# Author: Wei Xue <xuewei4d@gmail.com>
#         Thierry Guillemot <thierry.guillemot.work@gmail.com>
# License: BSD 3 clause

import itertools
import re
import sys
import copy
import warnings
import pytest

import numpy as np
from scipy import stats, linalg

from sklearn.cluster import KMeans
from sklearn.covariance import EmpiricalCovariance
from sklearn.datasets import make_spd_matrix
from io import StringIO
from sklearn.metrics.cluster import adjusted_rand_score
from sklearn.mixture import GaussianMixture
from sklearn.mixture._gaussian_mixture import (
    _estimate_gaussian_covariances_full,
    _estimate_gaussian_covariances_tied,
    _estimate_gaussian_covariances_diag,
    _estimate_gaussian_covariances_spherical,
    _estimate_gaussian_parameters,
    _compute_precision_cholesky,
    _compute_log_det_cholesky,
)
from sklearn.exceptions import ConvergenceWarning, NotFittedError
from sklearn.utils.extmath import fast_logdet
from sklearn.utils._testing import assert_allclose
from sklearn.utils._testing import assert_almost_equal
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.utils._testing import assert_array_equal
from sklearn.utils._testing import ignore_warnings


COVARIANCE_TYPE = ["full", "tied", "diag", "spherical"]


def generate_data(n_samples, n_features, weights, means, precisions, covariance_type):
    rng = np.random.RandomState(0)

    X = []
    if covariance_type == "spherical":
        for _, (w, m, c) in enumerate(zip(weights, means, precisions["spherical"])):
            X.append(
                rng.multivariate_normal(
                    m, c * np.eye(n_features), int(np.round(w * n_samples))
                )
            )
    if covariance_type == "diag":
        for _, (w, m, c) in enumerate(zip(weights, means, precisions["diag"])):
            X.append(
                rng.multivariate_normal(m, np.diag(c), int(np.round(w * n_samples)))
            )
    if covariance_type == "tied":
        for _, (w, m) in enumerate(zip(weights, means)):
            X.append(
                rng.multivariate_normal(
                    m, precisions["tied"], int(np.round(w * n_samples))
                )
            )
    if covariance_type == "full":
        for _, (w, m, c) in enumerate(zip(weights, means, precisions["full"])):
            X.append(rng.multivariate_normal(m, c, int(np.round(w * n_samples))))

    X = np.vstack(X)
    return X


class RandomData:
    def __init__(self, rng, n_samples=200, n_components=2, n_features=2, scale=50):
        self.n_samples = n_samples
        self.n_components = n_components
        self.n_features = n_features

        self.weights = rng.rand(n_components)
        self.weights = self.weights / self.weights.sum()
        self.means = rng.rand(n_components, n_features) * scale
        self.covariances = {
            "spherical": 0.5 + rng.rand(n_components),
            "diag": (0.5 + rng.rand(n_components, n_features)) ** 2,
            "tied": make_spd_matrix(n_features, random_state=rng),
            "full": np.array(
                [
                    make_spd_matrix(n_features, random_state=rng) * 0.5
                    for _ in range(n_components)
                ]
            ),
        }
        self.precisions = {
            "spherical": 1.0 / self.covariances["spherical"],
            "diag": 1.0 / self.covariances["diag"],
            "tied": linalg.inv(self.covariances["tied"]),
            "full": np.array(
                [linalg.inv(covariance) for covariance in self.covariances["full"]]
            ),
        }

        self.X = dict(
            zip(
                COVARIANCE_TYPE,
                [
                    generate_data(
                        n_samples,
                        n_features,
                        self.weights,
                        self.means,
                        self.covariances,
                        covar_type,
                    )
                    for covar_type in COVARIANCE_TYPE
                ],
            )
        )
        self.Y = np.hstack(
            [
                np.full(int(np.round(w * n_samples)), k, dtype=int)
                for k, w in enumerate(self.weights)
            ]
        )


def test_gaussian_mixture_attributes():
    # test bad parameters
    rng = np.random.RandomState(0)
    X = rng.rand(10, 2)

    # test good parameters
    n_components, tol, n_init, max_iter, reg_covar = 2, 1e-4, 3, 30, 1e-1
    covariance_type, init_params = "full", "random"
    gmm = GaussianMixture(
        n_components=n_components,
        tol=tol,
        n_init=n_init,
        max_iter=max_iter,
        reg_covar=reg_covar,
        covariance_type=covariance_type,
        init_params=init_params,
    ).fit(X)

    assert gmm.n_components == n_components
    assert gmm.covariance_type == covariance_type
    assert gmm.tol == tol
    assert gmm.reg_covar == reg_covar
    assert gmm.max_iter == max_iter
    assert gmm.n_init == n_init
    assert gmm.init_params == init_params


def test_check_weights():
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng)

    n_components = rand_data.n_components
    X = rand_data.X["full"]

    g = GaussianMixture(n_components=n_components)

    # Check bad shape
    weights_bad_shape = rng.rand(n_components, 1)
    g.weights_init = weights_bad_shape
    msg = re.escape(
        "The parameter 'weights' should have the shape of "
        f"({n_components},), but got {str(weights_bad_shape.shape)}"
    )
    with pytest.raises(ValueError, match=msg):
        g.fit(X)

    # Check bad range
    weights_bad_range = rng.rand(n_components) + 1
    g.weights_init = weights_bad_range
    msg = re.escape(
        "The parameter 'weights' should be in the range [0, 1], but got"
        f" max value {np.min(weights_bad_range):.5f}, "
        f"min value {np.max(weights_bad_range):.5f}"
    )
    with pytest.raises(ValueError, match=msg):
        g.fit(X)

