails():
"""
Check that write data raises an exception for non-zero return codes.
"""
# It's hard to make the C API function fail without causing a Segmentation
# Fault. Can't test this if by giving a bad file name because if
# output=='', GMT will just write to stdout and spaces are valid file
# names. Use a mock instead just to exercise this part of the code.
with clib.Session() as lib:
with mock(lib, "GMT_Write_Data", returns=1):
with pytest.raises(GMTCLibError):
lib.write_data(
"GMT_IS_VECTOR",
"GMT_IS_POINT",
"GMT_WRITE_SET",
[1] * 6,
"some-file-name",
None,
)
def test_dataarray_to_matrix_works():
"""
Check that dataarray_to_matrix returns correct output.
"""
data = np.diag(v=np.arange(3))
x = np.linspace(start=0, stop=4, num=3)
y = np.linspace(start=5, stop=9, num=3)
grid = xr.DataArray(data, coords=[("y", y), ("x", x)])
matrix, region, inc = dataarray_to_matrix(grid)
npt.assert_allclose(actual=matrix, desired=np.flipud(data))
npt.assert_allclose(actual=region, desired=[x.min(), x.max(), y.min(), y.max()])
npt.assert_allclose(actual=inc, desired=[x[1] - x[0], y[1] - y[0]])
def test_dataarray_to_matrix_negative_x_increment():
"""
Check if dataarray_to_matrix returns correct output with flipped x.
"""
data = np.diag(v=np.arange(3))
x = np.linspace(start=4, stop=0, num=3)
y = np.linspace(start=5, stop=9, num=3)
grid = xr.DataArray(data, coords=[("y", y), ("x", x)])
matrix, region, inc = dataarray_to_matrix(grid)
npt.assert_allclose(actual=matrix, desired=np.flip(data, axis=(0, 1)))
npt.assert_allclose(actual=region, desired=[x.min(), x.max(), y.min(), y.max()])
npt.assert_allclose(actual=inc, desired=[abs(x[1] - x[0]), abs(y[1] - y[0])])
def test_dataarray_to_matrix_negative_y_increment():
"""
Check that dataarray_to_matrix returns correct output with flipped y.
"""
data = np.diag(v=np.arange(3))
x = np.linspace(start=0, stop=4, num=3)
y = np.linspace(start=9, stop=5, num=3)
grid = xr.DataArray(data, coords=[("y", y), ("x", x)])
matrix, region, inc = dataarray_to_matrix(grid)
npt.assert_allclose(actual=matrix, desired=data)
npt.assert_allclose(actual=region, desired=[x.min(), x.max(), y.min(), y.max()])
npt.assert_allclose(actual=inc, desired=[abs(x[1] - x[0]), abs(y[1] - y[0])])
def test_dataarray_to_matrix_negative_x_and_y_increment():
"""
Check that dataarray_to_matrix returns correct output with flipped x/y.
"""
data = np.diag(v=np.arange(3))
x = np.linspace(start=4, stop=0, num=3)
y = np.linspace(start=9, stop=5, num=3)
grid = xr.DataArray(data, coords=[("y", y), ("x", x)])
matrix, region, inc = dataarray_to_matrix(grid)
npt.assert_allclose(actual=matrix, desired=np.fliplr(data))
npt.assert_allclose(actual=region, desired=[x.min(), x.max(), y.min(), y.max()])
npt.assert_allclose(actual=inc, desired=[abs(x[1] - x[0]), abs(y[1] - y[0])])
def test_dataarray_to_matrix_dims_fails():
"""
Check that it fails for > 2 dims.
"""
# Make a 3D regular grid
data = np.ones((10, 12, 11), dtype="float32")
x = np.arange(11)
y = np.arange(12)
z = | np.arange(10) | numpy.arange |
import numpy as np
import pytest
import theano
import theano.tensor as tt
# Don't import test classes otherwise they get tested as part of the file
from tests import unittest_tools as utt
from tests.gpuarray.config import mode_with_gpu, mode_without_gpu, test_ctx_name
from tests.tensor.test_basic import (
TestAlloc,
TestComparison,
TestJoinAndSplit,
TestReshape,
)
from tests.tensor.utils import rand, safe_make_node
from theano.gpuarray.basic_ops import (
GpuAlloc,
GpuAllocEmpty,
GpuContiguous,
GpuEye,
GpuFromHost,
GpuJoin,
GpuReshape,
GpuSplit,
GpuToGpu,
GpuTri,
HostFromGpu,
gpu_contiguous,
gpu_join,
host_from_gpu,
)
from theano.gpuarray.elemwise import GpuDimShuffle, GpuElemwise
from theano.gpuarray.subtensor import GpuSubtensor
from theano.gpuarray.type import GpuArrayType, get_context, gpuarray_shared_constructor
from theano.tensor import TensorType
from theano.tensor.basic import alloc
pygpu = pytest.importorskip("pygpu")
gpuarray = pygpu.gpuarray
utt.seed_rng()
rng = np.random.RandomState(seed=utt.fetch_seed())
def inplace_func(
inputs,
outputs,
mode=None,
allow_input_downcast=False,
on_unused_input="raise",
name=None,
):
if mode is None:
mode = mode_with_gpu
return theano.function(
inputs,
outputs,
mode=mode,
allow_input_downcast=allow_input_downcast,
accept_inplace=True,
on_unused_input=on_unused_input,
name=name,
)
def fake_shared(value, name=None, strict=False, allow_downcast=None, **kwargs):
from theano.tensor.sharedvar import scalar_constructor, tensor_constructor
for c in (gpuarray_shared_constructor, tensor_constructor, scalar_constructor):
try:
return c(
value, name=name, strict=strict, allow_downcast=allow_downcast, **kwargs
)
except TypeError:
continue
def rand_gpuarray(*shape, **kwargs):
r = rng.rand(*shape) * 2 - 1
dtype = kwargs.pop("dtype", theano.config.floatX)
cls = kwargs.pop("cls", None)
if len(kwargs) != 0:
raise TypeError("Unexpected argument %s", list(kwargs.keys())[0])
return gpuarray.array(r, dtype=dtype, cls=cls, context=get_context(test_ctx_name))
def makeTester(
name,
op,
gpu_op,
cases,
checks=None,
mode_gpu=mode_with_gpu,
mode_nogpu=mode_without_gpu,
skip=False,
eps=1e-10,
):
if checks is None:
checks = {}
_op = op
_gpu_op = gpu_op
_cases = cases
_skip = skip
_checks = checks
class Checker(utt.OptimizationTestMixin):
op = staticmethod(_op)
gpu_op = staticmethod(_gpu_op)
cases = _cases
skip = _skip
checks = _checks
def setup_method(self):
eval(self.__class__.__module__ + "." + self.__class__.__name__)
def test_all(self):
if skip:
pytest.skip(skip)
for testname, inputs in cases.items():
for _ in range(len(inputs)):
if type(inputs[_]) is float:
inputs[_] = np.asarray(inputs[_], dtype=theano.config.floatX)
self.run_case(testname, inputs)
def run_case(self, testname, inputs):
inputs_ref = [theano.shared(inp) for inp in inputs]
inputs_tst = [theano.shared(inp) for inp in inputs]
try:
node_ref = safe_make_node(self.op, *inputs_ref)
node_tst = safe_make_node(self.op, *inputs_tst)
except Exception as exc:
err_msg = (
"Test %s::%s: Error occurred while making " "a node with inputs %s"
) % (self.gpu_op, testname, inputs)
exc.args += (err_msg,)
raise
try:
f_ref = inplace_func([], node_ref.outputs, mode=mode_nogpu)
f_tst = inplace_func([], node_tst.outputs, mode=mode_gpu)
except Exception as exc:
err_msg = (
"Test %s::%s: Error occurred while trying to " "make a Function"
) % (self.gpu_op, testname)
exc.args += (err_msg,)
raise
self.assertFunctionContains1(f_tst, self.gpu_op)
ref_e = None
try:
expecteds = f_ref()
except Exception as exc:
ref_e = exc
try:
variables = f_tst()
except Exception as exc:
if ref_e is None:
err_msg = (
"Test %s::%s: exception when calling the " "Function"
) % (self.gpu_op, testname)
exc.args += (err_msg,)
raise
else:
# if we raised an exception of the same type we're good.
if isinstance(exc, type(ref_e)):
return
else:
err_msg = (
"Test %s::%s: exception raised during test "
"call was not the same as the reference "
"call (got: %s, expected %s)"
% (self.gpu_op, testname, type(exc), type(ref_e))
)
exc.args += (err_msg,)
raise
for i, (variable, expected) in enumerate(zip(variables, expecteds)):
condition = (
variable.dtype != expected.dtype
or variable.shape != expected.shape
or not TensorType.values_eq_approx(variable, expected)
)
assert not condition, (
"Test %s::%s: Output %s gave the wrong "
"value. With inputs %s, expected %s "
"(dtype %s), got %s (dtype %s)."
% (
self.op,
testname,
i,
inputs,
expected,
expected.dtype,
variable,
variable.dtype,
)
)
for description, check in self.checks.items():
assert check(inputs, variables), (
"Test %s::%s: Failed check: %s " "(inputs were %s, ouputs were %s)"
) % (self.op, testname, description, inputs, variables)
Checker.__name__ = name
if hasattr(Checker, "__qualname__"):
Checker.__qualname__ = name
return Checker
def test_transfer_cpu_gpu():
a = tt.fmatrix("a")
g = GpuArrayType(dtype="float32", broadcastable=(False, False))("g")
av = np.asarray(rng.rand(5, 4), dtype="float32")
gv = gpuarray.array(av, context=get_context(test_ctx_name))
f = theano.function([a], GpuFromHost(test_ctx_name)(a))
fv = f(av)
assert GpuArrayType.values_eq(fv, gv)
f = theano.function([g], host_from_gpu(g))
fv = f(gv)
assert np.all(fv == av)
def test_transfer_gpu_gpu():
g = GpuArrayType(
dtype="float32", broadcastable=(False, False), context_name=test_ctx_name
)()
av = np.asarray(rng.rand(5, 4), dtype="float32")
gv = gpuarray.array(av, context=get_context(test_ctx_name))
mode = mode_with_gpu.excluding(
"cut_gpua_host_transfers", "local_cut_gpua_host_gpua"
)
f = theano.function([g], GpuToGpu(test_ctx_name)(g), mode=mode)
topo = f.maker.fgraph.toposort()
assert len(topo) == 1
assert isinstance(topo[0].op, GpuToGpu)
fv = f(gv)
assert GpuArrayType.values_eq(fv, gv)
def test_transfer_strided():
# This is just to ensure that it works in theano
# libgpuarray has a much more comprehensive suit of tests to
# ensure correctness
a = tt.fmatrix("a")
g = GpuArrayType(dtype="float32", broadcastable=(False, False))("g")
av = np.asarray(rng.rand(5, 8), dtype="float32")
gv = gpuarray.array(av, context=get_context(test_ctx_name))
av = av[:, ::2]
gv = gv[:, ::2]
f = theano.function([a], GpuFromHost(test_ctx_name)(a))
fv = f(av)
assert GpuArrayType.values_eq(fv, gv)
f = theano.function([g], host_from_gpu(g))
fv = f(gv)
assert np.all(fv == av)
def gpu_alloc_expected(x, *shp):
g = gpuarray.empty(shp, dtype=x.dtype, context=get_context(test_ctx_name))
g[:] = x
return g
TestGpuAlloc = makeTester(
name="GpuAllocTester",
# The +1 is there to allow the lift to the GPU.
op=lambda *args: alloc(*args) + 1,
gpu_op=GpuAlloc(test_ctx_name),
cases=dict(
correct01=(rand(), np.int32(7)),
# just gives a DeepCopyOp with possibly wrong results on the CPU
# correct01_bcast=(rand(1), np.int32(7)),
correct02=(rand(), np.int32(4), np.int32(7)),
correct12=(rand(7), np.int32(4), np.int32(7)),
correct13=(rand(7), np.int32(2), np.int32(4), | np.int32(7) | numpy.int32 |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * | np.ones(101) | numpy.ones |
import numpy as np
from scipy import ndimage
def erode_value_blobs(array, steps=1, values_to_ignore=tuple(), new_value=0):
unique_values = list(np.unique(array))
all_entries_to_keep = | np.zeros(shape=array.shape, dtype=np.bool) | numpy.zeros |
import torch
import torchvision
import matplotlib
import matplotlib.pyplot as plt
from PIL import Image
from captum.attr import GuidedGradCam, GuidedBackprop
from captum.attr import LayerActivation, LayerConductance, LayerGradCam
from data_utils import *
from image_utils import *
from captum_utils import *
import numpy as np
from visualizers import GradCam
plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'
X, y, class_names = load_imagenet_val(num=5)
# FOR THIS SECTION ONLY, we need to use gradients. We introduce a new model we will use explicitly for GradCAM for this.
gc_model = torchvision.models.squeezenet1_1(pretrained=True)
gc = GradCam()
X_tensor = torch.cat([preprocess(Image.fromarray(x)) for x in X], dim=0).requires_grad_(True)
y_tensor = torch.LongTensor(y)
# Guided Back-Propagation
gbp_result = gc.guided_backprop(X_tensor,y_tensor, gc_model)
plt.figure(figsize=(24, 24))
for i in range(gbp_result.shape[0]):
plt.subplot(1, 5, i + 1)
img = gbp_result[i]
img = rescale(img)
plt.imshow(img)
plt.title(class_names[y[i]])
plt.axis('off')
plt.gcf().tight_layout()
plt.savefig('visualization/guided_backprop.png')
# GradCam
# GradCAM. We have given you which module(=layer) that we need to capture gradients from, which you can see in conv_module variable below
gc_model = torchvision.models.squeezenet1_1(pretrained=True)
for param in gc_model.parameters():
param.requires_grad = True
X_tensor = torch.cat([preprocess(Image.fromarray(x)) for x in X], dim=0).requires_grad_(True)
y_tensor = torch.LongTensor(y)
gradcam_result = gc.grad_cam(X_tensor, y_tensor, gc_model)
plt.figure(figsize=(24, 24))
for i in range(gradcam_result.shape[0]):
gradcam_val = gradcam_result[i]
img = X[i] + (matplotlib.cm.jet(gradcam_val)[:,:,:3]*255)
img = img / np.max(img)
plt.subplot(1, 5, i + 1)
plt.imshow(img)
plt.title(class_names[y[i]])
plt.axis('off')
plt.gcf().tight_layout()
plt.savefig('visualization/gradcam.png')
# As a final step, we can combine GradCam and Guided Backprop to get Guided GradCam.
X_tensor = torch.cat([preprocess(Image.fromarray(x)) for x in X], dim=0).requires_grad_(True)
y_tensor = torch.LongTensor(y)
gradcam_result = gc.grad_cam(X_tensor, y_tensor, gc_model)
gbp_result = gc.guided_backprop(X_tensor, y_tensor, gc_model)
plt.figure(figsize=(24, 24))
for i in range(gradcam_result.shape[0]):
gbp_val = gbp_result[i]
gradcam_val = | np.expand_dims(gradcam_result[i], axis=2) | numpy.expand_dims |
import argparse
import json
import numpy as np
import pandas as pd
import os
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report,f1_score
from keras.models import Sequential
from keras.layers import Dense, Dropout
from keras import backend as K
from keras.utils.vis_utils import plot_model
from sklearn.externals import joblib
import time
def f1(y_true, y_pred):
def recall(y_true, y_pred):
"""Recall metric.
Only computes a batch-wise average of recall.
Computes the recall, a metric for multi-label classification of
how many relevant items are selected.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
possible_positives = K.sum(K.round(K.clip(y_true, 0, 1)))
recall = true_positives / (possible_positives + K.epsilon())
return recall
def precision(y_true, y_pred):
"""Precision metric.
Only computes a batch-wise average of precision.
Computes the precision, a metric for multi-label classification of
how many selected items are relevant.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
predicted_positives = K.sum(K.round(K.clip(y_pred, 0, 1)))
precision = true_positives / (predicted_positives + K.epsilon())
return precision
precision = precision(y_true, y_pred)
recall = recall(y_true, y_pred)
return 2*((precision*recall)/(precision+recall+K.epsilon()))
def get_embeddings(sentences_list,layer_json):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:return: Dictionary with key each sentence of the sentences_list and as value the embedding
'''
sentences = dict()#dict with key the index of each line of the sentences_list.txt and as value the sentence
embeddings = dict()##dict with key the index of each sentence and as value the its embedding
sentence_emb = dict()#key:sentence,value:its embedding
with open(sentences_list,'r') as file:
for index,line in enumerate(file):
sentences[index] = line.strip()
with open(layer_json, 'r',encoding='utf-8') as f:
for line in f:
embeddings[json.loads(line)['linex_index']] = np.asarray(json.loads(line)['features'])
for key,value in sentences.items():
sentence_emb[value] = embeddings[key]
return sentence_emb
def train_classifier(sentences_list,layer_json,dataset_csv,filename):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:param dataset_csv: the path of the dataset
:param filename: The path of the pickle file that the model will be stored
:return:
'''
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list,layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = np.asarray(previous_emb)
print(previous_emb.shape)
section_emb = np.asarray(section_list)
print(sentence_emb.shape)
length = np.asarray(length)
print(length.shape)
label = np.asarray(label)
print(errors)
features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1)
features = np.column_stack([features, length]) # np.append(features,length,axis=1)
print(features.shape)
X_train, X_val, y_train, y_val = train_test_split(features, label, test_size=0.33, random_state=42)
log = LogisticRegression(random_state=0, solver='newton-cg', max_iter=1000, C=0.1)
log.fit(X_train, y_train)
#save the model
_ = joblib.dump(log, filename, compress=9)
predictions = log.predict(X_val)
print("###########################################")
print("Results using embeddings from the",layer_json,"file")
print(classification_report(y_val, predictions))
print("F1 score using Logistic Regression:",f1_score(y_val, predictions))
print("###########################################")
#train a DNN
f1_results = list()
for i in range(3):
model = Sequential()
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dense(128, activation='relu', trainable=True))
model.add(Dropout(0.30))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.25))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.35))
model.add(Dense(1, activation='sigmoid'))
# compile network
model.compile(loss='binary_crossentropy', optimizer='sgd', metrics=[f1])
# fit network
model.fit(X_train, y_train, epochs=100, batch_size=64)
loss, f_1 = model.evaluate(X_val, y_val, verbose=1)
print('\nTest F1: %f' % (f_1 * 100))
f1_results.append(f_1)
model = None
print("###########################################")
print("Results using embeddings from the", layer_json, "file")
# evaluate
print(np.mean(f1_results))
print("###########################################")
def parameter_tuning_LR(sentences_list,layer_json,dataset_csv):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:param dataset_csv: the path of the dataset
:return:
'''
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list,layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = np.asarray(previous_emb)
print(previous_emb.shape)
section_emb = np.asarray(section_list)
print(sentence_emb.shape)
length = np.asarray(length)
print(length.shape)
label = np.asarray(label)
print(errors)
features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1)
features = np.column_stack([features, length])
print(features.shape)
X_train, X_val, y_train, y_val = train_test_split(features, label, test_size=0.33, random_state=42)
C = [0.1,1,2,5,10]
solver = ['newton-cg','saga','sag']
best_params = dict()
best_score = 0.0
for c in C:
for s in solver:
start = time.time()
log = LogisticRegression(random_state=0, solver=s, max_iter=1000, C=c)
log.fit(X_train, y_train)
predictions = log.predict(X_val)
print("###########################################")
print("LR with C =",c,'and solver = ',s)
print("Results using embeddings from the", layer_json, "file")
print(classification_report(y_val, predictions))
f1 = f1_score(y_val, predictions)
if f1 > best_score:
best_score = f1
best_params['c'] = c
best_params['solver'] = s
print("F1 score using Logistic Regression:",f1)
print("###########################################")
end = time.time()
running_time = end - start
print("Running time:"+str(running_time))
def visualize_DNN(file_to_save):
'''
Save the DNN architecture to a png file. Better use the Visulize_DNN.ipynd
:param file_to_save: the png file that the architecture of the DNN will be saved.
:return: None
'''
model = Sequential()
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dense(128, activation='relu', trainable=True))
model.add(Dropout(0.30))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.25))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.35))
model.add(Dense(1, activation='sigmoid'))
plot_model(model, to_file=file_to_save, show_shapes=True)
def save_model(sentences_list,layer_json,dataset_csv,pkl):
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list, layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append( | np.zeros(768) | numpy.zeros |
"""Test the search module"""
from collections.abc import Iterable, Sized
from io import StringIO
from itertools import chain, product
from functools import partial
import pickle
import sys
from types import GeneratorType
import re
import numpy as np
import scipy.sparse as sp
import pytest
from sklearn.utils.fixes import sp_version
from sklearn.utils._testing import assert_raises
from sklearn.utils._testing import assert_warns
from sklearn.utils._testing import assert_warns_message
from sklearn.utils._testing import assert_raise_message
from sklearn.utils._testing import assert_array_equal
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.utils._testing import assert_allclose
from sklearn.utils._testing import assert_almost_equal
from sklearn.utils._testing import ignore_warnings
from sklearn.utils._mocking import CheckingClassifier, MockDataFrame
from scipy.stats import bernoulli, expon, uniform
from sklearn.base import BaseEstimator, ClassifierMixin
from sklearn.base import clone
from sklearn.exceptions import NotFittedError
from sklearn.datasets import make_classification
from sklearn.datasets import make_blobs
from sklearn.datasets import make_multilabel_classification
from sklearn.model_selection import fit_grid_point
from sklearn.model_selection import train_test_split
from sklearn.model_selection import KFold
from sklearn.model_selection import StratifiedKFold
from sklearn.model_selection import StratifiedShuffleSplit
from sklearn.model_selection import LeaveOneGroupOut
from sklearn.model_selection import LeavePGroupsOut
from sklearn.model_selection import GroupKFold
from sklearn.model_selection import GroupShuffleSplit
from sklearn.model_selection import GridSearchCV
from sklearn.model_selection import RandomizedSearchCV
from sklearn.model_selection import ParameterGrid
from sklearn.model_selection import ParameterSampler
from sklearn.model_selection._search import BaseSearchCV
from sklearn.model_selection._validation import FitFailedWarning
from sklearn.svm import LinearSVC, SVC
from sklearn.tree import DecisionTreeRegressor
from sklearn.tree import DecisionTreeClassifier
from sklearn.cluster import KMeans
from sklearn.neighbors import KernelDensity
from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import f1_score
from sklearn.metrics import recall_score
from sklearn.metrics import accuracy_score
from sklearn.metrics import make_scorer
from sklearn.metrics import roc_auc_score
from sklearn.metrics.pairwise import euclidean_distances
from sklearn.impute import SimpleImputer
from sklearn.pipeline import Pipeline
from sklearn.linear_model import Ridge, SGDClassifier, LinearRegression
from sklearn.experimental import enable_hist_gradient_boosting # noqa
from sklearn.ensemble import HistGradientBoostingClassifier
from sklearn.model_selection.tests.common import OneTimeSplitter
# Neither of the following two estimators inherit from BaseEstimator,
# to test hyperparameter search on user-defined classifiers.
class MockClassifier:
"""Dummy classifier to test the parameter search algorithms"""
def __init__(self, foo_param=0):
self.foo_param = foo_param
def fit(self, X, Y):
assert len(X) == len(Y)
self.classes_ = np.unique(Y)
return self
def predict(self, T):
return T.shape[0]
def transform(self, X):
return X + self.foo_param
def inverse_transform(self, X):
return X - self.foo_param
predict_proba = predict
predict_log_proba = predict
decision_function = predict
def score(self, X=None, Y=None):
if self.foo_param > 1:
score = 1.
else:
score = 0.
return score
def get_params(self, deep=False):
return {'foo_param': self.foo_param}
def set_params(self, **params):
self.foo_param = params['foo_param']
return self
class LinearSVCNoScore(LinearSVC):
"""An LinearSVC classifier that has no score method."""
@property
def score(self):
raise AttributeError
X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
y = np.array([1, 1, 2, 2])
def assert_grid_iter_equals_getitem(grid):
assert list(grid) == [grid[i] for i in range(len(grid))]
@pytest.mark.parametrize("klass", [ParameterGrid,
partial(ParameterSampler, n_iter=10)])
@pytest.mark.parametrize(
"input, error_type, error_message",
[(0, TypeError, r'Parameter .* is not a dict or a list \(0\)'),
([{'foo': [0]}, 0], TypeError, r'Parameter .* is not a dict \(0\)'),
({'foo': 0}, TypeError, "Parameter.* value is not iterable .*"
r"\(key='foo', value=0\)")]
)
def test_validate_parameter_input(klass, input, error_type, error_message):
with pytest.raises(error_type, match=error_message):
klass(input)
def test_parameter_grid():
# Test basic properties of ParameterGrid.
params1 = {"foo": [1, 2, 3]}
grid1 = ParameterGrid(params1)
assert isinstance(grid1, Iterable)
assert isinstance(grid1, Sized)
assert len(grid1) == 3
assert_grid_iter_equals_getitem(grid1)
params2 = {"foo": [4, 2],
"bar": ["ham", "spam", "eggs"]}
grid2 = ParameterGrid(params2)
assert len(grid2) == 6
# loop to assert we can iterate over the grid multiple times
for i in range(2):
# tuple + chain transforms {"a": 1, "b": 2} to ("a", 1, "b", 2)
points = set(tuple(chain(*(sorted(p.items())))) for p in grid2)
assert (points ==
set(("bar", x, "foo", y)
for x, y in product(params2["bar"], params2["foo"])))
assert_grid_iter_equals_getitem(grid2)
# Special case: empty grid (useful to get default estimator settings)
empty = ParameterGrid({})
assert len(empty) == 1
assert list(empty) == [{}]
assert_grid_iter_equals_getitem(empty)
assert_raises(IndexError, lambda: empty[1])
has_empty = ParameterGrid([{'C': [1, 10]}, {}, {'C': [.5]}])
assert len(has_empty) == 4
assert list(has_empty) == [{'C': 1}, {'C': 10}, {}, {'C': .5}]
assert_grid_iter_equals_getitem(has_empty)
def test_grid_search():
# Test that the best estimator contains the right value for foo_param
clf = MockClassifier()
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=3, verbose=3)
# make sure it selects the smallest parameter in case of ties
old_stdout = sys.stdout
sys.stdout = StringIO()
grid_search.fit(X, y)
sys.stdout = old_stdout
assert grid_search.best_estimator_.foo_param == 2
assert_array_equal(grid_search.cv_results_["param_foo_param"].data,
[1, 2, 3])
# Smoke test the score etc:
grid_search.score(X, y)
grid_search.predict_proba(X)
grid_search.decision_function(X)
grid_search.transform(X)
# Test exception handling on scoring
grid_search.scoring = 'sklearn'
assert_raises(ValueError, grid_search.fit, X, y)
def test_grid_search_pipeline_steps():
# check that parameters that are estimators are cloned before fitting
pipe = Pipeline([('regressor', LinearRegression())])
param_grid = {'regressor': [LinearRegression(), Ridge()]}
grid_search = GridSearchCV(pipe, param_grid, cv=2)
grid_search.fit(X, y)
regressor_results = grid_search.cv_results_['param_regressor']
assert isinstance(regressor_results[0], LinearRegression)
assert isinstance(regressor_results[1], Ridge)
assert not hasattr(regressor_results[0], 'coef_')
assert not hasattr(regressor_results[1], 'coef_')
assert regressor_results[0] is not grid_search.best_estimator_
assert regressor_results[1] is not grid_search.best_estimator_
# check that we didn't modify the parameter grid that was passed
assert not hasattr(param_grid['regressor'][0], 'coef_')
assert not hasattr(param_grid['regressor'][1], 'coef_')
@pytest.mark.parametrize("SearchCV", [GridSearchCV, RandomizedSearchCV])
def test_SearchCV_with_fit_params(SearchCV):
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
clf = CheckingClassifier(expected_fit_params=['spam', 'eggs'])
searcher = SearchCV(
clf, {'foo_param': [1, 2, 3]}, cv=2, error_score="raise"
)
# The CheckingClassifier generates an assertion error if
# a parameter is missing or has length != len(X).
err_msg = r"Expected fit parameter\(s\) \['eggs'\] not seen."
with pytest.raises(AssertionError, match=err_msg):
searcher.fit(X, y, spam=np.ones(10))
err_msg = "Fit parameter spam has length 1; expected"
with pytest.raises(AssertionError, match=err_msg):
searcher.fit(X, y, spam=np.ones(1), eggs=np.zeros(10))
searcher.fit(X, y, spam=np.ones(10), eggs=np.zeros(10))
@ignore_warnings
def test_grid_search_no_score():
# Test grid-search on classifier that has no score function.
clf = LinearSVC(random_state=0)
X, y = make_blobs(random_state=0, centers=2)
Cs = [.1, 1, 10]
clf_no_score = LinearSVCNoScore(random_state=0)
grid_search = GridSearchCV(clf, {'C': Cs}, scoring='accuracy')
grid_search.fit(X, y)
grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs},
scoring='accuracy')
# smoketest grid search
grid_search_no_score.fit(X, y)
# check that best params are equal
assert grid_search_no_score.best_params_ == grid_search.best_params_
# check that we can call score and that it gives the correct result
assert grid_search.score(X, y) == grid_search_no_score.score(X, y)
# giving no scoring function raises an error
grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs})
assert_raise_message(TypeError, "no scoring", grid_search_no_score.fit,
[[1]])
def test_grid_search_score_method():
X, y = make_classification(n_samples=100, n_classes=2, flip_y=.2,
random_state=0)
clf = LinearSVC(random_state=0)
grid = {'C': [.1]}
search_no_scoring = GridSearchCV(clf, grid, scoring=None).fit(X, y)
search_accuracy = GridSearchCV(clf, grid, scoring='accuracy').fit(X, y)
search_no_score_method_auc = GridSearchCV(LinearSVCNoScore(), grid,
scoring='roc_auc'
).fit(X, y)
search_auc = GridSearchCV(clf, grid, scoring='roc_auc').fit(X, y)
# Check warning only occurs in situation where behavior changed:
# estimator requires score method to compete with scoring parameter
score_no_scoring = search_no_scoring.score(X, y)
score_accuracy = search_accuracy.score(X, y)
score_no_score_auc = search_no_score_method_auc.score(X, y)
score_auc = search_auc.score(X, y)
# ensure the test is sane
assert score_auc < 1.0
assert score_accuracy < 1.0
assert score_auc != score_accuracy
assert_almost_equal(score_accuracy, score_no_scoring)
assert_almost_equal(score_auc, score_no_score_auc)
def test_grid_search_groups():
# Check if ValueError (when groups is None) propagates to GridSearchCV
# And also check if groups is correctly passed to the cv object
rng = np.random.RandomState(0)
X, y = make_classification(n_samples=15, n_classes=2, random_state=0)
groups = rng.randint(0, 3, 15)
clf = LinearSVC(random_state=0)
grid = {'C': [1]}
group_cvs = [LeaveOneGroupOut(), LeavePGroupsOut(2),
GroupKFold(n_splits=3), GroupShuffleSplit()]
for cv in group_cvs:
gs = GridSearchCV(clf, grid, cv=cv)
assert_raise_message(ValueError,
"The 'groups' parameter should not be None.",
gs.fit, X, y)
gs.fit(X, y, groups=groups)
non_group_cvs = [StratifiedKFold(), StratifiedShuffleSplit()]
for cv in non_group_cvs:
gs = GridSearchCV(clf, grid, cv=cv)
# Should not raise an error
gs.fit(X, y)
def test_classes__property():
# Test that classes_ property matches best_estimator_.classes_
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
Cs = [.1, 1, 10]
grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs})
grid_search.fit(X, y)
assert_array_equal(grid_search.best_estimator_.classes_,
grid_search.classes_)
# Test that regressors do not have a classes_ attribute
grid_search = GridSearchCV(Ridge(), {'alpha': [1.0, 2.0]})
grid_search.fit(X, y)
assert not hasattr(grid_search, 'classes_')
# Test that the grid searcher has no classes_ attribute before it's fit
grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs})
assert not hasattr(grid_search, 'classes_')
# Test that the grid searcher has no classes_ attribute without a refit
grid_search = GridSearchCV(LinearSVC(random_state=0),
{'C': Cs}, refit=False)
grid_search.fit(X, y)
assert not hasattr(grid_search, 'classes_')
def test_trivial_cv_results_attr():
# Test search over a "grid" with only one point.
clf = MockClassifier()
grid_search = GridSearchCV(clf, {'foo_param': [1]}, cv=3)
grid_search.fit(X, y)
assert hasattr(grid_search, "cv_results_")
random_search = RandomizedSearchCV(clf, {'foo_param': [0]}, n_iter=1, cv=3)
random_search.fit(X, y)
assert hasattr(grid_search, "cv_results_")
def test_no_refit():
# Test that GSCV can be used for model selection alone without refitting
clf = MockClassifier()
for scoring in [None, ['accuracy', 'precision']]:
grid_search = GridSearchCV(
clf, {'foo_param': [1, 2, 3]}, refit=False, cv=3
)
grid_search.fit(X, y)
assert not hasattr(grid_search, "best_estimator_") and \
hasattr(grid_search, "best_index_") and \
hasattr(grid_search, "best_params_")
# Make sure the functions predict/transform etc raise meaningful
# error messages
for fn_name in ('predict', 'predict_proba', 'predict_log_proba',
'transform', 'inverse_transform'):
assert_raise_message(NotFittedError,
('refit=False. %s is available only after '
'refitting on the best parameters'
% fn_name), getattr(grid_search, fn_name), X)
# Test that an invalid refit param raises appropriate error messages
for refit in ["", 5, True, 'recall', 'accuracy']:
assert_raise_message(ValueError, "For multi-metric scoring, the "
"parameter refit must be set to a scorer key",
GridSearchCV(clf, {}, refit=refit,
scoring={'acc': 'accuracy',
'prec': 'precision'}
).fit,
X, y)
def test_grid_search_error():
# Test that grid search will capture errors on data with different length
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
assert_raises(ValueError, cv.fit, X_[:180], y_)
def test_grid_search_one_grid_point():
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
param_dict = {"C": [1.0], "kernel": ["rbf"], "gamma": [0.1]}
clf = SVC(gamma='auto')
cv = GridSearchCV(clf, param_dict)
cv.fit(X_, y_)
clf = SVC(C=1.0, kernel="rbf", gamma=0.1)
clf.fit(X_, y_)
assert_array_equal(clf.dual_coef_, cv.best_estimator_.dual_coef_)
def test_grid_search_when_param_grid_includes_range():
# Test that the best estimator contains the right value for foo_param
clf = MockClassifier()
grid_search = None
grid_search = GridSearchCV(clf, {'foo_param': range(1, 4)}, cv=3)
grid_search.fit(X, y)
assert grid_search.best_estimator_.foo_param == 2
def test_grid_search_bad_param_grid():
param_dict = {"C": 1}
clf = SVC(gamma='auto')
assert_raise_message(
ValueError,
"Parameter grid for parameter (C) needs to"
" be a list or numpy array, but got (<class 'int'>)."
" Single values need to be wrapped in a list"
" with one element.",
GridSearchCV, clf, param_dict)
param_dict = {"C": []}
clf = SVC()
assert_raise_message(
ValueError,
"Parameter values for parameter (C) need to be a non-empty sequence.",
GridSearchCV, clf, param_dict)
param_dict = {"C": "1,2,3"}
clf = SVC(gamma='auto')
assert_raise_message(
ValueError,
"Parameter grid for parameter (C) needs to"
" be a list or numpy array, but got (<class 'str'>)."
