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
                try:
                    current_log_likelihood = gmm.fit(X).score(X)
                except ConvergenceWarning:
                    pass
                assert_greater_equal(current_log_likelihood,
                                     prev_log_likelihood)

                if gmm.converged_:
                    break

            assert gmm.converged_

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_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_equal(g._n_parameters(), n_params[cv_type])

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)
    assert_raise_message(NotFittedError,
                         "This GaussianMixture instance is not fitted "
                         "yet. Call 'fit' with appropriate arguments "
                         "before using this method.", 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_greater(gmm2.score(X), gmm1.score(X))

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
        assert_raise_message(NotFittedError, "This GaussianMixture instance "
                             "is not fitted", gmm.sample, 0)
        gmm.fit(X)

        assert_raise_message(ValueError, "Invalid value for 'n_samples",
                             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_equal(X_s.shape, (n_samples, n_features))

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

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_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)
    assert_raise_message(NotFittedError,
                         "This GaussianMixture instance is not fitted "
                         "yet. Call 'fit' with appropriate arguments "
                         "before using this method.", gmm.score_samples, X)

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

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=0.1)

def test_gaussian_mixture_fit_predict():
    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 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_greater(adjusted_rand_score(Y, Y_pred2), .95)

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. / gmm.covariances_)

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
    assert_raise_message(ValueError,
                         "The parameter 'means' should have the shape of ",
                         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_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)
            assert_raise_message(ValueError,
                                 "The algorithm has diverged because of too "
                                 "few samples per components. "
                                 "Try to decrease the number of components, "
                                 "or increase reg_covar.", gmm.fit, X)

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

def test_sample():
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng, scale=7)
    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
        assert_raise_message(NotFittedError, "This GaussianMixture instance "
                             "is not fitted", gmm.sample, 0)
        gmm.fit(X)

        assert_raise_message(ValueError, "Invalid value for 'n_samples",
                             gmm.sample, 0)

        # Just to make sure the class samples correctly
        X_s, y_s = gmm.sample(20000)
        for k in range(n_features):
            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_features)])
        assert_array_almost_equal(gmm.means_, means_s, decimal=1)

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
        assert_raise_message(NotFittedError,
                             "This GaussianMixture instance is not fitted "
                             "yet. Call 'fit' with appropriate arguments "
                             "before using this method.", 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_greater(adjusted_rand_score(Y, Y_pred), .95)

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_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)
            assert_raise_message(ValueError,
                                 "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.", gmm.fit, X)

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

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.

    precisions_not_positive = {
        'full': precisions_not_pos,
        'tied': precisions_not_pos[0],
        'diag': np.full((n_components, n_features), -1.),
        'spherical': np.full(n_components, -1.)}

    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]
        assert_raise_message(ValueError,
                             "The parameter '%s precision' should have "
                             "the shape of" % covar_type,
                             g.fit, X)

        # Check not positive precisions
        g.precisions_init = precisions_not_positive[covar_type]
        assert_raise_message(ValueError,
                             "'%s precision' should be %s"
                             % (covar_type, not_positive_errors[covar_type]),
                             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_check_covariances():
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng)

    n_components, n_features = rand_data.n_components, rand_data.n_features

    # Define the bad covariances for each covariance_type
    covariances_bad_shape = {
        'full': rng.rand(n_components + 1, n_features, n_features),
        'tied': rng.rand(n_features + 1, n_features + 1),
        'diag': rng.rand(n_components + 1, n_features),
        'spherical': rng.rand(n_components + 1)}

    # Define not positive-definite covariances
    covariances_not_pos = rng.rand(n_components, n_features, n_features)
    covariances_not_pos[0] = np.eye(n_features)
    covariances_not_pos[0, 0, 0] = -1.

    covariances_not_positive = {
        'full': covariances_not_pos,
        'tied': covariances_not_pos[0],
        'diag': -1. * np.ones((n_components, n_features)),
        'spherical': -1. * np.ones(n_components)}

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

    for cov_type in ['full', 'tied', 'diag', 'spherical']:
        X = rand_data.X[cov_type]
        g = GaussianMixture(n_components=n_components,
                            covariance_type=cov_type)

        # Check covariance with bad shapes
        g.covariances_init = covariances_bad_shape[cov_type]
        assert_raise_message(ValueError,
                             "The parameter '%s covariance' should have "
                             "the shape of" % cov_type,
                             g.fit, X)

        # Check not positive covariances
        g.covariances_init = covariances_not_positive[cov_type]
        assert_raise_message(ValueError,
                             "'%s covariance' should be %s"
                             % (cov_type, not_positive_errors[cov_type]),
                             g.fit, X)

        # Check the correct init of covariances_init
        g.covariances_init = rand_data.covariances[cov_type]
        g.fit(X)
        assert_array_equal(rand_data.covariances[cov_type], g.covariances_init)

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_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
    assert_raise_message(ValueError,
                         "The parameter 'weights' should have the shape of "
                         "(%d,), "
                         "but got %s" % (n_components,
                                         str(weights_bad_shape.shape)),
                         g.fit, X)

    # Check bad range
    weights_bad_range = rng.rand(n_components) + 1
    g.weights_init = weights_bad_range
    assert_raise_message(ValueError,
                         "The parameter 'weights' should be in the range "
                         "[0, 1], but got max value %.5f, min value %.5f"
                         % (np.min(weights_bad_range),
                            np.max(weights_bad_range)),
                         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
    assert_raise_message(ValueError,
                         "The parameter 'weights' should be normalized, "
                         "but got sum(weights) = %.5f"
                         % np.sum(weights_bad_norm),
                         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)