    # Check bad normalization
    weights_bad_norm = rng.rand(n_components)
    weights_bad_norm = weights_bad_norm / (weights_bad_norm.sum() + 1)
    g.weights_init = weights_bad_norm
    msg = re.escape(
        "The parameter 'weights' should be normalized, "
        f"but got sum(weights) = {np.sum(weights_bad_norm):.5f}"
    )
    with pytest.raises(ValueError, match=msg):
        g.fit(X)

    # Check good weights matrix
    weights = rand_data.weights
    g = GaussianMixture(weights_init=weights, n_components=n_components)
    g.fit(X)
    assert_array_equal(weights, g.weights_init)


def test_check_means():
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng)

    n_components, n_features = rand_data.n_components, rand_data.n_features
    X = rand_data.X["full"]

    g = GaussianMixture(n_components=n_components)

    # Check means bad shape
    means_bad_shape = rng.rand(n_components + 1, n_features)
    g.means_init = means_bad_shape
    msg = "The parameter 'means' should have the shape of "
    with pytest.raises(ValueError, match=msg):
        g.fit(X)

    # Check good means matrix
    means = rand_data.means
    g.means_init = means
    g.fit(X)
    assert_array_equal(means, g.means_init)


def test_check_precisions():
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng)

    n_components, n_features = rand_data.n_components, rand_data.n_features

    # Define the bad precisions for each covariance_type
    precisions_bad_shape = {
        "full": np.ones((n_components + 1, n_features, n_features)),
        "tied": np.ones((n_features + 1, n_features + 1)),
        "diag": np.ones((n_components + 1, n_features)),
        "spherical": np.ones((n_components + 1)),
    }

    # Define not positive-definite precisions
    precisions_not_pos = np.ones((n_components, n_features, n_features))
    precisions_not_pos[0] = np.eye(n_features)
    precisions_not_pos[0, 0, 0] = -1.0

    precisions_not_positive = {
        "full": precisions_not_pos,
        "tied": precisions_not_pos[0],
        "diag": np.full((n_components, n_features), -1.0),
        "spherical": np.full(n_components, -1.0),
    }

    not_positive_errors = {
        "full": "symmetric, positive-definite",
        "tied": "symmetric, positive-definite",
        "diag": "positive",
        "spherical": "positive",
    }

    for covar_type in COVARIANCE_TYPE:
        X = RandomData(rng).X[covar_type]
        g = GaussianMixture(
            n_components=n_components, covariance_type=covar_type, random_state=rng
        )

        # Check precisions with bad shapes
        g.precisions_init = precisions_bad_shape[covar_type]
        msg = f"The parameter '{covar_type} precision' should have the shape of"
        with pytest.raises(ValueError, match=msg):
            g.fit(X)

        # Check not positive precisions
        g.precisions_init = precisions_not_positive[covar_type]
        msg = f"'{covar_type} precision' should be {not_positive_errors[covar_type]}"
        with pytest.raises(ValueError, match=msg):
            g.fit(X)

        # Check the correct init of precisions_init
        g.precisions_init = rand_data.precisions[covar_type]
        g.fit(X)
        assert_array_equal(rand_data.precisions[covar_type], g.precisions_init)


def test_suffstat_sk_full():
    # compare the precision matrix compute from the
    # EmpiricalCovariance.covariance fitted on X*sqrt(resp)
    # with _sufficient_sk_full, n_components=1
    rng = np.random.RandomState(0)
    n_samples, n_features = 500, 2

    # special case 1, assuming data is "centered"
    X = rng.rand(n_samples, n_features)
    resp = rng.rand(n_samples, 1)
    X_resp = np.sqrt(resp) * X
    nk = np.array([n_samples])
    xk = np.zeros((1, n_features))
    covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
    ecov = EmpiricalCovariance(assume_centered=True)
    ecov.fit(X_resp)
    assert_almost_equal(ecov.error_norm(covars_pred[0], norm="frobenius"), 0)
    assert_almost_equal(ecov.error_norm(covars_pred[0], norm="spectral"), 0)

    # check the precision computation
    precs_chol_pred = _compute_precision_cholesky(covars_pred, "full")
    precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
    precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
    assert_array_almost_equal(precs_est, precs_pred)

    # special case 2, assuming resp are all ones
    resp = np.ones((n_samples, 1))
    nk = np.array([n_samples])
    xk = X.mean(axis=0).reshape((1, -1))
    covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
    ecov = EmpiricalCovariance(assume_centered=False)
    ecov.fit(X)
    assert_almost_equal(ecov.error_norm(covars_pred[0], norm="frobenius"), 0)
    assert_almost_equal(ecov.error_norm(covars_pred[0], norm="spectral"), 0)

    # check the precision computation
    precs_chol_pred = _compute_precision_cholesky(covars_pred, "full")
    precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
    precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
    assert_array_almost_equal(precs_est, precs_pred)


def test_suffstat_sk_tied():
    # use equation Nk * Sk / N = S_tied
    rng = np.random.RandomState(0)
    n_samples, n_features, n_components = 500, 2, 2

    resp = rng.rand(n_samples, n_components)
    resp = resp / resp.sum(axis=1)[:, np.newaxis]
    X = rng.rand(n_samples, n_features)
    nk = resp.sum(axis=0)
    xk = np.dot(resp.T, X) / nk[:, np.newaxis]

    covars_pred_full = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
    covars_pred_full = (
        np.sum(nk[:, np.newaxis, np.newaxis] * covars_pred_full, 0) / n_samples
    )

    covars_pred_tied = _estimate_gaussian_covariances_tied(resp, X, nk, xk, 0)

    ecov = EmpiricalCovariance()
    ecov.covariance_ = covars_pred_full
    assert_almost_equal(ecov.error_norm(covars_pred_tied, norm="frobenius"), 0)
    assert_almost_equal(ecov.error_norm(covars_pred_tied, norm="spectral"), 0)