" Single values need to be wrapped in a list"
" with one element.",
GridSearchCV, clf, param_dict)
param_dict = {"C": np.ones((3, 2))}
clf = SVC()
assert_raises(ValueError, GridSearchCV, clf, param_dict)
def test_grid_search_sparse():
# Test that grid search works with both dense and sparse matrices
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(X_[:180], y_[:180])
y_pred = cv.predict(X_[180:])
C = cv.best_estimator_.C
X_ = sp.csr_matrix(X_)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(X_[:180].tocoo(), y_[:180])
y_pred2 = cv.predict(X_[180:])
C2 = cv.best_estimator_.C
assert np.mean(y_pred == y_pred2) >= .9
assert C == C2
def test_grid_search_sparse_scoring():
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1")
cv.fit(X_[:180], y_[:180])
y_pred = cv.predict(X_[180:])
C = cv.best_estimator_.C
X_ = sp.csr_matrix(X_)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1")
cv.fit(X_[:180], y_[:180])
y_pred2 = cv.predict(X_[180:])
C2 = cv.best_estimator_.C
assert_array_equal(y_pred, y_pred2)
assert C == C2
# Smoke test the score
# np.testing.assert_allclose(f1_score(cv.predict(X_[:180]), y[:180]),
# cv.score(X_[:180], y[:180]))
# test loss where greater is worse
def f1_loss(y_true_, y_pred_):
return -f1_score(y_true_, y_pred_)
F1Loss = make_scorer(f1_loss, greater_is_better=False)
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring=F1Loss)
cv.fit(X_[:180], y_[:180])
y_pred3 = cv.predict(X_[180:])
C3 = cv.best_estimator_.C
assert C == C3
assert_array_equal(y_pred, y_pred3)
def test_grid_search_precomputed_kernel():
# Test that grid search works when the input features are given in the
# form of a precomputed kernel matrix
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
# compute the training kernel matrix corresponding to the linear kernel
K_train = np.dot(X_[:180], X_[:180].T)
y_train = y_[:180]
clf = SVC(kernel='precomputed')
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(K_train, y_train)
assert cv.best_score_ >= 0
# compute the test kernel matrix
K_test = np.dot(X_[180:], X_[:180].T)
y_test = y_[180:]
y_pred = cv.predict(K_test)
assert np.mean(y_pred == y_test) >= 0
# test error is raised when the precomputed kernel is not array-like
# or sparse
assert_raises(ValueError, cv.fit, K_train.tolist(), y_train)
def test_grid_search_precomputed_kernel_error_nonsquare():
# Test that grid search returns an error with a non-square precomputed
# training kernel matrix
K_train = np.zeros((10, 20))
y_train = np.ones((10, ))
clf = SVC(kernel='precomputed')
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
assert_raises(ValueError, cv.fit, K_train, y_train)
class BrokenClassifier(BaseEstimator):
"""Broken classifier that cannot be fit twice"""
def __init__(self, parameter=None):
self.parameter = parameter
def fit(self, X, y):
assert not hasattr(self, 'has_been_fit_')
self.has_been_fit_ = True
def predict(self, X):
return np.zeros(X.shape[0])
@ignore_warnings
def test_refit():
# Regression test for bug in refitting
# Simulates re-fitting a broken estimator; this used to break with
# sparse SVMs.
X = np.arange(100).reshape(10, 10)
y = | np.array([0] * 5 + [1] * 5) | numpy.array |
'''
<NAME>
set up :2020-1-9
intergrate img and label into one file
-- fiducial1024_v1
'''
import argparse
import sys, os
import pickle
import random
import collections
import json
import numpy as np
import scipy.io as io
import scipy.misc as m
import matplotlib.pyplot as plt
import glob
import math
import time
import threading
import multiprocessing as mp
from multiprocessing import Pool
import re
import cv2
# sys.path.append('/lustre/home/gwxie/hope/project/dewarp/datasets/') # /lustre/home/gwxie/program/project/unwarp/perturbed_imgaes/GAN
import utils
def getDatasets(dir):
return os.listdir(dir)
class perturbed(utils.BasePerturbed):
def __init__(self, path, bg_path, save_path, save_suffix):
self.path = path
self.bg_path = bg_path
self.save_path = save_path
self.save_suffix = save_suffix
def save_img(self, m, n, fold_curve='fold', repeat_time=4, fiducial_points = 16, relativeShift_position='relativeShift_v2'):
origin_img = cv2.imread(self.path, flags=cv2.IMREAD_COLOR)
save_img_shape = [512*2, 480*2] # 320
# reduce_value = np.random.choice([2**4, 2**5, 2**6, 2**7, 2**8], p=[0.01, 0.1, 0.4, 0.39, 0.1])
reduce_value = np.random.choice([2*2, 4*2, 8*2, 16*2, 24*2, 32*2, 40*2, 48*2], p=[0.02, 0.18, 0.2, 0.3, 0.1, 0.1, 0.08, 0.02])
# reduce_value = np.random.choice([8*2, 16*2, 24*2, 32*2, 40*2, 48*2], p=[0.01, 0.02, 0.2, 0.4, 0.19, 0.18])
# reduce_value = np.random.choice([16, 24, 32, 40, 48, 64], p=[0.01, 0.1, 0.2, 0.4, 0.2, 0.09])
base_img_shrink = save_img_shape[0] - reduce_value
# enlarge_img_shrink = [1024, 768]
# enlarge_img_shrink = [896, 672] # 420
enlarge_img_shrink = [512*4, 480*4] # 420
# enlarge_img_shrink = [896*2, 768*2] # 420
# enlarge_img_shrink = [896, 768] # 420
# enlarge_img_shrink = [768, 576] # 420
# enlarge_img_shrink = [640, 480] # 420
''''''
im_lr = origin_img.shape[0]
im_ud = origin_img.shape[1]
reduce_value_v2 = np.random.choice([2*2, 4*2, 8*2, 16*2, 24*2, 28*2, 32*2, 48*2], p=[0.02, 0.18, 0.2, 0.2, 0.1, 0.1, 0.1, 0.1])
# reduce_value_v2 = np.random.choice([16, 24, 28, 32, 48, 64], p=[0.01, 0.1, 0.2, 0.3, 0.25, 0.14])
if im_lr > im_ud:
im_ud = min(int(im_ud / im_lr * base_img_shrink), save_img_shape[1] - reduce_value_v2)
im_lr = save_img_shape[0] - reduce_value
else:
base_img_shrink = save_img_shape[1] - reduce_value
im_lr = min(int(im_lr / im_ud * base_img_shrink), save_img_shape[0] - reduce_value_v2)
im_ud = base_img_shrink
if round(im_lr / im_ud, 2) < 0.5 or round(im_ud / im_lr, 2) < 0.5:
repeat_time = min(repeat_time, 8)
edge_padding = 3
im_lr -= im_lr % (fiducial_points-1) - (2*edge_padding) # im_lr % (fiducial_points-1) - 1
im_ud -= im_ud % (fiducial_points-1) - (2*edge_padding) # im_ud % (fiducial_points-1) - 1
im_hight = np.linspace(edge_padding, im_lr - edge_padding, fiducial_points, dtype=np.int64)
im_wide = np.linspace(edge_padding, im_ud - edge_padding, fiducial_points, dtype=np.int64)
# im_lr -= im_lr % (fiducial_points-1) - (1+2*edge_padding) # im_lr % (fiducial_points-1) - 1
# im_ud -= im_ud % (fiducial_points-1) - (1+2*edge_padding) # im_ud % (fiducial_points-1) - 1
# im_hight = np.linspace(edge_padding, im_lr - (1+edge_padding), fiducial_points, dtype=np.int64)
# im_wide = np.linspace(edge_padding, im_ud - (1+edge_padding), fiducial_points, dtype=np.int64)
im_x, im_y = np.meshgrid(im_hight, im_wide)
segment_x = (im_lr) // (fiducial_points-1)
segment_y = (im_ud) // (fiducial_points-1)
# plt.plot(im_x, im_y,
# color='limegreen',
# marker='.',
# linestyle='')
# plt.grid(True)
# plt.show()
self.origin_img = cv2.resize(origin_img, (im_ud, im_lr), interpolation=cv2.INTER_CUBIC)
perturbed_bg_ = getDatasets(self.bg_path)
perturbed_bg_img_ = self.bg_path+random.choice(perturbed_bg_)
perturbed_bg_img = cv2.imread(perturbed_bg_img_, flags=cv2.IMREAD_COLOR)
mesh_shape = self.origin_img.shape[:2]
self.synthesis_perturbed_img = np.full((enlarge_img_shrink[0], enlarge_img_shrink[1], 3), 256, dtype=np.float32)#np.zeros_like(perturbed_bg_img)
# self.synthesis_perturbed_img = np.full((enlarge_img_shrink[0], enlarge_img_shrink[1], 3), 0, dtype=np.int16)#np.zeros_like(perturbed_bg_img)
self.new_shape = self.synthesis_perturbed_img.shape[:2]
perturbed_bg_img = cv2.resize(perturbed_bg_img, (save_img_shape[1], save_img_shape[0]), cv2.INPAINT_TELEA)
origin_pixel_position = np.argwhere(np.zeros(mesh_shape, dtype=np.uint32) == 0).reshape(mesh_shape[0], mesh_shape[1], 2)
pixel_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape(self.new_shape[0], self.new_shape[1], 2)
self.perturbed_xy_ = np.zeros((self.new_shape[0], self.new_shape[1], 2))
# self.perturbed_xy_ = pixel_position.copy().astype(np.float32)
# fiducial_points_grid = origin_pixel_position[im_x, im_y]
self.synthesis_perturbed_label = np.zeros((self.new_shape[0], self.new_shape[1], 2))
x_min, y_min, x_max, y_max = self.adjust_position_v2(0, 0, mesh_shape[0], mesh_shape[1], save_img_shape)
origin_pixel_position += [x_min, y_min]
x_min, y_min, x_max, y_max = self.adjust_position(0, 0, mesh_shape[0], mesh_shape[1])
x_shift = random.randint(-enlarge_img_shrink[0]//16, enlarge_img_shrink[0]//16)
y_shift = random.randint(-enlarge_img_shrink[1]//16, enlarge_img_shrink[1]//16)
x_min += x_shift
x_max += x_shift
y_min += y_shift
y_max += y_shift
'''im_x,y'''
im_x += x_min
im_y += y_min
self.synthesis_perturbed_img[x_min:x_max, y_min:y_max] = self.origin_img
self.synthesis_perturbed_label[x_min:x_max, y_min:y_max] = origin_pixel_position
synthesis_perturbed_img_map = self.synthesis_perturbed_img.copy()
synthesis_perturbed_label_map = self.synthesis_perturbed_label.copy()
foreORbackground_label = np.full((mesh_shape), 1, dtype=np.int16)
foreORbackground_label_map = np.full((self.new_shape), 0, dtype=np.int16)
foreORbackground_label_map[x_min:x_max, y_min:y_max] = foreORbackground_label
# synthesis_perturbed_img_map = self.pad(self.synthesis_perturbed_img.copy(), x_min, y_min, x_max, y_max)
# synthesis_perturbed_label_map = self.pad(synthesis_perturbed_label_map, x_min, y_min, x_max, y_max)
'''*****************************************************************'''
is_normalizationFun_mixture = self.is_perform(0.2, 0.8)
# if not is_normalizationFun_mixture:
normalizationFun_0_1 = False
# normalizationFun_0_1 = self.is_perform(0.5, 0.5)
if fold_curve == 'fold':
fold_curve_random = True
# is_normalizationFun_mixture = False
normalizationFun_0_1 = self.is_perform(0.2, 0.8)
if is_normalizationFun_mixture:
alpha_perturbed = random.randint(80, 120) / 100
else:
if normalizationFun_0_1 and repeat_time < 8:
alpha_perturbed = random.randint(50, 70) / 100
else:
alpha_perturbed = random.randint(70, 130) / 100
else:
fold_curve_random = self.is_perform(0.1, 0.9) # False # self.is_perform(0.01, 0.99)
alpha_perturbed = random.randint(80, 160) / 100
# is_normalizationFun_mixture = False # self.is_perform(0.01, 0.99)
synthesis_perturbed_img = np.full_like(self.synthesis_perturbed_img, 256)
# synthesis_perturbed_img = np.full_like(self.synthesis_perturbed_img, 0, dtype=np.int16)
synthesis_perturbed_label = np.zeros_like(self.synthesis_perturbed_label)
alpha_perturbed_change = self.is_perform(0.5, 0.5)
p_pp_choice = self.is_perform(0.8, 0.2) if fold_curve == 'fold' else self.is_perform(0.1, 0.9)
for repeat_i in range(repeat_time):
if alpha_perturbed_change:
if fold_curve == 'fold':
if is_normalizationFun_mixture:
alpha_perturbed = random.randint(80, 120) / 100
else:
if normalizationFun_0_1 and repeat_time < 8:
alpha_perturbed = random.randint(50, 70) / 100
else:
alpha_perturbed = random.randint(70, 130) / 100
else:
alpha_perturbed = random.randint(80, 160) / 100
''''''
linspace_x = [0, (self.new_shape[0] - im_lr) // 2 - 1,
self.new_shape[0] - (self.new_shape[0] - im_lr) // 2 - 1, self.new_shape[0] - 1]
linspace_y = [0, (self.new_shape[1] - im_ud) // 2 - 1,
self.new_shape[1] - (self.new_shape[1] - im_ud) // 2 - 1, self.new_shape[1] - 1]
linspace_x_seq = [1, 2, 3]
linspace_y_seq = [1, 2, 3]
r_x = random.choice(linspace_x_seq)
r_y = random.choice(linspace_y_seq)
perturbed_p = np.array(
[random.randint(linspace_x[r_x-1] * 10, linspace_x[r_x] * 10),
random.randint(linspace_y[r_y-1] * 10, linspace_y[r_y] * 10)])/10
if ((r_x == 1 or r_x == 3) and (r_y == 1 or r_y == 3)) and p_pp_choice:
linspace_x_seq.remove(r_x)
linspace_y_seq.remove(r_y)
r_x = random.choice(linspace_x_seq)
r_y = random.choice(linspace_y_seq)
perturbed_pp = np.array(
[random.randint(linspace_x[r_x-1] * 10, linspace_x[r_x] * 10),
random.randint(linspace_y[r_y-1] * 10, linspace_y[r_y] * 10)])/10
# perturbed_p, perturbed_pp = np.array(
# [random.randint(0, self.new_shape[0] * 10) / 10,
# random.randint(0, self.new_shape[1] * 10) / 10]) \
# , np.array([random.randint(0, self.new_shape[0] * 10) / 10,
# random.randint(0, self.new_shape[1] * 10) / 10])
# perturbed_p, perturbed_pp = np.array(
# [random.randint((self.new_shape[0]-im_lr)//2*10, (self.new_shape[0]-(self.new_shape[0]-im_lr)//2) * 10) / 10,
# random.randint((self.new_shape[1]-im_ud)//2*10, (self.new_shape[1]-(self.new_shape[1]-im_ud)//2) * 10) / 10]) \
# , np.array([random.randint((self.new_shape[0]-im_lr)//2*10, (self.new_shape[0]-(self.new_shape[0]-im_lr)//2) * 10) / 10,
# random.randint((self.new_shape[1]-im_ud)//2*10, (self.new_shape[1]-(self.new_shape[1]-im_ud)//2) * 10) / 10])
''''''
perturbed_vp = perturbed_pp - perturbed_p
perturbed_vp_norm = np.linalg.norm(perturbed_vp)
perturbed_distance_vertex_and_line = np.dot((perturbed_p - pixel_position), perturbed_vp) / perturbed_vp_norm
''''''
# perturbed_v = np.array([random.randint(-3000, 3000) / 100, random.randint(-3000, 3000) / 100])
# perturbed_v = np.array([random.randint(-4000, 4000) / 100, random.randint(-4000, 4000) / 100])
if fold_curve == 'fold' and self.is_perform(0.6, 0.4): # self.is_perform(0.3, 0.7):
# perturbed_v = np.array([random.randint(-9000, 9000) / 100, random.randint(-9000, 9000) / 100])
perturbed_v = np.array([random.randint(-10000, 10000) / 100, random.randint(-10000, 10000) / 100])
# perturbed_v = np.array([random.randint(-11000, 11000) / 100, random.randint(-11000, 11000) / 100])
else:
# perturbed_v = np.array([random.randint(-9000, 9000) / 100, random.randint(-9000, 9000) / 100])
# perturbed_v = np.array([random.randint(-16000, 16000) / 100, random.randint(-16000, 16000) / 100])
perturbed_v = np.array([random.randint(-8000, 8000) / 100, random.randint(-8000, 8000) / 100])
# perturbed_v = np.array([random.randint(-3500, 3500) / 100, random.randint(-3500, 3500) / 100])
# perturbed_v = np.array([random.randint(-600, 600) / 10, random.randint(-600, 600) / 10])
''''''
if fold_curve == 'fold':
if is_normalizationFun_mixture:
if self.is_perform(0.5, 0.5):
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
else:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), random.randint(1, 2))
else:
if normalizationFun_0_1:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), 2)
else:
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
else:
if is_normalizationFun_mixture:
if self.is_perform(0.5, 0.5):
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
else:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), random.randint(1, 2))
else:
if normalizationFun_0_1:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), 2)
else:
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
''''''
if fold_curve_random:
# omega_perturbed = (alpha_perturbed+0.2) / (perturbed_d + alpha_perturbed)
# omega_perturbed = alpha_perturbed**perturbed_d
omega_perturbed = alpha_perturbed / (perturbed_d + alpha_perturbed)
else:
omega_perturbed = 1 - perturbed_d ** alpha_perturbed
'''shadow'''
if self.is_perform(0.6, 0.4):
synthesis_perturbed_img_map[x_min:x_max, y_min:y_max] = np.minimum(np.maximum(synthesis_perturbed_img_map[x_min:x_max, y_min:y_max] - np.int16(np.round(omega_perturbed[x_min:x_max, y_min:y_max].repeat(3).reshape(x_max-x_min, y_max-y_min, 3) * abs(np.linalg.norm(perturbed_v//2))*np.array([0.4-random.random()*0.1, 0.4-random.random()*0.1, 0.4-random.random()*0.1]))), 0), 255)
''''''
if relativeShift_position in ['position', 'relativeShift_v2']:
self.perturbed_xy_ += | np.array([omega_perturbed * perturbed_v[0], omega_perturbed * perturbed_v[1]]) | numpy.array |
"""Routines for numerical differentiation."""
from __future__ import division
import numpy as np
from numpy.linalg import norm
from scipy.sparse.linalg import LinearOperator
from ..sparse import issparse, csc_matrix, csr_matrix, coo_matrix, find
from ._group_columns import group_dense, group_sparse
EPS = np.finfo(np.float64).eps
def _adjust_scheme_to_bounds(x0, h, num_steps, scheme, lb, ub):
"""Adjust final difference scheme to the presence of bounds.
Parameters
----------
x0 : ndarray, shape (n,)
Point at which we wish to estimate derivative.
h : ndarray, shape (n,)
Desired finite difference steps.
num_steps : int
Number of `h` steps in one direction required to implement finite
difference scheme. For example, 2 means that we need to evaluate
f(x0 + 2 * h) or f(x0 - 2 * h)
scheme : {'1-sided', '2-sided'}
Whether steps in one or both directions are required. In other
words '1-sided' applies to forward and backward schemes, '2-sided'
applies to center schemes.
lb : ndarray, shape (n,)
Lower bounds on independent variables.
ub : ndarray, shape (n,)
Upper bounds on independent variables.
Returns
-------
h_adjusted : ndarray, shape (n,)
Adjusted step sizes. Step size decreases only if a sign flip or
switching to one-sided scheme doesn't allow to take a full step.
use_one_sided : ndarray of bool, shape (n,)
Whether to switch to one-sided scheme. Informative only for
``scheme='2-sided'``.
"""
if scheme == '1-sided':
use_one_sided = np.ones_like(h, dtype=bool)
elif scheme == '2-sided':
h = np.abs(h)
use_one_sided = np.zeros_like(h, dtype=bool)
else:
raise ValueError("`scheme` must be '1-sided' or '2-sided'.")
if np.all((lb == -np.inf) & (ub == np.inf)):
return h, use_one_sided
h_total = h * num_steps
h_adjusted = h.copy()
lower_dist = x0 - lb
upper_dist = ub - x0
if scheme == '1-sided':
x = x0 + h_total
violated = (x < lb) | (x > ub)
fitting = | np.abs(h_total) | numpy.abs |
# -*- coding: utf-8 -*-
"""
Created on Thu Nov 28 12:10:11 2019
@author: Omer
"""
## File handler
## This file was initially intended purely to generate the matrices for the near earth code found in: https://public.ccsds.org/Pubs/131x1o2e2s.pdf
## The values from the above pdf were copied manually to a txt file, and it is the purpose of this file to parse it.
## The emphasis here is on correctness, I currently do not see a reason to generalise this file, since matrices will be saved in either json or some matrix friendly format.
import numpy as np
from scipy.linalg import circulant
#import matplotlib.pyplot as plt
import scipy.io
import common
import hashlib
import os
projectDir = os.environ.get('LDPC')
if projectDir == None:
import pathlib
projectDir = pathlib.Path(__file__).parent.absolute()
## <NAME>: added on 01/12/2020, need to make sure this doesn't break anything.
import sys
sys.path.insert(1, projectDir)
FILE_HANDLER_INT_DATA_TYPE = np.int32
GENERAL_CODE_MATRIX_DATA_TYPE = np.int32
NIBBLE_CONVERTER = np.array([8, 4, 2, 1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
def nibbleToHex(inputArray):
n = NIBBLE_CONVERTER.dot(inputArray)
if n == 10:
h = 'A'
elif n== 11:
h = 'B'
elif n== 12:
h = 'C'
elif n== 13:
h = 'D'
elif n== 14:
h = 'E'
elif n== 15:
h = 'F'
else:
h = str(n)
return h
def binaryArraytoHex(inputArray):
d1 = len(inputArray)
assert (d1 % 4 == 0)
outputArray = np.zeros(d1//4, dtype = str)
outputString = ''
for j in range(d1//4):
nibble = inputArray[4 * j : 4 * j + 4]
h = nibbleToHex(nibble)
outputArray[j] = h
outputString = outputString + h
return outputArray, outputString
def hexStringToBinaryArray(hexString):
outputBinary = np.array([], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
for i in hexString:
if i == '0':
nibble = np.array([0,0,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '1':
nibble = np.array([0,0,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '2':
nibble = np.array([0,0,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '3':
nibble = np.array([0,0,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '4':
nibble = np.array([0,1,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '5':
nibble = np.array([0,1,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '6':
nibble = np.array([0,1,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '7':
nibble = np.array([0,1,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '8':
nibble = np.array([1,0,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == '9':
nibble = np.array([1,0,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == 'A':
nibble = np.array([1,0,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == 'B':
nibble = np.array([1,0,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)
elif i == 'C':
nibble = | np.array([1,1,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) | numpy.array |
"""
YTArray class.
"""
from __future__ import print_function
#-----------------------------------------------------------------------------
# Copyright (c) 2013, yt Development Team.
#
# Distributed under the terms of the Modified BSD License.
#
# The full license is in the file COPYING.txt, distributed with this software.
#-----------------------------------------------------------------------------
import copy
import numpy as np
from distutils.version import LooseVersion
from functools import wraps
from numpy import \
add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, \
floor_divide, negative, power, remainder, mod, absolute, rint, \
sign, conj, exp, exp2, log, log2, log10, expm1, log1p, sqrt, square, \
reciprocal, sin, cos, tan, arcsin, arccos, arctan, arctan2, \
hypot, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad, rad2deg, \
bitwise_and, bitwise_or, bitwise_xor, invert, left_shift, right_shift, \
greater, greater_equal, less, less_equal, not_equal, equal, logical_and, \
logical_or, logical_xor, logical_not, maximum, minimum, fmax, fmin, \
isreal, iscomplex, isfinite, isinf, isnan, signbit, copysign, nextafter, \
modf, ldexp, frexp, fmod, floor, ceil, trunc, fabs, spacing
try:
# numpy 1.13 or newer
from numpy import positive, divmod as divmod_, isnat, heaviside
except ImportError:
positive, divmod_, isnat, heaviside = (None,)*4
from yt.units.unit_object import Unit, UnitParseError
from yt.units.unit_registry import UnitRegistry
from yt.units.dimensions import \
angle, \
current_mks, \
dimensionless, \
em_dimensions
from yt.utilities.exceptions import \
YTUnitOperationError, YTUnitConversionError, \
YTUfuncUnitError, YTIterableUnitCoercionError, \
YTInvalidUnitEquivalence, YTEquivalentDimsError
from yt.utilities.lru_cache import lru_cache
from numbers import Number as numeric_type
from yt.utilities.on_demand_imports import _astropy
from sympy import Rational
from yt.units.unit_lookup_table import \
default_unit_symbol_lut
from yt.units.equivalencies import equivalence_registry
from yt.utilities.logger import ytLogger as mylog
from .pint_conversions import convert_pint_units
NULL_UNIT = Unit()
POWER_SIGN_MAPPING = {multiply: 1, divide: -1}
# redefine this here to avoid a circular import from yt.funcs
def iterable(obj):
try: len(obj)
except: return False
return True
def return_arr(func):
@wraps(func)
def wrapped(*args, **kwargs):
ret, units = func(*args, **kwargs)
if ret.shape == ():
return YTQuantity(ret, units)
else:
# This could be a subclass, so don't call YTArray directly.
return type(args[0])(ret, units)
return wrapped
@lru_cache(maxsize=128, typed=False)
def sqrt_unit(unit):
return unit**0.5
@lru_cache(maxsize=128, typed=False)
def multiply_units(unit1, unit2):
return unit1 * unit2
def preserve_units(unit1, unit2=None):
return unit1
@lru_cache(maxsize=128, typed=False)
def power_unit(unit, power):
return unit**power
@lru_cache(maxsize=128, typed=False)
def square_unit(unit):
return unit*unit
@lru_cache(maxsize=128, typed=False)
def divide_units(unit1, unit2):
return unit1/unit2
@lru_cache(maxsize=128, typed=False)
def reciprocal_unit(unit):
return unit**-1
def passthrough_unit(unit, unit2=None):
return unit
def return_without_unit(unit, unit2=None):
return None
def arctan2_unit(unit1, unit2):
return NULL_UNIT
def comparison_unit(unit1, unit2=None):
return None
def invert_units(unit):
raise TypeError(
"Bit-twiddling operators are not defined for YTArray instances")
def bitop_units(unit1, unit2):
raise TypeError(
"Bit-twiddling operators are not defined for YTArray instances")
def get_inp_u_unary(ufunc, inputs, out_arr=None):
inp = inputs[0]
u = getattr(inp, 'units', None)
if u is None:
u = NULL_UNIT
if u.dimensions is angle and ufunc in trigonometric_operators:
inp = inp.in_units('radian').v
if out_arr is not None:
out_arr = ufunc(inp).view(np.ndarray)
return out_arr, inp, u
def get_inp_u_binary(ufunc, inputs):
inp1 = coerce_iterable_units(inputs[0])
inp2 = coerce_iterable_units(inputs[1])
unit1 = getattr(inp1, 'units', None)
unit2 = getattr(inp2, 'units', None)
ret_class = get_binary_op_return_class(type(inp1), type(inp2))
if unit1 is None:
unit1 = Unit(registry=getattr(unit2, 'registry', None))
if unit2 is None and ufunc is not power:
unit2 = Unit(registry=getattr(unit1, 'registry', None))
elif ufunc is power:
unit2 = inp2
if isinstance(unit2, np.ndarray):
if isinstance(unit2, YTArray):
if unit2.units.is_dimensionless:
pass
else:
raise YTUnitOperationError(ufunc, unit1, unit2)
unit2 = 1.0
return (inp1, inp2), (unit1, unit2), ret_class
def handle_preserve_units(inps, units, ufunc, ret_class):
if units[0] != units[1]:
any_nonzero = [np.any(inps[0]), np.any(inps[1])]
if any_nonzero[0] == np.bool_(False):
units = (units[1], units[1])
elif any_nonzero[1] == np.bool_(False):
units = (units[0], units[0])
else:
if not units[0].same_dimensions_as(units[1]):
raise YTUnitOperationError(ufunc, *units)
inps = (inps[0], ret_class(inps[1]).to(
ret_class(inps[0]).units))
return inps, units
def handle_comparison_units(inps, units, ufunc, ret_class, raise_error=False):
if units[0] != units[1]:
u1d = units[0].is_dimensionless
u2d = units[1].is_dimensionless
any_nonzero = [np.any(inps[0]), np.any(inps[1])]
if any_nonzero[0] == np.bool_(False):
units = (units[1], units[1])
elif any_nonzero[1] == np.bool_(False):
units = (units[0], units[0])
elif not any([u1d, u2d]):
if not units[0].same_dimensions_as(units[1]):
raise YTUnitOperationError(ufunc, *units)
else:
if raise_error:
raise YTUfuncUnitError(ufunc, *units)
inps = (inps[0], ret_class(inps[1]).to(
ret_class(inps[0]).units))
return inps, units
def handle_multiply_divide_units(unit, units, out, out_arr):
if unit.is_dimensionless and unit.base_value != 1.0:
if not units[0].is_dimensionless:
if units[0].dimensions == units[1].dimensions:
out_arr = np.multiply(out_arr.view(np.ndarray),
unit.base_value, out=out)
unit = Unit(registry=unit.registry)
return out, out_arr, unit
def coerce_iterable_units(input_object):
if isinstance(input_object, np.ndarray):
return input_object
if iterable(input_object):
if any([isinstance(o, YTArray) for o in input_object]):
ff = getattr(input_object[0], 'units', NULL_UNIT, )
if any([ff != getattr(_, 'units', NULL_UNIT) for _ in input_object]):
raise YTIterableUnitCoercionError(input_object)
# This will create a copy of the data in the iterable.
return YTArray(input_object)
return input_object
else:
return input_object
def sanitize_units_mul(this_object, other_object):
inp = coerce_iterable_units(this_object)
ret = coerce_iterable_units(other_object)
# If the other object is a YTArray and has the same dimensions as the object
# under consideration, convert so we don't mix units with the same
# dimensions.
if isinstance(ret, YTArray):
if inp.units.same_dimensions_as(ret.units):
ret.in_units(inp.units)
return ret
def sanitize_units_add(this_object, other_object, op_string):
inp = coerce_iterable_units(this_object)
ret = coerce_iterable_units(other_object)
# Make sure the other object is a YTArray before we use the `units`
# attribute.
if isinstance(ret, YTArray):
if not inp.units.same_dimensions_as(ret.units):
# handle special case of adding or subtracting with zero or
# array filled with zero
if not np.any(other_object):
return ret.view(np.ndarray)
elif not np.any(this_object):
return ret
raise YTUnitOperationError(op_string, inp.units, ret.units)
ret = ret.in_units(inp.units)
else:
# If the other object is not a YTArray, then one of the arrays must be
# dimensionless or filled with zeros
if not inp.units.is_dimensionless and np.any(ret):
raise YTUnitOperationError(op_string, inp.units, dimensionless)
return ret
def validate_comparison_units(this, other, op_string):
# Check that other is a YTArray.
if hasattr(other, 'units'):
if this.units.expr is other.units.expr:
if this.units.base_value == other.units.base_value:
return other
if not this.units.same_dimensions_as(other.units):
raise YTUnitOperationError(op_string, this.units, other.units)
return other.in_units(this.units)
return other
@lru_cache(maxsize=128, typed=False)
def _unit_repr_check_same(my_units, other_units):
"""
Takes a Unit object, or string of known unit symbol, and check that it
is compatible with this quantity. Returns Unit object.
"""
# let Unit() handle units arg if it's not already a Unit obj.
if not isinstance(other_units, Unit):
other_units = Unit(other_units, registry=my_units.registry)
equiv_dims = em_dimensions.get(my_units.dimensions, None)
if equiv_dims == other_units.dimensions:
if current_mks in equiv_dims.free_symbols:
base = "SI"
else:
base = "CGS"
raise YTEquivalentDimsError(my_units, other_units, base)
if not my_units.same_dimensions_as(other_units):
raise YTUnitConversionError(
my_units, my_units.dimensions, other_units, other_units.dimensions)
return other_units
unary_operators = (
negative, absolute, rint, sign, conj, exp, exp2, log, log2,
log10, expm1, log1p, sqrt, square, reciprocal, sin, cos, tan, arcsin,
arccos, arctan, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad,
rad2deg, invert, logical_not, isreal, iscomplex, isfinite, isinf, isnan,
signbit, floor, ceil, trunc, modf, frexp, fabs, spacing, positive, isnat,
)
binary_operators = (
add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, power,
remainder, mod, arctan2, hypot, bitwise_and, bitwise_or, bitwise_xor,
left_shift, right_shift, greater, greater_equal, less, less_equal,
not_equal, equal, logical_and, logical_or, logical_xor, maximum, minimum,
fmax, fmin, copysign, nextafter, ldexp, fmod, divmod_, heaviside
)
trigonometric_operators = (
sin, cos, tan,
)
class YTArray(np.ndarray):
"""
An ndarray subclass that attaches a symbolic unit object to the array data.
Parameters
----------
input_array : :obj:`!iterable`
A tuple, list, or array to attach units to
input_units : String unit specification, unit symbol object, or astropy units
The units of the array. Powers must be specified using python
syntax (cm**3, not cm^3).
registry : ~yt.units.unit_registry.UnitRegistry
The registry to create units from. If input_units is already associated
with a unit registry and this is specified, this will be used instead of
the registry associated with the unit object.
dtype : data-type
The dtype of the array data. Defaults to the dtype of the input data,
or, if none is found, uses np.float64
bypass_validation : boolean
If True, all input validation is skipped. Using this option may produce
corrupted, invalid units or array data, but can lead to significant
speedups in the input validation logic adds significant overhead. If set,
input_units *must* be a valid unit object. Defaults to False.
Examples
--------
>>> from yt import YTArray
>>> a = YTArray([1, 2, 3], 'cm')
>>> b = YTArray([4, 5, 6], 'm')
>>> a + b
YTArray([ 401., 502., 603.]) cm
>>> b + a
YTArray([ 4.01, 5.02, 6.03]) m
NumPy ufuncs will pass through units where appropriate.
>>> import numpy as np
>>> a = YTArray(np.arange(8) - 4, 'g/cm**3')
>>> np.abs(a)
YTArray([4, 3, 2, 1, 0, 1, 2, 3]) g/cm**3
and strip them when it would be annoying to deal with them.
