#!/usr/bin/env python
#
# Copyright 2015 Free Software Foundation, Inc.
#
# This file is part of GNU Radio
#
# GNU Radio 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, or (at your option)
# any later version.
#
# GNU Radio 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 GNU Radio; see the file COPYING.  If not, write to
# the Free Software Foundation, Inc., 51 Franklin Street,
# Boston, MA 02110-1301, USA.
#

from __future__ import print_function
from __future__ import division
from __future__ import unicode_literals
from gnuradio import gr
import numpy as np
from scipy.stats import norm, laplace, rayleigh
from matplotlib import pyplot as plt

# NOTE: scipy and matplotlib are optional packages and not included in the default gnuradio dependencies

#*** SETUP ***#

# Number of realisations per histogram
num_tests = 1000000

# Set number of bins in histograms
uniform_num_bins = 31
gauss_num_bins = 31
rayleigh_num_bins = 31
laplace_num_bins = 31

rndm = gr.random() # instance of gnuradio random class (gr::random)

print('All histograms contain',num_tests,'realisations.')

#*** GENERATE DATA ***#

uniform_values = np.zeros(num_tests)
gauss_values = np.zeros(num_tests)
rayleigh_values = np.zeros(num_tests)
laplace_values = np.zeros(num_tests)

for k in range(num_tests):
    uniform_values[k] = rndm.ran1()
    gauss_values[k] = rndm.gasdev()
    rayleigh_values[k] = rndm.rayleigh()
    laplace_values[k] = rndm.laplacian()

#*** HISTOGRAM DATA AND CALCULATE EXPECTED COUNTS ***#

uniform_bins = np.linspace(0,1,uniform_num_bins)
gauss_bins = np.linspace(-8,8,gauss_num_bins)
laplace_bins = np.linspace(-8,8,laplace_num_bins)
rayleigh_bins = np.linspace(0,10,rayleigh_num_bins)

uniform_hist = np.histogram(uniform_values,uniform_bins)
gauss_hist = np.histogram(gauss_values,gauss_bins)
rayleigh_hist = np.histogram(rayleigh_values,rayleigh_bins)
laplace_hist = np.histogram(laplace_values,laplace_bins)

uniform_expected = np.zeros(uniform_num_bins-1)
gauss_expected = np.zeros(gauss_num_bins-1)
rayleigh_expected = np.zeros(rayleigh_num_bins-1)
laplace_expected = np.zeros(laplace_num_bins-1)

for k in range(len(uniform_hist[0])):
    uniform_expected[k] = num_tests / float(uniform_num_bins-1)

for k in range(len(gauss_hist[0])):
    gauss_expected[k] = float(norm.cdf(gauss_hist[1][k+1])-norm.cdf(gauss_hist[1][k]))*num_tests

for k in range(len(rayleigh_hist[0])):
    rayleigh_expected[k] = float(rayleigh.cdf(rayleigh_hist[1][k+1])-rayleigh.cdf(rayleigh_hist[1][k]))*num_tests

for k in range(len(laplace_hist[0])):
    laplace_expected[k] = float(laplace.cdf(laplace_hist[1][k+1])-laplace.cdf(laplace_hist[1][k]))*num_tests

#*** PLOT HISTOGRAMS AND EXPECTATIONS TAKEN FROM SCIPY ***#

uniform_bins_center = uniform_bins[0:-1]+(uniform_bins[1]-uniform_bins[0]) / 2.0
gauss_bins_center = gauss_bins[0:-1]+(gauss_bins[1]-gauss_bins[0]) / 2.0
rayleigh_bins_center = rayleigh_bins[0:-1]+(rayleigh_bins[1]-rayleigh_bins[0]) / 2.0
laplace_bins_center = laplace_bins[0:-1]+(laplace_bins[1]-laplace_bins[0]) / 2.0

plt.figure(1)

plt.subplot(2,1,1)
plt.plot(uniform_bins_center,uniform_hist[0],'s--',uniform_bins_center,uniform_expected,'o:')
plt.xlabel('Bins'), plt.ylabel('Count'), plt.title('Uniform: Distribution')
plt.legend(['histogram gr::random','calculation scipy'],loc=1)

plt.subplot(2,1,2)
plt.plot(uniform_bins_center,uniform_hist[0] / uniform_expected,'rs--')
plt.xlabel('Bins'), plt.ylabel('Relative deviation'), plt.title('Uniform: Relative deviation to scipy')

plt.figure(2)

plt.subplot(2,1,1)
plt.plot(gauss_bins_center,gauss_hist[0],'s--',gauss_bins_center,gauss_expected,'o:')
plt.xlabel('Bins'), plt.ylabel('Count'), plt.title('Gauss: Distribution')
plt.legend(['histogram gr::random','calculation scipy'],loc=1)

plt.subplot(2,1,2)
plt.plot(gauss_bins_center,gauss_hist[0] / gauss_expected,'rs--')
plt.xlabel('Bins'), plt.ylabel('Relative deviation'), plt.title('Gauss: Relative deviation to scipy')

plt.figure(3)

plt.subplot(2,1,1)
plt.plot(rayleigh_bins_center,rayleigh_hist[0],'s--',rayleigh_bins_center,rayleigh_expected,'o:')
plt.xlabel('Bins'), plt.ylabel('Count'), plt.title('Rayleigh: Distribution')
plt.legend(['histogram gr::random','calculation scipy'],loc=1)


plt.subplot(2,1,2)
plt.plot(rayleigh_bins_center,rayleigh_hist[0] / rayleigh_expected,'rs--')
plt.xlabel('Bins'), plt.ylabel('Relative deviation'), plt.title('Rayleigh: Relative deviation to scipy')

plt.figure(4)

plt.subplot(2,1,1)
plt.plot(laplace_bins_center,laplace_hist[0],'s--',laplace_bins_center,laplace_expected,'o:')
plt.xlabel('Bins'), plt.ylabel('Count'), plt.title('Laplace: Distribution')
plt.legend(['histogram gr::random','calculation scipy'],loc=1)

plt.subplot(2,1,2)
plt.plot(laplace_bins_center,laplace_hist[0] / laplace_expected,'rs--')
plt.xlabel('Bins'), plt.ylabel('Relative deviation'), plt.title('Laplace: Relative deviation to scipy')

plt.show()