    # check the precision computation
    precs_chol_pred = _compute_precision_cholesky(covars_pred_tied, "tied")
    precs_pred = np.dot(precs_chol_pred, precs_chol_pred.T)
    precs_est = linalg.inv(covars_pred_tied)
    assert_array_almost_equal(precs_est, precs_pred)


def test_suffstat_sk_diag():
    # test against 'full' case
    rng = np.random.RandomState(0)
    n_samples, n_features, n_components = 500, 2, 2

    resp = rng.rand(n_samples, n_components)
    resp = resp / resp.sum(axis=1)[:, np.newaxis]
    X = rng.rand(n_samples, n_features)
    nk = resp.sum(axis=0)
    xk = np.dot(resp.T, X) / nk[:, np.newaxis]
    covars_pred_full = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
    covars_pred_diag = _estimate_gaussian_covariances_diag(resp, X, nk, xk, 0)

    ecov = EmpiricalCovariance()
    for cov_full, cov_diag in zip(covars_pred_full, covars_pred_diag):
        ecov.covariance_ = np.diag(np.diag(cov_full))
        cov_diag = np.diag(cov_diag)
        assert_almost_equal(ecov.error_norm(cov_diag, norm="frobenius"), 0)
        assert_almost_equal(ecov.error_norm(cov_diag, norm="spectral"), 0)

    # check the precision computation
    precs_chol_pred = _compute_precision_cholesky(covars_pred_diag, "diag")
    assert_almost_equal(covars_pred_diag, 1.0 / precs_chol_pred**2)


def test_gaussian_suffstat_sk_spherical():
    # computing spherical covariance equals to the variance of one-dimension
    # data after flattening, n_components=1
    rng = np.random.RandomState(0)
    n_samples, n_features = 500, 2

    X = rng.rand(n_samples, n_features)
    X = X - X.mean()
    resp = np.ones((n_samples, 1))
    nk = np.array([n_samples])
    xk = X.mean()
    covars_pred_spherical = _estimate_gaussian_covariances_spherical(resp, X, nk, xk, 0)
    covars_pred_spherical2 = np.dot(X.flatten().T, X.flatten()) / (
        n_features * n_samples
    )
    assert_almost_equal(covars_pred_spherical, covars_pred_spherical2)

    # check the precision computation
    precs_chol_pred = _compute_precision_cholesky(covars_pred_spherical, "spherical")
    assert_almost_equal(covars_pred_spherical, 1.0 / precs_chol_pred**2)


def test_compute_log_det_cholesky():
    n_features = 2
    rand_data = RandomData(np.random.RandomState(0))

    for covar_type in COVARIANCE_TYPE:
        covariance = rand_data.covariances[covar_type]

        if covar_type == "full":
            predected_det = np.array([linalg.det(cov) for cov in covariance])
        elif covar_type == "tied":
            predected_det = linalg.det(covariance)
        elif covar_type == "diag":
            predected_det = np.array([np.prod(cov) for cov in covariance])
        elif covar_type == "spherical":
            predected_det = covariance**n_features

        # We compute the cholesky decomposition of the covariance matrix
        expected_det = _compute_log_det_cholesky(
            _compute_precision_cholesky(covariance, covar_type),
            covar_type,
            n_features=n_features,
        )
        assert_array_almost_equal(expected_det, -0.5 * np.log(predected_det))


def _naive_lmvnpdf_diag(X, means, covars):
    resp = np.empty((len(X), len(means)))
    stds = np.sqrt(covars)
    for i, (mean, std) in enumerate(zip(means, stds)):
        resp[:, i] = stats.norm.logpdf(X, mean, std).sum(axis=1)
    return resp


def test_gaussian_mixture_log_probabilities():
    from sklearn.mixture._gaussian_mixture import _estimate_log_gaussian_prob

    # test against with _naive_lmvnpdf_diag
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng)
    n_samples = 500
    n_features = rand_data.n_features
    n_components = rand_data.n_components

    means = rand_data.means
    covars_diag = rng.rand(n_components, n_features)
    X = rng.rand(n_samples, n_features)
    log_prob_naive = _naive_lmvnpdf_diag(X, means, covars_diag)

    # full covariances
    precs_full = np.array([np.diag(1.0 / np.sqrt(x)) for x in covars_diag])

    log_prob = _estimate_log_gaussian_prob(X, means, precs_full, "full")
    assert_array_almost_equal(log_prob, log_prob_naive)

    # diag covariances
    precs_chol_diag = 1.0 / np.sqrt(covars_diag)
    log_prob = _estimate_log_gaussian_prob(X, means, precs_chol_diag, "diag")
    assert_array_almost_equal(log_prob, log_prob_naive)

    # tied
    covars_tied = np.array([x for x in covars_diag]).mean(axis=0)
    precs_tied = np.diag(np.sqrt(1.0 / covars_tied))

    log_prob_naive = _naive_lmvnpdf_diag(X, means, [covars_tied] * n_components)
    log_prob = _estimate_log_gaussian_prob(X, means, precs_tied, "tied")

    assert_array_almost_equal(log_prob, log_prob_naive)