>>> np.log10(a)
array([ -inf, 0. , 0.30103 , 0.47712125, 0.60205999,
0.69897 , 0.77815125, 0.84509804])
YTArray is tightly integrated with yt datasets:
>>> import yt
>>> ds = yt.load('IsolatedGalaxy/galaxy0030/galaxy0030')
>>> a = ds.arr(np.ones(5), 'code_length')
>>> a.in_cgs()
YTArray([ 3.08600000e+24, 3.08600000e+24, 3.08600000e+24,
3.08600000e+24, 3.08600000e+24]) cm
This is equivalent to:
>>> b = YTArray(np.ones(5), 'code_length', registry=ds.unit_registry)
>>> np.all(a == b)
True
"""
_ufunc_registry = {
add: preserve_units,
subtract: preserve_units,
multiply: multiply_units,
divide: divide_units,
logaddexp: return_without_unit,
logaddexp2: return_without_unit,
true_divide: divide_units,
floor_divide: divide_units,
negative: passthrough_unit,
power: power_unit,
remainder: preserve_units,
mod: preserve_units,
fmod: preserve_units,
absolute: passthrough_unit,
fabs: passthrough_unit,
rint: return_without_unit,
sign: return_without_unit,
conj: passthrough_unit,
exp: return_without_unit,
exp2: return_without_unit,
log: return_without_unit,
log2: return_without_unit,
log10: return_without_unit,
expm1: return_without_unit,
log1p: return_without_unit,
sqrt: sqrt_unit,
square: square_unit,
reciprocal: reciprocal_unit,
sin: return_without_unit,
cos: return_without_unit,
tan: return_without_unit,
sinh: return_without_unit,
cosh: return_without_unit,
tanh: return_without_unit,
arcsin: return_without_unit,
arccos: return_without_unit,
arctan: return_without_unit,
arctan2: arctan2_unit,
arcsinh: return_without_unit,
arccosh: return_without_unit,
arctanh: return_without_unit,
hypot: preserve_units,
deg2rad: return_without_unit,
rad2deg: return_without_unit,
bitwise_and: bitop_units,
bitwise_or: bitop_units,
bitwise_xor: bitop_units,
invert: invert_units,
left_shift: bitop_units,
right_shift: bitop_units,
greater: comparison_unit,
greater_equal: comparison_unit,
less: comparison_unit,
less_equal: comparison_unit,
not_equal: comparison_unit,
equal: comparison_unit,
logical_and: comparison_unit,
logical_or: comparison_unit,
logical_xor: comparison_unit,
logical_not: return_without_unit,
maximum: preserve_units,
minimum: preserve_units,
fmax: preserve_units,
fmin: preserve_units,
isreal: return_without_unit,
iscomplex: return_without_unit,
isfinite: return_without_unit,
isinf: return_without_unit,
isnan: return_without_unit,
signbit: return_without_unit,
copysign: passthrough_unit,
nextafter: preserve_units,
modf: passthrough_unit,
ldexp: bitop_units,
frexp: return_without_unit,
floor: passthrough_unit,
ceil: passthrough_unit,
trunc: passthrough_unit,
spacing: passthrough_unit,
positive: passthrough_unit,
divmod_: passthrough_unit,
isnat: return_without_unit,
heaviside: preserve_units,
}
__array_priority__ = 2.0
def __new__(cls, input_array, input_units=None, registry=None, dtype=None,
bypass_validation=False):
if dtype is None:
dtype = getattr(input_array, 'dtype', np.float64)
if bypass_validation is True:
obj = np.asarray(input_array, dtype=dtype).view(cls)
obj.units = input_units
if registry is not None:
obj.units.registry = registry
return obj
if input_array is NotImplemented:
return input_array.view(cls)
if registry is None and isinstance(input_units, (str, bytes)):
if input_units.startswith('code_'):
raise UnitParseError(
"Code units used without referring to a dataset. \n"
"Perhaps you meant to do something like this instead: \n"
"ds.arr(%s, \"%s\")" % (input_array, input_units)
)
if isinstance(input_array, YTArray):
ret = input_array.view(cls)
if input_units is None:
if registry is None:
ret.units = input_array.units
else:
units = Unit(str(input_array.units), registry=registry)
ret.units = units
elif isinstance(input_units, Unit):
ret.units = input_units
else:
ret.units = Unit(input_units, registry=registry)
return ret
elif isinstance(input_array, np.ndarray):
pass
elif iterable(input_array) and input_array:
if isinstance(input_array[0], YTArray):
return YTArray(np.array(input_array, dtype=dtype),
input_array[0].units, registry=registry)
# Input array is an already formed ndarray instance
# We first cast to be our class type
obj = np.asarray(input_array, dtype=dtype).view(cls)
# Check units type
if input_units is None:
# Nothing provided. Make dimensionless...
units = Unit()
elif isinstance(input_units, Unit):
if registry and registry is not input_units.registry:
units = Unit(str(input_units), registry=registry)
else:
units = input_units
else:
# units kwarg set, but it's not a Unit object.
# don't handle all the cases here, let the Unit class handle if
# it's a str.
units = Unit(input_units, registry=registry)
# Attach the units
obj.units = units
return obj
def __repr__(self):
"""
"""
return super(YTArray, self).__repr__()+' '+self.units.__repr__()
def __str__(self):
"""
"""
return str(self.view(np.ndarray)) + ' ' + str(self.units)
#
# Start unit conversion methods
#
def convert_to_units(self, units):
"""
Convert the array and units to the given units.
Parameters
----------
units : Unit object or str
The units you want to convert to.
"""
new_units = _unit_repr_check_same(self.units, units)
(conversion_factor, offset) = self.units.get_conversion_factor(new_units)
self.units = new_units
values = self.d
values *= conversion_factor
if offset:
np.subtract(self, offset*self.uq, self)
return self
def convert_to_base(self, unit_system="cgs"):
"""
Convert the array and units to the equivalent base units in
the specified unit system.
Parameters
----------
unit_system : string, optional
The unit system to be used in the conversion. If not specified,
the default base units of cgs are used.
Examples
--------
>>> E = YTQuantity(2.5, "erg/s")
>>> E.convert_to_base(unit_system="galactic")
"""
return self.convert_to_units(self.units.get_base_equivalent(unit_system))
def convert_to_cgs(self):
"""
Convert the array and units to the equivalent cgs units.
"""
return self.convert_to_units(self.units.get_cgs_equivalent())
def convert_to_mks(self):
"""
Convert the array and units to the equivalent mks units.
"""
return self.convert_to_units(self.units.get_mks_equivalent())
def in_units(self, units, equivalence=None, **kwargs):
"""
Creates a copy of this array with the data in the supplied
units, and returns it.
Optionally, an equivalence can be specified to convert to an
equivalent quantity which is not in the same dimensions.
.. note::
All additional keyword arguments are passed to the
equivalency, which should be used if that particular
equivalency requires them.
Parameters
----------
units : Unit object or string
The units you want to get a new quantity in.
equivalence : string, optional
The equivalence you wish to use. To see which
equivalencies are supported for this unitful
quantity, try the :meth:`list_equivalencies`
method. Default: None
Returns
-------
YTArray
"""
if equivalence is None:
new_units = _unit_repr_check_same(self.units, units)
(conversion_factor, offset) = self.units.get_conversion_factor(new_units)
new_array = type(self)(self.ndview * conversion_factor, new_units)
if offset:
np.subtract(new_array, offset*new_array.uq, new_array)
return new_array
else:
return self.to_equivalent(units, equivalence, **kwargs)
def to(self, units, equivalence=None, **kwargs):
"""
An alias for YTArray.in_units().
See the docstrings of that function for details.
"""
return self.in_units(units, equivalence=equivalence, **kwargs)
def to_value(self, units=None, equivalence=None, **kwargs):
"""
Creates a copy of this array with the data in the supplied
units, and returns it without units. Output is therefore a
bare NumPy array.
Optionally, an equivalence can be specified to convert to an
equivalent quantity which is not in the same dimensions.
.. note::
All additional keyword arguments are passed to the
equivalency, which should be used if that particular
equivalency requires them.
Parameters
----------
units : Unit object or string, optional
The units you want to get the bare quantity in. If not
specified, the value will be returned in the current units.
equivalence : string, optional
The equivalence you wish to use. To see which
equivalencies are supported for this unitful
quantity, try the :meth:`list_equivalencies`
method. Default: None
Returns
-------
NumPy array
"""
if units is None:
v = self.value
else:
v = self.in_units(units, equivalence=equivalence, **kwargs).value
if isinstance(self, YTQuantity):
return float(v)
else:
return v
def in_base(self, unit_system="cgs"):
"""
Creates a copy of this array with the data in the specified unit system,
and returns it in that system's base units.
Parameters
----------
unit_system : string, optional
The unit system to be used in the conversion. If not specified,
the default base units of cgs are used.
Examples
--------
>>> E = YTQuantity(2.5, "erg/s")
>>> E_new = E.in_base(unit_system="galactic")
"""
return self.in_units(self.units.get_base_equivalent(unit_system))
def in_cgs(self):
"""
Creates a copy of this array with the data in the equivalent cgs units,
and returns it.
Returns
-------
Quantity object with data converted to cgs units.
"""
return self.in_units(self.units.get_cgs_equivalent())
def in_mks(self):
"""
Creates a copy of this array with the data in the equivalent mks units,
and returns it.
Returns
-------
Quantity object with data converted to mks units.
"""
return self.in_units(self.units.get_mks_equivalent())
def to_equivalent(self, unit, equiv, **kwargs):
"""
Convert a YTArray or YTQuantity to an equivalent, e.g., something that is
related by only a constant factor but not in the same units.
Parameters
----------
unit : string
The unit that you wish to convert to.
equiv : string
The equivalence you wish to use. To see which equivalencies are
supported for this unitful quantity, try the
:meth:`list_equivalencies` method.
Examples
--------
>>> a = yt.YTArray(1.0e7,"K")
>>> a.to_equivalent("keV", "thermal")
"""
conv_unit = Unit(unit, registry=self.units.registry)
if self.units.same_dimensions_as(conv_unit):
return self.in_units(conv_unit)
this_equiv = equivalence_registry[equiv]()
oneway_or_equivalent = (
conv_unit.has_equivalent(equiv) or this_equiv._one_way)
if self.has_equivalent(equiv) and oneway_or_equivalent:
new_arr = this_equiv.convert(
self, conv_unit.dimensions, **kwargs)
if isinstance(new_arr, tuple):
try:
return type(self)(new_arr[0], new_arr[1]).in_units(unit)
except YTUnitConversionError:
raise YTInvalidUnitEquivalence(equiv, self.units, unit)
else:
return new_arr.in_units(unit)
else:
raise YTInvalidUnitEquivalence(equiv, self.units, unit)
def list_equivalencies(self):
"""
Lists the possible equivalencies associated with this YTArray or
YTQuantity.
"""
self.units.list_equivalencies()
def has_equivalent(self, equiv):
"""
Check to see if this YTArray or YTQuantity has an equivalent unit in
*equiv*.
"""
return self.units.has_equivalent(equiv)
def ndarray_view(self):
"""
Returns a view into the array, but as an ndarray rather than ytarray.
Returns
-------
View of this array's data.
"""
return self.view(np.ndarray)
def to_ndarray(self):
"""
Creates a copy of this array with the unit information stripped
"""
return np.array(self)
@classmethod
def from_astropy(cls, arr, unit_registry=None):
"""
Convert an AstroPy "Quantity" to a YTArray or YTQuantity.
Parameters
----------
arr : AstroPy Quantity
The Quantity to convert from.
unit_registry : yt UnitRegistry, optional
A yt unit registry to use in the conversion. If one is not
supplied, the default one will be used.
"""
# Converting from AstroPy Quantity
u = arr.unit
ap_units = []
for base, exponent in zip(u.bases, u.powers):
unit_str = base.to_string()
# we have to do this because AstroPy is silly and defines
# hour as "h"
if unit_str == "h": unit_str = "hr"
ap_units.append("%s**(%s)" % (unit_str, Rational(exponent)))
ap_units = "*".join(ap_units)
if isinstance(arr.value, np.ndarray):
return YTArray(arr.value, ap_units, registry=unit_registry)
else:
return YTQuantity(arr.value, ap_units, registry=unit_registry)
def to_astropy(self, **kwargs):
"""
Creates a new AstroPy quantity with the same unit information.
"""
if _astropy.units is None:
raise ImportError("You don't have AstroPy installed, so you can't convert to " +
"an AstroPy quantity.")
return self.value*_astropy.units.Unit(str(self.units), **kwargs)
@classmethod
def from_pint(cls, arr, unit_registry=None):
"""
Convert a Pint "Quantity" to a YTArray or YTQuantity.
Parameters
----------
arr : Pint Quantity
The Quantity to convert from.
unit_registry : yt UnitRegistry, optional
A yt unit registry to use in the conversion. If one is not
supplied, the default one will be used.
Examples
--------
>>> from pint import UnitRegistry
>>> import numpy as np
>>> ureg = UnitRegistry()
>>> a = np.random.random(10)
>>> b = ureg.Quantity(a, "erg/cm**3")
>>> c = yt.YTArray.from_pint(b)
"""
p_units = []
for base, exponent in arr._units.items():
bs = convert_pint_units(base)
p_units.append("%s**(%s)" % (bs, Rational(exponent)))
p_units = "*".join(p_units)
if isinstance(arr.magnitude, np.ndarray):
return YTArray(arr.magnitude, p_units, registry=unit_registry)
else:
return YTQuantity(arr.magnitude, p_units, registry=unit_registry)
def to_pint(self, unit_registry=None):
"""
Convert a YTArray or YTQuantity to a Pint Quantity.
Parameters
----------
arr : YTArray or YTQuantity
The unitful quantity to convert from.
unit_registry : Pint UnitRegistry, optional
The Pint UnitRegistry to use in the conversion. If one is not
supplied, the default one will be used. NOTE: This is not
the same as a yt UnitRegistry object.
Examples
--------
>>> a = YTQuantity(4.0, "cm**2/s")
>>> b = a.to_pint()
"""
from pint import UnitRegistry
if unit_registry is None:
unit_registry = UnitRegistry()
powers_dict = self.units.expr.as_powers_dict()
units = []
for unit, pow in powers_dict.items():
# we have to do this because Pint doesn't recognize
# "yr" as "year"
if str(unit).endswith("yr") and len(str(unit)) in [2,3]:
unit = str(unit).replace("yr","year")
units.append("%s**(%s)" % (unit, Rational(pow)))
units = "*".join(units)
return unit_registry.Quantity(self.value, units)
#
# End unit conversion methods
#
def write_hdf5(self, filename, dataset_name=None, info=None, group_name=None):
r"""Writes a YTArray to hdf5 file.
Parameters
----------
filename: string
The filename to create and write a dataset to
dataset_name: string
The name of the dataset to create in the file.
info: dictionary
A dictionary of supplementary info to write to append as attributes
to the dataset.
group_name: string
An optional group to write the arrays to. If not specified, the arrays
are datasets at the top level by default.
Examples
--------
>>> a = YTArray([1,2,3], 'cm')
>>> myinfo = {'field':'dinosaurs', 'type':'field_data'}
>>> a.write_hdf5('test_array_data.h5', dataset_name='dinosaurs',
... info=myinfo)
"""
from yt.utilities.on_demand_imports import _h5py as h5py
from yt.extern.six.moves import cPickle as pickle
if info is None:
info = {}
info['units'] = str(self.units)
info['unit_registry'] = np.void(pickle.dumps(self.units.registry.lut))
if dataset_name is None:
dataset_name = 'array_data'
f = h5py.File(filename)
if group_name is not None:
if group_name in f:
g = f[group_name]
else:
g = f.create_group(group_name)
else:
g = f
if dataset_name in g.keys():
d = g[dataset_name]
# Overwrite without deleting if we can get away with it.
if d.shape == self.shape and d.dtype == self.dtype:
d[...] = self
for k in d.attrs.keys():
del d.attrs[k]
else:
del f[dataset_name]
d = g.create_dataset(dataset_name, data=self)
else:
d = g.create_dataset(dataset_name, data=self)
for k, v in info.items():
d.attrs[k] = v
f.close()
@classmethod
def from_hdf5(cls, filename, dataset_name=None, group_name=None):
r"""Attempts read in and convert a dataset in an hdf5 file into a
YTArray.
Parameters
----------
filename: string
The filename to of the hdf5 file.
dataset_name: string
The name of the dataset to read from. If the dataset has a units
attribute, attempt to infer units as well.
group_name: string
An optional group to read the arrays from. If not specified, the
arrays are datasets at the top level by default.
"""
import h5py
from yt.extern.six.moves import cPickle as pickle
if dataset_name is None:
dataset_name = 'array_data'
f = h5py.File(filename)
if group_name is not None:
g = f[group_name]
else:
g = f
dataset = g[dataset_name]
data = dataset[:]
units = dataset.attrs.get('units', '')
if 'unit_registry' in dataset.attrs.keys():
unit_lut = pickle.loads(dataset.attrs['unit_registry'].tostring())
else:
unit_lut = None
f.close()
registry = UnitRegistry(lut=unit_lut, add_default_symbols=False)
return cls(data, units, registry=registry)
#
# Start convenience methods
#
@property
def value(self):
"""Get a copy of the array data as a numpy ndarray"""
return np.array(self)
v = value
@property
def ndview(self):
"""Get a view of the array data."""
return self.ndarray_view()
d = ndview
@property
def unit_quantity(self):
"""Get a YTQuantity with the same unit as this array and a value of
1.0"""
return YTQuantity(1.0, self.units)
uq = unit_quantity
@property
def unit_array(self):
"""Get a YTArray filled with ones with the same unit and shape as this
array"""
return np.ones_like(self)
ua = unit_array
def __getitem__(self, item):
ret = super(YTArray, self).__getitem__(item)
if ret.shape == ():
return YTQuantity(ret, self.units, bypass_validation=True)
else:
if hasattr(self, 'units'):
ret.units = self.units
return ret
#
# Start operation methods
#
if LooseVersion(np.__version__) < LooseVersion('1.13.0'):
def __add__(self, right_object):
"""
Add this ytarray to the object on the right of the `+` operator.
Must check for the correct (same dimension) units.
"""
ro = sanitize_units_add(self, right_object, "addition")
return super(YTArray, self).__add__(ro)
def __radd__(self, left_object):
""" See __add__. """
lo = sanitize_units_add(self, left_object, "addition")
return super(YTArray, self).__radd__(lo)
def __iadd__(self, other):
""" See __add__. """
oth = sanitize_units_add(self, other, "addition")
np.add(self, oth, out=self)
return self
def __sub__(self, right_object):
"""
Subtract the object on the right of the `-` from this ytarray. Must
check for the correct (same dimension) units.
"""
ro = sanitize_units_add(self, right_object, "subtraction")
return super(YTArray, self).__sub__(ro)
def __rsub__(self, left_object):
""" See __sub__. """
lo = sanitize_units_add(self, left_object, "subtraction")
return super(YTArray, self).__rsub__(lo)
def __isub__(self, other):
""" See __sub__. """
oth = sanitize_units_add(self, other, "subtraction")
np.subtract(self, oth, out=self)
return self
def __neg__(self):
""" Negate the data. """
return super(YTArray, self).__neg__()
def __mul__(self, right_object):
"""
Multiply this YTArray by the object on the right of the `*`
operator. The unit objects handle being multiplied.
"""
ro = sanitize_units_mul(self, right_object)
return super(YTArray, self).__mul__(ro)
def __rmul__(self, left_object):
""" See __mul__. """
lo = sanitize_units_mul(self, left_object)
return super(YTArray, self).__rmul__(lo)
def __imul__(self, other):
""" See __mul__. """
oth = sanitize_units_mul(self, other)
np.multiply(self, oth, out=self)
return self
def __div__(self, right_object):
"""
Divide this YTArray by the object on the right of the `/` operator.
"""
ro = sanitize_units_mul(self, right_object)
return super(YTArray, self).__div__(ro)
def __rdiv__(self, left_object):
""" See __div__. """
lo = sanitize_units_mul(self, left_object)
return super(YTArray, self).__rdiv__(lo)
def __idiv__(self, other):
""" See __div__. """
oth = sanitize_units_mul(self, other)
np.divide(self, oth, out=self)
return self
def __truediv__(self, right_object):
ro = sanitize_units_mul(self, right_object)
return super(YTArray, self).__truediv__(ro)
def __rtruediv__(self, left_object):
""" See __div__. """
lo = sanitize_units_mul(self, left_object)
return super(YTArray, self).__rtruediv__(lo)
def __itruediv__(self, other):
""" See __div__. """
oth = sanitize_units_mul(self, other)
np.true_divide(self, oth, out=self)
return self
def __floordiv__(self, right_object):
ro = sanitize_units_mul(self, right_object)
return super(YTArray, self).__floordiv__(ro)
def __rfloordiv__(self, left_object):
""" See __div__. """
lo = sanitize_units_mul(self, left_object)
return super(YTArray, self).__rfloordiv__(lo)
def __ifloordiv__(self, other):
""" See __div__. """
oth = sanitize_units_mul(self, other)
np.floor_divide(self, oth, out=self)
return self
def __or__(self, right_object):
return super(YTArray, self).__or__(right_object)
def __ror__(self, left_object):
return super(YTArray, self).__ror__(left_object)
def __ior__(self, other):
np.bitwise_or(self, other, out=self)
return self
def __xor__(self, right_object):
return super(YTArray, self).__xor__(right_object)
def __rxor__(self, left_object):
return super(YTArray, self).__rxor__(left_object)
def __ixor__(self, other):
np.bitwise_xor(self, other, out=self)
return self
def __and__(self, right_object):
return super(YTArray, self).__and__(right_object)
def __rand__(self, left_object):
return super(YTArray, self).__rand__(left_object)
def __iand__(self, other):
np.bitwise_and(self, other, out=self)
return self
def __pow__(self, power):
"""
Raise this YTArray to some power.
Parameters
----------
power : float or dimensionless YTArray.
The pow value.
"""
if isinstance(power, YTArray):
if not power.units.is_dimensionless:
raise YTUnitOperationError('power', power.unit)
# Work around a sympy issue (I think?)
#
# If I don't do this, super(YTArray, self).__pow__ returns a YTArray
# with a unit attribute set to the sympy expression 1/1 rather than
# a dimensionless Unit object.
if self.units.is_dimensionless and power == -1:
ret = super(YTArray, self).__pow__(power)
return type(self)(ret, input_units='')
return super(YTArray, self).__pow__(power)
def __abs__(self):
""" Return a YTArray with the abs of the data. """
return super(YTArray, self).__abs__()
#
# Start comparison operators.
#
def __lt__(self, other):
""" Test if this is less than the object on the right. """
# converts if possible
oth = validate_comparison_units(self, other, 'less_than')
return super(YTArray, self).__lt__(oth)
def __le__(self, other):
"""Test if this is less than or equal to the object on the right.
"""
oth = validate_comparison_units(self, other, 'less_than or equal')
return super(YTArray, self).__le__(oth)
def __eq__(self, other):
""" Test if this is equal to the object on the right. """
# Check that other is a YTArray.
if other is None:
# self is a YTArray, so it can't be None.
return False
oth = validate_comparison_units(self, other, 'equal')
return super(YTArray, self).__eq__(oth)
def __ne__(self, other):
""" Test if this is not equal to the object on the right. """
# Check that the other is a YTArray.
if other is None:
return True
oth = validate_comparison_units(self, other, 'not equal')
return super(YTArray, self).__ne__(oth)
def __ge__(self, other):
""" Test if this is greater than or equal to other. """
# Check that the other is a YTArray.
oth = validate_comparison_units(
self, other, 'greater than or equal')
return super(YTArray, self).__ge__(oth)
def __gt__(self, other):
""" Test if this is greater than the object on the right. """
# Check that the other is a YTArray.
oth = validate_comparison_units(self, other, 'greater than')
return super(YTArray, self).__gt__(oth)
#
# End comparison operators
#
#
# Begin reduction operators
#
@return_arr
def prod(self, axis=None, dtype=None, out=None):
if axis is not None:
units = self.units**self.shape[axis]
else:
units = self.units**self.size
return super(YTArray, self).prod(axis, dtype, out), units
@return_arr
def mean(self, axis=None, dtype=None, out=None):
return super(YTArray, self).mean(axis, dtype, out), self.units
@return_arr
def sum(self, axis=None, dtype=None, out=None):
return super(YTArray, self).sum(axis, dtype, out), self.units
@return_arr
def std(self, axis=None, dtype=None, out=None, ddof=0):
return super(YTArray, self).std(axis, dtype, out, ddof), self.units
def __array_wrap__(self, out_arr, context=None):
ret = super(YTArray, self).__array_wrap__(out_arr, context)
if isinstance(ret, YTQuantity) and ret.shape != ():
ret = ret.view(YTArray)
if context is None:
if ret.shape == ():
return ret[()]
else:
return ret
ufunc = context[0]
inputs = context[1]
if ufunc in unary_operators:
out_arr, inp, u = get_inp_u_unary(ufunc, inputs, out_arr)
unit = self._ufunc_registry[context[0]](u)
ret_class = type(self)
elif ufunc in binary_operators:
unit_operator = self._ufunc_registry[context[0]]
inps, units, ret_class = get_inp_u_binary(ufunc, inputs)
if unit_operator in (preserve_units, comparison_unit,
arctan2_unit):
inps, units = handle_comparison_units(
inps, units, ufunc, ret_class, raise_error=True)
unit = unit_operator(*units)
if unit_operator in (multiply_units, divide_units):
out_arr, out_arr, unit = handle_multiply_divide_units(
unit, units, out_arr, out_arr)
else:
raise RuntimeError(
"Support for the %s ufunc has not been added "
"to YTArray." % str(context[0]))
if unit is None:
out_arr = np.array(out_arr, copy=False)
return out_arr
out_arr.units = unit
if out_arr.size == 1:
return YTQuantity(np.array(out_arr), unit)
else:
if ret_class is YTQuantity:
# This happens if you do ndarray * YTQuantity. Explicitly
# casting to YTArray avoids creating a YTQuantity with
# size > 1
return YTArray(np.array(out_arr), unit)
return ret_class(np.array(out_arr, copy=False), unit)
else: # numpy version equal to or newer than 1.13
def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
func = getattr(ufunc, method)
if 'out' in kwargs:
out_orig = kwargs.pop('out')
out = np.asarray(out_orig[0])
else:
out = None
if len(inputs) == 1:
_, inp, u = get_inp_u_unary(ufunc, inputs)
out_arr = func(np.asarray(inp), out=out, **kwargs)
if ufunc in (multiply, divide) and method == 'reduce':
power_sign = POWER_SIGN_MAPPING[ufunc]
if 'axis' in kwargs and kwargs['axis'] is not None:
unit = u**(power_sign*inp.shape[kwargs['axis']])
else:
unit = u**(power_sign*inp.size)
else:
unit = self._ufunc_registry[ufunc](u)
ret_class = type(self)
elif len(inputs) == 2:
unit_operator = self._ufunc_registry[ufunc]
inps, units, ret_class = get_inp_u_binary(ufunc, inputs)
if unit_operator in (comparison_unit, arctan2_unit):
inps, units = handle_comparison_units(
inps, units, ufunc, ret_class)
elif unit_operator is preserve_units:
inps, units = handle_preserve_units(
inps, units, ufunc, ret_class)
unit = unit_operator(*units)
out_arr = func(np.asarray(inps[0]), np.asarray(inps[1]),
out=out, **kwargs)
if unit_operator in (multiply_units, divide_units):
out, out_arr, unit = handle_multiply_divide_units(
unit, units, out, out_arr)
else:
raise RuntimeError(
"Support for the %s ufunc with %i inputs has not been"
"added to YTArray." % (str(ufunc), len(inputs)))
if unit is None:
out_arr = np.array(out_arr, copy=False)
elif ufunc in (modf, divmod_):
out_arr = tuple((ret_class(o, unit) for o in out_arr))
elif out_arr.size == 1:
out_arr = YTQuantity(np.asarray(out_arr), unit)
else:
if ret_class is YTQuantity:
# This happens if you do ndarray * YTQuantity. Explicitly
# casting to YTArray avoids creating a YTQuantity with
# size > 1
out_arr = YTArray(np.asarray(out_arr), unit)
else:
out_arr = ret_class(np.asarray(out_arr), unit)
if out is not None:
out_orig[0].flat[:] = out.flat[:]
if isinstance(out_orig[0], YTArray):
out_orig[0].units = unit
return out_arr
def copy(self, order='C'):
return type(self)(np.copy( | np.asarray(self) | numpy.asarray |
from data.data_loader_dad import (
NASA_Anomaly,
WADI
)
from exp.exp_basic import Exp_Basic
from models.model import Informer
from utils.tools import EarlyStopping, adjust_learning_rate
from utils.metrics import metric
from sklearn.metrics import classification_report
import numpy as np
import torch
import torch.nn as nn
from torch import optim
from torch.utils.data import DataLoader
import os
import time
import warnings
warnings.filterwarnings('ignore')
class Exp_Informer_DAD(Exp_Basic):
def __init__(self, args):
super(Exp_Informer_DAD, self).__init__(args)
def _build_model(self):
model_dict = {
'informer':Informer,
}
if self.args.model=='informer':
model = model_dict[self.args.model](
self.args.enc_in,
self.args.dec_in,
self.args.c_out,
self.args.seq_len,
self.args.label_len,
self.args.pred_len,
self.args.factor,
self.args.d_model,
self.args.n_heads,
self.args.e_layers,
self.args.d_layers,
self.args.d_ff,
self.args.dropout,
self.args.attn,
self.args.embed,
self.args.data[:-1],
self.args.activation,
self.device
)
return model.double()
def _get_data(self, flag):
args = self.args
data_dict = {
'SMAP':NASA_Anomaly,
'MSL':NASA_Anomaly,
'WADI':WADI,
}
Data = data_dict[self.args.data]
if flag == 'test':
shuffle_flag = False; drop_last = True; batch_size = args.batch_size
else:
shuffle_flag = True; drop_last = True; batch_size = args.batch_size
data_set = Data(
root_path=args.root_path,
data_path=args.data_path,
flag=flag,
size=[args.seq_len, args.label_len, args.pred_len],
features=args.features,
target=args.target
)
print(flag, len(data_set))
data_loader = DataLoader(
data_set,
batch_size=batch_size,
shuffle=shuffle_flag,
num_workers=args.num_workers,
drop_last=drop_last)
return data_set, data_loader
def _select_optimizer(self):
model_optim = optim.Adam(self.model.parameters(), lr=self.args.learning_rate)
return model_optim
def _select_criterion(self):
criterion = nn.MSELoss()
return criterion
def vali(self, vali_data, vali_loader, criterion):
self.model.eval()
total_loss = []
for i, (batch_x,batch_y,batch_x_mark,batch_y_mark,batch_label) in enumerate(vali_loader):
batch_x = batch_x.double().to(self.device)
batch_y = batch_y.double()
batch_x_mark = batch_x_mark.double().to(self.device)
batch_y_mark = batch_y_mark.double().to(self.device)
# decoder input
dec_inp = torch.zeros_like(batch_y[:,-self.args.pred_len:,:]).double()
dec_inp = torch.cat([batch_y[:,:self.args.label_len,:], dec_inp], dim=1).double().to(self.device)
# encoder - decoder
outputs = self.model(batch_x, batch_x_mark, dec_inp, batch_y_mark)
batch_y = batch_y[:,-self.args.pred_len:,:].to(self.device)
pred = outputs.detach().cpu()
true = batch_y.detach().cpu()
loss = criterion(pred, true)
total_loss.append(loss)
total_loss = np.average(total_loss)
self.model.train()
return total_loss
def train(self, setting):
train_data, train_loader = self._get_data(flag = 'train')
vali_data, vali_loader = self._get_data(flag = 'val')
test_data, test_loader = self._get_data(flag = 'test')
path = './checkpoints/'+setting
if not os.path.exists(path):
os.makedirs(path)
time_now = time.time()
train_steps = len(train_loader)
early_stopping = EarlyStopping(patience=self.args.patience, verbose=True)
model_optim = self._select_optimizer()
criterion = self._select_criterion()
for epoch in range(self.args.train_epochs):
iter_count = 0
train_loss = []
self.model.train()
for i, (batch_x,batch_y,batch_x_mark,batch_y_mark) in enumerate(train_loader):
iter_count += 1
model_optim.zero_grad()
batch_x = batch_x.double().to(self.device)
batch_y = batch_y.double()
batch_x_mark = batch_x_mark.double().to(self.device)
batch_y_mark = batch_y_mark.double().to(self.device)
# decoder input
dec_inp = torch.zeros_like(batch_y[:,-self.args.pred_len:,:]).double()
dec_inp = torch.cat([batch_y[:,:self.args.label_len,:], dec_inp], dim=1).double().to(self.device)
# encoder - decoder
outputs = self.model(batch_x, batch_x_mark, dec_inp, batch_y_mark)
batch_y = batch_y[:,-self.args.pred_len:,:].to(self.device)
loss = criterion(outputs, batch_y)
train_loss.append(loss.item())
if (i+1) % 100==0:
print("\titers: {0}, epoch: {1} | loss: {2:.7f}".format(i + 1, epoch + 1, loss.item()))
speed = (time.time()-time_now)/iter_count
left_time = speed*((self.args.train_epochs - epoch)*train_steps - i)
print('\tspeed: {:.4f}s/iter; left time: {:.4f}s'.format(speed, left_time))
iter_count = 0
time_now = time.time()
loss.backward()
model_optim.step()
train_loss = np.average(train_loss)
vali_loss = self.vali(vali_data, vali_loader, criterion)
test_loss = self.vali(test_data, test_loader, criterion)
print("Epoch: {0}, Steps: {1} | Train Loss: {2:.7f} Vali Loss: {3:.7f} Test Loss: {4:.7f}".format(
epoch + 1, train_steps, train_loss, vali_loss, test_loss))
early_stopping(vali_loss, self.model, path)
if early_stopping.early_stop:
print("Early stopping")
break
adjust_learning_rate(model_optim, epoch+1, self.args)
best_model_path = path+'/'+'checkpoint.pth'
self.model.load_state_dict(torch.load(best_model_path))
return self.model
def test(self, setting):
test_data, test_loader = self._get_data(flag='test')
self.model.eval()
preds = []
trues = []
labels = []
with torch.no_grad():
for i, (batch_x,batch_y,batch_x_mark,batch_y_mark,batch_label) in enumerate(test_loader):
batch_x = batch_x.double().to(self.device)
batch_y = batch_y.double()
batch_x_mark = batch_x_mark.double().to(self.device)
batch_y_mark = batch_y_mark.double().to(self.device)
# decoder input
dec_inp = torch.zeros_like(batch_y[:,-self.args.pred_len:,:]).double()
dec_inp = torch.cat([batch_y[:,:self.args.label_len,:], dec_inp], dim=1).double().to(self.device)
# encoder - decoder
outputs = self.model(batch_x, batch_x_mark, dec_inp, batch_y_mark)
batch_y = batch_y[:,-self.args.pred_len:,:].to(self.device)
pred = outputs.detach().cpu().numpy()#.squeeze()
true = batch_y.detach().cpu().numpy()#.squeeze()
batch_label = batch_label.long().detach().numpy()
preds.append(pred)
trues.append(true)
labels.append(batch_label)
preds = np.array(preds)
trues = | np.array(trues) | numpy.array |
#!/usr/bin/env python3
from __future__ import absolute_import, division, print_function
import curses
import sys
from collections import deque
from datetime import datetime
import numpy as np
import rospy
from diagnostic_msgs.msg import DiagnosticArray, DiagnosticStatus
from geometry_msgs.msg import PoseStamped
from mavros_msgs.msg import ExtendedState, PositionTarget, State # StatusText
from scipy.spatial.transform import Rotation as R
from sensor_msgs.msg import BatteryState, Image, NavSatFix
GPS_FIX_DICT = {
0: ('No GPS', curses.COLOR_RED),
1: ('No fix', curses.COLOR_RED),
2: ('2D lock', curses.COLOR_BLUE),
3: ('3D lock', curses.COLOR_BLUE),
4: ('DGPS', curses.COLOR_MAGENTA),
5: ('RTK float', curses.COLOR_YELLOW),
6: ('RTK fix', curses.COLOR_GREEN)
}
def get_color(color):
return curses.color_pair(color)
def frequency_from_messages(messages):
durations = []
for i in range(len(messages) - 1):
duration = messages[i + 1].header.stamp - messages[i].header.stamp
durations.append(duration.to_sec())
frequency = 1 / | np.mean(durations) | numpy.mean |
import numpy as np
from stumpff import C, S
from CelestialBody import BODIES
from numerical import newton, laguerre
from lagrange import calc_f, calc_fd, calc_g, calc_gd
def kepler_chi(chi, alpha, r0, vr0, mu, dt):
''' Kepler's Equation of the universal anomaly, modified
for use in numerical solvers. '''
z = alpha*chi**2
return (r0*vr0/np.sqrt(mu))*chi**2*C(z) + \
(1 - alpha*r0)*chi**3*S(z) + \
r0*chi - np.sqrt(mu)*dt
def dkepler_dchi(chi, alpha, r0, vr0, mu, dt):
''' Derivative of Kepler's Equation of the universal anomaly,
modified for use in numerical solvers. '''
z = alpha*chi**2
return (r0*vr0/np.sqrt(mu))*chi*(1 - alpha*chi**2*S(z)) + \
(1 - alpha*r0)*chi**2*C(z) + r0
def d2kepler_dchi2(chi, alpha, r0, vr0, mu, dt):
''' Second derivative of Kepler's Equation of the universal
anomaly, modified for use in numerical solvers. '''
z = alpha*chi**2
S_ = S(z)
return (r0*vr0/np.sqrt(mu))*(1 - 3*z*S_ + z*(C(z) - 3*S_)) + \
chi*(1 - z*S_)*(1 - alpha*r0)
def solve_kepler_chi(r_0, v_0, dt, body=BODIES['Earth'], method='laguerre', tol=1e-7, max_iters=100):
''' Solve Kepler's Equation of the universal anomaly chi using the specified
numerical method. Applies Algorithm 3.4 from Orbital Mechanics for Engineering
Students, 4 ed, Curtis.
