import numpy as np

import pytest

from sklearn.utils.testing import (assert_allclose, assert_raises,
                                   assert_equal)
from sklearn.neighbors import KernelDensity, KDTree, NearestNeighbors
from sklearn.neighbors.ball_tree import kernel_norm
from sklearn.pipeline import make_pipeline
from sklearn.datasets import make_blobs
from sklearn.model_selection import GridSearchCV
from sklearn.preprocessing import StandardScaler


def compute_kernel_slow(Y, X, kernel, h):
    d = np.sqrt(((Y[:, None, :] - X) ** 2).sum(-1))
    norm = kernel_norm(h, X.shape[1], kernel) / X.shape[0]

    if kernel == 'gaussian':
        return norm * np.exp(-0.5 * (d * d) / (h * h)).sum(-1)
    elif kernel == 'tophat':
        return norm * (d < h).sum(-1)
    elif kernel == 'epanechnikov':
        return norm * ((1.0 - (d * d) / (h * h)) * (d < h)).sum(-1)
    elif kernel == 'exponential':
        return norm * (np.exp(-d / h)).sum(-1)
    elif kernel == 'linear':
        return norm * ((1 - d / h) * (d < h)).sum(-1)
    elif kernel == 'cosine':
        return norm * (np.cos(0.5 * np.pi * d / h) * (d < h)).sum(-1)
    else:
        raise ValueError('kernel not recognized')


def check_results(kernel, bandwidth, atol, rtol, X, Y, dens_true):
    kde = KernelDensity(kernel=kernel, bandwidth=bandwidth,
                        atol=atol, rtol=rtol)
    log_dens = kde.fit(X).score_samples(Y)
    assert_allclose(np.exp(log_dens), dens_true,
                    atol=atol, rtol=max(1E-7, rtol))
    assert_allclose(np.exp(kde.score(Y)),
                    np.prod(dens_true),
                    atol=atol, rtol=max(1E-7, rtol))


@pytest.mark.parametrize(
        'kernel',
        ['gaussian', 'tophat', 'epanechnikov',
         'exponential', 'linear', 'cosine'])
@pytest.mark.parametrize('bandwidth', [0.01, 0.1, 1])
def test_kernel_density(kernel, bandwidth):
    n_samples, n_features = (100, 3)

    rng = np.random.RandomState(0)
    X = rng.randn(n_samples, n_features)
    Y = rng.randn(n_samples, n_features)

    dens_true = compute_kernel_slow(Y, X, kernel, bandwidth)

    for rtol in [0, 1E-5]:
        for atol in [1E-6, 1E-2]:
            for breadth_first in (True, False):
                check_results(kernel, bandwidth, atol, rtol,
                              X, Y, dens_true)


def test_kernel_density_sampling(n_samples=100, n_features=3):
    rng = np.random.RandomState(0)
    X = rng.randn(n_samples, n_features)

    bandwidth = 0.2

    for kernel in ['gaussian', 'tophat']:
        # draw a tophat sample
        kde = KernelDensity(bandwidth, kernel=kernel).fit(X)
        samp = kde.sample(100)
        assert_equal(X.shape, samp.shape)

        # check that samples are in the right range
        nbrs = NearestNeighbors(n_neighbors=1).fit(X)
        dist, ind = nbrs.kneighbors(X, return_distance=True)

        if kernel == 'tophat':
            assert np.all(dist < bandwidth)
        elif kernel == 'gaussian':
            # 5 standard deviations is safe for 100 samples, but there's a
            # very small chance this test could fail.
            assert np.all(dist < 5 * bandwidth)

    # check unsupported kernels
    for kernel in ['epanechnikov', 'exponential', 'linear', 'cosine']:
        kde = KernelDensity(bandwidth, kernel=kernel).fit(X)
        assert_raises(NotImplementedError, kde.sample, 100)

    # non-regression test: used to return a scalar
    X = rng.randn(4, 1)
    kde = KernelDensity(kernel="gaussian").fit(X)
    assert_equal(kde.sample().shape, (1, 1))