    # spherical
    covars_spherical = covars_diag.mean(axis=1)
    precs_spherical = 1.0 / np.sqrt(covars_diag.mean(axis=1))
    log_prob_naive = _naive_lmvnpdf_diag(
        X, means, [[k] * n_features for k in covars_spherical]
    )
    log_prob = _estimate_log_gaussian_prob(X, means, precs_spherical, "spherical")
    assert_array_almost_equal(log_prob, log_prob_naive)


# skip tests on weighted_log_probabilities, log_weights


def test_gaussian_mixture_estimate_log_prob_resp():
    # test whether responsibilities are normalized
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng, scale=5)
    n_samples = rand_data.n_samples
    n_features = rand_data.n_features
    n_components = rand_data.n_components

    X = rng.rand(n_samples, n_features)
    for covar_type in COVARIANCE_TYPE:
        weights = rand_data.weights
        means = rand_data.means
        precisions = rand_data.precisions[covar_type]
        g = GaussianMixture(
            n_components=n_components,
            random_state=rng,
            weights_init=weights,
            means_init=means,
            precisions_init=precisions,
            covariance_type=covar_type,
        )
        g.fit(X)
        resp = g.predict_proba(X)
        assert_array_almost_equal(resp.sum(axis=1), np.ones(n_samples))
        assert_array_equal(g.weights_init, weights)
        assert_array_equal(g.means_init, means)
        assert_array_equal(g.precisions_init, precisions)


def test_gaussian_mixture_predict_predict_proba():
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng)
    for covar_type in COVARIANCE_TYPE:
        X = rand_data.X[covar_type]
        Y = rand_data.Y
        g = GaussianMixture(
            n_components=rand_data.n_components,
            random_state=rng,
            weights_init=rand_data.weights,
            means_init=rand_data.means,
            precisions_init=rand_data.precisions[covar_type],
            covariance_type=covar_type,
        )

        # Check a warning message arrive if we don't do fit
        msg = (
            "This GaussianMixture instance is not fitted yet. Call 'fit' "
            "with appropriate arguments before using this estimator."
        )
        with pytest.raises(NotFittedError, match=msg):
            g.predict(X)

        g.fit(X)
        Y_pred = g.predict(X)
        Y_pred_proba = g.predict_proba(X).argmax(axis=1)
        assert_array_equal(Y_pred, Y_pred_proba)
        assert adjusted_rand_score(Y, Y_pred) > 0.95


@pytest.mark.filterwarnings("ignore:.*did not converge.*")
@pytest.mark.parametrize(
    "seed, max_iter, tol",
    [
        (0, 2, 1e-7),  # strict non-convergence
        (1, 2, 1e-1),  # loose non-convergence
        (3, 300, 1e-7),  # strict convergence
        (4, 300, 1e-1),  # loose convergence
    ],
)
def test_gaussian_mixture_fit_predict(seed, max_iter, tol):
    rng = np.random.RandomState(seed)
    rand_data = RandomData(rng)
    for covar_type in COVARIANCE_TYPE:
        X = rand_data.X[covar_type]
        Y = rand_data.Y
        g = GaussianMixture(
            n_components=rand_data.n_components,
            random_state=rng,
            weights_init=rand_data.weights,
            means_init=rand_data.means,
            precisions_init=rand_data.precisions[covar_type],
            covariance_type=covar_type,
            max_iter=max_iter,
            tol=tol,
        )

        # check if fit_predict(X) is equivalent to fit(X).predict(X)
        f = copy.deepcopy(g)
        Y_pred1 = f.fit(X).predict(X)
        Y_pred2 = g.fit_predict(X)
        assert_array_equal(Y_pred1, Y_pred2)
        assert adjusted_rand_score(Y, Y_pred2) > 0.95


def test_gaussian_mixture_fit_predict_n_init():
    # Check that fit_predict is equivalent to fit.predict, when n_init > 1
    X = np.random.RandomState(0).randn(1000, 5)
    gm = GaussianMixture(n_components=5, n_init=5, random_state=0)
    y_pred1 = gm.fit_predict(X)
    y_pred2 = gm.predict(X)
    assert_array_equal(y_pred1, y_pred2)


def test_gaussian_mixture_fit():
    # recover the ground truth
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng)
    n_features = rand_data.n_features
    n_components = rand_data.n_components

    for covar_type in COVARIANCE_TYPE:
        X = rand_data.X[covar_type]
        g = GaussianMixture(
            n_components=n_components,
            n_init=20,
            reg_covar=0,
            random_state=rng,
            covariance_type=covar_type,
        )
        g.fit(X)