:param r_0: `iterable` (km) initial position 3-vector
:param v_0: `iterable` (km/s) initial velocity 3-vector
:param dt: `float` (s) time after initial state to solve for r, v as 3-vectors
:param body: `CelestialBody` (--) the celestial body to use for orbital parameters
:param method: `str` (--) which numerical method to use to solve Kepler's Equation
:param tol: `float` (--) decimal tolerance for numerical method (default 1e-7 is IEEE 745 single precision)
:param max_iters: `int` (--) maximum number of iterations in numerical method before breaking
:return: (km) final position 3-vector, (km/s) final velocity 3-vector
'''
VALID_METHODS = ('laguerre', 'newton')
mu = body.mu # (km**3/s**2) gravitational parameter of the specified primary body
r0 = np.linalg.norm(r_0) # (km) initial position magnitude
v0 = np.linalg.norm(v_0) # (km/s) initial velocity magnitude
vr0 = np.dot(v_0, r_0)/r0 # (km/s) initial radial velocity magnitude
alpha = 2/r0 - v0**2/mu # (1/km) inverse of semi-major axis
chi0 = np.sqrt(mu)*np.abs(alpha)*dt
if method not in VALID_METHODS:
print(f'Method \'{method}\' is not valid, must be one of {VALID_METHODS}.\nDefaulting to laguerre method.')
chi, _, _ = laguerre(chi0, kepler_chi, dkepler_dchi, d2kepler_dchi2, alpha, r0, vr0, mu, dt)
elif method == 'newton':
chi, _, _ = newton(chi0, kepler_chi, dkepler_dchi, alpha, r0, vr0, mu, dt)
else: # method == 'laguerre'
chi, _, _ = laguerre(chi0, kepler_chi, dkepler_dchi, d2kepler_dchi2, alpha, r0, vr0, mu, dt)
f = calc_f(chi, r0, alpha)
g = calc_g(dt, mu, chi, alpha)
r_1 = f*r_0 + g*v_0
r1 = np.linalg.norm(r_1)
fd = calc_fd(mu, r1, r0, alpha, chi)
gd = calc_gd(chi, r1, alpha)
v_1 = fd*r_0 + gd*v_0
return r_1, v_1
def solve_kepler_E(e, Me, tol=1e-7, max_iters=100):
''' Solve Kepler's Equation in the form containing Eccentric Anomaly (E),
eccentricity (e), and Mean Anomaly of Ellipse (Me). Uses Algorithm 3.1 from Orbital
Mechanics for Engineering Students, 4 ed, Curtis. '''
# TODO: have this function make use of one of the numerical methods in numerical.py
def f(E, e, Me):
return E - e*np.sin(E) - Me
def fp(E, e):
return 1 - e*np.cos(E)
E = Me + e/2 if Me < np.pi else Me - e/2
ratio = f(E, e, Me)/fp(E, e)
iters = 0
while abs(ratio) > tol and iters < max_iters:
E -= ratio
ratio = f(E, e, Me)/fp(E, e)
iters += 1
E -= ratio
converged = np.abs(ratio) <= tol
return E, iters, converged
def test():
''' Test the functionality of solve_kepler_chi
and solve_kepler_laguerre using Problem 3.20 from
Orbital Mechanics for Engineering Students, 4 ed, Curtis.
'''
# given starting information
Earth = BODIES['Earth'] # `CelestialBody` (--) Earth and all the Earth things
r_0 = np.array([20000, -105000, -19000]) # (km) initial position vector
v_0 = np.array([0.9, -3.4, -1.5]) # (km/s) initial velocity vector
dt = 2*60*60 # (s) time of interest after initial time
# given correct answer from textbook
correct_r_1 = np.array([26338, -128750, -29656]) # (km) final position vector
correct_v_1 = np.array([0.86280, -3.2116, -1.4613]) # (km/s) final velocity vector
# solve using above methods
r_n, v_n = solve_kepler_chi(r_0, v_0, dt, Earth, method='newton')
r_l, v_l = solve_kepler_chi(r_0, v_0, dt, Earth, method='laguerre')
# check correctness
# tolerance based on significant figures of given answers
newton_valid = np.allclose(r_n, correct_r_1, atol=1) and | np.allclose(v_n, correct_v_1, atol=1e-4) | numpy.allclose |
# coding: utf-8
# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Test the Logarithmic Units and Quantities
"""
from __future__ import (absolute_import, unicode_literals, division,
print_function)
from ...extern import six
from ...extern.six.moves import zip
import pickle
import itertools
import pytest
import numpy as np
from numpy.testing.utils import assert_allclose
from ...tests.helper import assert_quantity_allclose
from ... import units as u, constants as c
lu_units = [u.dex, u.mag, u.decibel]
lu_subclasses = [u.DexUnit, u.MagUnit, u.DecibelUnit]
lq_subclasses = [u.Dex, u.Magnitude, u.Decibel]
pu_sample = (u.dimensionless_unscaled, u.m, u.g/u.s**2, u.Jy)
class TestLogUnitCreation(object):
def test_logarithmic_units(self):
"""Check logarithmic units are set up correctly."""
assert u.dB.to(u.dex) == 0.1
assert u.dex.to(u.mag) == -2.5
assert u.mag.to(u.dB) == -4
@pytest.mark.parametrize('lu_unit, lu_cls', zip(lu_units, lu_subclasses))
def test_callable_units(self, lu_unit, lu_cls):
assert isinstance(lu_unit, u.UnitBase)
assert callable(lu_unit)
assert lu_unit._function_unit_class is lu_cls
@pytest.mark.parametrize('lu_unit', lu_units)
def test_equality_to_normal_unit_for_dimensionless(self, lu_unit):
lu = lu_unit()
assert lu == lu._default_function_unit # eg, MagUnit() == u.mag
assert lu._default_function_unit == lu # and u.mag == MagUnit()
@pytest.mark.parametrize('lu_unit, physical_unit',
itertools.product(lu_units, pu_sample))
def test_call_units(self, lu_unit, physical_unit):
"""Create a LogUnit subclass using the callable unit and physical unit,
and do basic check that output is right."""
lu1 = lu_unit(physical_unit)
assert lu1.physical_unit == physical_unit
assert lu1.function_unit == lu1._default_function_unit
def test_call_invalid_unit(self):
with pytest.raises(TypeError):
u.mag([])
with pytest.raises(ValueError):
u.mag(u.mag())
@pytest.mark.parametrize('lu_cls, physical_unit', itertools.product(
lu_subclasses + [u.LogUnit], pu_sample))
def test_subclass_creation(self, lu_cls, physical_unit):
"""Create a LogUnit subclass object for given physical unit,
and do basic check that output is right."""
lu1 = lu_cls(physical_unit)
assert lu1.physical_unit == physical_unit
assert lu1.function_unit == lu1._default_function_unit
lu2 = lu_cls(physical_unit,
function_unit=2*lu1._default_function_unit)
assert lu2.physical_unit == physical_unit
assert lu2.function_unit == u.Unit(2*lu2._default_function_unit)
with pytest.raises(ValueError):
lu_cls(physical_unit, u.m)
def test_predefined_magnitudes():
assert_quantity_allclose((-21.1*u.STmag).physical,
1.*u.erg/u.cm**2/u.s/u.AA)
assert_quantity_allclose((-48.6*u.ABmag).physical,
1.*u.erg/u.cm**2/u.s/u.Hz)
assert_quantity_allclose((0*u.M_bol).physical, c.L_bol0)
assert_quantity_allclose((0*u.m_bol).physical,
c.L_bol0/(4.*np.pi*(10.*c.pc)**2))
def test_predefined_reinitialisation():
assert u.mag('ST') == u.STmag
assert u.mag('AB') == u.ABmag
assert u.mag('Bol') == u.M_bol
assert u.mag('bol') == u.m_bol
def test_predefined_string_roundtrip():
"""Ensure roundtripping; see #5015"""
with u.magnitude_zero_points.enable():
assert u.Unit(u.STmag.to_string()) == u.STmag
assert u.Unit(u.ABmag.to_string()) == u.ABmag
assert u.Unit(u.M_bol.to_string()) == u.M_bol
assert u.Unit(u.m_bol.to_string()) == u.m_bol
def test_inequality():
"""Check __ne__ works (regresssion for #5342)."""
lu1 = u.mag(u.Jy)
lu2 = u.dex(u.Jy)
lu3 = u.mag(u.Jy**2)
lu4 = lu3 - lu1
assert lu1 != lu2
assert lu1 != lu3
assert lu1 == lu4
class TestLogUnitStrings(object):
def test_str(self):
"""Do some spot checks that str, repr, etc. work as expected."""
lu1 = u.mag(u.Jy)
assert str(lu1) == 'mag(Jy)'
assert repr(lu1) == 'Unit("mag(Jy)")'
assert lu1.to_string('generic') == 'mag(Jy)'
with pytest.raises(ValueError):
lu1.to_string('fits')
lu2 = u.dex()
assert str(lu2) == 'dex'
assert repr(lu2) == 'Unit("dex(1)")'
assert lu2.to_string() == 'dex(1)'
lu3 = u.MagUnit(u.Jy, function_unit=2*u.mag)
assert str(lu3) == '2 mag(Jy)'
assert repr(lu3) == 'MagUnit("Jy", unit="2 mag")'
assert lu3.to_string() == '2 mag(Jy)'
lu4 = u.mag(u.ct)
assert lu4.to_string('generic') == 'mag(ct)'
assert lu4.to_string('latex') == ('$\\mathrm{mag}$$\\mathrm{\\left( '
'\\mathrm{ct} \\right)}$')
assert lu4._repr_latex_() == lu4.to_string('latex')
class TestLogUnitConversion(object):
@pytest.mark.parametrize('lu_unit, physical_unit',
itertools.product(lu_units, pu_sample))
def test_physical_unit_conversion(self, lu_unit, physical_unit):
"""Check various LogUnit subclasses are equivalent and convertible
to their non-log counterparts."""
lu1 = lu_unit(physical_unit)
assert lu1.is_equivalent(physical_unit)
assert lu1.to(physical_unit, 0.) == 1.
assert physical_unit.is_equivalent(lu1)
assert physical_unit.to(lu1, 1.) == 0.
pu = u.Unit(8.*physical_unit)
assert lu1.is_equivalent(physical_unit)
assert lu1.to(pu, 0.) == 0.125
assert pu.is_equivalent(lu1)
assert_allclose(pu.to(lu1, 0.125), 0., atol=1.e-15)
# Check we round-trip.
value = np.linspace(0., 10., 6)
assert_allclose(pu.to(lu1, lu1.to(pu, value)), value, atol=1.e-15)
# And that we're not just returning True all the time.
pu2 = u.g
assert not lu1.is_equivalent(pu2)
with pytest.raises(u.UnitsError):
lu1.to(pu2)
assert not pu2.is_equivalent(lu1)
with pytest.raises(u.UnitsError):
pu2.to(lu1)
@pytest.mark.parametrize('lu_unit', lu_units)
def test_container_unit_conversion(self, lu_unit):
"""Check that conversion to logarithmic units (u.mag, u.dB, u.dex)
is only possible when the physical unit is dimensionless."""
values = np.linspace(0., 10., 6)
lu1 = lu_unit(u.dimensionless_unscaled)
assert lu1.is_equivalent(lu1.function_unit)
assert_allclose(lu1.to(lu1.function_unit, values), values)
lu2 = lu_unit(u.Jy)
assert not lu2.is_equivalent(lu2.function_unit)
with pytest.raises(u.UnitsError):
lu2.to(lu2.function_unit, values)
@pytest.mark.parametrize(
'flu_unit, tlu_unit, physical_unit',
itertools.product(lu_units, lu_units, pu_sample))
def test_subclass_conversion(self, flu_unit, tlu_unit, physical_unit):
"""Check various LogUnit subclasses are equivalent and convertible
to each other if they correspond to equivalent physical units."""
values = np.linspace(0., 10., 6)
flu = flu_unit(physical_unit)
tlu = tlu_unit(physical_unit)
assert flu.is_equivalent(tlu)
assert_allclose(flu.to(tlu), flu.function_unit.to(tlu.function_unit))
assert_allclose(flu.to(tlu, values),
values * flu.function_unit.to(tlu.function_unit))
tlu2 = tlu_unit(u.Unit(100.*physical_unit))
assert flu.is_equivalent(tlu2)
# Check that we round-trip.
assert_allclose(flu.to(tlu2, tlu2.to(flu, values)), values, atol=1.e-15)
tlu3 = tlu_unit(physical_unit.to_system(u.si)[0])
assert flu.is_equivalent(tlu3)
assert_allclose(flu.to(tlu3, tlu3.to(flu, values)), values, atol=1.e-15)
tlu4 = tlu_unit(u.g)
assert not flu.is_equivalent(tlu4)
with pytest.raises(u.UnitsError):
flu.to(tlu4, values)
def test_unit_decomposition(self):
lu = u.mag(u.Jy)
assert lu.decompose() == u.mag(u.Jy.decompose())
assert lu.decompose().physical_unit.bases == [u.kg, u.s]
assert lu.si == u.mag(u.Jy.si)
assert lu.si.physical_unit.bases == [u.kg, u.s]
assert lu.cgs == u.mag(u.Jy.cgs)
assert lu.cgs.physical_unit.bases == [u.g, u.s]
def test_unit_multiple_possible_equivalencies(self):
lu = u.mag(u.Jy)
assert lu.is_equivalent(pu_sample)
class TestLogUnitArithmetic(object):
def test_multiplication_division(self):
"""Check that multiplication/division with other units is only
possible when the physical unit is dimensionless, and that this
turns the unit into a normal one."""
lu1 = u.mag(u.Jy)
with pytest.raises(u.UnitsError):
lu1 * u.m
with pytest.raises(u.UnitsError):
u.m * lu1
with pytest.raises(u.UnitsError):
lu1 / lu1
for unit in (u.dimensionless_unscaled, u.m, u.mag, u.dex):
with pytest.raises(u.UnitsError):
lu1 / unit
lu2 = u.mag(u.dimensionless_unscaled)
with pytest.raises(u.UnitsError):
lu2 * lu1
with pytest.raises(u.UnitsError):
lu2 / lu1
# But dimensionless_unscaled can be cancelled.
assert lu2 / lu2 == u.dimensionless_unscaled
# With dimensionless, normal units are OK, but we return a plain unit.
tf = lu2 * u.m
tr = u.m * lu2
for t in (tf, tr):
assert not isinstance(t, type(lu2))
assert t == lu2.function_unit * u.m
with u.set_enabled_equivalencies(u.logarithmic()):
with pytest.raises(u.UnitsError):
t.to(lu2.physical_unit)
# Now we essentially have a LogUnit with a prefactor of 100,
# so should be equivalent again.
t = tf / u.cm
with u.set_enabled_equivalencies(u.logarithmic()):
assert t.is_equivalent(lu2.function_unit)
assert_allclose(t.to(u.dimensionless_unscaled, np.arange(3.)/100.),
lu2.to(lu2.physical_unit, np.arange(3.)))
# If we effectively remove lu1, a normal unit should be returned.
t2 = tf / lu2
assert not isinstance(t2, type(lu2))
assert t2 == u.m
t3 = tf / lu2.function_unit
assert not isinstance(t3, type(lu2))
assert t3 == u.m
# For completeness, also ensure non-sensical operations fail
with pytest.raises(TypeError):
lu1 * object()
with pytest.raises(TypeError):
slice(None) * lu1
with pytest.raises(TypeError):
lu1 / []
with pytest.raises(TypeError):
1 / lu1
@pytest.mark.parametrize('power', (2, 0.5, 1, 0))
def test_raise_to_power(self, power):
"""Check that raising LogUnits to some power is only possible when the
physical unit is dimensionless, and that conversion is turned off when
the resulting logarithmic unit (such as mag**2) is incompatible."""
lu1 = u.mag(u.Jy)
if power == 0:
assert lu1 ** power == u.dimensionless_unscaled
elif power == 1:
assert lu1 ** power == lu1
else:
with pytest.raises(u.UnitsError):
lu1 ** power
# With dimensionless, though, it works, but returns a normal unit.
lu2 = u.mag(u.dimensionless_unscaled)
t = lu2**power
if power == 0:
assert t == u.dimensionless_unscaled
elif power == 1:
assert t == lu2
else:
assert not isinstance(t, type(lu2))
assert t == lu2.function_unit**power
# also check we roundtrip
t2 = t**(1./power)
assert t2 == lu2.function_unit
with u.set_enabled_equivalencies(u.logarithmic()):
assert_allclose(t2.to(u.dimensionless_unscaled, np.arange(3.)),
lu2.to(lu2.physical_unit, np.arange(3.)))
@pytest.mark.parametrize('other', pu_sample)
def test_addition_subtraction_to_normal_units_fails(self, other):
lu1 = u.mag(u.Jy)
with pytest.raises(u.UnitsError):
lu1 + other
with pytest.raises(u.UnitsError):
lu1 - other
with pytest.raises(u.UnitsError):
other - lu1
def test_addition_subtraction_to_non_units_fails(self):
lu1 = u.mag(u.Jy)
with pytest.raises(TypeError):
lu1 + 1.
with pytest.raises(TypeError):
lu1 - [1., 2., 3.]
@pytest.mark.parametrize(
'other', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m),
u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag)))
def test_addition_subtraction(self, other):
"""Check physical units are changed appropriately"""
lu1 = u.mag(u.Jy)
other_pu = getattr(other, 'physical_unit', u.dimensionless_unscaled)
lu_sf = lu1 + other
assert lu_sf.is_equivalent(lu1.physical_unit * other_pu)
lu_sr = other + lu1
assert lu_sr.is_equivalent(lu1.physical_unit * other_pu)
lu_df = lu1 - other
assert lu_df.is_equivalent(lu1.physical_unit / other_pu)
lu_dr = other - lu1
assert lu_dr.is_equivalent(other_pu / lu1.physical_unit)
def test_complicated_addition_subtraction(self):
"""for fun, a more complicated example of addition and subtraction"""
dm0 = u.Unit('DM', 1./(4.*np.pi*(10.*u.pc)**2))
lu_dm = u.mag(dm0)
lu_absST = u.STmag - lu_dm
assert lu_absST.is_equivalent(u.erg/u.s/u.AA)
def test_neg_pos(self):
lu1 = u.mag(u.Jy)
neg_lu = -lu1
assert neg_lu != lu1
assert neg_lu.physical_unit == u.Jy**-1
assert -neg_lu == lu1
pos_lu = +lu1
assert pos_lu is not lu1
assert pos_lu == lu1
def test_pickle():
lu1 = u.dex(u.cm/u.s**2)
s = pickle.dumps(lu1)
lu2 = pickle.loads(s)
assert lu1 == lu2
def test_hashable():
lu1 = u.dB(u.mW)
lu2 = u.dB(u.m)
lu3 = u.dB(u.mW)
assert hash(lu1) != hash(lu2)
assert hash(lu1) == hash(lu3)
luset = {lu1, lu2, lu3}
assert len(luset) == 2
class TestLogQuantityCreation(object):
@pytest.mark.parametrize('lq, lu', zip(lq_subclasses + [u.LogQuantity],
lu_subclasses + [u.LogUnit]))
def test_logarithmic_quantities(self, lq, lu):
"""Check logarithmic quantities are all set up correctly"""
assert lq._unit_class == lu
assert type(lu()._quantity_class(1.)) is lq
@pytest.mark.parametrize('lq_cls, physical_unit',
itertools.product(lq_subclasses, pu_sample))
def test_subclass_creation(self, lq_cls, physical_unit):
"""Create LogQuantity subclass objects for some physical units,
and basic check on transformations"""
value = np.arange(1., 10.)
log_q = lq_cls(value * physical_unit)
assert log_q.unit.physical_unit == physical_unit
assert log_q.unit.function_unit == log_q.unit._default_function_unit
assert_allclose(log_q.physical.value, value)
with pytest.raises(ValueError):
lq_cls(value, physical_unit)
@pytest.mark.parametrize(
'unit', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m),
u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag),
u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag)))
def test_different_units(self, unit):
q = u.Magnitude(1.23, unit)
assert q.unit.function_unit == getattr(unit, 'function_unit', unit)
assert q.unit.physical_unit is getattr(unit, 'physical_unit',
u.dimensionless_unscaled)
@pytest.mark.parametrize('value, unit', (
(1.*u.mag(u.Jy), None),
(1.*u.dex(u.Jy), None),
(1.*u.mag(u.W/u.m**2/u.Hz), u.mag(u.Jy)),
(1.*u.dex(u.W/u.m**2/u.Hz), u.mag(u.Jy))))
def test_function_values(self, value, unit):
lq = u.Magnitude(value, unit)
assert lq == value
assert lq.unit.function_unit == u.mag
assert lq.unit.physical_unit == getattr(unit, 'physical_unit',
value.unit.physical_unit)
@pytest.mark.parametrize(
'unit', (u.mag(), u.mag(u.Jy), u.mag(u.m), u.MagUnit('', 2.*u.mag),
u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag)))
def test_indirect_creation(self, unit):
q1 = 2.5 * unit
assert isinstance(q1, u.Magnitude)
assert q1.value == 2.5
assert q1.unit == unit
pv = 100. * unit.physical_unit
q2 = unit * pv
assert q2.unit == unit
assert q2.unit.physical_unit == pv.unit
assert q2.to_value(unit.physical_unit) == 100.
assert (q2._function_view / u.mag).to_value(1) == -5.
q3 = unit / 0.4
assert q3 == q1
def test_from_view(self):
# Cannot view a physical quantity as a function quantity, since the
# values would change.
q = [100., 1000.] * u.cm/u.s**2
with pytest.raises(TypeError):
q.view(u.Dex)
# But fine if we have the right magnitude.
q = [2., 3.] * u.dex
lq = q.view(u.Dex)
assert isinstance(lq, u.Dex)
assert lq.unit.physical_unit == u.dimensionless_unscaled
assert np.all(q == lq)
def test_using_quantity_class(self):
"""Check that we can use Quantity if we have subok=True"""
# following issue #5851
lu = u.dex(u.AA)
with pytest.raises(u.UnitTypeError):
u.Quantity(1., lu)
q = u.Quantity(1., lu, subok=True)
assert type(q) is lu._quantity_class
def test_conversion_to_and_from_physical_quantities():
"""Ensures we can convert from regular quantities."""
mst = [10., 12., 14.] * u.STmag
flux_lambda = mst.physical
mst_roundtrip = flux_lambda.to(u.STmag)
# check we return a logquantity; see #5178.
assert isinstance(mst_roundtrip, u.Magnitude)
assert mst_roundtrip.unit == mst.unit
assert_allclose(mst_roundtrip.value, mst.value)
wave = [4956.8, 4959.55, 4962.3] * u.AA
flux_nu = mst.to(u.Jy, equivalencies=u.spectral_density(wave))
mst_roundtrip2 = flux_nu.to(u.STmag, u.spectral_density(wave))
assert isinstance(mst_roundtrip2, u.Magnitude)
assert mst_roundtrip2.unit == mst.unit
assert_allclose(mst_roundtrip2.value, mst.value)
def test_quantity_decomposition():
lq = 10.*u.mag(u.Jy)
assert lq.decompose() == lq
assert lq.decompose().unit.physical_unit.bases == [u.kg, u.s]
assert lq.si == lq
assert lq.si.unit.physical_unit.bases == [u.kg, u.s]
assert lq.cgs == lq
assert lq.cgs.unit.physical_unit.bases == [u.g, u.s]
class TestLogQuantityViews(object):
def setup(self):
self.lq = u.Magnitude(np.arange(10.) * u.Jy)
self.lq2 = u.Magnitude(np.arange(5.))
def test_value_view(self):
lq_value = self.lq.value
assert type(lq_value) is np.ndarray
lq_value[2] = -1.
assert np.all(self.lq.value == lq_value)
def test_function_view(self):
lq_fv = self.lq._function_view
assert type(lq_fv) is u.Quantity
assert lq_fv.unit is self.lq.unit.function_unit
lq_fv[3] = -2. * lq_fv.unit
assert np.all(self.lq.value == lq_fv.value)
def test_quantity_view(self):
# Cannot view as Quantity, since the unit cannot be represented.
with pytest.raises(TypeError):
self.lq.view(u.Quantity)
# But a dimensionless one is fine.
q2 = self.lq2.view(u.Quantity)
assert q2.unit is u.mag
assert np.all(q2.value == self.lq2.value)
lq3 = q2.view(u.Magnitude)
assert type(lq3.unit) is u.MagUnit
assert lq3.unit.physical_unit == u.dimensionless_unscaled
assert np.all(lq3 == self.lq2)
class TestLogQuantitySlicing(object):
def test_item_get_and_set(self):
lq1 = u.Magnitude(np.arange(1., 11.)*u.Jy)
assert lq1[9] == u.Magnitude(10.*u.Jy)
lq1[2] = 100.*u.Jy
assert lq1[2] == u.Magnitude(100.*u.Jy)
with pytest.raises(u.UnitsError):
lq1[2] = 100.*u.m
with pytest.raises(u.UnitsError):
lq1[2] = 100.*u.mag
with pytest.raises(u.UnitsError):
lq1[2] = u.Magnitude(100.*u.m)
assert lq1[2] == u.Magnitude(100.*u.Jy)
def test_slice_get_and_set(self):
lq1 = u.Magnitude(np.arange(1., 10.)*u.Jy)
lq1[2:4] = 100.*u.Jy
assert np.all(lq1[2:4] == u.Magnitude(100.*u.Jy))
with pytest.raises(u.UnitsError):
lq1[2:4] = 100.*u.m
with pytest.raises(u.UnitsError):
lq1[2:4] = 100.*u.mag
with pytest.raises(u.UnitsError):
lq1[2:4] = u.Magnitude(100.*u.m)
assert np.all(lq1[2] == u.Magnitude(100.*u.Jy))
class TestLogQuantityArithmetic(object):
def test_multiplication_division(self):
"""Check that multiplication/division with other quantities is only
possible when the physical unit is dimensionless, and that this turns
the result into a normal quantity."""
lq = u.Magnitude( | np.arange(1., 11.) | numpy.arange |
from abc import ABCMeta, abstractmethod
import os
from vmaf.tools.misc import make_absolute_path, run_process
from vmaf.tools.stats import ListStats
__copyright__ = "Copyright 2016-2018, Netflix, Inc."
__license__ = "Apache, Version 2.0"
import re
import numpy as np
import ast
from vmaf import ExternalProgramCaller, to_list
from vmaf.config import VmafConfig, VmafExternalConfig
from vmaf.core.executor import Executor
from vmaf.core.result import Result
from vmaf.tools.reader import YuvReader
class FeatureExtractor(Executor):
"""
FeatureExtractor takes in a list of assets, and run feature extraction on
them, and return a list of corresponding results. A FeatureExtractor must
specify a unique type and version combination (by the TYPE and VERSION
attribute), so that the Result generated by it can be identified.
A derived class of FeatureExtractor must:
1) Override TYPE and VERSION
2) Override _generate_result(self, asset), which call a
command-line executable and generate feature scores in a log file.
3) Override _get_feature_scores(self, asset), which read the feature
scores from the log file, and return the scores in a dictionary format.
For an example, follow VmafFeatureExtractor.
"""
__metaclass__ = ABCMeta
@property
@abstractmethod
def ATOM_FEATURES(self):
raise NotImplementedError
def _read_result(self, asset):
result = {}
result.update(self._get_feature_scores(asset))
executor_id = self.executor_id
return Result(asset, executor_id, result)
@classmethod
def get_scores_key(cls, atom_feature):
return "{type}_{atom_feature}_scores".format(
type=cls.TYPE, atom_feature=atom_feature)
@classmethod
def get_score_key(cls, atom_feature):
return "{type}_{atom_feature}_score".format(
type=cls.TYPE, atom_feature=atom_feature)
def _get_feature_scores(self, asset):
# routine to read the feature scores from the log file, and return
# the scores in a dictionary format.
log_file_path = self._get_log_file_path(asset)
atom_feature_scores_dict = {}
atom_feature_idx_dict = {}
for atom_feature in self.ATOM_FEATURES:
atom_feature_scores_dict[atom_feature] = []
atom_feature_idx_dict[atom_feature] = 0
with open(log_file_path, 'rt') as log_file:
for line in log_file.readlines():
for atom_feature in self.ATOM_FEATURES:
re_template = "{af}: ([0-9]+) ([a-zA-Z0-9.-]+)".format(af=atom_feature)
mo = re.match(re_template, line)
if mo:
cur_idx = int(mo.group(1))
assert cur_idx == atom_feature_idx_dict[atom_feature]
# parse value, allowing NaN and inf
val = float(mo.group(2))
if np.isnan(val) or np.isinf(val):
val = None
atom_feature_scores_dict[atom_feature].append(val)
atom_feature_idx_dict[atom_feature] += 1
continue
len_score = len(atom_feature_scores_dict[self.ATOM_FEATURES[0]])
assert len_score != 0
for atom_feature in self.ATOM_FEATURES[1:]:
assert len_score == len(atom_feature_scores_dict[atom_feature]), \
"Feature data possibly corrupt. Run cleanup script and try again."
feature_result = {}
for atom_feature in self.ATOM_FEATURES:
scores_key = self.get_scores_key(atom_feature)
feature_result[scores_key] = atom_feature_scores_dict[atom_feature]
return feature_result
class VmafFeatureExtractor(FeatureExtractor):
TYPE = "VMAF_feature"
# VERSION = '0.1' # vmaf_study; Anush's VIF fix
# VERSION = '0.2' # expose vif_num, vif_den, adm_num, adm_den, anpsnr
# VERSION = '0.2.1' # expose vif num/den of each scale
# VERSION = '0.2.2' # adm abs-->fabs, corrected border handling, uniform reading with option of offset for input YUV, updated VIF corner case
# VERSION = '0.2.2b' # expose adm_den/num_scalex
# VERSION = '0.2.3' # AVX for VMAF convolution; update adm features by folding noise floor into per coef
# VERSION = '0.2.4' # Fix a bug in adm feature passing scale into dwt_quant_step
# VERSION = '0.2.4b' # Modify by adding ADM noise floor outside cube root; add derived feature motion2
VERSION = '0.2.4c' # Modify by moving motion2 to c code
ATOM_FEATURES = ['vif', 'adm', 'ansnr', 'motion', 'motion2',
'vif_num', 'vif_den', 'adm_num', 'adm_den', 'anpsnr',
'vif_num_scale0', 'vif_den_scale0',
'vif_num_scale1', 'vif_den_scale1',
'vif_num_scale2', 'vif_den_scale2',
'vif_num_scale3', 'vif_den_scale3',
'adm_num_scale0', 'adm_den_scale0',
'adm_num_scale1', 'adm_den_scale1',
'adm_num_scale2', 'adm_den_scale2',
'adm_num_scale3', 'adm_den_scale3',
]
DERIVED_ATOM_FEATURES = ['vif_scale0', 'vif_scale1', 'vif_scale2', 'vif_scale3',
'vif2', 'adm2', 'adm3',
'adm_scale0', 'adm_scale1', 'adm_scale2', 'adm_scale3',
]
ADM2_CONSTANT = 0
ADM_SCALE_CONSTANT = 0
def _generate_result(self, asset):
# routine to call the command-line executable and generate feature
# scores in the log file.
quality_width, quality_height = asset.quality_width_height
log_file_path = self._get_log_file_path(asset)
yuv_type=self._get_workfile_yuv_type(asset)
ref_path=asset.ref_workfile_path
dis_path=asset.dis_workfile_path
w=quality_width
h=quality_height
logger = self.logger
ExternalProgramCaller.call_vmaf_feature(yuv_type, ref_path, dis_path, w, h, log_file_path, logger)
@classmethod
def _post_process_result(cls, result):
# override Executor._post_process_result
result = super(VmafFeatureExtractor, cls)._post_process_result(result)
# adm2 =
# (adm_num + ADM2_CONSTANT) / (adm_den + ADM2_CONSTANT)
adm2_scores_key = cls.get_scores_key('adm2')
adm_num_scores_key = cls.get_scores_key('adm_num')
adm_den_scores_key = cls.get_scores_key('adm_den')
result.result_dict[adm2_scores_key] = list(
(np.array(result.result_dict[adm_num_scores_key]) + cls.ADM2_CONSTANT) /
(np.array(result.result_dict[adm_den_scores_key]) + cls.ADM2_CONSTANT)
)
# vif_scalei = vif_num_scalei / vif_den_scalei, i = 0, 1, 2, 3
vif_num_scale0_scores_key = cls.get_scores_key('vif_num_scale0')
vif_den_scale0_scores_key = cls.get_scores_key('vif_den_scale0')
vif_num_scale1_scores_key = cls.get_scores_key('vif_num_scale1')
vif_den_scale1_scores_key = cls.get_scores_key('vif_den_scale1')
vif_num_scale2_scores_key = cls.get_scores_key('vif_num_scale2')
vif_den_scale2_scores_key = cls.get_scores_key('vif_den_scale2')
vif_num_scale3_scores_key = cls.get_scores_key('vif_num_scale3')
vif_den_scale3_scores_key = cls.get_scores_key('vif_den_scale3')
vif_scale0_scores_key = cls.get_scores_key('vif_scale0')
vif_scale1_scores_key = cls.get_scores_key('vif_scale1')
vif_scale2_scores_key = cls.get_scores_key('vif_scale2')
vif_scale3_scores_key = cls.get_scores_key('vif_scale3')
result.result_dict[vif_scale0_scores_key] = list(
(np.array(result.result_dict[vif_num_scale0_scores_key])
/ np.array(result.result_dict[vif_den_scale0_scores_key]))
)
result.result_dict[vif_scale1_scores_key] = list(
(np.array(result.result_dict[vif_num_scale1_scores_key])
/ np.array(result.result_dict[vif_den_scale1_scores_key]))
)
result.result_dict[vif_scale2_scores_key] = list(
(np.array(result.result_dict[vif_num_scale2_scores_key])
/ np.array(result.result_dict[vif_den_scale2_scores_key]))
)
result.result_dict[vif_scale3_scores_key] = list(
(np.array(result.result_dict[vif_num_scale3_scores_key])
/ np.array(result.result_dict[vif_den_scale3_scores_key]))
)
# vif2 =
# ((vif_num_scale0 / vif_den_scale0) + (vif_num_scale1 / vif_den_scale1) +
# (vif_num_scale2 / vif_den_scale2) + (vif_num_scale3 / vif_den_scale3)) / 4.0
vif_scores_key = cls.get_scores_key('vif2')
result.result_dict[vif_scores_key] = list(
(
(np.array(result.result_dict[vif_num_scale0_scores_key])
/ | np.array(result.result_dict[vif_den_scale0_scores_key]) | numpy.array |
'''
-------------------------------------------------------------------------------------------------
This code accompanies the paper titled "Human injury-based safety decision of automated vehicles"
Author: <NAME>, <NAME>, <NAME>, <NAME>
Corresponding author: <NAME> (<EMAIL>)
-------------------------------------------------------------------------------------------------
'''
import torch
import numpy as np
from torch import nn
from torch.nn.utils import weight_norm
__author__ = "<NAME>"
def Collision_cond(veh_striking_list, V1_v, V2_v, delta_angle, veh_param):
''' Estimate the collision condition. '''
(veh_l, veh_w, veh_cgf, veh_cgs, veh_k, veh_m) = veh_param
delta_angle_2 = np.arccos(np.abs(np.cos(delta_angle)))
if -1e-6 < delta_angle_2 < 1e-6:
delta_angle_2 = 1e-6
delta_v1_list = []
delta_v2_list = []
# Estimate the collision condition (delat-v) according to the principal impact direction.
for veh_striking in veh_striking_list:
if veh_striking[0] == 1:
veh_ca = np.arctan(veh_cgf[0] / veh_cgs[0])
veh_a2 = np.abs(veh_cgs[1] - veh_striking[3])
veh_RDS = np.abs(V1_v * np.cos(delta_angle) - V2_v)
veh_a1 = np.abs(np.sqrt(veh_cgf[0] ** 2 + veh_cgs[0] ** 2) * np.cos(veh_ca + delta_angle_2))
if (veh_striking[1]+1) in [16, 1, 2, 3, 17, 20, 21] and (veh_striking[2]+1) in [16, 1, 2, 3, 17, 20, 21]:
veh_e = 2 / veh_RDS
else:
veh_e = 0.5 / veh_RDS
elif veh_striking[0] == 2:
veh_ca = np.arctan(veh_cgf[0] / veh_cgs[0])
veh_a2 = np.abs(veh_cgf[1] - veh_striking[3])
veh_a1 = np.abs(np.sqrt(veh_cgf[0] ** 2 + veh_cgs[0] ** 2) * np.cos(delta_angle_2 - veh_ca + np.pi / 2))
veh_RDS = V1_v * np.sin(delta_angle_2)
veh_e = 1.5 / veh_RDS
elif veh_striking[0] == 3:
veh_ca = np.arctan(veh_cgf[1] / veh_cgs[1])
veh_a1 = np.abs(veh_cgs[0] - veh_striking[3])
veh_RDS = np.abs(V2_v * np.cos(delta_angle) - V1_v)
veh_a2 = np.abs(np.sqrt(veh_cgf[1] ** 2 + veh_cgs[1] ** 2) * np.cos(veh_ca + delta_angle_2))
if (veh_striking[1]+1) in [16, 1, 2, 3, 17, 20, 21] and (veh_striking[2]+1) in [16, 1, 2, 3, 17, 20, 21]:
veh_e = 2 / veh_RDS
else:
veh_e = 0.5 / veh_RDS
elif veh_striking[0] == 4:
veh_ca = np.arctan(veh_cgf[1] / veh_cgs[1])
veh_a1 = np.abs(veh_cgf[0] - veh_striking[3])
veh_a2 = np.abs(np.sqrt(veh_cgf[1] ** 2 + veh_cgs[1] ** 2) * np.cos(delta_angle_2 - veh_ca + np.pi / 2))
veh_RDS = V2_v * | np.sin(delta_angle_2) | numpy.sin |
from gtrain import Model
import numpy as np
import tensorflow as tf
class NetForHypinv(Model):
"""
Implementaion of the crutial function for the HypINV algorithm.