@pytest.mark.parametrize('algorithm', ['auto', 'ball_tree', 'kd_tree'])
@pytest.mark.parametrize('metric',
                         ['euclidean', 'minkowski', 'manhattan',
                          'chebyshev', 'haversine'])
def test_kde_algorithm_metric_choice(algorithm, metric):
    # Smoke test for various metrics and algorithms
    rng = np.random.RandomState(0)
    X = rng.randn(10, 2)    # 2 features required for haversine dist.
    Y = rng.randn(10, 2)

    if algorithm == 'kd_tree' and metric not in KDTree.valid_metrics:
        assert_raises(ValueError, KernelDensity,
                      algorithm=algorithm, metric=metric)
    else:
        kde = KernelDensity(algorithm=algorithm, metric=metric)
        kde.fit(X)
        y_dens = kde.score_samples(Y)
        assert_equal(y_dens.shape, Y.shape[:1])


def test_kde_score(n_samples=100, n_features=3):
    pass
    # FIXME
    # rng = np.random.RandomState(0)
    # X = rng.random_sample((n_samples, n_features))
    # Y = rng.random_sample((n_samples, n_features))


def test_kde_badargs():
    assert_raises(ValueError, KernelDensity,
                  algorithm='blah')
    assert_raises(ValueError, KernelDensity,
                  bandwidth=0)
    assert_raises(ValueError, KernelDensity,
                  kernel='blah')
    assert_raises(ValueError, KernelDensity,
                  metric='blah')
    assert_raises(ValueError, KernelDensity,
                  algorithm='kd_tree', metric='blah')
    kde = KernelDensity()
    assert_raises(ValueError, kde.fit, np.random.random((200, 10)),
                  sample_weight=np.random.random((200, 10)))
    assert_raises(ValueError, kde.fit, np.random.random((200, 10)),
                  sample_weight=-np.random.random(200))


def test_kde_pipeline_gridsearch():
    # test that kde plays nice in pipelines and grid-searches
    X, _ = make_blobs(cluster_std=.1, random_state=1,
                      centers=[[0, 1], [1, 0], [0, 0]])
    pipe1 = make_pipeline(StandardScaler(with_mean=False, with_std=False),
                          KernelDensity(kernel="gaussian"))
    params = dict(kerneldensity__bandwidth=[0.001, 0.01, 0.1, 1, 10])
    search = GridSearchCV(pipe1, param_grid=params, cv=5)
    search.fit(X)
    assert_equal(search.best_params_['kerneldensity__bandwidth'], .1)


def test_kde_sample_weights():
    n_samples = 400
    size_test = 20
    weights_neutral = 3 * np.ones(n_samples)
    for d in [1, 2, 10]:
        rng = np.random.RandomState(0)
        X = rng.rand(n_samples, d)
        weights = 1 + (10 * X.sum(axis=1)).astype(np.int8)
        X_repetitions = np.repeat(X, weights, axis=0)
        n_samples_test = size_test // d
        test_points = rng.rand(n_samples_test, d)
        for algorithm in ['auto', 'ball_tree', 'kd_tree']:
            for metric in ['euclidean', 'minkowski', 'manhattan',
                           'chebyshev']:
                if algorithm != 'kd_tree' or metric in KDTree.valid_metrics:
                    kde = KernelDensity(algorithm=algorithm, metric=metric)

                    # Test that adding a constant sample weight has no effect
                    kde.fit(X, sample_weight=weights_neutral)
                    scores_const_weight = kde.score_samples(test_points)
                    sample_const_weight = kde.sample(random_state=1234)
                    kde.fit(X)
                    scores_no_weight = kde.score_samples(test_points)
                    sample_no_weight = kde.sample(random_state=1234)
                    assert_allclose(scores_const_weight, scores_no_weight)
                    assert_allclose(sample_const_weight, sample_no_weight)

                    # Test equivalence between sampling and (integer) weights
                    kde.fit(X, sample_weight=weights)
                    scores_weight = kde.score_samples(test_points)
                    sample_weight = kde.sample(random_state=1234)
                    kde.fit(X_repetitions)
                    scores_ref_sampling = kde.score_samples(test_points)
                    sample_ref_sampling = kde.sample(random_state=1234)
                    assert_allclose(scores_weight, scores_ref_sampling)
                    assert_allclose(sample_weight, sample_ref_sampling)

                    # Test that sample weights has a non-trivial effect
                    diff = np.max(np.abs(scores_no_weight - scores_weight))
                    assert diff > 0.001

                    # Test invariance with respect to arbitrary scaling
                    scale_factor = rng.rand()
                    kde.fit(X, sample_weight=(scale_factor * weights))
                    scores_scaled_weight = kde.score_samples(test_points)
                    assert_allclose(scores_scaled_weight, scores_weight)