        # needs more data to pass the test with rtol=1e-7
        assert_allclose(
            np.sort(g.weights_), np.sort(rand_data.weights), rtol=0.1, atol=1e-2
        )

        arg_idx1 = g.means_[:, 0].argsort()
        arg_idx2 = rand_data.means[:, 0].argsort()
        assert_allclose(
            g.means_[arg_idx1], rand_data.means[arg_idx2], rtol=0.1, atol=1e-2
        )

        if covar_type == "full":
            prec_pred = g.precisions_
            prec_test = rand_data.precisions["full"]
        elif covar_type == "tied":
            prec_pred = np.array([g.precisions_] * n_components)
            prec_test = np.array([rand_data.precisions["tied"]] * n_components)
        elif covar_type == "spherical":
            prec_pred = np.array([np.eye(n_features) * c for c in g.precisions_])
            prec_test = np.array(
                [np.eye(n_features) * c for c in rand_data.precisions["spherical"]]
            )
        elif covar_type == "diag":
            prec_pred = np.array([np.diag(d) for d in g.precisions_])
            prec_test = np.array([np.diag(d) for d in rand_data.precisions["diag"]])

        arg_idx1 = np.trace(prec_pred, axis1=1, axis2=2).argsort()
        arg_idx2 = np.trace(prec_test, axis1=1, axis2=2).argsort()
        for k, h in zip(arg_idx1, arg_idx2):
            ecov = EmpiricalCovariance()
            ecov.covariance_ = prec_test[h]
            # the accuracy depends on the number of data and randomness, rng
            assert_allclose(ecov.error_norm(prec_pred[k]), 0, atol=0.15)


def test_gaussian_mixture_fit_best_params():
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng)
    n_components = rand_data.n_components
    n_init = 10
    for covar_type in COVARIANCE_TYPE:
        X = rand_data.X[covar_type]
        g = GaussianMixture(
            n_components=n_components,
            n_init=1,
            reg_covar=0,
            random_state=rng,
            covariance_type=covar_type,
        )
        ll = []
        for _ in range(n_init):
            g.fit(X)
            ll.append(g.score(X))
        ll = np.array(ll)
        g_best = GaussianMixture(
            n_components=n_components,
            n_init=n_init,
            reg_covar=0,
            random_state=rng,
            covariance_type=covar_type,
        )
        g_best.fit(X)
        assert_almost_equal(ll.min(), g_best.score(X))


def test_gaussian_mixture_fit_convergence_warning():
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng, scale=1)
    n_components = rand_data.n_components
    max_iter = 1
    for covar_type in COVARIANCE_TYPE:
        X = rand_data.X[covar_type]
        g = GaussianMixture(
            n_components=n_components,
            n_init=1,
            max_iter=max_iter,
            reg_covar=0,
            random_state=rng,
            covariance_type=covar_type,
        )
        msg = (
            f"Initialization {max_iter} did not converge. Try different init "
            "parameters, or increase max_iter, tol or check for degenerate"
            " data."
        )
        with pytest.warns(ConvergenceWarning, match=msg):
            g.fit(X)


def test_multiple_init():
    # Test that multiple inits does not much worse than a single one
    rng = np.random.RandomState(0)
    n_samples, n_features, n_components = 50, 5, 2
    X = rng.randn(n_samples, n_features)
    for cv_type in COVARIANCE_TYPE:
        train1 = (
            GaussianMixture(
                n_components=n_components, covariance_type=cv_type, random_state=0
            )
            .fit(X)
            .score(X)
        )
        train2 = (
            GaussianMixture(
                n_components=n_components,
                covariance_type=cv_type,
                random_state=0,
                n_init=5,
            )
            .fit(X)
            .score(X)
        )
        assert train2 >= train1


def test_gaussian_mixture_n_parameters():
    # Test that the right number of parameters is estimated
    rng = np.random.RandomState(0)
    n_samples, n_features, n_components = 50, 5, 2
    X = rng.randn(n_samples, n_features)
    n_params = {"spherical": 13, "diag": 21, "tied": 26, "full": 41}
    for cv_type in COVARIANCE_TYPE:
        g = GaussianMixture(
            n_components=n_components, covariance_type=cv_type, random_state=rng
        ).fit(X)
        assert g._n_parameters() == n_params[cv_type]


def test_bic_1d_1component():
    # Test all of the covariance_types return the same BIC score for
    # 1-dimensional, 1 component fits.
    rng = np.random.RandomState(0)
    n_samples, n_dim, n_components = 100, 1, 1
    X = rng.randn(n_samples, n_dim)
    bic_full = (
        GaussianMixture(
            n_components=n_components, covariance_type="full", random_state=rng
        )
        .fit(X)
        .bic(X)
    )
    for covariance_type in ["tied", "diag", "spherical"]:
        bic = (
            GaussianMixture(
                n_components=n_components,
                covariance_type=covariance_type,
                random_state=rng,
            )
            .fit(X)
            .bic(X)
        )
        assert_almost_equal(bic_full, bic)


def test_gaussian_mixture_aic_bic():
    # Test the aic and bic criteria
    rng = np.random.RandomState(0)
    n_samples, n_features, n_components = 50, 3, 2
    X = rng.randn(n_samples, n_features)
    # standard gaussian entropy
    sgh = 0.5 * (
        fast_logdet(np.cov(X.T, bias=1)) + n_features * (1 + np.log(2 * np.pi))
    )
    for cv_type in COVARIANCE_TYPE:
        g = GaussianMixture(
            n_components=n_components,
            covariance_type=cv_type,
            random_state=rng,
            max_iter=200,
        )
        g.fit(X)
        aic = 2 * n_samples * sgh + 2 * g._n_parameters()
        bic = 2 * n_samples * sgh + np.log(n_samples) * g._n_parameters()
        bound = n_features / np.sqrt(n_samples)
        assert (g.aic(X) - aic) / n_samples < bound
        assert (g.bic(X) - bic) / n_samples < bound


def test_gaussian_mixture_verbose():
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng)
    n_components = rand_data.n_components
    for covar_type in COVARIANCE_TYPE:
        X = rand_data.X[covar_type]
        g = GaussianMixture(
            n_components=n_components,
            n_init=1,
            reg_covar=0,
            random_state=rng,
            covariance_type=covar_type,
            verbose=1,
        )
        h = GaussianMixture(
            n_components=n_components,
            n_init=1,
            reg_covar=0,
            random_state=rng,
            covariance_type=covar_type,
            verbose=2,
        )
        old_stdout = sys.stdout
        sys.stdout = StringIO()
        try:
            g.fit(X)
            h.fit(X)
        finally:
            sys.stdout = old_stdout