Warning: Do not use this class but implement its subclass, for example see FCNetForHypinv
"""
def __init__(self, weights):
self.eval_session = None
self.grad_session = None
self.initial_x = None
self.center = None
self.weights = weights
self.out_for_eval = None #(going to be filled in build_for_eval method)
self.boundary_out_for_eval = None
self.trained_x = None
self.training_class_index = None
self.x = None # tf variable for inversion (going to be filled in build method)
self.x_for_eval = None
self.out = None
self.boundary_out = None # list of tf tensorf for each class of softmax class vs others output
self.loss = None
self.boundary_loss = None
self.t = None #target
self.boundary_t = None
self.x1 = None # this attribute is used of purposes of modified loss function
def __del__(self):
# close arr sessions
if self.eval_session:
self.eval_session.close()
if self.grad_session:
self.grad_session.close()
def set_initial_x(self, initial_x):
# sets starting point for the search of the closest point
self.initial_x = initial_x
def set_center(self, center):
# sets center point
self.center = center / | np.linalg.norm(center) | numpy.linalg.norm |
# -*- coding: utf-8 -*-
# -----------------------------------------------------------------------------
# (C) British Crown Copyright 2017-2021 Met Office.
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# * Redistributions of source code must retain the above copyright notice, this
# list of conditions and the following disclaimer.
#
# * Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
#
# * Neither the name of the copyright holder nor the names of its
# contributors may be used to endorse or promote products derived from
# this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
""" Tests of precipitation_type utilities"""
import numpy as np
import pytest
from iris.exceptions import CoordinateNotFoundError
from improver.metadata.constants import FLOAT_DTYPE
from improver.precipitation_type.utilities import make_shower_condition_cube
from improver.synthetic_data.set_up_test_cubes import set_up_probability_cube
def set_up_test_cube(n_thresholds=1):
"""Set up a cube testing shower condition conversion"""
thresholds = | np.arange(n_thresholds) | numpy.arange |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = | np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) | numpy.linspace |
"""Routines for numerical differentiation."""
from __future__ import division
import numpy as np
from numpy.linalg import norm
from scipy.sparse.linalg import LinearOperator
from ..sparse import issparse, csc_matrix, csr_matrix, coo_matrix, find
from ._group_columns import group_dense, group_sparse
EPS = np.finfo(np.float64).eps
def _adjust_scheme_to_bounds(x0, h, num_steps, scheme, lb, ub):
"""Adjust final difference scheme to the presence of bounds.
Parameters
----------
x0 : ndarray, shape (n,)
Point at which we wish to estimate derivative.
h : ndarray, shape (n,)
Desired finite difference steps.
num_steps : int
Number of `h` steps in one direction required to implement finite
difference scheme. For example, 2 means that we need to evaluate
f(x0 + 2 * h) or f(x0 - 2 * h)
scheme : {'1-sided', '2-sided'}
Whether steps in one or both directions are required. In other
words '1-sided' applies to forward and backward schemes, '2-sided'
applies to center schemes.
lb : ndarray, shape (n,)
Lower bounds on independent variables.
ub : ndarray, shape (n,)
Upper bounds on independent variables.
Returns
-------
h_adjusted : ndarray, shape (n,)
Adjusted step sizes. Step size decreases only if a sign flip or
switching to one-sided scheme doesn't allow to take a full step.
use_one_sided : ndarray of bool, shape (n,)
Whether to switch to one-sided scheme. Informative only for
``scheme='2-sided'``.
"""
if scheme == '1-sided':
use_one_sided = np.ones_like(h, dtype=bool)
elif scheme == '2-sided':
h = np.abs(h)
use_one_sided = np.zeros_like(h, dtype=bool)
else:
raise ValueError("`scheme` must be '1-sided' or '2-sided'.")
if np.all((lb == -np.inf) & (ub == np.inf)):
return h, use_one_sided
h_total = h * num_steps
h_adjusted = h.copy()
lower_dist = x0 - lb
upper_dist = ub - x0
if scheme == '1-sided':
x = x0 + h_total
violated = (x < lb) | (x > ub)
fitting = np.abs(h_total) <= np.maximum(lower_dist, upper_dist)
h_adjusted[violated & fitting] *= -1
forward = (upper_dist >= lower_dist) & ~fitting
h_adjusted[forward] = upper_dist[forward] / num_steps
backward = (upper_dist < lower_dist) & ~fitting
h_adjusted[backward] = -lower_dist[backward] / num_steps
elif scheme == '2-sided':
central = (lower_dist >= h_total) & (upper_dist >= h_total)
forward = (upper_dist >= lower_dist) & ~central
h_adjusted[forward] = np.minimum(
h[forward], 0.5 * upper_dist[forward] / num_steps)
use_one_sided[forward] = True
backward = (upper_dist < lower_dist) & ~central
h_adjusted[backward] = -np.minimum(
h[backward], 0.5 * lower_dist[backward] / num_steps)
use_one_sided[backward] = True
min_dist = | np.minimum(upper_dist, lower_dist) | numpy.minimum |
#
# Copyright (c) 2021 The GPflux Contributors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
import abc
import numpy as np
import pytest
import tensorflow as tf
import tensorflow_probability as tfp
from gpflow.kullback_leiblers import gauss_kl
from gpflux.encoders import DirectlyParameterizedNormalDiag
from gpflux.layers import LatentVariableLayer, LayerWithObservations, TrackableLayer
tf.keras.backend.set_floatx("float64")
############
# Utilities
############
def _zero_one_normal_prior(w_dim):
""" N(0, I) prior """
return tfp.distributions.MultivariateNormalDiag(loc=np.zeros(w_dim), scale_diag=np.ones(w_dim))
def get_distributions_with_w_dim():
distributions = []
for d in [1, 5]:
mean = np.zeros(d)
scale_tri_l = np.eye(d)
mvn = tfp.distributions.MultivariateNormalTriL(mean, scale_tri_l)
std = np.ones(d)
mvn_diag = tfp.distributions.MultivariateNormalDiag(mean, std)
distributions.append((mvn, d))
distributions.append((mvn_diag, d))
return distributions
############
# Tests
############
@pytest.mark.parametrize("distribution, w_dim", get_distributions_with_w_dim())
def test_local_kls(distribution, w_dim):
lv = LatentVariableLayer(encoder=None, prior=distribution)
# test kl is 0 when posteriors == priors
posterior = distribution
assert lv._local_kls(posterior) == 0
# test kl > 0 when posteriors != priors
batch_size = 10
params = distribution.parameters
posterior_params = {
k: [v + 0.5 for _ in range(batch_size)]
for k, v in params.items()
if isinstance(v, np.ndarray)
}
posterior = lv.distribution_class(**posterior_params)
local_kls = lv._local_kls(posterior)
assert np.all(local_kls > 0)
assert local_kls.shape == (batch_size,)
@pytest.mark.parametrize("w_dim", [1, 5])
def test_local_kl_gpflow_consistency(w_dim):
num_data = 400
means = np.random.randn(num_data, w_dim)
encoder = DirectlyParameterizedNormalDiag(num_data, w_dim, means)
lv = LatentVariableLayer(encoder=encoder, prior=_zero_one_normal_prior(w_dim))
posteriors = lv._inference_posteriors(
[np.random.randn(num_data, 3), np.random.randn(num_data, 2)]
)
q_mu = posteriors.parameters["loc"]
q_sqrt = posteriors.parameters["scale_diag"]
gpflow_local_kls = gauss_kl(q_mu, q_sqrt)
tfp_local_kls = tf.reduce_sum(lv._local_kls(posteriors))
np.testing.assert_allclose(tfp_local_kls, gpflow_local_kls, rtol=1e-10)
class ArrayMatcher:
def __init__(self, expected):
self.expected = expected
def __eq__(self, actual):
return np.allclose(actual, self.expected, equal_nan=True)
@pytest.mark.parametrize("w_dim", [1, 5])
def test_latent_variable_layer_losses(mocker, w_dim):
num_data, x_dim, y_dim = 43, 3, 1
prior_shape = (w_dim,)
posteriors_shape = (num_data, w_dim)
prior = tfp.distributions.MultivariateNormalDiag(
loc=np.random.randn(*prior_shape),
scale_diag=np.random.randn(*prior_shape) ** 2,
)
posteriors = tfp.distributions.MultivariateNormalDiag(
loc=np.random.randn(*posteriors_shape),
scale_diag=np.random.randn(*posteriors_shape) ** 2,
)
encoder = mocker.Mock(return_value=(posteriors.loc, posteriors.scale.diag))
lv = LatentVariableLayer(encoder=encoder, prior=prior)
inputs = np.full((num_data, x_dim), np.nan)
targets = | np.full((num_data, y_dim), np.nan) | numpy.full |
# pvtrace is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# pvtrace is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import numpy as np
from external.transformations import translation_matrix, rotation_matrix
import external.transformations as tf
from Trace import Photon
from Geometry import Box, Cylinder, FinitePlane, transform_point, transform_direction, rotation_matrix_from_vector_alignment, norm
from Materials import Spectrum
def random_spherecial_vector():
# This method of calculating isotropic vectors is taken from GNU Scientific Library
LOOP = True
while LOOP:
x = -1. + 2. * np.random.uniform()
y = -1. + 2. * np.random.uniform()
s = x**2 + y**2
if s <= 1.0:
LOOP = False
z = -1. + 2. * s
a = 2 * np.sqrt(1 - s)
x = a * x
y = a * y
return | np.array([x,y,z]) | numpy.array |
"""
YTArray class.
"""
from __future__ import print_function
#-----------------------------------------------------------------------------
# Copyright (c) 2013, yt Development Team.
#
# Distributed under the terms of the Modified BSD License.
#
# The full license is in the file COPYING.txt, distributed with this software.
#-----------------------------------------------------------------------------
import copy
import numpy as np
from distutils.version import LooseVersion
from functools import wraps
from numpy import \
add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, \
floor_divide, negative, power, remainder, mod, absolute, rint, \
sign, conj, exp, exp2, log, log2, log10, expm1, log1p, sqrt, square, \
reciprocal, sin, cos, tan, arcsin, arccos, arctan, arctan2, \
hypot, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad, rad2deg, \
bitwise_and, bitwise_or, bitwise_xor, invert, left_shift, right_shift, \
greater, greater_equal, less, less_equal, not_equal, equal, logical_and, \
logical_or, logical_xor, logical_not, maximum, minimum, fmax, fmin, \
isreal, iscomplex, isfinite, isinf, isnan, signbit, copysign, nextafter, \
modf, ldexp, frexp, fmod, floor, ceil, trunc, fabs, spacing
try:
# numpy 1.13 or newer
from numpy import positive, divmod as divmod_, isnat, heaviside
except ImportError:
positive, divmod_, isnat, heaviside = (None,)*4
from yt.units.unit_object import Unit, UnitParseError
from yt.units.unit_registry import UnitRegistry
from yt.units.dimensions import \
angle, \
current_mks, \
dimensionless, \
em_dimensions
from yt.utilities.exceptions import \
YTUnitOperationError, YTUnitConversionError, \
YTUfuncUnitError, YTIterableUnitCoercionError, \
YTInvalidUnitEquivalence, YTEquivalentDimsError
from yt.utilities.lru_cache import lru_cache
from numbers import Number as numeric_type
from yt.utilities.on_demand_imports import _astropy
from sympy import Rational
from yt.units.unit_lookup_table import \
default_unit_symbol_lut
from yt.units.equivalencies import equivalence_registry
from yt.utilities.logger import ytLogger as mylog
from .pint_conversions import convert_pint_units
NULL_UNIT = Unit()
POWER_SIGN_MAPPING = {multiply: 1, divide: -1}
# redefine this here to avoid a circular import from yt.funcs
def iterable(obj):
try: len(obj)
except: return False
return True
def return_arr(func):
@wraps(func)
def wrapped(*args, **kwargs):
ret, units = func(*args, **kwargs)
if ret.shape == ():
return YTQuantity(ret, units)
else:
# This could be a subclass, so don't call YTArray directly.
return type(args[0])(ret, units)
return wrapped
@lru_cache(maxsize=128, typed=False)
def sqrt_unit(unit):
return unit**0.5
@lru_cache(maxsize=128, typed=False)
def multiply_units(unit1, unit2):
return unit1 * unit2
def preserve_units(unit1, unit2=None):
return unit1
@lru_cache(maxsize=128, typed=False)
def power_unit(unit, power):
return unit**power
@lru_cache(maxsize=128, typed=False)
def square_unit(unit):
return unit*unit
@lru_cache(maxsize=128, typed=False)
def divide_units(unit1, unit2):
return unit1/unit2
@lru_cache(maxsize=128, typed=False)
def reciprocal_unit(unit):
return unit**-1
def passthrough_unit(unit, unit2=None):
return unit
def return_without_unit(unit, unit2=None):
return None
def arctan2_unit(unit1, unit2):
return NULL_UNIT
def comparison_unit(unit1, unit2=None):
return None
def invert_units(unit):
raise TypeError(
"Bit-twiddling operators are not defined for YTArray instances")
def bitop_units(unit1, unit2):
raise TypeError(
"Bit-twiddling operators are not defined for YTArray instances")
def get_inp_u_unary(ufunc, inputs, out_arr=None):
inp = inputs[0]
u = getattr(inp, 'units', None)
if u is None:
u = NULL_UNIT
if u.dimensions is angle and ufunc in trigonometric_operators:
inp = inp.in_units('radian').v
if out_arr is not None:
out_arr = ufunc(inp).view(np.ndarray)
return out_arr, inp, u
def get_inp_u_binary(ufunc, inputs):
inp1 = coerce_iterable_units(inputs[0])
inp2 = coerce_iterable_units(inputs[1])
unit1 = getattr(inp1, 'units', None)
unit2 = getattr(inp2, 'units', None)
ret_class = get_binary_op_return_class(type(inp1), type(inp2))
if unit1 is None:
unit1 = Unit(registry=getattr(unit2, 'registry', None))
if unit2 is None and ufunc is not power:
unit2 = Unit(registry=getattr(unit1, 'registry', None))
elif ufunc is power:
unit2 = inp2
if isinstance(unit2, np.ndarray):
if isinstance(unit2, YTArray):
if unit2.units.is_dimensionless:
pass
else:
raise YTUnitOperationError(ufunc, unit1, unit2)
unit2 = 1.0
return (inp1, inp2), (unit1, unit2), ret_class
def handle_preserve_units(inps, units, ufunc, ret_class):
if units[0] != units[1]:
any_nonzero = [np.any(inps[0]), np.any(inps[1])]
if any_nonzero[0] == np.bool_(False):
units = (units[1], units[1])
elif any_nonzero[1] == np.bool_(False):
units = (units[0], units[0])
else:
if not units[0].same_dimensions_as(units[1]):
raise YTUnitOperationError(ufunc, *units)
inps = (inps[0], ret_class(inps[1]).to(
ret_class(inps[0]).units))
return inps, units
def handle_comparison_units(inps, units, ufunc, ret_class, raise_error=False):
if units[0] != units[1]:
u1d = units[0].is_dimensionless
u2d = units[1].is_dimensionless
any_nonzero = [np.any(inps[0]), np.any(inps[1])]
if any_nonzero[0] == np.bool_(False):
units = (units[1], units[1])
elif any_nonzero[1] == np.bool_(False):
units = (units[0], units[0])
elif not any([u1d, u2d]):
if not units[0].same_dimensions_as(units[1]):
raise YTUnitOperationError(ufunc, *units)
else:
if raise_error:
raise YTUfuncUnitError(ufunc, *units)
inps = (inps[0], ret_class(inps[1]).to(
ret_class(inps[0]).units))
return inps, units
def handle_multiply_divide_units(unit, units, out, out_arr):
if unit.is_dimensionless and unit.base_value != 1.0:
if not units[0].is_dimensionless:
if units[0].dimensions == units[1].dimensions:
out_arr = np.multiply(out_arr.view(np.ndarray),
unit.base_value, out=out)
unit = Unit(registry=unit.registry)
return out, out_arr, unit
def coerce_iterable_units(input_object):
if isinstance(input_object, np.ndarray):
return input_object
if iterable(input_object):
if any([isinstance(o, YTArray) for o in input_object]):
ff = getattr(input_object[0], 'units', NULL_UNIT, )
if any([ff != getattr(_, 'units', NULL_UNIT) for _ in input_object]):
raise YTIterableUnitCoercionError(input_object)
# This will create a copy of the data in the iterable.
return YTArray(input_object)
return input_object
else:
return input_object
def sanitize_units_mul(this_object, other_object):
inp = coerce_iterable_units(this_object)
ret = coerce_iterable_units(other_object)
# If the other object is a YTArray and has the same dimensions as the object
# under consideration, convert so we don't mix units with the same
# dimensions.
if isinstance(ret, YTArray):
if inp.units.same_dimensions_as(ret.units):
ret.in_units(inp.units)
return ret
def sanitize_units_add(this_object, other_object, op_string):
inp = coerce_iterable_units(this_object)
ret = coerce_iterable_units(other_object)
# Make sure the other object is a YTArray before we use the `units`
# attribute.
if isinstance(ret, YTArray):
if not inp.units.same_dimensions_as(ret.units):
# handle special case of adding or subtracting with zero or
# array filled with zero
if not np.any(other_object):
return ret.view(np.ndarray)
elif not np.any(this_object):
return ret
raise YTUnitOperationError(op_string, inp.units, ret.units)
ret = ret.in_units(inp.units)
else:
# If the other object is not a YTArray, then one of the arrays must be
# dimensionless or filled with zeros
if not inp.units.is_dimensionless and np.any(ret):
raise YTUnitOperationError(op_string, inp.units, dimensionless)
return ret
def validate_comparison_units(this, other, op_string):
# Check that other is a YTArray.
if hasattr(other, 'units'):
if this.units.expr is other.units.expr:
if this.units.base_value == other.units.base_value:
return other
if not this.units.same_dimensions_as(other.units):
raise YTUnitOperationError(op_string, this.units, other.units)
return other.in_units(this.units)
return other
@lru_cache(maxsize=128, typed=False)
def _unit_repr_check_same(my_units, other_units):
"""
Takes a Unit object, or string of known unit symbol, and check that it
is compatible with this quantity. Returns Unit object.
"""
# let Unit() handle units arg if it's not already a Unit obj.
if not isinstance(other_units, Unit):
other_units = Unit(other_units, registry=my_units.registry)
equiv_dims = em_dimensions.get(my_units.dimensions, None)
if equiv_dims == other_units.dimensions:
if current_mks in equiv_dims.free_symbols:
base = "SI"
else:
base = "CGS"
raise YTEquivalentDimsError(my_units, other_units, base)
if not my_units.same_dimensions_as(other_units):
raise YTUnitConversionError(
my_units, my_units.dimensions, other_units, other_units.dimensions)
return other_units
unary_operators = (
negative, absolute, rint, sign, conj, exp, exp2, log, log2,
log10, expm1, log1p, sqrt, square, reciprocal, sin, cos, tan, arcsin,
arccos, arctan, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad,
rad2deg, invert, logical_not, isreal, iscomplex, isfinite, isinf, isnan,
signbit, floor, ceil, trunc, modf, frexp, fabs, spacing, positive, isnat,
)
binary_operators = (
add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, power,
remainder, mod, arctan2, hypot, bitwise_and, bitwise_or, bitwise_xor,
left_shift, right_shift, greater, greater_equal, less, less_equal,
not_equal, equal, logical_and, logical_or, logical_xor, maximum, minimum,
fmax, fmin, copysign, nextafter, ldexp, fmod, divmod_, heaviside
)
trigonometric_operators = (
sin, cos, tan,
)
class YTArray(np.ndarray):
"""
An ndarray subclass that attaches a symbolic unit object to the array data.
Parameters
----------
input_array : :obj:`!iterable`
A tuple, list, or array to attach units to
input_units : String unit specification, unit symbol object, or astropy units
The units of the array. Powers must be specified using python
syntax (cm**3, not cm^3).
registry : ~yt.units.unit_registry.UnitRegistry
The registry to create units from. If input_units is already associated
with a unit registry and this is specified, this will be used instead of
the registry associated with the unit object.
dtype : data-type
The dtype of the array data. Defaults to the dtype of the input data,
or, if none is found, uses np.float64
bypass_validation : boolean
If True, all input validation is skipped. Using this option may produce
corrupted, invalid units or array data, but can lead to significant
speedups in the input validation logic adds significant overhead. If set,
input_units *must* be a valid unit object. Defaults to False.
Examples
--------
>>> from yt import YTArray
>>> a = YTArray([1, 2, 3], 'cm')
>>> b = YTArray([4, 5, 6], 'm')
>>> a + b
YTArray([ 401., 502., 603.]) cm
>>> b + a
YTArray([ 4.01, 5.02, 6.03]) m
NumPy ufuncs will pass through units where appropriate.
>>> import numpy as np
>>> a = YTArray(np.arange(8) - 4, 'g/cm**3')
>>> np.abs(a)
YTArray([4, 3, 2, 1, 0, 1, 2, 3]) g/cm**3
and strip them when it would be annoying to deal with them.
>>> np.log10(a)
array([ -inf, 0. , 0.30103 , 0.47712125, 0.60205999,
0.69897 , 0.77815125, 0.84509804])
YTArray is tightly integrated with yt datasets:
>>> import yt
>>> ds = yt.load('IsolatedGalaxy/galaxy0030/galaxy0030')
>>> a = ds.arr(np.ones(5), 'code_length')
>>> a.in_cgs()
YTArray([ 3.08600000e+24, 3.08600000e+24, 3.08600000e+24,
3.08600000e+24, 3.08600000e+24]) cm
This is equivalent to:
>>> b = YTArray(np.ones(5), 'code_length', registry=ds.unit_registry)
>>> np.all(a == b)
True
"""
_ufunc_registry = {
add: preserve_units,
subtract: preserve_units,
multiply: multiply_units,
divide: divide_units,
logaddexp: return_without_unit,
logaddexp2: return_without_unit,
true_divide: divide_units,
floor_divide: divide_units,
negative: passthrough_unit,
power: power_unit,
remainder: preserve_units,
mod: preserve_units,
fmod: preserve_units,
absolute: passthrough_unit,
fabs: passthrough_unit,
rint: return_without_unit,
sign: return_without_unit,
conj: passthrough_unit,
exp: return_without_unit,
exp2: return_without_unit,
log: return_without_unit,
log2: return_without_unit,
log10: return_without_unit,
expm1: return_without_unit,
log1p: return_without_unit,
sqrt: sqrt_unit,
square: square_unit,
reciprocal: reciprocal_unit,
sin: return_without_unit,
cos: return_without_unit,
tan: return_without_unit,
sinh: return_without_unit,
cosh: return_without_unit,
tanh: return_without_unit,
arcsin: return_without_unit,
arccos: return_without_unit,
arctan: return_without_unit,
arctan2: arctan2_unit,
arcsinh: return_without_unit,
arccosh: return_without_unit,
arctanh: return_without_unit,
hypot: preserve_units,
deg2rad: return_without_unit,
rad2deg: return_without_unit,
bitwise_and: bitop_units,
bitwise_or: bitop_units,
bitwise_xor: bitop_units,
invert: invert_units,
left_shift: bitop_units,
right_shift: bitop_units,
greater: comparison_unit,
greater_equal: comparison_unit,
less: comparison_unit,
less_equal: comparison_unit,
not_equal: comparison_unit,
equal: comparison_unit,
logical_and: comparison_unit,
logical_or: comparison_unit,
logical_xor: comparison_unit,
logical_not: return_without_unit,
maximum: preserve_units,
minimum: preserve_units,
fmax: preserve_units,
fmin: preserve_units,
isreal: return_without_unit,
iscomplex: return_without_unit,
isfinite: return_without_unit,
isinf: return_without_unit,
isnan: return_without_unit,
signbit: return_without_unit,
copysign: passthrough_unit,
nextafter: preserve_units,
modf: passthrough_unit,
ldexp: bitop_units,
frexp: return_without_unit,
floor: passthrough_unit,
ceil: passthrough_unit,
trunc: passthrough_unit,
spacing: passthrough_unit,
positive: passthrough_unit,
divmod_: passthrough_unit,
isnat: return_without_unit,
heaviside: preserve_units,
}
__array_priority__ = 2.0
def __new__(cls, input_array, input_units=None, registry=None, dtype=None,
bypass_validation=False):
if dtype is None:
dtype = getattr(input_array, 'dtype', np.float64)
if bypass_validation is True:
obj = np.asarray(input_array, dtype=dtype).view(cls)
obj.units = input_units
if registry is not None:
obj.units.registry = registry
return obj
if input_array is NotImplemented:
return input_array.view(cls)
if registry is None and isinstance(input_units, (str, bytes)):
if input_units.startswith('code_'):
raise UnitParseError(
"Code units used without referring to a dataset. \n"
"Perhaps you meant to do something like this instead: \n"
"ds.arr(%s, \"%s\")" % (input_array, input_units)
)
if isinstance(input_array, YTArray):
ret = input_array.view(cls)
if input_units is None:
if registry is None:
ret.units = input_array.units
else:
units = Unit(str(input_array.units), registry=registry)
ret.units = units
elif isinstance(input_units, Unit):
ret.units = input_units
else:
ret.units = Unit(input_units, registry=registry)
return ret
elif isinstance(input_array, np.ndarray):
pass
elif iterable(input_array) and input_array:
if isinstance(input_array[0], YTArray):
return YTArray(np.array(input_array, dtype=dtype),
input_array[0].units, registry=registry)
# Input array is an already formed ndarray instance
# We first cast to be our class type
obj = np.asarray(input_array, dtype=dtype).view(cls)
# Check units type
if input_units is None:
# Nothing provided. Make dimensionless...
units = Unit()
elif isinstance(input_units, Unit):
if registry and registry is not input_units.registry:
units = Unit(str(input_units), registry=registry)
else:
units = input_units
else:
# units kwarg set, but it's not a Unit object.
# don't handle all the cases here, let the Unit class handle if
# it's a str.
units = Unit(input_units, registry=registry)
# Attach the units
obj.units = units
return obj
def __repr__(self):
"""
"""
return super(YTArray, self).__repr__()+' '+self.units.__repr__()
def __str__(self):
"""
"""
return str(self.view(np.ndarray)) + ' ' + str(self.units)
#
# Start unit conversion methods
#
def convert_to_units(self, units):
"""
Convert the array and units to the given units.
Parameters
----------
units : Unit object or str
The units you want to convert to.
"""
new_units = _unit_repr_check_same(self.units, units)
(conversion_factor, offset) = self.units.get_conversion_factor(new_units)
self.units = new_units
values = self.d
values *= conversion_factor
if offset:
np.subtract(self, offset*self.uq, self)
return self
def convert_to_base(self, unit_system="cgs"):
"""
Convert the array and units to the equivalent base units in
the specified unit system.
Parameters
----------
unit_system : string, optional
The unit system to be used in the conversion. If not specified,
the default base units of cgs are used.
Examples
--------
>>> E = YTQuantity(2.5, "erg/s")
>>> E.convert_to_base(unit_system="galactic")
"""
return self.convert_to_units(self.units.get_base_equivalent(unit_system))
def convert_to_cgs(self):
"""
Convert the array and units to the equivalent cgs units.
"""
return self.convert_to_units(self.units.get_cgs_equivalent())
def convert_to_mks(self):
"""
Convert the array and units to the equivalent mks units.
"""
return self.convert_to_units(self.units.get_mks_equivalent())
def in_units(self, units, equivalence=None, **kwargs):
"""
Creates a copy of this array with the data in the supplied
units, and returns it.
Optionally, an equivalence can be specified to convert to an
equivalent quantity which is not in the same dimensions.
.. note::
All additional keyword arguments are passed to the
equivalency, which should be used if that particular
equivalency requires them.
Parameters
----------
units : Unit object or string
The units you want to get a new quantity in.
equivalence : string, optional
The equivalence you wish to use. To see which
equivalencies are supported for this unitful
quantity, try the :meth:`list_equivalencies`
method. Default: None
Returns
-------
YTArray
"""
if equivalence is None:
new_units = _unit_repr_check_same(self.units, units)
(conversion_factor, offset) = self.units.get_conversion_factor(new_units)
new_array = type(self)(self.ndview * conversion_factor, new_units)
if offset:
| np.subtract(new_array, offset*new_array.uq, new_array) | numpy.subtract |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = | np.linspace(minima_y[-1], slope_based_maximum, 101) | numpy.linspace |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = | np.linspace(time_series[-1], minima_y[-1], 101) | numpy.linspace |
from sklearn.metrics import f1_score,accuracy_score
import numpy as np
from utilities.tools import load_model
import pandas as pd
def predict_MSRP_test_data(n_models,nb_words,nlp_f,test_data_1,test_data_2,test_labels):
models=[]
n_h_features=nlp_f.shape[1]
print('loading the models...')
for i in range(n_models):
models.append(load_model(i+1,nb_words,n_h_features))
preds=[]
print('predicting the test data...\n')
i=0
for m in models:
i+=1
preds_prob=m.predict([test_data_1, test_data_2,nlp_f], batch_size=64, verbose=0)
preds.append(preds_prob[:,1])
preds= | np.asarray(preds) | numpy.asarray |
#
# Copyright (c) 2021 The GPflux Contributors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
import abc
import numpy as np
import pytest
import tensorflow as tf
import tensorflow_probability as tfp
from gpflow.kullback_leiblers import gauss_kl
from gpflux.encoders import DirectlyParameterizedNormalDiag
from gpflux.layers import LatentVariableLayer, LayerWithObservations, TrackableLayer
tf.keras.backend.set_floatx("float64")
############
# Utilities
############
def _zero_one_normal_prior(w_dim):
""" N(0, I) prior """
return tfp.distributions.MultivariateNormalDiag(loc=np.zeros(w_dim), scale_diag=np.ones(w_dim))
def get_distributions_with_w_dim():
distributions = []
for d in [1, 5]:
mean = np.zeros(d)
scale_tri_l = np.eye(d)
mvn = tfp.distributions.MultivariateNormalTriL(mean, scale_tri_l)
std = np.ones(d)
mvn_diag = tfp.distributions.MultivariateNormalDiag(mean, std)
distributions.append((mvn, d))
distributions.append((mvn_diag, d))
return distributions
############
# Tests
############
@pytest.mark.parametrize("distribution, w_dim", get_distributions_with_w_dim())
def test_local_kls(distribution, w_dim):
lv = LatentVariableLayer(encoder=None, prior=distribution)
# test kl is 0 when posteriors == priors
posterior = distribution
assert lv._local_kls(posterior) == 0
# test kl > 0 when posteriors != priors
batch_size = 10
params = distribution.parameters
posterior_params = {
k: [v + 0.5 for _ in range(batch_size)]
for k, v in params.items()
if isinstance(v, np.ndarray)
}
posterior = lv.distribution_class(**posterior_params)
local_kls = lv._local_kls(posterior)
assert np.all(local_kls > 0)
assert local_kls.shape == (batch_size,)
@pytest.mark.parametrize("w_dim", [1, 5])
def test_local_kl_gpflow_consistency(w_dim):
num_data = 400
means = np.random.randn(num_data, w_dim)
encoder = DirectlyParameterizedNormalDiag(num_data, w_dim, means)
lv = LatentVariableLayer(encoder=encoder, prior=_zero_one_normal_prior(w_dim))
posteriors = lv._inference_posteriors(
[np.random.randn(num_data, 3), np.random.randn(num_data, 2)]
)
q_mu = posteriors.parameters["loc"]
q_sqrt = posteriors.parameters["scale_diag"]
gpflow_local_kls = gauss_kl(q_mu, q_sqrt)
tfp_local_kls = tf.reduce_sum(lv._local_kls(posteriors))
np.testing.assert_allclose(tfp_local_kls, gpflow_local_kls, rtol=1e-10)
class ArrayMatcher:
def __init__(self, expected):
self.expected = expected
def __eq__(self, actual):
return np.allclose(actual, self.expected, equal_nan=True)
@pytest.mark.parametrize("w_dim", [1, 5])
def test_latent_variable_layer_losses(mocker, w_dim):
num_data, x_dim, y_dim = 43, 3, 1
prior_shape = (w_dim,)
posteriors_shape = (num_data, w_dim)
prior = tfp.distributions.MultivariateNormalDiag(
loc=np.random.randn(*prior_shape),
scale_diag=np.random.randn(*prior_shape) ** 2,
)
posteriors = tfp.distributions.MultivariateNormalDiag(
loc=np.random.randn(*posteriors_shape),
scale_diag= | np.random.randn(*posteriors_shape) | numpy.random.randn |
'''
<NAME>
set up :2020-1-9
intergrate img and label into one file
-- fiducial1024_v1
'''
import argparse
import sys, os
import pickle
import random
import collections
import json
import numpy as np
import scipy.io as io
import scipy.misc as m
import matplotlib.pyplot as plt
import glob
import math
import time
import threading
import multiprocessing as mp
from multiprocessing import Pool
import re
import cv2
# sys.path.append('/lustre/home/gwxie/hope/project/dewarp/datasets/') # /lustre/home/gwxie/program/project/unwarp/perturbed_imgaes/GAN
import utils
def getDatasets(dir):
return os.listdir(dir)
class perturbed(utils.BasePerturbed):
def __init__(self, path, bg_path, save_path, save_suffix):
self.path = path
self.bg_path = bg_path
self.save_path = save_path
self.save_suffix = save_suffix
def save_img(self, m, n, fold_curve='fold', repeat_time=4, fiducial_points = 16, relativeShift_position='relativeShift_v2'):
origin_img = cv2.imread(self.path, flags=cv2.IMREAD_COLOR)
save_img_shape = [512*2, 480*2] # 320
# reduce_value = np.random.choice([2**4, 2**5, 2**6, 2**7, 2**8], p=[0.01, 0.1, 0.4, 0.39, 0.1])
reduce_value = np.random.choice([2*2, 4*2, 8*2, 16*2, 24*2, 32*2, 40*2, 48*2], p=[0.02, 0.18, 0.2, 0.3, 0.1, 0.1, 0.08, 0.02])
# reduce_value = np.random.choice([8*2, 16*2, 24*2, 32*2, 40*2, 48*2], p=[0.01, 0.02, 0.2, 0.4, 0.19, 0.18])
# reduce_value = np.random.choice([16, 24, 32, 40, 48, 64], p=[0.01, 0.1, 0.2, 0.4, 0.2, 0.09])
base_img_shrink = save_img_shape[0] - reduce_value
# enlarge_img_shrink = [1024, 768]
# enlarge_img_shrink = [896, 672] # 420
enlarge_img_shrink = [512*4, 480*4] # 420
# enlarge_img_shrink = [896*2, 768*2] # 420
# enlarge_img_shrink = [896, 768] # 420
# enlarge_img_shrink = [768, 576] # 420
# enlarge_img_shrink = [640, 480] # 420
''''''
im_lr = origin_img.shape[0]
im_ud = origin_img.shape[1]
reduce_value_v2 = np.random.choice([2*2, 4*2, 8*2, 16*2, 24*2, 28*2, 32*2, 48*2], p=[0.02, 0.18, 0.2, 0.2, 0.1, 0.1, 0.1, 0.1])
# reduce_value_v2 = np.random.choice([16, 24, 28, 32, 48, 64], p=[0.01, 0.1, 0.2, 0.3, 0.25, 0.14])
if im_lr > im_ud:
im_ud = min(int(im_ud / im_lr * base_img_shrink), save_img_shape[1] - reduce_value_v2)
im_lr = save_img_shape[0] - reduce_value
else:
base_img_shrink = save_img_shape[1] - reduce_value
im_lr = min(int(im_lr / im_ud * base_img_shrink), save_img_shape[0] - reduce_value_v2)
im_ud = base_img_shrink
if round(im_lr / im_ud, 2) < 0.5 or round(im_ud / im_lr, 2) < 0.5:
repeat_time = min(repeat_time, 8)
edge_padding = 3
im_lr -= im_lr % (fiducial_points-1) - (2*edge_padding) # im_lr % (fiducial_points-1) - 1
im_ud -= im_ud % (fiducial_points-1) - (2*edge_padding) # im_ud % (fiducial_points-1) - 1
im_hight = np.linspace(edge_padding, im_lr - edge_padding, fiducial_points, dtype=np.int64)
im_wide = np.linspace(edge_padding, im_ud - edge_padding, fiducial_points, dtype=np.int64)
# im_lr -= im_lr % (fiducial_points-1) - (1+2*edge_padding) # im_lr % (fiducial_points-1) - 1
# im_ud -= im_ud % (fiducial_points-1) - (1+2*edge_padding) # im_ud % (fiducial_points-1) - 1
# im_hight = np.linspace(edge_padding, im_lr - (1+edge_padding), fiducial_points, dtype=np.int64)
# im_wide = np.linspace(edge_padding, im_ud - (1+edge_padding), fiducial_points, dtype=np.int64)
im_x, im_y = np.meshgrid(im_hight, im_wide)
segment_x = (im_lr) // (fiducial_points-1)
segment_y = (im_ud) // (fiducial_points-1)
# plt.plot(im_x, im_y,
# color='limegreen',
# marker='.',
# linestyle='')
# plt.grid(True)
# plt.show()
self.origin_img = cv2.resize(origin_img, (im_ud, im_lr), interpolation=cv2.INTER_CUBIC)
perturbed_bg_ = getDatasets(self.bg_path)
perturbed_bg_img_ = self.bg_path+random.choice(perturbed_bg_)
perturbed_bg_img = cv2.imread(perturbed_bg_img_, flags=cv2.IMREAD_COLOR)
mesh_shape = self.origin_img.shape[:2]
self.synthesis_perturbed_img = np.full((enlarge_img_shrink[0], enlarge_img_shrink[1], 3), 256, dtype=np.float32)#np.zeros_like(perturbed_bg_img)
# self.synthesis_perturbed_img = np.full((enlarge_img_shrink[0], enlarge_img_shrink[1], 3), 0, dtype=np.int16)#np.zeros_like(perturbed_bg_img)
self.new_shape = self.synthesis_perturbed_img.shape[:2]
perturbed_bg_img = cv2.resize(perturbed_bg_img, (save_img_shape[1], save_img_shape[0]), cv2.INPAINT_TELEA)
origin_pixel_position = np.argwhere(np.zeros(mesh_shape, dtype=np.uint32) == 0).reshape(mesh_shape[0], mesh_shape[1], 2)
pixel_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape(self.new_shape[0], self.new_shape[1], 2)
self.perturbed_xy_ = np.zeros((self.new_shape[0], self.new_shape[1], 2))
# self.perturbed_xy_ = pixel_position.copy().astype(np.float32)
# fiducial_points_grid = origin_pixel_position[im_x, im_y]
self.synthesis_perturbed_label = np.zeros((self.new_shape[0], self.new_shape[1], 2))
x_min, y_min, x_max, y_max = self.adjust_position_v2(0, 0, mesh_shape[0], mesh_shape[1], save_img_shape)
origin_pixel_position += [x_min, y_min]
x_min, y_min, x_max, y_max = self.adjust_position(0, 0, mesh_shape[0], mesh_shape[1])
x_shift = random.randint(-enlarge_img_shrink[0]//16, enlarge_img_shrink[0]//16)
y_shift = random.randint(-enlarge_img_shrink[1]//16, enlarge_img_shrink[1]//16)
x_min += x_shift
x_max += x_shift
y_min += y_shift
y_max += y_shift
'''im_x,y'''
im_x += x_min
im_y += y_min
self.synthesis_perturbed_img[x_min:x_max, y_min:y_max] = self.origin_img
self.synthesis_perturbed_label[x_min:x_max, y_min:y_max] = origin_pixel_position
synthesis_perturbed_img_map = self.synthesis_perturbed_img.copy()
synthesis_perturbed_label_map = self.synthesis_perturbed_label.copy()
foreORbackground_label = np.full((mesh_shape), 1, dtype=np.int16)
foreORbackground_label_map = np.full((self.new_shape), 0, dtype=np.int16)
foreORbackground_label_map[x_min:x_max, y_min:y_max] = foreORbackground_label
# synthesis_perturbed_img_map = self.pad(self.synthesis_perturbed_img.copy(), x_min, y_min, x_max, y_max)
# synthesis_perturbed_label_map = self.pad(synthesis_perturbed_label_map, x_min, y_min, x_max, y_max)
'''*****************************************************************'''
is_normalizationFun_mixture = self.is_perform(0.2, 0.8)
# if not is_normalizationFun_mixture:
normalizationFun_0_1 = False
# normalizationFun_0_1 = self.is_perform(0.5, 0.5)
if fold_curve == 'fold':
fold_curve_random = True
# is_normalizationFun_mixture = False
normalizationFun_0_1 = self.is_perform(0.2, 0.8)
if is_normalizationFun_mixture:
alpha_perturbed = random.randint(80, 120) / 100
else:
if normalizationFun_0_1 and repeat_time < 8:
alpha_perturbed = random.randint(50, 70) / 100
else:
alpha_perturbed = random.randint(70, 130) / 100
else:
fold_curve_random = self.is_perform(0.1, 0.9) # False # self.is_perform(0.01, 0.99)
alpha_perturbed = random.randint(80, 160) / 100
# is_normalizationFun_mixture = False # self.is_perform(0.01, 0.99)
synthesis_perturbed_img = np.full_like(self.synthesis_perturbed_img, 256)
# synthesis_perturbed_img = np.full_like(self.synthesis_perturbed_img, 0, dtype=np.int16)
synthesis_perturbed_label = np.zeros_like(self.synthesis_perturbed_label)
alpha_perturbed_change = self.is_perform(0.5, 0.5)
p_pp_choice = self.is_perform(0.8, 0.2) if fold_curve == 'fold' else self.is_perform(0.1, 0.9)
for repeat_i in range(repeat_time):
if alpha_perturbed_change:
if fold_curve == 'fold':
if is_normalizationFun_mixture:
alpha_perturbed = random.randint(80, 120) / 100
else:
if normalizationFun_0_1 and repeat_time < 8:
alpha_perturbed = random.randint(50, 70) / 100
else:
alpha_perturbed = random.randint(70, 130) / 100
else:
alpha_perturbed = random.randint(80, 160) / 100
''''''
linspace_x = [0, (self.new_shape[0] - im_lr) // 2 - 1,
self.new_shape[0] - (self.new_shape[0] - im_lr) // 2 - 1, self.new_shape[0] - 1]
linspace_y = [0, (self.new_shape[1] - im_ud) // 2 - 1,
self.new_shape[1] - (self.new_shape[1] - im_ud) // 2 - 1, self.new_shape[1] - 1]
linspace_x_seq = [1, 2, 3]
linspace_y_seq = [1, 2, 3]
r_x = random.choice(linspace_x_seq)
r_y = random.choice(linspace_y_seq)
perturbed_p = np.array(
[random.randint(linspace_x[r_x-1] * 10, linspace_x[r_x] * 10),
random.randint(linspace_y[r_y-1] * 10, linspace_y[r_y] * 10)])/10
if ((r_x == 1 or r_x == 3) and (r_y == 1 or r_y == 3)) and p_pp_choice:
linspace_x_seq.remove(r_x)
linspace_y_seq.remove(r_y)
r_x = random.choice(linspace_x_seq)
r_y = random.choice(linspace_y_seq)
perturbed_pp = np.array(
[random.randint(linspace_x[r_x-1] * 10, linspace_x[r_x] * 10),
random.randint(linspace_y[r_y-1] * 10, linspace_y[r_y] * 10)])/10
# perturbed_p, perturbed_pp = np.array(
# [random.randint(0, self.new_shape[0] * 10) / 10,
# random.randint(0, self.new_shape[1] * 10) / 10]) \
# , np.array([random.randint(0, self.new_shape[0] * 10) / 10,
# random.randint(0, self.new_shape[1] * 10) / 10])
# perturbed_p, perturbed_pp = np.array(
# [random.randint((self.new_shape[0]-im_lr)//2*10, (self.new_shape[0]-(self.new_shape[0]-im_lr)//2) * 10) / 10,
# random.randint((self.new_shape[1]-im_ud)//2*10, (self.new_shape[1]-(self.new_shape[1]-im_ud)//2) * 10) / 10]) \
# , np.array([random.randint((self.new_shape[0]-im_lr)//2*10, (self.new_shape[0]-(self.new_shape[0]-im_lr)//2) * 10) / 10,
# random.randint((self.new_shape[1]-im_ud)//2*10, (self.new_shape[1]-(self.new_shape[1]-im_ud)//2) * 10) / 10])
''''''
perturbed_vp = perturbed_pp - perturbed_p
perturbed_vp_norm = np.linalg.norm(perturbed_vp)
perturbed_distance_vertex_and_line = np.dot((perturbed_p - pixel_position), perturbed_vp) / perturbed_vp_norm
''''''
# perturbed_v = np.array([random.randint(-3000, 3000) / 100, random.randint(-3000, 3000) / 100])
# perturbed_v = np.array([random.randint(-4000, 4000) / 100, random.randint(-4000, 4000) / 100])
if fold_curve == 'fold' and self.is_perform(0.6, 0.4): # self.is_perform(0.3, 0.7):
# perturbed_v = np.array([random.randint(-9000, 9000) / 100, random.randint(-9000, 9000) / 100])
perturbed_v = np.array([random.randint(-10000, 10000) / 100, random.randint(-10000, 10000) / 100])
# perturbed_v = np.array([random.randint(-11000, 11000) / 100, random.randint(-11000, 11000) / 100])
else:
# perturbed_v = np.array([random.randint(-9000, 9000) / 100, random.randint(-9000, 9000) / 100])
# perturbed_v = np.array([random.randint(-16000, 16000) / 100, random.randint(-16000, 16000) / 100])
perturbed_v = np.array([random.randint(-8000, 8000) / 100, random.randint(-8000, 8000) / 100])
# perturbed_v = np.array([random.randint(-3500, 3500) / 100, random.randint(-3500, 3500) / 100])
# perturbed_v = np.array([random.randint(-600, 600) / 10, random.randint(-600, 600) / 10])
''''''
if fold_curve == 'fold':
if is_normalizationFun_mixture:
if self.is_perform(0.5, 0.5):
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
else:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), random.randint(1, 2))
else:
if normalizationFun_0_1:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), 2)
else:
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
else:
if is_normalizationFun_mixture:
if self.is_perform(0.5, 0.5):
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
else:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), random.randint(1, 2))
else:
if normalizationFun_0_1:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), 2)
else:
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
''''''
if fold_curve_random:
# omega_perturbed = (alpha_perturbed+0.2) / (perturbed_d + alpha_perturbed)
# omega_perturbed = alpha_perturbed**perturbed_d
omega_perturbed = alpha_perturbed / (perturbed_d + alpha_perturbed)
else:
omega_perturbed = 1 - perturbed_d ** alpha_perturbed
'''shadow'''
if self.is_perform(0.6, 0.4):
synthesis_perturbed_img_map[x_min:x_max, y_min:y_max] = np.minimum(np.maximum(synthesis_perturbed_img_map[x_min:x_max, y_min:y_max] - np.int16(np.round(omega_perturbed[x_min:x_max, y_min:y_max].repeat(3).reshape(x_max-x_min, y_max-y_min, 3) * abs(np.linalg.norm(perturbed_v//2))*np.array([0.4-random.random()*0.1, 0.4-random.random()*0.1, 0.4-random.random()*0.1]))), 0), 255)
''''''
if relativeShift_position in ['position', 'relativeShift_v2']:
self.perturbed_xy_ += np.array([omega_perturbed * perturbed_v[0], omega_perturbed * perturbed_v[1]]).transpose(1, 2, 0)
else:
print('relativeShift_position error')
exit()
'''
flat_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape(
self.new_shape[0] * self.new_shape[1], 2)
vtx, wts = self.interp_weights(self.perturbed_xy_.reshape(self.new_shape[0] * self.new_shape[1], 2), flat_position)
wts_sum = np.abs(wts).sum(-1)
# flat_img.reshape(flat_shape[0] * flat_shape[1], 3)[:] = interpolate(pixel, vtx, wts)
wts = wts[wts_sum <= 1, :]
vtx = vtx[wts_sum <= 1, :]
synthesis_perturbed_img.reshape(self.new_shape[0] * self.new_shape[1], 3)[wts_sum <= 1,
:] = self.interpolate(synthesis_perturbed_img_map.reshape(self.new_shape[0] * self.new_shape[1], 3), vtx, wts)
synthesis_perturbed_label.reshape(self.new_shape[0] * self.new_shape[1], 2)[wts_sum <= 1,
:] = self.interpolate(synthesis_perturbed_label_map.reshape(self.new_shape[0] * self.new_shape[1], 2), vtx, wts)
foreORbackground_label = np.zeros(self.new_shape)
foreORbackground_label.reshape(self.new_shape[0] * self.new_shape[1], 1)[wts_sum <= 1, :] = self.interpolate(foreORbackground_label_map.reshape(self.new_shape[0] * self.new_shape[1], 1), vtx, wts)
foreORbackground_label[foreORbackground_label < 0.99] = 0
foreORbackground_label[foreORbackground_label >= 0.99] = 1
# synthesis_perturbed_img = np.around(synthesis_perturbed_img).astype(np.uint8)
synthesis_perturbed_label[:, :, 0] *= foreORbackground_label
synthesis_perturbed_label[:, :, 1] *= foreORbackground_label
synthesis_perturbed_img[:, :, 0] *= foreORbackground_label
synthesis_perturbed_img[:, :, 1] *= foreORbackground_label
synthesis_perturbed_img[:, :, 2] *= foreORbackground_label
self.synthesis_perturbed_img = synthesis_perturbed_img
self.synthesis_perturbed_label = synthesis_perturbed_label
'''
'''perspective'''
perspective_shreshold = random.randint(26, 36)*10 # 280
x_min_per, y_min_per, x_max_per, y_max_per = self.adjust_position(perspective_shreshold, perspective_shreshold, self.new_shape[0]-perspective_shreshold, self.new_shape[1]-perspective_shreshold)
pts1 = np.float32([[x_min_per, y_min_per], [x_max_per, y_min_per], [x_min_per, y_max_per], [x_max_per, y_max_per]])
e_1_ = x_max_per - x_min_per
e_2_ = y_max_per - y_min_per
e_3_ = e_2_
e_4_ = e_1_
perspective_shreshold_h = e_1_*0.02
perspective_shreshold_w = e_2_*0.02
a_min_, a_max_ = 70, 110
# if self.is_perform(1, 0):
if fold_curve == 'curve' and self.is_perform(0.5, 0.5):
if self.is_perform(0.5, 0.5):
while True:
pts2 = np.around(
np.float32([[x_min_per - (random.random()) * perspective_shreshold, y_min_per + (random.random()) * perspective_shreshold],
[x_max_per - (random.random()) * perspective_shreshold, y_min_per - (random.random()) * perspective_shreshold],
[x_min_per + (random.random()) * perspective_shreshold, y_max_per + (random.random()) * perspective_shreshold],
[x_max_per + (random.random()) * perspective_shreshold, y_max_per - (random.random()) * perspective_shreshold]])) # right
e_1 = np.linalg.norm(pts2[0]-pts2[1])
e_2 = np.linalg.norm(pts2[0]-pts2[2])
e_3 = np.linalg.norm(pts2[1]-pts2[3])
e_4 = np.linalg.norm(pts2[2]-pts2[3])
if e_1_+perspective_shreshold_h > e_1 and e_2_+perspective_shreshold_w > e_2 and e_3_+perspective_shreshold_w > e_3 and e_4_+perspective_shreshold_h > e_4 and \
e_1_ - perspective_shreshold_h < e_1 and e_2_ - perspective_shreshold_w < e_2 and e_3_ - perspective_shreshold_w < e_3 and e_4_ - perspective_shreshold_h < e_4 and \
abs(e_1-e_4) < perspective_shreshold_h and abs(e_2-e_3) < perspective_shreshold_w:
a0_, a1_, a2_, a3_ = self.get_angle_4(pts2)
if (a0_ > a_min_ and a0_ < a_max_) or (a1_ > a_min_ and a1_ < a_max_) or (a2_ > a_min_ and a2_ < a_max_) or (a3_ > a_min_ and a3_ < a_max_):
break
else:
while True:
pts2 = np.around(
np.float32([[x_min_per + (random.random()) * perspective_shreshold, y_min_per - (random.random()) * perspective_shreshold],
[x_max_per + (random.random()) * perspective_shreshold, y_min_per + (random.random()) * perspective_shreshold],
[x_min_per - (random.random()) * perspective_shreshold, y_max_per - (random.random()) * perspective_shreshold],
[x_max_per - (random.random()) * perspective_shreshold, y_max_per + (random.random()) * perspective_shreshold]]))
e_1 = np.linalg.norm(pts2[0]-pts2[1])
e_2 = np.linalg.norm(pts2[0]-pts2[2])
e_3 = np.linalg.norm(pts2[1]-pts2[3])
e_4 = np.linalg.norm(pts2[2]-pts2[3])
if e_1_+perspective_shreshold_h > e_1 and e_2_+perspective_shreshold_w > e_2 and e_3_+perspective_shreshold_w > e_3 and e_4_+perspective_shreshold_h > e_4 and \
e_1_ - perspective_shreshold_h < e_1 and e_2_ - perspective_shreshold_w < e_2 and e_3_ - perspective_shreshold_w < e_3 and e_4_ - perspective_shreshold_h < e_4 and \
abs(e_1-e_4) < perspective_shreshold_h and abs(e_2-e_3) < perspective_shreshold_w:
a0_, a1_, a2_, a3_ = self.get_angle_4(pts2)
if (a0_ > a_min_ and a0_ < a_max_) or (a1_ > a_min_ and a1_ < a_max_) or (a2_ > a_min_ and a2_ < a_max_) or (a3_ > a_min_ and a3_ < a_max_):
break
else:
while True:
pts2 = np.around(np.float32([[x_min_per+(random.random()-0.5)*perspective_shreshold, y_min_per+(random.random()-0.5)*perspective_shreshold],
[x_max_per+(random.random()-0.5)*perspective_shreshold, y_min_per+(random.random()-0.5)*perspective_shreshold],
[x_min_per+(random.random()-0.5)*perspective_shreshold, y_max_per+(random.random()-0.5)*perspective_shreshold],
[x_max_per+(random.random()-0.5)*perspective_shreshold, y_max_per+(random.random()-0.5)*perspective_shreshold]]))
e_1 = np.linalg.norm(pts2[0]-pts2[1])
e_2 = np.linalg.norm(pts2[0]-pts2[2])
e_3 = np.linalg.norm(pts2[1]-pts2[3])
e_4 = np.linalg.norm(pts2[2]-pts2[3])
if e_1_+perspective_shreshold_h > e_1 and e_2_+perspective_shreshold_w > e_2 and e_3_+perspective_shreshold_w > e_3 and e_4_+perspective_shreshold_h > e_4 and \
e_1_ - perspective_shreshold_h < e_1 and e_2_ - perspective_shreshold_w < e_2 and e_3_ - perspective_shreshold_w < e_3 and e_4_ - perspective_shreshold_h < e_4 and \
abs(e_1-e_4) < perspective_shreshold_h and abs(e_2-e_3) < perspective_shreshold_w:
a0_, a1_, a2_, a3_ = self.get_angle_4(pts2)
if (a0_ > a_min_ and a0_ < a_max_) or (a1_ > a_min_ and a1_ < a_max_) or (a2_ > a_min_ and a2_ < a_max_) or (a3_ > a_min_ and a3_ < a_max_):
break
M = cv2.getPerspectiveTransform(pts1, pts2)
one = np.ones((self.new_shape[0], self.new_shape[1], 1), dtype=np.int16)
matr = np.dstack((pixel_position, one))
new = np.dot(M, matr.reshape(-1, 3).T).T.reshape(self.new_shape[0], self.new_shape[1], 3)
x = new[:, :, 0]/new[:, :, 2]
y = new[:, :, 1]/new[:, :, 2]
perturbed_xy_ = np.dstack((x, y))
# perturbed_xy_round_int = np.around(cv2.bilateralFilter(perturbed_xy_round_int, 9, 75, 75))
# perturbed_xy_round_int = np.around(cv2.blur(perturbed_xy_, (17, 17)))
# perturbed_xy_round_int = cv2.blur(perturbed_xy_round_int, (17, 17))
# perturbed_xy_round_int = cv2.GaussianBlur(perturbed_xy_round_int, (7, 7), 0)
perturbed_xy_ = perturbed_xy_-np.min(perturbed_xy_.T.reshape(2, -1), 1)
# perturbed_xy_round_int = np.around(perturbed_xy_round_int-np.min(perturbed_xy_round_int.T.reshape(2, -1), 1)).astype(np.int16)
self.perturbed_xy_ += perturbed_xy_
'''perspective end'''
'''to img'''
flat_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape(
self.new_shape[0] * self.new_shape[1], 2)
# self.perturbed_xy_ = cv2.blur(self.perturbed_xy_, (7, 7))
self.perturbed_xy_ = cv2.GaussianBlur(self.perturbed_xy_, (7, 7), 0)
'''get fiducial points'''
fiducial_points_coordinate = self.perturbed_xy_[im_x, im_y]
vtx, wts = self.interp_weights(self.perturbed_xy_.reshape(self.new_shape[0] * self.new_shape[1], 2), flat_position)
wts_sum = np.abs(wts).sum(-1)
# flat_img.reshape(flat_shape[0] * flat_shape[1], 3)[:] = interpolate(pixel, vtx, wts)
wts = wts[wts_sum <= 1, :]
vtx = vtx[wts_sum <= 1, :]
synthesis_perturbed_img.reshape(self.new_shape[0] * self.new_shape[1], 3)[wts_sum <= 1,
:] = self.interpolate(synthesis_perturbed_img_map.reshape(self.new_shape[0] * self.new_shape[1], 3), vtx, wts)
synthesis_perturbed_label.reshape(self.new_shape[0] * self.new_shape[1], 2)[wts_sum <= 1,
:] = self.interpolate(synthesis_perturbed_label_map.reshape(self.new_shape[0] * self.new_shape[1], 2), vtx, wts)
foreORbackground_label = np.zeros(self.new_shape)
foreORbackground_label.reshape(self.new_shape[0] * self.new_shape[1], 1)[wts_sum <= 1, :] = self.interpolate(foreORbackground_label_map.reshape(self.new_shape[0] * self.new_shape[1], 1), vtx, wts)
foreORbackground_label[foreORbackground_label < 0.99] = 0
foreORbackground_label[foreORbackground_label >= 0.99] = 1
self.synthesis_perturbed_img = synthesis_perturbed_img
self.synthesis_perturbed_label = synthesis_perturbed_label
self.foreORbackground_label = foreORbackground_label
'''draw fiducial points
stepSize = 0
fiducial_points_synthesis_perturbed_img = self.synthesis_perturbed_img.copy()
for l in fiducial_points_coordinate.astype(np.int64).reshape(-1,2):
cv2.circle(fiducial_points_synthesis_perturbed_img, (l[1] + math.ceil(stepSize / 2), l[0] + math.ceil(stepSize / 2)), 5, (0, 0, 255), -1)
cv2.imwrite('/lustre/home/gwxie/program/project/unwarp/unwarp_perturbed/TPS/img/cv_TPS_large.jpg', fiducial_points_synthesis_perturbed_img)
'''
'''clip'''
perturbed_x_min, perturbed_y_min, perturbed_x_max, perturbed_y_max = -1, -1, self.new_shape[0], self.new_shape[1]
for x in range(self.new_shape[0] // 2, perturbed_x_max):
if np.sum(self.synthesis_perturbed_img[x, :]) == 768 * self.new_shape[1] and perturbed_x_max - 1 > x:
perturbed_x_max = x
break
for x in range(self.new_shape[0] // 2, perturbed_x_min, -1):
if np.sum(self.synthesis_perturbed_img[x, :]) == 768 * self.new_shape[1] and x > 0:
perturbed_x_min = x
break
for y in range(self.new_shape[1] // 2, perturbed_y_max):
if np.sum(self.synthesis_perturbed_img[:, y]) == 768 * self.new_shape[0] and perturbed_y_max - 1 > y:
perturbed_y_max = y
break
for y in range(self.new_shape[1] // 2, perturbed_y_min, -1):
if np.sum(self.synthesis_perturbed_img[:, y]) == 768 * self.new_shape[0] and y > 0:
perturbed_y_min = y
break
if perturbed_x_min == 0 or perturbed_x_max == self.new_shape[0] or perturbed_y_min == self.new_shape[1] or perturbed_y_max == self.new_shape[1]:
raise Exception('clip error')
if perturbed_x_max - perturbed_x_min < im_lr//2 or perturbed_y_max - perturbed_y_min < im_ud//2:
raise Exception('clip error')
perfix_ = self.save_suffix+'_'+str(m)+'_'+str(n)
is_shrink = False
if perturbed_x_max - perturbed_x_min > save_img_shape[0] or perturbed_y_max - perturbed_y_min > save_img_shape[1]:
is_shrink = True
synthesis_perturbed_img = cv2.resize(self.synthesis_perturbed_img[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max, :].copy(), (im_ud, im_lr), interpolation=cv2.INTER_LINEAR)
synthesis_perturbed_label = cv2.resize(self.synthesis_perturbed_label[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max, :].copy(), (im_ud, im_lr), interpolation=cv2.INTER_LINEAR)
foreORbackground_label = cv2.resize(self.foreORbackground_label[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max].copy(), (im_ud, im_lr), interpolation=cv2.INTER_LINEAR)
foreORbackground_label[foreORbackground_label < 0.99] = 0
foreORbackground_label[foreORbackground_label >= 0.99] = 1
'''shrink fiducial points'''
center_x_l, center_y_l = perturbed_x_min + (perturbed_x_max - perturbed_x_min) // 2, perturbed_y_min + (perturbed_y_max - perturbed_y_min) // 2
fiducial_points_coordinate_copy = fiducial_points_coordinate.copy()
shrink_x = im_lr/(perturbed_x_max - perturbed_x_min)
shrink_y = im_ud/(perturbed_y_max - perturbed_y_min)
fiducial_points_coordinate *= [shrink_x, shrink_y]
center_x_l *= shrink_x
center_y_l *= shrink_y
# fiducial_points_coordinate[1:, 1:] *= [shrink_x, shrink_y]
# fiducial_points_coordinate[1:, :1, 0] *= shrink_x
# fiducial_points_coordinate[:1, 1:, 1] *= shrink_y
# perturbed_x_min_copy, perturbed_y_min_copy, perturbed_x_max_copy, perturbed_y_max_copy = perturbed_x_min, perturbed_y_min, perturbed_x_max, perturbed_y_max
perturbed_x_min, perturbed_y_min, perturbed_x_max, perturbed_y_max = self.adjust_position_v2(0, 0, im_lr, im_ud, self.new_shape)
self.synthesis_perturbed_img = np.full_like(self.synthesis_perturbed_img, 256)
self.synthesis_perturbed_label = np.zeros_like(self.synthesis_perturbed_label)
self.foreORbackground_label = np.zeros_like(self.foreORbackground_label)
self.synthesis_perturbed_img[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max, :] = synthesis_perturbed_img
self.synthesis_perturbed_label[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max, :] = synthesis_perturbed_label
self.foreORbackground_label[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max] = foreORbackground_label
center_x, center_y = perturbed_x_min + (perturbed_x_max - perturbed_x_min) // 2, perturbed_y_min + (perturbed_y_max - perturbed_y_min) // 2
if is_shrink:
fiducial_points_coordinate += [center_x-center_x_l, center_y-center_y_l]
'''draw fiducial points
stepSize = 0
fiducial_points_synthesis_perturbed_img = self.synthesis_perturbed_img.copy()
for l in fiducial_points_coordinate.astype(np.int64).reshape(-1, 2):
cv2.circle(fiducial_points_synthesis_perturbed_img,
(l[1] + math.ceil(stepSize / 2), l[0] + math.ceil(stepSize / 2)), 5, (0, 0, 255), -1)
cv2.imwrite('/lustre/home/gwxie/program/project/unwarp/unwarp_perturbed/TPS/img/cv_TPS_small.jpg',fiducial_points_synthesis_perturbed_img)
'''
self.new_shape = save_img_shape
self.synthesis_perturbed_img = self.synthesis_perturbed_img[
center_x - self.new_shape[0] // 2:center_x + self.new_shape[0] // 2,
center_y - self.new_shape[1] // 2:center_y + self.new_shape[1] // 2,
:].copy()
self.synthesis_perturbed_label = self.synthesis_perturbed_label[
center_x - self.new_shape[0] // 2:center_x + self.new_shape[0] // 2,
center_y - self.new_shape[1] // 2:center_y + self.new_shape[1] // 2,
:].copy()
self.foreORbackground_label = self.foreORbackground_label[
center_x - self.new_shape[0] // 2:center_x + self.new_shape[0] // 2,
center_y - self.new_shape[1] // 2:center_y + self.new_shape[1] // 2].copy()
perturbed_x_ = max(self.new_shape[0] - (perturbed_x_max - perturbed_x_min), 0)
perturbed_x_min = perturbed_x_ // 2
perturbed_x_max = self.new_shape[0] - perturbed_x_ // 2 if perturbed_x_%2 == 0 else self.new_shape[0] - (perturbed_x_ // 2 + 1)
perturbed_y_ = max(self.new_shape[1] - (perturbed_y_max - perturbed_y_min), 0)
perturbed_y_min = perturbed_y_ // 2
perturbed_y_max = self.new_shape[1] - perturbed_y_ // 2 if perturbed_y_%2 == 0 else self.new_shape[1] - (perturbed_y_ // 2 + 1)
'''clip
perturbed_x_min, perturbed_y_min, perturbed_x_max, perturbed_y_max = -1, -1, self.new_shape[0], self.new_shape[1]
for x in range(self.new_shape[0] // 2, perturbed_x_max):
if np.sum(self.synthesis_perturbed_img[x, :]) == 768 * self.new_shape[1] and perturbed_x_max - 1 > x:
perturbed_x_max = x
break
for x in range(self.new_shape[0] // 2, perturbed_x_min, -1):
if np.sum(self.synthesis_perturbed_img[x, :]) == 768 * self.new_shape[1] and x > 0:
perturbed_x_min = x
break
for y in range(self.new_shape[1] // 2, perturbed_y_max):
if np.sum(self.synthesis_perturbed_img[:, y]) == 768 * self.new_shape[0] and perturbed_y_max - 1 > y:
perturbed_y_max = y
break
for y in range(self.new_shape[1] // 2, perturbed_y_min, -1):
if np.sum(self.synthesis_perturbed_img[:, y]) == 768 * self.new_shape[0] and y > 0:
perturbed_y_min = y
break
center_x, center_y = perturbed_x_min+(perturbed_x_max - perturbed_x_min)//2, perturbed_y_min+(perturbed_y_max - perturbed_y_min)//2
perfix_ = self.save_suffix+'_'+str(m)+'_'+str(n)
self.new_shape = save_img_shape
perturbed_x_ = max(self.new_shape[0] - (perturbed_x_max - perturbed_x_min), 0)
perturbed_x_min = perturbed_x_ // 2
perturbed_x_max = self.new_shape[0] - perturbed_x_ // 2 if perturbed_x_%2 == 0 else self.new_shape[0] - (perturbed_x_ // 2 + 1)
perturbed_y_ = max(self.new_shape[1] - (perturbed_y_max - perturbed_y_min), 0)
perturbed_y_min = perturbed_y_ // 2
perturbed_y_max = self.new_shape[1] - perturbed_y_ // 2 if perturbed_y_%2 == 0 else self.new_shape[1] - (perturbed_y_ // 2 + 1)
self.synthesis_perturbed_img = self.synthesis_perturbed_img[center_x-self.new_shape[0]//2:center_x+self.new_shape[0]//2, center_y-self.new_shape[1]//2:center_y+self.new_shape[1]//2, :].copy()