@pytest.mark.filterwarnings("ignore:.*did not converge.*")
@pytest.mark.parametrize("seed", (0, 1, 2))
def test_warm_start(seed):
    random_state = seed
    rng = np.random.RandomState(random_state)
    n_samples, n_features, n_components = 500, 2, 2
    X = rng.rand(n_samples, n_features)

    # Assert the warm_start give the same result for the same number of iter
    g = GaussianMixture(
        n_components=n_components,
        n_init=1,
        max_iter=2,
        reg_covar=0,
        random_state=random_state,
        warm_start=False,
    )
    h = GaussianMixture(
        n_components=n_components,
        n_init=1,
        max_iter=1,
        reg_covar=0,
        random_state=random_state,
        warm_start=True,
    )

    g.fit(X)
    score1 = h.fit(X).score(X)
    score2 = h.fit(X).score(X)

    assert_almost_equal(g.weights_, h.weights_)
    assert_almost_equal(g.means_, h.means_)
    assert_almost_equal(g.precisions_, h.precisions_)
    assert score2 > score1

    # Assert that by using warm_start we can converge to a good solution
    g = GaussianMixture(
        n_components=n_components,
        n_init=1,
        max_iter=5,
        reg_covar=0,
        random_state=random_state,
        warm_start=False,
        tol=1e-6,
    )
    h = GaussianMixture(
        n_components=n_components,
        n_init=1,
        max_iter=5,
        reg_covar=0,
        random_state=random_state,
        warm_start=True,
        tol=1e-6,
    )

    g.fit(X)
    assert not g.converged_

    h.fit(X)
    # depending on the data there is large variability in the number of
    # refit necessary to converge due to the complete randomness of the
    # data
    for _ in range(1000):
        h.fit(X)
        if h.converged_:
            break
    assert h.converged_


@ignore_warnings(category=ConvergenceWarning)
def test_convergence_detected_with_warm_start():
    # We check that convergence is detected when warm_start=True
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng)
    n_components = rand_data.n_components
    X = rand_data.X["full"]

    for max_iter in (1, 2, 50):
        gmm = GaussianMixture(
            n_components=n_components,
            warm_start=True,
            max_iter=max_iter,
            random_state=rng,
        )
        for _ in range(100):
            gmm.fit(X)
            if gmm.converged_:
                break
        assert gmm.converged_
        assert max_iter >= gmm.n_iter_


def test_score():
    covar_type = "full"
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng, scale=7)
    n_components = rand_data.n_components
    X = rand_data.X[covar_type]

    # Check the error message if we don't call fit
    gmm1 = GaussianMixture(
        n_components=n_components,
        n_init=1,
        max_iter=1,
        reg_covar=0,
        random_state=rng,
        covariance_type=covar_type,
    )
    msg = (
        "This GaussianMixture instance is not fitted yet. Call 'fit' with "
        "appropriate arguments before using this estimator."
    )
    with pytest.raises(NotFittedError, match=msg):
        gmm1.score(X)

    # Check score value
    with warnings.catch_warnings():
        warnings.simplefilter("ignore", ConvergenceWarning)
        gmm1.fit(X)
    gmm_score = gmm1.score(X)
    gmm_score_proba = gmm1.score_samples(X).mean()
    assert_almost_equal(gmm_score, gmm_score_proba)

    # Check if the score increase
    gmm2 = GaussianMixture(
        n_components=n_components,
        n_init=1,
        reg_covar=0,
        random_state=rng,
        covariance_type=covar_type,
    ).fit(X)
    assert gmm2.score(X) > gmm1.score(X)


def test_score_samples():
    covar_type = "full"
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng, scale=7)
    n_components = rand_data.n_components
    X = rand_data.X[covar_type]

    # Check the error message if we don't call fit
    gmm = GaussianMixture(
        n_components=n_components,
        n_init=1,
        reg_covar=0,
        random_state=rng,
        covariance_type=covar_type,
    )
    msg = (
        "This GaussianMixture instance is not fitted yet. Call 'fit' with "
        "appropriate arguments before using this estimator."
    )
    with pytest.raises(NotFittedError, match=msg):
        gmm.score_samples(X)

    gmm_score_samples = gmm.fit(X).score_samples(X)
    assert gmm_score_samples.shape[0] == rand_data.n_samples


def test_monotonic_likelihood():
    # We check that each step of the EM without regularization improve
    # monotonically the training set likelihood
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng, scale=7)
    n_components = rand_data.n_components

    for covar_type in COVARIANCE_TYPE:
        X = rand_data.X[covar_type]
        gmm = GaussianMixture(
            n_components=n_components,
            covariance_type=covar_type,
            reg_covar=0,
            warm_start=True,
            max_iter=1,
            random_state=rng,
            tol=1e-7,
        )
        current_log_likelihood = -np.infty
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", ConvergenceWarning)
            # Do one training iteration at a time so we can make sure that the
            # training log likelihood increases after each iteration.
            for _ in range(600):
                prev_log_likelihood = current_log_likelihood
                current_log_likelihood = gmm.fit(X).score(X)
                assert current_log_likelihood >= prev_log_likelihood

                if gmm.converged_:
                    break

            assert gmm.converged_


def test_regularisation():
    # We train the GaussianMixture on degenerate data by defining two clusters
    # of a 0 covariance.
    rng = np.random.RandomState(0)
    n_samples, n_features = 10, 5

    X = np.vstack(
        (np.ones((n_samples // 2, n_features)), np.zeros((n_samples // 2, n_features)))
    )

    for covar_type in COVARIANCE_TYPE:
        gmm = GaussianMixture(
            n_components=n_samples,
            reg_covar=0,
            covariance_type=covar_type,
            random_state=rng,
        )

        with warnings.catch_warnings():
            warnings.simplefilter("ignore", RuntimeWarning)
            msg = re.escape(
                "Fitting the mixture model failed because some components have"
                " ill-defined empirical covariance (for instance caused by "
                "singleton or collapsed samples). Try to decrease the number "
                "of components, or increase reg_covar."
            )
            with pytest.raises(ValueError, match=msg):
                gmm.fit(X)

            gmm.set_params(reg_covar=1e-6).fit(X)


def test_property():
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng, scale=7)
    n_components = rand_data.n_components

    for covar_type in COVARIANCE_TYPE:
        X = rand_data.X[covar_type]
        gmm = GaussianMixture(
            n_components=n_components,
            covariance_type=covar_type,
            random_state=rng,
            n_init=5,
        )
        gmm.fit(X)
        if covar_type == "full":
            for prec, covar in zip(gmm.precisions_, gmm.covariances_):

                assert_array_almost_equal(linalg.inv(prec), covar)
        elif covar_type == "tied":
            assert_array_almost_equal(linalg.inv(gmm.precisions_), gmm.covariances_)
        else:
            assert_array_almost_equal(gmm.precisions_, 1.0 / gmm.covariances_)


def test_sample():
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng, scale=7, n_components=3)
    n_features, n_components = rand_data.n_features, rand_data.n_components

    for covar_type in COVARIANCE_TYPE:
        X = rand_data.X[covar_type]

        gmm = GaussianMixture(
            n_components=n_components, covariance_type=covar_type, random_state=rng
        )
        # To sample we need that GaussianMixture is fitted
        msg = "This GaussianMixture instance is not fitted"
        with pytest.raises(NotFittedError, match=msg):
            gmm.sample(0)
        gmm.fit(X)

        msg = "Invalid value for 'n_samples'"
        with pytest.raises(ValueError, match=msg):
            gmm.sample(0)

        # Just to make sure the class samples correctly
        n_samples = 20000
        X_s, y_s = gmm.sample(n_samples)

        for k in range(n_components):
            if covar_type == "full":
                assert_array_almost_equal(
                    gmm.covariances_[k], np.cov(X_s[y_s == k].T), decimal=1
                )
            elif covar_type == "tied":
                assert_array_almost_equal(
                    gmm.covariances_, np.cov(X_s[y_s == k].T), decimal=1
                )
            elif covar_type == "diag":
                assert_array_almost_equal(
                    gmm.covariances_[k], np.diag(np.cov(X_s[y_s == k].T)), decimal=1
                )
            else:
                assert_array_almost_equal(
                    gmm.covariances_[k],
                    np.var(X_s[y_s == k] - gmm.means_[k]),
                    decimal=1,
                )

        means_s = np.array([np.mean(X_s[y_s == k], 0) for k in range(n_components)])
        assert_array_almost_equal(gmm.means_, means_s, decimal=1)

        # Check shapes of sampled data, see
        # https://github.com/scikit-learn/scikit-learn/issues/7701
        assert X_s.shape == (n_samples, n_features)

        for sample_size in range(1, 100):
            X_s, _ = gmm.sample(sample_size)
            assert X_s.shape == (sample_size, n_features)


@ignore_warnings(category=ConvergenceWarning)
def test_init():
    # We check that by increasing the n_init number we have a better solution
    for random_state in range(15):
        rand_data = RandomData(
            np.random.RandomState(random_state), n_samples=50, scale=1
        )
        n_components = rand_data.n_components
        X = rand_data.X["full"]

        gmm1 = GaussianMixture(
            n_components=n_components, n_init=1, max_iter=1, random_state=random_state
        ).fit(X)
        gmm2 = GaussianMixture(
            n_components=n_components, n_init=10, max_iter=1, random_state=random_state
        ).fit(X)

        assert gmm2.lower_bound_ >= gmm1.lower_bound_


def test_gaussian_mixture_setting_best_params():
    """`GaussianMixture`'s best_parameters, `n_iter_` and `lower_bound_`
    must be set appropriately in the case of divergence.

    Non-regression test for:
    https://github.com/scikit-learn/scikit-learn/issues/18216
    """
    rnd = np.random.RandomState(0)
    n_samples = 30
    X = rnd.uniform(size=(n_samples, 3))