self.synthesis_perturbed_label = self.synthesis_perturbed_label[center_x-self.new_shape[0]//2:center_x+self.new_shape[0]//2, center_y-self.new_shape[1]//2:center_y+self.new_shape[1]//2, :].copy()
self.foreORbackground_label = self.foreORbackground_label[center_x-self.new_shape[0]//2:center_x+self.new_shape[0]//2, center_y-self.new_shape[1]//2:center_y+self.new_shape[1]//2].copy()
'''
'''save'''
pixel_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape(self.new_shape[0], self.new_shape[1], 2)
if relativeShift_position == 'relativeShift_v2':
self.synthesis_perturbed_label -= pixel_position
fiducial_points_coordinate -= [center_x - self.new_shape[0] // 2, center_y - self.new_shape[1] // 2]
self.synthesis_perturbed_label[:, :, 0] *= self.foreORbackground_label
self.synthesis_perturbed_label[:, :, 1] *= self.foreORbackground_label
self.synthesis_perturbed_img[:, :, 0] *= self.foreORbackground_label
self.synthesis_perturbed_img[:, :, 1] *= self.foreORbackground_label
self.synthesis_perturbed_img[:, :, 2] *= self.foreORbackground_label
'''
synthesis_perturbed_img_filter = self.synthesis_perturbed_img.copy()
synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (3, 3), 0)
# if self.is_perform(0.9, 0.1) or repeat_time > 5:
# # if self.is_perform(0.1, 0.9) and repeat_time > 9:
# # synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (7, 7), 0)
# # else:
# synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (5, 5), 0)
# else:
# synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (3, 3), 0)
self.synthesis_perturbed_img[self.foreORbackground_label == 1] = synthesis_perturbed_img_filter[self.foreORbackground_label == 1]
'''
'''
perturbed_bg_img = perturbed_bg_img.astype(np.float32)
perturbed_bg_img[:, :, 0] *= 1 - self.foreORbackground_label
perturbed_bg_img[:, :, 1] *= 1 - self.foreORbackground_label
perturbed_bg_img[:, :, 2] *= 1 - self.foreORbackground_label
self.synthesis_perturbed_img += perturbed_bg_img
HSV
perturbed_bg_img = perturbed_bg_img.astype(np.float32)
if self.is_perform(0.1, 0.9):
if self.is_perform(0.2, 0.8):
synthesis_perturbed_img_clip_HSV = self.synthesis_perturbed_img.copy()
synthesis_perturbed_img_clip_HSV = cv2.cvtColor(synthesis_perturbed_img_clip_HSV, cv2.COLOR_RGB2HSV)
H_, S_, V_ = (random.random()-0.2)*20, (random.random()-0.2)/8, (random.random()-0.2)*20
synthesis_perturbed_img_clip_HSV[:, :, 0], synthesis_perturbed_img_clip_HSV[:, :, 1], synthesis_perturbed_img_clip_HSV[:, :, 2] = synthesis_perturbed_img_clip_HSV[:, :, 0]-H_, synthesis_perturbed_img_clip_HSV[:, :, 1]-S_, synthesis_perturbed_img_clip_HSV[:, :, 2]-V_
synthesis_perturbed_img_clip_HSV = cv2.cvtColor(synthesis_perturbed_img_clip_HSV, cv2.COLOR_HSV2RGB)
perturbed_bg_img[:, :, 0] *= 1-self.foreORbackground_label
perturbed_bg_img[:, :, 1] *= 1-self.foreORbackground_label
perturbed_bg_img[:, :, 2] *= 1-self.foreORbackground_label
synthesis_perturbed_img_clip_HSV += perturbed_bg_img
self.synthesis_perturbed_img = synthesis_perturbed_img_clip_HSV
else:
perturbed_bg_img_HSV = perturbed_bg_img
perturbed_bg_img_HSV = cv2.cvtColor(perturbed_bg_img_HSV, cv2.COLOR_RGB2HSV)
H_, S_, V_ = (random.random()-0.5)*20, (random.random()-0.5)/8, (random.random()-0.2)*20
perturbed_bg_img_HSV[:, :, 0], perturbed_bg_img_HSV[:, :, 1], perturbed_bg_img_HSV[:, :, 2] = perturbed_bg_img_HSV[:, :, 0]-H_, perturbed_bg_img_HSV[:, :, 1]-S_, perturbed_bg_img_HSV[:, :, 2]-V_
perturbed_bg_img_HSV = cv2.cvtColor(perturbed_bg_img_HSV, cv2.COLOR_HSV2RGB)
perturbed_bg_img_HSV[:, :, 0] *= 1-self.foreORbackground_label
perturbed_bg_img_HSV[:, :, 1] *= 1-self.foreORbackground_label
perturbed_bg_img_HSV[:, :, 2] *= 1-self.foreORbackground_label
self.synthesis_perturbed_img += perturbed_bg_img_HSV
# self.synthesis_perturbed_img[np.sum(self.synthesis_perturbed_img, 2) == 771] = perturbed_bg_img_HSV[np.sum(self.synthesis_perturbed_img, 2) == 771]
else:
synthesis_perturbed_img_clip_HSV = self.synthesis_perturbed_img.copy()
perturbed_bg_img[:, :, 0] *= 1 - self.foreORbackground_label
perturbed_bg_img[:, :, 1] *= 1 - self.foreORbackground_label
perturbed_bg_img[:, :, 2] *= 1 - self.foreORbackground_label
synthesis_perturbed_img_clip_HSV += perturbed_bg_img
# synthesis_perturbed_img_clip_HSV[np.sum(self.synthesis_perturbed_img, 2) == 771] = perturbed_bg_img[np.sum(self.synthesis_perturbed_img, 2) == 771]
synthesis_perturbed_img_clip_HSV = cv2.cvtColor(synthesis_perturbed_img_clip_HSV, cv2.COLOR_RGB2HSV)
H_, S_, V_ = (random.random()-0.5)*20, (random.random()-0.5)/10, (random.random()-0.4)*20
synthesis_perturbed_img_clip_HSV[:, :, 0], synthesis_perturbed_img_clip_HSV[:, :, 1], synthesis_perturbed_img_clip_HSV[:, :, 2] = synthesis_perturbed_img_clip_HSV[:, :, 0]-H_, synthesis_perturbed_img_clip_HSV[:, :, 1]-S_, synthesis_perturbed_img_clip_HSV[:, :, 2]-V_
synthesis_perturbed_img_clip_HSV = cv2.cvtColor(synthesis_perturbed_img_clip_HSV, cv2.COLOR_HSV2RGB)
self.synthesis_perturbed_img = synthesis_perturbed_img_clip_HSV
'''
'''HSV_v2'''
perturbed_bg_img = perturbed_bg_img.astype(np.float32)
# if self.is_perform(1, 0):
# if self.is_perform(1, 0):
if self.is_perform(0.1, 0.9):
if self.is_perform(0.2, 0.8):
synthesis_perturbed_img_clip_HSV = self.synthesis_perturbed_img.copy()
synthesis_perturbed_img_clip_HSV = self.HSV_v1(synthesis_perturbed_img_clip_HSV)
perturbed_bg_img[:, :, 0] *= 1-self.foreORbackground_label
perturbed_bg_img[:, :, 1] *= 1-self.foreORbackground_label
perturbed_bg_img[:, :, 2] *= 1-self.foreORbackground_label
synthesis_perturbed_img_clip_HSV += perturbed_bg_img
self.synthesis_perturbed_img = synthesis_perturbed_img_clip_HSV
else:
perturbed_bg_img_HSV = perturbed_bg_img
perturbed_bg_img_HSV = self.HSV_v1(perturbed_bg_img_HSV)
perturbed_bg_img_HSV[:, :, 0] *= 1-self.foreORbackground_label
perturbed_bg_img_HSV[:, :, 1] *= 1-self.foreORbackground_label
perturbed_bg_img_HSV[:, :, 2] *= 1-self.foreORbackground_label
self.synthesis_perturbed_img += perturbed_bg_img_HSV
# self.synthesis_perturbed_img[np.sum(self.synthesis_perturbed_img, 2) == 771] = perturbed_bg_img_HSV[np.sum(self.synthesis_perturbed_img, 2) == 771]
else:
synthesis_perturbed_img_clip_HSV = self.synthesis_perturbed_img.copy()
perturbed_bg_img[:, :, 0] *= 1 - self.foreORbackground_label
perturbed_bg_img[:, :, 1] *= 1 - self.foreORbackground_label
perturbed_bg_img[:, :, 2] *= 1 - self.foreORbackground_label
synthesis_perturbed_img_clip_HSV += perturbed_bg_img
synthesis_perturbed_img_clip_HSV = self.HSV_v1(synthesis_perturbed_img_clip_HSV)
self.synthesis_perturbed_img = synthesis_perturbed_img_clip_HSV
''''''
# cv2.imwrite(self.save_path+'clip/'+perfix_+'_'+fold_curve+str(perturbed_time)+'-'+str(repeat_time)+'.png', synthesis_perturbed_img_clip)
self.synthesis_perturbed_img[self.synthesis_perturbed_img < 0] = 0
self.synthesis_perturbed_img[self.synthesis_perturbed_img > 255] = 255
self.synthesis_perturbed_img = | np.around(self.synthesis_perturbed_img) | numpy.around |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
min_1_y_time = minima_x[-1] * np.ones_like(min_1_y)
dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101)
dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Characteristic Wave Effects Example')
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10))
plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10))
plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4,
label=textwrap.fill('Coughlin maximum', 14))
plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4,
label=textwrap.fill('Coughlin minimum', 14))
plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4,
label=textwrap.fill('Average maximum', 14))
plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4,
label=textwrap.fill('Average minimum', 14))
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14))
plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14))
plt.plot(max_2_x_time, max_2_x, 'k-')
plt.plot(max_2_x_time_side, max_2_x, 'k-')
plt.plot(min_2_x_time, min_2_x, 'k-')
plt.plot(min_2_x_time_side, min_2_x, 'k-')
plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--')
plt.text(5.16 * np.pi, 0.85, r'$2a_2$')
plt.plot(max_2_y_time, max_2_y, 'k-')
plt.plot(max_2_y_time, max_2_y_side, 'k-')
plt.plot(min_2_y_time, min_2_y, 'k-')
plt.plot(min_2_y_time, min_2_y_side, 'k-')
plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--')
plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$')
plt.plot(max_1_x_time, max_1_x, 'k-')
plt.plot(max_1_x_time_side, max_1_x, 'k-')
plt.plot(min_1_x_time, min_1_x, 'k-')
plt.plot(min_1_x_time_side, min_1_x, 'k-')
plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--')
plt.text(5.42 * np.pi, -0.1, r'$2a_1$')
plt.plot(max_1_y_time, max_1_y, 'k-')
plt.plot(max_1_y_time, max_1_y_side, 'k-')
plt.plot(min_1_y_time, min_1_y, 'k-')
plt.plot(min_1_y_time, min_1_y_side, 'k-')
plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--')
plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$')
plt.xlim(3.9 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_characteristic_wave.png')
plt.show()
# plot 6
t = np.linspace(5, 95, 100)
signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200)
util_nn = emd_utils.Utility(time=t, time_series=signal_orig)
maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()]
minima = signal_orig[util_nn.min_bool_func_1st_order_fd()]
cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima)
cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima)
time = np.linspace(0, 5 * np.pi, 1001)
lsq_signal = np.cos(time) + np.cos(5 * time)
knots = np.linspace(0, 5 * np.pi, 101)
time_extended = time_extension(time)
time_series_extended = np.zeros_like(time_extended) / 0
time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal
neural_network_m = 200
neural_network_k = 100
# forward ->
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))]
P[-1, col] = 1 # for additive constant
t = lsq_signal[-neural_network_m:]
# test - top
seed_weights = np.ones(neural_network_k) / neural_network_k
weights = 0 * seed_weights.copy()
train_input = P[:-1, :]
lr = 0.01
for iterations in range(1000):
output = np.matmul(weights, train_input)
error = (t - output)
gradients = error * (- train_input)
# guess average gradients
average_gradients = np.mean(gradients, axis=1)
# steepest descent
max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients)))
adjustment = - lr * average_gradients
# adjustment = - lr * max_gradient_vector
weights += adjustment
# test - bottom
weights_right = np.hstack((weights, 0))
max_count_right = 0
min_count_right = 0
i_right = 0
while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1):
time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \
sum(weights_right * np.hstack((time_series_extended[
int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right):
int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1)))
i_right += 1
if i_right > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_right += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_right += 1
# backward <-
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)]
P[-1, col] = 1 # for additive constant
t = lsq_signal[:neural_network_m]
vx = cvx.Variable(int(neural_network_k + 1))
objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary
prob = cvx.Problem(objective)
result = prob.solve(verbose=True, solver=cvx.ECOS)
weights_left = np.array(vx.value)
max_count_left = 0
min_count_left = 0
i_left = 0
while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1):
time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \
2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left):
int(len(lsq_signal) - 1 - i_left + neural_network_k)],
1))) + 1
i_left += 1
if i_left > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_left += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_left += 1
lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal)
utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended)
maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()]
maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()]
maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()]
minima_time = time[lsq_utils.min_bool_func_1st_order_fd()]
minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Single Neuron Neural Network Example')
plt.plot(time, lsq_signal, zorder=2, label='Signal')
plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12))
plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima')
plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima')
plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3,
label=textwrap.fill('Extrapolated maxima', 12))
plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4,
label=textwrap.fill('Extrapolated minima', 12))
plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k',
label=textwrap.fill('Neural network inputs', 13))
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k')
plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k')
plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed',
label=textwrap.fill('Neural network targets', 13))
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray')
plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray',
linestyle='dashed')
plt.xlim(3.4 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/neural_network.png')
plt.show()
# plot 6a
np.random.seed(0)
time = np.linspace(0, 5 * np.pi, 1001)
knots_51 = np.linspace(0, 5 * np.pi, 51)
time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time)
noise = np.random.normal(0, 1, len(time_series))
time_series += noise
advemdpy = EMD(time=time, time_series=time_series)
imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_31 = np.linspace(0, 5 * np.pi, 31)
imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_11 = np.linspace(0, 5 * np.pi, 11)
imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1,
edge_effect='symmetric_anchor', verbose=False)[:3]
fig, axs = plt.subplots(3, 1)
plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40))
plt.subplots_adjust(hspace=0.1)
axs[0].plot(time, time_series, label='Time series')
axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21))
print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}')
for knot in knots_51:
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[0].set_xticklabels(['', '', '', '', '', ''])
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[1].plot(time, time_series, label='Time series')
axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19))
axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19))
print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}')
for knot in knots_31:
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[1].set_xticklabels(['', '', '', '', '', ''])
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[1].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[1].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
axs[2].plot(time, time_series, label='Time series')
axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots')
axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots')
axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots')
print(f'DFA fluctuation with 11 knots: {np.round(np.var(time_series - imfs_51[3, :]), 3)}')
for knot in knots_11:
axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[2].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[2].set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$', r'$5\pi$'])
box_2 = axs[2].get_position()
axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height])
axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[2].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[2].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
plt.savefig('jss_figures/DFA_different_trends.png')
plt.show()
# plot 6b
fig, axs = plt.subplots(3, 1)
plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences Zoomed Region', 40))
plt.subplots_adjust(hspace=0.1)
axs[0].plot(time, time_series, label='Time series')
axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21))
for knot in knots_51:
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[0].set_xticklabels(['', '', '', '', '', ''])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[0].set_ylim(-5.5, 5.5)
axs[0].set_xlim(0.95 * np.pi, 1.55 * np.pi)
axs[1].plot(time, time_series, label='Time series')
axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19))
axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19))
for knot in knots_31:
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[1].set_xticklabels(['', '', '', '', '', ''])
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[1].set_ylim(-5.5, 5.5)
axs[1].set_xlim(0.95 * np.pi, 1.55 * np.pi)
axs[2].plot(time, time_series, label='Time series')
axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots')
axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots')
axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots')
for knot in knots_11:
axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[2].set_xticks([np.pi, (3 / 2) * np.pi])
axs[2].set_xticklabels([r'$\pi$', r'$\frac{3}{2}\pi$'])
box_2 = axs[2].get_position()
axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height])
axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[2].set_ylim(-5.5, 5.5)
axs[2].set_xlim(0.95 * np.pi, 1.55 * np.pi)
plt.savefig('jss_figures/DFA_different_trends_zoomed.png')
plt.show()
hs_ouputs = hilbert_spectrum(time, imfs_51, hts_51, ifs_51, max_frequency=12, plot=False)
# plot 6c
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Simple Sinusoidal Time Seres with Added Noise', 50))
x_hs, y, z = hs_ouputs
z_min, z_max = 0, np.abs(z).max()
ax.pcolormesh(x_hs, y, np.abs(z), cmap='gist_rainbow', vmin=z_min, vmax=z_max)
ax.plot(x_hs[0, :], 8 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 8$', Linewidth=3)
ax.plot(x_hs[0, :], 4 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 4$', Linewidth=3)
ax.plot(x_hs[0, :], 2 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 2$', Linewidth=3)
ax.set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi])
ax.set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$'])
plt.ylabel(r'Frequency (rad.s$^{-1}$)')
plt.xlabel('Time (s)')
box_0 = ax.get_position()
ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.85, box_0.height * 0.9])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/DFA_hilbert_spectrum.png')
plt.show()
# plot 6c
time = np.linspace(0, 5 * np.pi, 1001)
time_series = | np.cos(time) | numpy.cos |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * | np.ones_like(max_dash_time) | numpy.ones_like |
import numpy as np
import tensorflow as tf
H = 2
N = 2
M = 3
BS = 10
def my_softmax(arr):
max_elements = np.reshape(np.max(arr, axis = 2), (BS, N, 1))
arr = arr - max_elements
exp_array = np.exp(arr)
print (exp_array)
sum_array = np.reshape(np.sum(exp_array, axis=2), (BS, N, 1))
return exp_array /sum_array
def masked_softmax(logits, mask, dim):
"""
Takes masked softmax over given dimension of logits.
Inputs:
logits: Numpy array. We want to take softmax over dimension dim.
mask: Numpy array of same shape as logits.
Has 1s where there's real data in logits, 0 where there's padding
dim: int. dimension over which to take softmax
Returns:
masked_logits: Numpy array same shape as logits.
This is the same as logits, but with 1e30 subtracted
(i.e. very large negative number) in the padding locations.
prob_dist: Numpy array same shape as logits.
The result of taking softmax over masked_logits in given dimension.
Should be 0 in padding locations.
Should sum to 1 over given dimension.
"""
exp_mask = (1 - tf.cast(mask, 'float64')) * (-1e30) # -large where there's padding, 0 elsewhere
print (exp_mask)
masked_logits = tf.add(logits, exp_mask) # where there's padding, set logits to -large
prob_dist = tf.nn.softmax(masked_logits, dim)
return masked_logits, prob_dist
def test_build_similarity(contexts, questions):
w_sim_1 = tf.get_variable('w_sim_1',
initializer=w_1) # 2 * H
w_sim_2 = tf.get_variable('w_sim_2',
initializer=w_2) # 2 * self.hidden_size
w_sim_3 = tf.get_variable('w_sim_3',
initializer=w_3) # 2 * self.hidden_size
q_tile = tf.tile(tf.expand_dims(questions, 0), [N, 1, 1, 1]) # N x BS x M x 2H
q_tile = tf.transpose(q_tile, (1, 0, 3, 2)) # BS x N x 2H x M
contexts = tf.expand_dims(contexts, -1) # BS x N x 2H x 1
result = (contexts * q_tile) # BS x N x 2H x M
tf.assert_equal(tf.shape(result), [BS, N, 2 * H, M])
result = tf.transpose(result, (0, 1, 3, 2)) # BS x N x M x 2H
result = tf.reshape(result, (-1, N * M, 2 * H)) # BS x (NxM) x 2H
tf.assert_equal(tf.shape(result), [BS, N*M, 2*H])
# w_sim_1 = tf.tile(tf.expand_dims(w_sim_1, 0), [BS, 1])
# w_sim_2 = tf.tile(tf.expand_dims(w_sim_2, 0), [BS, 1])
# w_sim_3 = tf.tile(tf.expand_dims(w_sim_3, 0), [BS, 1])
term1 = tf.matmul(tf.reshape(contexts, (BS * N, 2*H)), tf.expand_dims(w_sim_1, -1)) # BS x N
term1 = tf.reshape(term1, (-1, N))
term2 = tf.matmul(tf.reshape(questions, (BS * M, 2*H)), tf.expand_dims(w_sim_2, -1)) # BS x M
term2 = tf.reshape(term2, (-1, M))
term3 = tf.matmul(tf.reshape(result, (BS * N * M, 2* H)), tf.expand_dims(w_sim_3, -1))
term3 = tf.reshape(term3, (-1, N, M)) # BS x N x M
S = tf.reshape(term1,(-1, N, 1)) + term3 + tf.reshape(term2, (-1, 1, M))
return S
def test_build_sim_mask():
context_mask = np.array([True, True]) # BS x N
question_mask = np.array([True, True, False]) # BS x M
context_mask = np.tile(context_mask, [BS, 1])
question_mask = | np.tile(question_mask, [BS, 1]) | numpy.tile |
try:
import importlib.resources as pkg_resources
except ImportError:
# Try backported to PY<37 `importlib_resources`.
import importlib_resources as pkg_resources
from . import images
from gym import Env, spaces
from time import time
import numpy as np
from copy import copy
import colorsys
import pygame
from pygame.transform import scale
class MinesweeperEnv(Env):
def __init__(self, grid_shape=(10, 15), bombs_density=0.1, n_bombs=None, impact_size=3, max_time=999, chicken=False):
self.grid_shape = grid_shape
self.grid_size = np.prod(grid_shape)
self.n_bombs = max(1, int(bombs_density * self.grid_size)) if n_bombs is None else n_bombs
self.n_bombs = min(self.grid_size - 1, self.n_bombs)
self.flaged_bombs = 0
self.flaged_empty = 0
self.max_time = max_time
if impact_size % 2 == 0:
raise ValueError('Impact_size must be an odd number !')
self.impact_size = impact_size
# Define constants
self.HIDDEN = 0
self.REVEAL = 1
self.FLAG = 2
self.BOMB = self.impact_size ** 2
# Setting up gym Env conventions
nvec_observation = (self.BOMB + 2) * np.ones(self.grid_shape)
self.observation_space = spaces.MultiDiscrete(nvec_observation)
nvec_action = np.array(self.grid_shape + (2,))
self.action_space = spaces.MultiDiscrete(nvec_action)
# Initalize state
self.state = np.zeros(self.grid_shape + (2,), dtype=np.uint8)
## Setup bombs places
idx = np.indices(self.grid_shape).reshape(2, -1)
bombs_ids = np.random.choice(range(self.grid_size), size=self.n_bombs, replace=False)
self.bombs_positions = idx[0][bombs_ids], idx[1][bombs_ids]
## Place numbers
self.semi_impact_size = (self.impact_size-1)//2
bomb_impact = np.ones((self.impact_size, self.impact_size), dtype=np.uint8)
for bombs_id in bombs_ids:
bomb_x, bomb_y = idx[0][bombs_id], idx[1][bombs_id]
x_min, x_max, dx_min, dx_max = self.clip_index(bomb_x, 0)
y_min, y_max, dy_min, dy_max = self.clip_index(bomb_y, 1)
bomb_region = self.state[x_min:x_max, y_min:y_max, 0]
bomb_region += bomb_impact[dx_min:dx_max, dy_min:dy_max]
## Place bombs
self.state[self.bombs_positions + (0,)] = self.BOMB
self.start_time = time()
self.time_left = int(time() - self.start_time)
# Setup rendering
self.pygame_is_init = False
self.chicken = chicken
self.done = False
self.score = 0
def get_observation(self):
observation = copy(self.state[:, :, 1])
revealed = observation == 1
flaged = observation == 2
observation += self.impact_size ** 2 + 1
observation[revealed] = copy(self.state[:, :, 0][revealed])
observation[flaged] -= 1
return observation
def reveal_around(self, coords, reward, done, without_loss=False):
if not done:
x_min, x_max, _, _ = self.clip_index(coords[0], 0)
y_min, y_max, _, _ = self.clip_index(coords[1], 1)
region = self.state[x_min:x_max, y_min:y_max, :]
unseen_around = np.sum(region[..., 1] == 0)
if unseen_around == 0:
if not without_loss:
reward -= 0.001
return
flags_around = np.sum(region[..., 1] == 2)
if flags_around == self.state[coords + (0,)]:
unrevealed_zeros_around = np.logical_and(region[..., 0] == 0, region[..., 1] == self.HIDDEN)
if np.any(unrevealed_zeros_around):
zeros_coords = np.argwhere(unrevealed_zeros_around)
for zero in zeros_coords:
coord = (x_min + zero[0], y_min + zero[1])
self.state[coord + (1,)] = 1
self.reveal_around(coord, reward, done, without_loss=True)
self.state[x_min:x_max, y_min:y_max, 1][self.state[x_min:x_max, y_min:y_max, 1] != self.FLAG] = 1
unflagged_bombs_around = np.logical_and(region[..., 0] == self.BOMB, region[..., 1] != self.FLAG)
if | np.any(unflagged_bombs_around) | numpy.any |
import argparse
import json
import numpy as np
import pandas as pd
import os
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report,f1_score
from keras.models import Sequential
from keras.layers import Dense, Dropout
from keras import backend as K
from keras.utils.vis_utils import plot_model
from sklearn.externals import joblib
import time
def f1(y_true, y_pred):
def recall(y_true, y_pred):
"""Recall metric.
Only computes a batch-wise average of recall.
Computes the recall, a metric for multi-label classification of
how many relevant items are selected.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
possible_positives = K.sum(K.round(K.clip(y_true, 0, 1)))
recall = true_positives / (possible_positives + K.epsilon())
return recall
def precision(y_true, y_pred):
"""Precision metric.
Only computes a batch-wise average of precision.
Computes the precision, a metric for multi-label classification of
how many selected items are relevant.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
predicted_positives = K.sum(K.round(K.clip(y_pred, 0, 1)))
precision = true_positives / (predicted_positives + K.epsilon())
return precision
precision = precision(y_true, y_pred)
recall = recall(y_true, y_pred)
return 2*((precision*recall)/(precision+recall+K.epsilon()))
def get_embeddings(sentences_list,layer_json):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:return: Dictionary with key each sentence of the sentences_list and as value the embedding
'''
sentences = dict()#dict with key the index of each line of the sentences_list.txt and as value the sentence
embeddings = dict()##dict with key the index of each sentence and as value the its embedding
sentence_emb = dict()#key:sentence,value:its embedding
with open(sentences_list,'r') as file:
for index,line in enumerate(file):
sentences[index] = line.strip()
with open(layer_json, 'r',encoding='utf-8') as f:
for line in f:
embeddings[json.loads(line)['linex_index']] = np.asarray(json.loads(line)['features'])
for key,value in sentences.items():
sentence_emb[value] = embeddings[key]
return sentence_emb
def train_classifier(sentences_list,layer_json,dataset_csv,filename):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:param dataset_csv: the path of the dataset
:param filename: The path of the pickle file that the model will be stored
:return:
'''
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list,layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = np.asarray(previous_emb)
print(previous_emb.shape)
section_emb = np.asarray(section_list)
print(sentence_emb.shape)
length = np.asarray(length)
print(length.shape)
label = np.asarray(label)
print(errors)
features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1)
features = np.column_stack([features, length]) # np.append(features,length,axis=1)
print(features.shape)
X_train, X_val, y_train, y_val = train_test_split(features, label, test_size=0.33, random_state=42)
log = LogisticRegression(random_state=0, solver='newton-cg', max_iter=1000, C=0.1)
log.fit(X_train, y_train)
#save the model
_ = joblib.dump(log, filename, compress=9)
predictions = log.predict(X_val)
print("###########################################")
print("Results using embeddings from the",layer_json,"file")
print(classification_report(y_val, predictions))
print("F1 score using Logistic Regression:",f1_score(y_val, predictions))
print("###########################################")
#train a DNN
f1_results = list()
for i in range(3):
model = Sequential()
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dense(128, activation='relu', trainable=True))
model.add(Dropout(0.30))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.25))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.35))
model.add(Dense(1, activation='sigmoid'))
# compile network
model.compile(loss='binary_crossentropy', optimizer='sgd', metrics=[f1])
# fit network
model.fit(X_train, y_train, epochs=100, batch_size=64)
loss, f_1 = model.evaluate(X_val, y_val, verbose=1)
print('\nTest F1: %f' % (f_1 * 100))
f1_results.append(f_1)
model = None
print("###########################################")
print("Results using embeddings from the", layer_json, "file")
# evaluate
print( | np.mean(f1_results) | numpy.mean |
# coding: utf-8
# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Test the Logarithmic Units and Quantities
"""
from __future__ import (absolute_import, unicode_literals, division,
print_function)
from ...extern import six
from ...extern.six.moves import zip
import pickle
import itertools
import pytest
import numpy as np
from numpy.testing.utils import assert_allclose
from ...tests.helper import assert_quantity_allclose
from ... import units as u, constants as c
lu_units = [u.dex, u.mag, u.decibel]
lu_subclasses = [u.DexUnit, u.MagUnit, u.DecibelUnit]
lq_subclasses = [u.Dex, u.Magnitude, u.Decibel]
pu_sample = (u.dimensionless_unscaled, u.m, u.g/u.s**2, u.Jy)
class TestLogUnitCreation(object):
def test_logarithmic_units(self):
"""Check logarithmic units are set up correctly."""
assert u.dB.to(u.dex) == 0.1
assert u.dex.to(u.mag) == -2.5
assert u.mag.to(u.dB) == -4
@pytest.mark.parametrize('lu_unit, lu_cls', zip(lu_units, lu_subclasses))
def test_callable_units(self, lu_unit, lu_cls):
assert isinstance(lu_unit, u.UnitBase)
assert callable(lu_unit)
assert lu_unit._function_unit_class is lu_cls
@pytest.mark.parametrize('lu_unit', lu_units)
def test_equality_to_normal_unit_for_dimensionless(self, lu_unit):
lu = lu_unit()
assert lu == lu._default_function_unit # eg, MagUnit() == u.mag
assert lu._default_function_unit == lu # and u.mag == MagUnit()
@pytest.mark.parametrize('lu_unit, physical_unit',
itertools.product(lu_units, pu_sample))
def test_call_units(self, lu_unit, physical_unit):
"""Create a LogUnit subclass using the callable unit and physical unit,
and do basic check that output is right."""
lu1 = lu_unit(physical_unit)
assert lu1.physical_unit == physical_unit
assert lu1.function_unit == lu1._default_function_unit
def test_call_invalid_unit(self):
with pytest.raises(TypeError):
u.mag([])
with pytest.raises(ValueError):
u.mag(u.mag())
@pytest.mark.parametrize('lu_cls, physical_unit', itertools.product(
lu_subclasses + [u.LogUnit], pu_sample))
def test_subclass_creation(self, lu_cls, physical_unit):
"""Create a LogUnit subclass object for given physical unit,
and do basic check that output is right."""
lu1 = lu_cls(physical_unit)
assert lu1.physical_unit == physical_unit
assert lu1.function_unit == lu1._default_function_unit
lu2 = lu_cls(physical_unit,
function_unit=2*lu1._default_function_unit)
assert lu2.physical_unit == physical_unit
assert lu2.function_unit == u.Unit(2*lu2._default_function_unit)
with pytest.raises(ValueError):
lu_cls(physical_unit, u.m)
def test_predefined_magnitudes():
assert_quantity_allclose((-21.1*u.STmag).physical,
1.*u.erg/u.cm**2/u.s/u.AA)
assert_quantity_allclose((-48.6*u.ABmag).physical,
1.*u.erg/u.cm**2/u.s/u.Hz)
assert_quantity_allclose((0*u.M_bol).physical, c.L_bol0)
assert_quantity_allclose((0*u.m_bol).physical,
c.L_bol0/(4.*np.pi*(10.*c.pc)**2))
def test_predefined_reinitialisation():
assert u.mag('ST') == u.STmag
assert u.mag('AB') == u.ABmag
assert u.mag('Bol') == u.M_bol
assert u.mag('bol') == u.m_bol
def test_predefined_string_roundtrip():
"""Ensure roundtripping; see #5015"""
with u.magnitude_zero_points.enable():
assert u.Unit(u.STmag.to_string()) == u.STmag
assert u.Unit(u.ABmag.to_string()) == u.ABmag
assert u.Unit(u.M_bol.to_string()) == u.M_bol
assert u.Unit(u.m_bol.to_string()) == u.m_bol
def test_inequality():
"""Check __ne__ works (regresssion for #5342)."""
lu1 = u.mag(u.Jy)
lu2 = u.dex(u.Jy)
lu3 = u.mag(u.Jy**2)
lu4 = lu3 - lu1
assert lu1 != lu2
assert lu1 != lu3
assert lu1 == lu4
class TestLogUnitStrings(object):
def test_str(self):
"""Do some spot checks that str, repr, etc. work as expected."""