    # following initialization parameters were found to lead to divergence
    means_init = np.array(
        [
            [0.670637869618158, 0.21038256107384043, 0.12892629765485303],
            [0.09394051075844147, 0.5759464955561779, 0.929296197576212],
            [0.5033230372781258, 0.9569852381759425, 0.08654043447295741],
            [0.18578301420435747, 0.5531158970919143, 0.19388943970532435],
            [0.4548589928173794, 0.35182513658825276, 0.568146063202464],
            [0.609279894978321, 0.7929063819678847, 0.9620097270828052],
        ]
    )
    precisions_init = np.array(
        [
            999999.999604483,
            999999.9990869573,
            553.7603944542167,
            204.78596008931834,
            15.867423501783637,
            85.4595728389735,
        ]
    )
    weights_init = [
        0.03333333333333341,
        0.03333333333333341,
        0.06666666666666674,
        0.06666666666666674,
        0.7000000000000001,
        0.10000000000000007,
    ]

    gmm = GaussianMixture(
        covariance_type="spherical",
        reg_covar=0,
        means_init=means_init,
        weights_init=weights_init,
        random_state=rnd,
        n_components=len(weights_init),
        precisions_init=precisions_init,
        max_iter=1,
    )
    # ensure that no error is thrown during fit
    gmm.fit(X)

    # check that the fit did not converge
    assert not gmm.converged_

    # check that parameters are set for gmm
    for attr in [
        "weights_",
        "means_",
        "covariances_",
        "precisions_cholesky_",
        "n_iter_",
        "lower_bound_",
    ]:
        assert hasattr(gmm, attr)


@pytest.mark.parametrize(
    "init_params", ["random", "random_from_data", "k-means++", "kmeans"]
)
def test_init_means_not_duplicated(init_params, global_random_seed):
    # Check that all initialisations provide not duplicated starting means
    rng = np.random.RandomState(global_random_seed)
    rand_data = RandomData(rng, scale=5)
    n_components = rand_data.n_components
    X = rand_data.X["full"]

    gmm = GaussianMixture(
        n_components=n_components, init_params=init_params, random_state=rng, max_iter=0
    )
    gmm.fit(X)

    means = gmm.means_
    for i_mean, j_mean in itertools.combinations(means, r=2):
        assert not np.allclose(i_mean, j_mean)


@pytest.mark.parametrize(
    "init_params", ["random", "random_from_data", "k-means++", "kmeans"]
)
def test_means_for_all_inits(init_params, global_random_seed):
    # Check fitted means properties for all initializations
    rng = np.random.RandomState(global_random_seed)
    rand_data = RandomData(rng, scale=5)
    n_components = rand_data.n_components
    X = rand_data.X["full"]

    gmm = GaussianMixture(
        n_components=n_components, init_params=init_params, random_state=rng
    )
    gmm.fit(X)

    assert gmm.means_.shape == (n_components, X.shape[1])
    assert np.all(X.min(axis=0) <= gmm.means_)
    assert np.all(gmm.means_ <= X.max(axis=0))
    assert gmm.converged_


def test_max_iter_zero():
    # Check that max_iter=0 returns initialisation as expected
    # Pick arbitrary initial means and check equal to max_iter=0
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng, scale=5)
    n_components = rand_data.n_components
    X = rand_data.X["full"]
    means_init = [[20, 30], [30, 25]]
    gmm = GaussianMixture(
        n_components=n_components,
        random_state=rng,
        means_init=means_init,
        tol=1e-06,
        max_iter=0,
    )
    gmm.fit(X)

    assert_allclose(gmm.means_, means_init)


def test_gaussian_mixture_precisions_init_diag():
    """Check that we properly initialize `precision_cholesky_` when we manually
    provide the precision matrix.

    In this regard, we check the consistency between estimating the precision
    matrix and providing the same precision matrix as initialization. It should
    lead to the same results with the same number of iterations.

    If the initialization is wrong then the number of iterations will increase.

    Non-regression test for:
    https://github.com/scikit-learn/scikit-learn/issues/16944
    """
    # generate a toy dataset
    n_samples = 300
    rng = np.random.RandomState(0)
    shifted_gaussian = rng.randn(n_samples, 2) + np.array([20, 20])
    C = np.array([[0.0, -0.7], [3.5, 0.7]])
    stretched_gaussian = np.dot(rng.randn(n_samples, 2), C)
    X = np.vstack([shifted_gaussian, stretched_gaussian])

    # common parameters to check the consistency of precision initialization
    n_components, covariance_type, reg_covar, random_state = 2, "diag", 1e-6, 0

    # execute the manual initialization to compute the precision matrix:
    # - run KMeans to have an initial guess
    # - estimate the covariance
    # - compute the precision matrix from the estimated covariance
    resp = np.zeros((X.shape[0], n_components))
    label = (
        KMeans(n_clusters=n_components, n_init=1, random_state=random_state)
        .fit(X)
        .labels_
    )
    resp[np.arange(X.shape[0]), label] = 1
    _, _, covariance = _estimate_gaussian_parameters(
        X, resp, reg_covar=reg_covar, covariance_type=covariance_type
    )
    precisions_init = 1 / covariance

    gm_with_init = GaussianMixture(
        n_components=n_components,
        covariance_type=covariance_type,
        reg_covar=reg_covar,
        precisions_init=precisions_init,
        random_state=random_state,
    ).fit(X)

    gm_without_init = GaussianMixture(
        n_components=n_components,
        covariance_type=covariance_type,
        reg_covar=reg_covar,
        random_state=random_state,
    ).fit(X)

    assert gm_without_init.n_iter_ == gm_with_init.n_iter_
    assert_allclose(
        gm_with_init.precisions_cholesky_, gm_without_init.precisions_cholesky_
    )


def test_gaussian_mixture_single_component_stable():
    """
    Non-regression test for #23032 ensuring 1-component GM works on only a
    few samples.
    """
    rng = np.random.RandomState(0)
    X = rng.multivariate_normal(np.zeros(2), np.identity(2), size=3)
    gm = GaussianMixture(n_components=1)
    gm.fit(X).sample()