lu1 = u.mag(u.Jy)
assert str(lu1) == 'mag(Jy)'
assert repr(lu1) == 'Unit("mag(Jy)")'
assert lu1.to_string('generic') == 'mag(Jy)'
with pytest.raises(ValueError):
lu1.to_string('fits')
lu2 = u.dex()
assert str(lu2) == 'dex'
assert repr(lu2) == 'Unit("dex(1)")'
assert lu2.to_string() == 'dex(1)'
lu3 = u.MagUnit(u.Jy, function_unit=2*u.mag)
assert str(lu3) == '2 mag(Jy)'
assert repr(lu3) == 'MagUnit("Jy", unit="2 mag")'
assert lu3.to_string() == '2 mag(Jy)'
lu4 = u.mag(u.ct)
assert lu4.to_string('generic') == 'mag(ct)'
assert lu4.to_string('latex') == ('$\\mathrm{mag}$$\\mathrm{\\left( '
'\\mathrm{ct} \\right)}$')
assert lu4._repr_latex_() == lu4.to_string('latex')
class TestLogUnitConversion(object):
@pytest.mark.parametrize('lu_unit, physical_unit',
itertools.product(lu_units, pu_sample))
def test_physical_unit_conversion(self, lu_unit, physical_unit):
"""Check various LogUnit subclasses are equivalent and convertible
to their non-log counterparts."""
lu1 = lu_unit(physical_unit)
assert lu1.is_equivalent(physical_unit)
assert lu1.to(physical_unit, 0.) == 1.
assert physical_unit.is_equivalent(lu1)
assert physical_unit.to(lu1, 1.) == 0.
pu = u.Unit(8.*physical_unit)
assert lu1.is_equivalent(physical_unit)
assert lu1.to(pu, 0.) == 0.125
assert pu.is_equivalent(lu1)
assert_allclose(pu.to(lu1, 0.125), 0., atol=1.e-15)
# Check we round-trip.
value = np.linspace(0., 10., 6)
assert_allclose(pu.to(lu1, lu1.to(pu, value)), value, atol=1.e-15)
# And that we're not just returning True all the time.
pu2 = u.g
assert not lu1.is_equivalent(pu2)
with pytest.raises(u.UnitsError):
lu1.to(pu2)
assert not pu2.is_equivalent(lu1)
with pytest.raises(u.UnitsError):
pu2.to(lu1)
@pytest.mark.parametrize('lu_unit', lu_units)
def test_container_unit_conversion(self, lu_unit):
"""Check that conversion to logarithmic units (u.mag, u.dB, u.dex)
is only possible when the physical unit is dimensionless."""
values = np.linspace(0., 10., 6)
lu1 = lu_unit(u.dimensionless_unscaled)
assert lu1.is_equivalent(lu1.function_unit)
assert_allclose(lu1.to(lu1.function_unit, values), values)
lu2 = lu_unit(u.Jy)
assert not lu2.is_equivalent(lu2.function_unit)
with pytest.raises(u.UnitsError):
lu2.to(lu2.function_unit, values)
@pytest.mark.parametrize(
'flu_unit, tlu_unit, physical_unit',
itertools.product(lu_units, lu_units, pu_sample))
def test_subclass_conversion(self, flu_unit, tlu_unit, physical_unit):
"""Check various LogUnit subclasses are equivalent and convertible
to each other if they correspond to equivalent physical units."""
values = np.linspace(0., 10., 6)
flu = flu_unit(physical_unit)
tlu = tlu_unit(physical_unit)
assert flu.is_equivalent(tlu)
assert_allclose(flu.to(tlu), flu.function_unit.to(tlu.function_unit))
assert_allclose(flu.to(tlu, values),
values * flu.function_unit.to(tlu.function_unit))
tlu2 = tlu_unit(u.Unit(100.*physical_unit))
assert flu.is_equivalent(tlu2)
# Check that we round-trip.
assert_allclose(flu.to(tlu2, tlu2.to(flu, values)), values, atol=1.e-15)
tlu3 = tlu_unit(physical_unit.to_system(u.si)[0])
assert flu.is_equivalent(tlu3)
assert_allclose(flu.to(tlu3, tlu3.to(flu, values)), values, atol=1.e-15)
tlu4 = tlu_unit(u.g)
assert not flu.is_equivalent(tlu4)
with pytest.raises(u.UnitsError):
flu.to(tlu4, values)
def test_unit_decomposition(self):
lu = u.mag(u.Jy)
assert lu.decompose() == u.mag(u.Jy.decompose())
assert lu.decompose().physical_unit.bases == [u.kg, u.s]
assert lu.si == u.mag(u.Jy.si)
assert lu.si.physical_unit.bases == [u.kg, u.s]
assert lu.cgs == u.mag(u.Jy.cgs)
assert lu.cgs.physical_unit.bases == [u.g, u.s]
def test_unit_multiple_possible_equivalencies(self):
lu = u.mag(u.Jy)
assert lu.is_equivalent(pu_sample)
class TestLogUnitArithmetic(object):
def test_multiplication_division(self):
"""Check that multiplication/division with other units is only
possible when the physical unit is dimensionless, and that this
turns the unit into a normal one."""
lu1 = u.mag(u.Jy)
with pytest.raises(u.UnitsError):
lu1 * u.m
with pytest.raises(u.UnitsError):
u.m * lu1
with pytest.raises(u.UnitsError):
lu1 / lu1
for unit in (u.dimensionless_unscaled, u.m, u.mag, u.dex):
with pytest.raises(u.UnitsError):
lu1 / unit
lu2 = u.mag(u.dimensionless_unscaled)
with pytest.raises(u.UnitsError):
lu2 * lu1
with pytest.raises(u.UnitsError):
lu2 / lu1
# But dimensionless_unscaled can be cancelled.
assert lu2 / lu2 == u.dimensionless_unscaled
# With dimensionless, normal units are OK, but we return a plain unit.
tf = lu2 * u.m
tr = u.m * lu2
for t in (tf, tr):
assert not isinstance(t, type(lu2))
assert t == lu2.function_unit * u.m
with u.set_enabled_equivalencies(u.logarithmic()):
with pytest.raises(u.UnitsError):
t.to(lu2.physical_unit)
# Now we essentially have a LogUnit with a prefactor of 100,
# so should be equivalent again.
t = tf / u.cm
with u.set_enabled_equivalencies(u.logarithmic()):
assert t.is_equivalent(lu2.function_unit)
assert_allclose(t.to(u.dimensionless_unscaled, np.arange(3.)/100.),
lu2.to(lu2.physical_unit, np.arange(3.)))
# If we effectively remove lu1, a normal unit should be returned.
t2 = tf / lu2
assert not isinstance(t2, type(lu2))
assert t2 == u.m
t3 = tf / lu2.function_unit
assert not isinstance(t3, type(lu2))
assert t3 == u.m
# For completeness, also ensure non-sensical operations fail
with pytest.raises(TypeError):
lu1 * object()
with pytest.raises(TypeError):
slice(None) * lu1
with pytest.raises(TypeError):
lu1 / []
with pytest.raises(TypeError):
1 / lu1
@pytest.mark.parametrize('power', (2, 0.5, 1, 0))
def test_raise_to_power(self, power):
"""Check that raising LogUnits to some power is only possible when the
physical unit is dimensionless, and that conversion is turned off when
the resulting logarithmic unit (such as mag**2) is incompatible."""
lu1 = u.mag(u.Jy)
if power == 0:
assert lu1 ** power == u.dimensionless_unscaled
elif power == 1:
assert lu1 ** power == lu1
else:
with pytest.raises(u.UnitsError):
lu1 ** power
# With dimensionless, though, it works, but returns a normal unit.
lu2 = u.mag(u.dimensionless_unscaled)
t = lu2**power
if power == 0:
assert t == u.dimensionless_unscaled
elif power == 1:
assert t == lu2
else:
assert not isinstance(t, type(lu2))
assert t == lu2.function_unit**power
# also check we roundtrip
t2 = t**(1./power)
assert t2 == lu2.function_unit
with u.set_enabled_equivalencies(u.logarithmic()):
assert_allclose(t2.to(u.dimensionless_unscaled, np.arange(3.)),
lu2.to(lu2.physical_unit, np.arange(3.)))
@pytest.mark.parametrize('other', pu_sample)
def test_addition_subtraction_to_normal_units_fails(self, other):
lu1 = u.mag(u.Jy)
with pytest.raises(u.UnitsError):
lu1 + other
with pytest.raises(u.UnitsError):
lu1 - other
with pytest.raises(u.UnitsError):
other - lu1
def test_addition_subtraction_to_non_units_fails(self):
lu1 = u.mag(u.Jy)
with pytest.raises(TypeError):
lu1 + 1.
with pytest.raises(TypeError):
lu1 - [1., 2., 3.]
@pytest.mark.parametrize(
'other', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m),
u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag)))
def test_addition_subtraction(self, other):
"""Check physical units are changed appropriately"""
lu1 = u.mag(u.Jy)
other_pu = getattr(other, 'physical_unit', u.dimensionless_unscaled)
lu_sf = lu1 + other
assert lu_sf.is_equivalent(lu1.physical_unit * other_pu)
lu_sr = other + lu1
assert lu_sr.is_equivalent(lu1.physical_unit * other_pu)
lu_df = lu1 - other
assert lu_df.is_equivalent(lu1.physical_unit / other_pu)
lu_dr = other - lu1
assert lu_dr.is_equivalent(other_pu / lu1.physical_unit)
def test_complicated_addition_subtraction(self):
"""for fun, a more complicated example of addition and subtraction"""
dm0 = u.Unit('DM', 1./(4.*np.pi*(10.*u.pc)**2))
lu_dm = u.mag(dm0)
lu_absST = u.STmag - lu_dm
assert lu_absST.is_equivalent(u.erg/u.s/u.AA)
def test_neg_pos(self):
lu1 = u.mag(u.Jy)
neg_lu = -lu1
assert neg_lu != lu1
assert neg_lu.physical_unit == u.Jy**-1
assert -neg_lu == lu1
pos_lu = +lu1
assert pos_lu is not lu1
assert pos_lu == lu1
def test_pickle():
lu1 = u.dex(u.cm/u.s**2)
s = pickle.dumps(lu1)
lu2 = pickle.loads(s)
assert lu1 == lu2
def test_hashable():
lu1 = u.dB(u.mW)
lu2 = u.dB(u.m)
lu3 = u.dB(u.mW)
assert hash(lu1) != hash(lu2)
assert hash(lu1) == hash(lu3)
luset = {lu1, lu2, lu3}
assert len(luset) == 2
class TestLogQuantityCreation(object):
@pytest.mark.parametrize('lq, lu', zip(lq_subclasses + [u.LogQuantity],
lu_subclasses + [u.LogUnit]))
def test_logarithmic_quantities(self, lq, lu):
"""Check logarithmic quantities are all set up correctly"""
assert lq._unit_class == lu
assert type(lu()._quantity_class(1.)) is lq
@pytest.mark.parametrize('lq_cls, physical_unit',
itertools.product(lq_subclasses, pu_sample))
def test_subclass_creation(self, lq_cls, physical_unit):
"""Create LogQuantity subclass objects for some physical units,
and basic check on transformations"""
value = np.arange(1., 10.)
log_q = lq_cls(value * physical_unit)
assert log_q.unit.physical_unit == physical_unit
assert log_q.unit.function_unit == log_q.unit._default_function_unit
assert_allclose(log_q.physical.value, value)
with pytest.raises(ValueError):
lq_cls(value, physical_unit)
@pytest.mark.parametrize(
'unit', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m),
u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag),
u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag)))
def test_different_units(self, unit):
q = u.Magnitude(1.23, unit)
assert q.unit.function_unit == getattr(unit, 'function_unit', unit)
assert q.unit.physical_unit is getattr(unit, 'physical_unit',
u.dimensionless_unscaled)
@pytest.mark.parametrize('value, unit', (
(1.*u.mag(u.Jy), None),
(1.*u.dex(u.Jy), None),
(1.*u.mag(u.W/u.m**2/u.Hz), u.mag(u.Jy)),
(1.*u.dex(u.W/u.m**2/u.Hz), u.mag(u.Jy))))
def test_function_values(self, value, unit):
lq = u.Magnitude(value, unit)
assert lq == value
assert lq.unit.function_unit == u.mag
assert lq.unit.physical_unit == getattr(unit, 'physical_unit',
value.unit.physical_unit)
@pytest.mark.parametrize(
'unit', (u.mag(), u.mag(u.Jy), u.mag(u.m), u.MagUnit('', 2.*u.mag),
u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag)))
def test_indirect_creation(self, unit):
q1 = 2.5 * unit
assert isinstance(q1, u.Magnitude)
assert q1.value == 2.5
assert q1.unit == unit
pv = 100. * unit.physical_unit
q2 = unit * pv
assert q2.unit == unit
assert q2.unit.physical_unit == pv.unit
assert q2.to_value(unit.physical_unit) == 100.
assert (q2._function_view / u.mag).to_value(1) == -5.
q3 = unit / 0.4
assert q3 == q1
def test_from_view(self):
# Cannot view a physical quantity as a function quantity, since the
# values would change.
q = [100., 1000.] * u.cm/u.s**2
with pytest.raises(TypeError):
q.view(u.Dex)
# But fine if we have the right magnitude.
q = [2., 3.] * u.dex
lq = q.view(u.Dex)
assert isinstance(lq, u.Dex)
assert lq.unit.physical_unit == u.dimensionless_unscaled
assert np.all(q == lq)
def test_using_quantity_class(self):
"""Check that we can use Quantity if we have subok=True"""
# following issue #5851
lu = u.dex(u.AA)
with pytest.raises(u.UnitTypeError):
u.Quantity(1., lu)
q = u.Quantity(1., lu, subok=True)
assert type(q) is lu._quantity_class
def test_conversion_to_and_from_physical_quantities():
"""Ensures we can convert from regular quantities."""
mst = [10., 12., 14.] * u.STmag
flux_lambda = mst.physical
mst_roundtrip = flux_lambda.to(u.STmag)
# check we return a logquantity; see #5178.
assert isinstance(mst_roundtrip, u.Magnitude)
assert mst_roundtrip.unit == mst.unit
assert_allclose(mst_roundtrip.value, mst.value)
wave = [4956.8, 4959.55, 4962.3] * u.AA
flux_nu = mst.to(u.Jy, equivalencies=u.spectral_density(wave))
mst_roundtrip2 = flux_nu.to(u.STmag, u.spectral_density(wave))
assert isinstance(mst_roundtrip2, u.Magnitude)
assert mst_roundtrip2.unit == mst.unit
assert_allclose(mst_roundtrip2.value, mst.value)
def test_quantity_decomposition():
lq = 10.*u.mag(u.Jy)
assert lq.decompose() == lq
assert lq.decompose().unit.physical_unit.bases == [u.kg, u.s]
assert lq.si == lq
assert lq.si.unit.physical_unit.bases == [u.kg, u.s]
assert lq.cgs == lq
assert lq.cgs.unit.physical_unit.bases == [u.g, u.s]
class TestLogQuantityViews(object):
def setup(self):
self.lq = u.Magnitude(np.arange(10.) * u.Jy)
self.lq2 = u.Magnitude(np.arange(5.))
def test_value_view(self):
lq_value = self.lq.value
assert type(lq_value) is np.ndarray
lq_value[2] = -1.
assert np.all(self.lq.value == lq_value)
def test_function_view(self):
lq_fv = self.lq._function_view
assert type(lq_fv) is u.Quantity
assert lq_fv.unit is self.lq.unit.function_unit
lq_fv[3] = -2. * lq_fv.unit
assert np.all(self.lq.value == lq_fv.value)
def test_quantity_view(self):
# Cannot view as Quantity, since the unit cannot be represented.
with pytest.raises(TypeError):
self.lq.view(u.Quantity)
# But a dimensionless one is fine.
q2 = self.lq2.view(u.Quantity)
assert q2.unit is u.mag
assert np.all(q2.value == self.lq2.value)
lq3 = q2.view(u.Magnitude)
assert type(lq3.unit) is u.MagUnit
assert lq3.unit.physical_unit == u.dimensionless_unscaled
assert np.all(lq3 == self.lq2)
class TestLogQuantitySlicing(object):
def test_item_get_and_set(self):
lq1 = u.Magnitude(np.arange(1., 11.)*u.Jy)
assert lq1[9] == u.Magnitude(10.*u.Jy)
lq1[2] = 100.*u.Jy
assert lq1[2] == u.Magnitude(100.*u.Jy)
with pytest.raises(u.UnitsError):
lq1[2] = 100.*u.m
with pytest.raises(u.UnitsError):
lq1[2] = 100.*u.mag
with pytest.raises(u.UnitsError):
lq1[2] = u.Magnitude(100.*u.m)
assert lq1[2] == u.Magnitude(100.*u.Jy)
def test_slice_get_and_set(self):
lq1 = u.Magnitude(np.arange(1., 10.)*u.Jy)
lq1[2:4] = 100.*u.Jy
assert np.all(lq1[2:4] == u.Magnitude(100.*u.Jy))
with pytest.raises(u.UnitsError):
lq1[2:4] = 100.*u.m
with pytest.raises(u.UnitsError):
lq1[2:4] = 100.*u.mag
with pytest.raises(u.UnitsError):
lq1[2:4] = u.Magnitude(100.*u.m)
assert np.all(lq1[2] == u.Magnitude(100.*u.Jy))
class TestLogQuantityArithmetic(object):
def test_multiplication_division(self):
"""Check that multiplication/division with other quantities is only
possible when the physical unit is dimensionless, and that this turns
the result into a normal quantity."""
lq = u.Magnitude(np.arange(1., 11.)*u.Jy)
with pytest.raises(u.UnitsError):
lq * (1.*u.m)
with pytest.raises(u.UnitsError):
(1.*u.m) * lq
with pytest.raises(u.UnitsError):
lq / lq
for unit in (u.m, u.mag, u.dex):
with pytest.raises(u.UnitsError):
lq / unit
lq2 = u.Magnitude(np.arange(1, 11.))
with pytest.raises(u.UnitsError):
lq2 * lq
with pytest.raises(u.UnitsError):
lq2 / lq
with pytest.raises(u.UnitsError):
lq / lq2
# but dimensionless_unscaled can be cancelled
r = lq2 / u.Magnitude(2.)
assert r.unit == u.dimensionless_unscaled
assert np.all(r.value == lq2.value/2.)
# with dimensionless, normal units OK, but return normal quantities
tf = lq2 * u.m
tr = u.m * lq2
for t in (tf, tr):
assert not isinstance(t, type(lq2))
assert t.unit == lq2.unit.function_unit * u.m
with u.set_enabled_equivalencies(u.logarithmic()):
with pytest.raises(u.UnitsError):
t.to(lq2.unit.physical_unit)
t = tf / (50.*u.cm)
# now we essentially have the same quantity but with a prefactor of 2
assert t.unit.is_equivalent(lq2.unit.function_unit)
assert_allclose(t.to(lq2.unit.function_unit), lq2._function_view*2)
@pytest.mark.parametrize('power', (2, 0.5, 1, 0))
def test_raise_to_power(self, power):
"""Check that raising LogQuantities to some power is only possible when
the physical unit is dimensionless, and that conversion is turned off
when the resulting logarithmic unit (say, mag**2) is incompatible."""
lq = u.Magnitude(np.arange(1., 4.)*u.Jy)
if power == 0:
assert np.all(lq ** power == 1.)
elif power == 1:
assert np.all(lq ** power == lq)
else:
with pytest.raises(u.UnitsError):
lq ** power
# with dimensionless, it works, but falls back to normal quantity
# (except for power=1)
lq2 = u.Magnitude(np.arange(10.))
t = lq2**power
if power == 0:
assert t.unit is u.dimensionless_unscaled
assert np.all(t.value == 1.)
elif power == 1:
assert np.all(t == lq2)
else:
assert not isinstance(t, type(lq2))
assert t.unit == lq2.unit.function_unit ** power
with u.set_enabled_equivalencies(u.logarithmic()):
with pytest.raises(u.UnitsError):
t.to(u.dimensionless_unscaled)
def test_error_on_lq_as_power(self):
lq = u.Magnitude(np.arange(1., 4.)*u.Jy)
with pytest.raises(TypeError):
lq ** lq
@pytest.mark.parametrize('other', pu_sample)
def test_addition_subtraction_to_normal_units_fails(self, other):
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
q = 1.23 * other
with pytest.raises(u.UnitsError):
lq + q
with pytest.raises(u.UnitsError):
lq - q
with pytest.raises(u.UnitsError):
q - lq
@pytest.mark.parametrize(
'other', (1.23 * u.mag, 2.34 * u.mag(),
u.Magnitude(3.45 * u.Jy), u.Magnitude(4.56 * u.m),
5.67 * u.Unit(2*u.mag), u.Magnitude(6.78, 2.*u.mag)))
def test_addition_subtraction(self, other):
"""Check that addition/subtraction with quantities with magnitude or
MagUnit units works, and that it changes the physical units
appropriately."""
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
other_physical = other.to(getattr(other.unit, 'physical_unit',
u.dimensionless_unscaled),
equivalencies=u.logarithmic())
lq_sf = lq + other
assert_allclose(lq_sf.physical, lq.physical * other_physical)
lq_sr = other + lq
assert_allclose(lq_sr.physical, lq.physical * other_physical)
lq_df = lq - other
assert_allclose(lq_df.physical, lq.physical / other_physical)
lq_dr = other - lq
assert_allclose(lq_dr.physical, other_physical / lq.physical)
@pytest.mark.parametrize('other', pu_sample)
def test_inplace_addition_subtraction_unit_checks(self, other):
lu1 = u.mag(u.Jy)
lq1 = u.Magnitude(np.arange(1., 10.), lu1)
with pytest.raises(u.UnitsError):
lq1 += other
assert np.all(lq1.value == np.arange(1., 10.))
assert lq1.unit == lu1
with pytest.raises(u.UnitsError):
lq1 -= other
assert np.all(lq1.value == np.arange(1., 10.))
assert lq1.unit == lu1
@pytest.mark.parametrize(
'other', (1.23 * u.mag, 2.34 * u.mag(),
u.Magnitude(3.45 * u.Jy), u.Magnitude(4.56 * u.m),
5.67 * u.Unit(2*u.mag), u.Magnitude(6.78, 2.*u.mag)))
def test_inplace_addition_subtraction(self, other):
"""Check that inplace addition/subtraction with quantities with
magnitude or MagUnit units works, and that it changes the physical
units appropriately."""
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
other_physical = other.to(getattr(other.unit, 'physical_unit',
u.dimensionless_unscaled),
equivalencies=u.logarithmic())
lq_sf = lq.copy()
lq_sf += other
| assert_allclose(lq_sf.physical, lq.physical * other_physical) | numpy.testing.utils.assert_allclose |
# pylint: disable=protected-access
"""
Test the wrappers for the C API.
"""
import os
from contextlib import contextmanager
import numpy as np
import numpy.testing as npt
import pandas as pd
import pytest
import xarray as xr
from packaging.version import Version
from pygmt import Figure, clib
from pygmt.clib.conversion import dataarray_to_matrix
from pygmt.clib.session import FAMILIES, VIAS
from pygmt.exceptions import (
GMTCLibError,
GMTCLibNoSessionError,
GMTInvalidInput,
GMTVersionError,
)
from pygmt.helpers import GMTTempFile
TEST_DATA_DIR = os.path.join(os.path.dirname(__file__), "data")
with clib.Session() as _lib:
gmt_version = Version(_lib.info["version"])
@contextmanager
def mock(session, func, returns=None, mock_func=None):
"""
Mock a GMT C API function to make it always return a given value.
Used to test that exceptions are raised when API functions fail by
producing a NULL pointer as output or non-zero status codes.
Needed because it's not easy to get some API functions to fail without
inducing a Segmentation Fault (which is a good thing because libgmt usually
only fails with errors).
"""
if mock_func is None:
def mock_api_function(*args): # pylint: disable=unused-argument
"""
A mock GMT API function that always returns a given value.
"""
return returns
mock_func = mock_api_function
get_libgmt_func = session.get_libgmt_func
def mock_get_libgmt_func(name, argtypes=None, restype=None):
"""
Return our mock function.
"""
if name == func:
return mock_func
return get_libgmt_func(name, argtypes, restype)
setattr(session, "get_libgmt_func", mock_get_libgmt_func)
yield
setattr(session, "get_libgmt_func", get_libgmt_func)
def test_getitem():
"""
Test that I can get correct constants from the C lib.
"""
ses = clib.Session()
assert ses["GMT_SESSION_EXTERNAL"] != -99999
assert ses["GMT_MODULE_CMD"] != -99999
assert ses["GMT_PAD_DEFAULT"] != -99999
assert ses["GMT_DOUBLE"] != -99999
with pytest.raises(GMTCLibError):
ses["A_WHOLE_LOT_OF_JUNK"] # pylint: disable=pointless-statement
def test_create_destroy_session():
"""
Test that create and destroy session are called without errors.
"""
# Create two session and make sure they are not pointing to the same memory
session1 = clib.Session()
session1.create(name="test_session1")
assert session1.session_pointer is not None
session2 = clib.Session()
session2.create(name="test_session2")
assert session2.session_pointer is not None
assert session2.session_pointer != session1.session_pointer
session1.destroy()
session2.destroy()
# Create and destroy a session twice
ses = clib.Session()
for __ in range(2):
with pytest.raises(GMTCLibNoSessionError):
ses.session_pointer # pylint: disable=pointless-statement
ses.create("session1")
assert ses.session_pointer is not None
ses.destroy()
with pytest.raises(GMTCLibNoSessionError):
ses.session_pointer # pylint: disable=pointless-statement
def test_create_session_fails():
"""
Check that an exception is raised when failing to create a session.
"""
ses = clib.Session()
with mock(ses, "GMT_Create_Session", returns=None):
with pytest.raises(GMTCLibError):
ses.create("test-session-name")
# Should fail if trying to create a session before destroying the old one.
ses.create("test1")
with pytest.raises(GMTCLibError):
ses.create("test2")
def test_destroy_session_fails():
"""
Fail to destroy session when given bad input.
"""
ses = clib.Session()
with pytest.raises(GMTCLibNoSessionError):
ses.destroy()
ses.create("test-session")
with mock(ses, "GMT_Destroy_Session", returns=1):
with pytest.raises(GMTCLibError):
ses.destroy()
ses.destroy()
def test_call_module():
"""
Run a command to see if call_module works.
"""
data_fname = os.path.join(TEST_DATA_DIR, "points.txt")
out_fname = "test_call_module.txt"
with clib.Session() as lib:
with GMTTempFile() as out_fname:
lib.call_module("info", "{} -C ->{}".format(data_fname, out_fname.name))
assert os.path.exists(out_fname.name)
output = out_fname.read().strip()
assert output == "11.5309 61.7074 -2.9289 7.8648 0.1412 0.9338"
def test_call_module_invalid_arguments():
"""
Fails for invalid module arguments.
"""
with clib.Session() as lib:
with pytest.raises(GMTCLibError):
lib.call_module("info", "bogus-data.bla")
def test_call_module_invalid_name():
"""
Fails when given bad input.
"""
with clib.Session() as lib:
with pytest.raises(GMTCLibError):
lib.call_module("meh", "")
def test_call_module_error_message():
"""
Check is the GMT error message was captured.
"""
with clib.Session() as lib:
try:
lib.call_module("info", "bogus-data.bla")
except GMTCLibError as error:
assert "Module 'info' failed with status code" in str(error)
assert "gmtinfo [ERROR]: Cannot find file bogus-data.bla" in str(error)
def test_method_no_session():
"""
Fails when not in a session.
"""
# Create an instance of Session without "with" so no session is created.
lib = clib.Session()
with pytest.raises(GMTCLibNoSessionError):
lib.call_module("gmtdefaults", "")
with pytest.raises(GMTCLibNoSessionError):
lib.session_pointer # pylint: disable=pointless-statement
def test_parse_constant_single():
"""
Parsing a single family argument correctly.
"""
lib = clib.Session()
for family in FAMILIES:
parsed = lib._parse_constant(family, valid=FAMILIES)
assert parsed == lib[family]
def test_parse_constant_composite():
"""
Parsing a composite constant argument (separated by |) correctly.
"""
lib = clib.Session()
test_cases = ((family, via) for family in FAMILIES for via in VIAS)
for family, via in test_cases:
composite = "|".join([family, via])
expected = lib[family] + lib[via]
parsed = lib._parse_constant(composite, valid=FAMILIES, valid_modifiers=VIAS)
assert parsed == expected
def test_parse_constant_fails():
"""
Check if the function fails when given bad input.
"""
lib = clib.Session()
test_cases = [
"SOME_random_STRING",
"GMT_IS_DATASET|GMT_VIA_MATRIX|GMT_VIA_VECTOR",
"GMT_IS_DATASET|NOT_A_PROPER_VIA",
"NOT_A_PROPER_FAMILY|GMT_VIA_MATRIX",
"NOT_A_PROPER_FAMILY|ALSO_INVALID",
]
for test_case in test_cases:
with pytest.raises(GMTInvalidInput):
lib._parse_constant(test_case, valid=FAMILIES, valid_modifiers=VIAS)
# Should also fail if not given valid modifiers but is using them anyway.
# This should work...
lib._parse_constant(
"GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=VIAS
)
# But this shouldn't.
with pytest.raises(GMTInvalidInput):
lib._parse_constant(
"GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=None
)
def test_create_data_dataset():
"""
Run the function to make sure it doesn't fail badly.
"""
with clib.Session() as lib:
# Dataset from vectors
data_vector = lib.create_data(
family="GMT_IS_DATASET|GMT_VIA_VECTOR",
geometry="GMT_IS_POINT",
mode="GMT_CONTAINER_ONLY",
dim=[10, 20, 1, 0], # columns, rows, layers, dtype
)
# Dataset from matrices
data_matrix = lib.create_data(
family="GMT_IS_DATASET|GMT_VIA_MATRIX",
geometry="GMT_IS_POINT",
mode="GMT_CONTAINER_ONLY",
dim=[10, 20, 1, 0],
)
assert data_vector != data_matrix
def test_create_data_grid_dim():
"""
Create a grid ignoring range and inc.
"""
with clib.Session() as lib:
# Grids from matrices using dim
lib.create_data(
family="GMT_IS_GRID|GMT_VIA_MATRIX",
geometry="GMT_IS_SURFACE",
mode="GMT_CONTAINER_ONLY",
dim=[10, 20, 1, 0],
)
def test_create_data_grid_range():
"""
Create a grid specifying range and inc instead of dim.
"""
with clib.Session() as lib:
# Grids from matrices using range and int
lib.create_data(
family="GMT_IS_GRID|GMT_VIA_MATRIX",
geometry="GMT_IS_SURFACE",
mode="GMT_CONTAINER_ONLY",
ranges=[150.0, 250.0, -20.0, 20.0],
inc=[0.1, 0.2],
)
def test_create_data_fails():
"""
Check that create_data raises exceptions for invalid input and output.
"""
# Passing in invalid mode
with pytest.raises(GMTInvalidInput):
with clib.Session() as lib:
lib.create_data(
family="GMT_IS_DATASET",
geometry="GMT_IS_SURFACE",
mode="Not_a_valid_mode",
dim=[0, 0, 1, 0],
ranges=[150.0, 250.0, -20.0, 20.0],
inc=[0.1, 0.2],
)
# Passing in invalid geometry
with pytest.raises(GMTInvalidInput):
with clib.Session() as lib:
lib.create_data(
family="GMT_IS_GRID",
geometry="Not_a_valid_geometry",
mode="GMT_CONTAINER_ONLY",
dim=[0, 0, 1, 0],
ranges=[150.0, 250.0, -20.0, 20.0],
inc=[0.1, 0.2],
)
# If the data pointer returned is None (NULL pointer)
with pytest.raises(GMTCLibError):
with clib.Session() as lib:
with mock(lib, "GMT_Create_Data", returns=None):
lib.create_data(
family="GMT_IS_DATASET",
geometry="GMT_IS_SURFACE",
mode="GMT_CONTAINER_ONLY",
dim=[11, 10, 2, 0],
)
def test_virtual_file():
"""
Test passing in data via a virtual file with a Dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
shape = (5, 3)
for dtype in dtypes:
with clib.Session() as lib:
family = "GMT_IS_DATASET|GMT_VIA_MATRIX"
geometry = "GMT_IS_POINT"
dataset = lib.create_data(
family=family,
geometry=geometry,
mode="GMT_CONTAINER_ONLY",
dim=[shape[1], shape[0], 1, 0], # columns, rows, layers, dtype
)
data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape)
lib.put_matrix(dataset, matrix=data)
# Add the dataset to a virtual file and pass it along to gmt info
vfargs = (family, geometry, "GMT_IN|GMT_IS_REFERENCE", dataset)
with lib.open_virtual_file(*vfargs) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T]
)
expected = "<matrix memory>: N = {}\t{}\n".format(shape[0], bounds)
assert output == expected
def test_virtual_file_fails():
"""
Check that opening and closing virtual files raises an exception for non-
zero return codes.
"""
vfargs = (
"GMT_IS_DATASET|GMT_VIA_MATRIX",
"GMT_IS_POINT",
"GMT_IN|GMT_IS_REFERENCE",
None,
)
# Mock Open_VirtualFile to test the status check when entering the context.
# If the exception is raised, the code won't get to the closing of the
# virtual file.
with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=1):
with pytest.raises(GMTCLibError):
with lib.open_virtual_file(*vfargs):
print("Should not get to this code")
# Test the status check when closing the virtual file
# Mock the opening to return 0 (success) so that we don't open a file that
# we won't close later.
with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=0), mock(
lib, "GMT_Close_VirtualFile", returns=1
):
with pytest.raises(GMTCLibError):
with lib.open_virtual_file(*vfargs):
pass
print("Shouldn't get to this code either")
def test_virtual_file_bad_direction():
"""
Test passing an invalid direction argument.
"""
with clib.Session() as lib:
vfargs = (
"GMT_IS_DATASET|GMT_VIA_MATRIX",
"GMT_IS_POINT",
"GMT_IS_GRID", # The invalid direction argument
0,
)
with pytest.raises(GMTInvalidInput):
with lib.open_virtual_file(*vfargs):
print("This should have failed")
def test_virtualfile_from_vectors():
"""
Test the automation for transforming vectors to virtual file dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
size = 10
for dtype in dtypes:
x = np.arange(size, dtype=dtype)
y = np.arange(size, size * 2, 1, dtype=dtype)
z = np.arange(size * 2, size * 3, 1, dtype=dtype)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(x, y, z) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(i.min(), i.max()) for i in (x, y, z)]
)
expected = "<vector memory>: N = {}\t{}\n".format(size, bounds)
assert output == expected
@pytest.mark.parametrize("dtype", [str, object])
def test_virtualfile_from_vectors_one_string_or_object_column(dtype):
"""
Test passing in one column with string or object dtype into virtual file
dataset.
"""
size = 5
x = np.arange(size, dtype=np.int32)
y = np.arange(size, size * 2, 1, dtype=np.int32)
strings = np.array(["a", "bc", "defg", "hijklmn", "opqrst"], dtype=dtype)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(x, y, strings) as vfile:
with GMTTempFile() as outfile:
lib.call_module("convert", f"{vfile} ->{outfile.name}")
output = outfile.read(keep_tabs=True)
expected = "".join(f"{i}\t{j}\t{k}\n" for i, j, k in zip(x, y, strings))
assert output == expected
@pytest.mark.parametrize("dtype", [str, object])
def test_virtualfile_from_vectors_two_string_or_object_columns(dtype):
"""
Test passing in two columns of string or object dtype into virtual file
dataset.
"""
size = 5
x = np.arange(size, dtype=np.int32)
y = | np.arange(size, size * 2, 1, dtype=np.int32) | numpy.arange |