Uploaded Test files

venv/Lib/site-packages/sklearn/decomposition/tests/test_dict_learning.py

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+import pytest
+
+import numpy as np
+import itertools
+
+from sklearn.exceptions import ConvergenceWarning
+
+from sklearn.utils import check_array
+
+from sklearn.utils._testing import assert_array_almost_equal
+from sklearn.utils._testing import assert_array_equal
+from sklearn.utils._testing import ignore_warnings
+from sklearn.utils._testing import TempMemmap
+
+from sklearn.decomposition import DictionaryLearning
+from sklearn.decomposition import MiniBatchDictionaryLearning
+from sklearn.decomposition import SparseCoder
+from sklearn.decomposition import dict_learning
+from sklearn.decomposition import dict_learning_online
+from sklearn.decomposition import sparse_encode
+
+
+rng_global = np.random.RandomState(0)
+n_samples, n_features = 10, 8
+X = rng_global.randn(n_samples, n_features)
+
+
+def test_sparse_encode_shapes_omp():
+    rng = np.random.RandomState(0)
+    algorithms = ['omp', 'lasso_lars', 'lasso_cd', 'lars', 'threshold']
+    for n_components, n_samples in itertools.product([1, 5], [1, 9]):
+        X_ = rng.randn(n_samples, n_features)
+        dictionary = rng.randn(n_components, n_features)
+        for algorithm, n_jobs in itertools.product(algorithms, [1, 3]):
+            code = sparse_encode(X_, dictionary, algorithm=algorithm,
+                                 n_jobs=n_jobs)
+            assert code.shape == (n_samples, n_components)
+
+
+def test_dict_learning_shapes():
+    n_components = 5
+    dico = DictionaryLearning(n_components, random_state=0).fit(X)
+    assert dico.components_.shape == (n_components, n_features)
+
+    n_components = 1
+    dico = DictionaryLearning(n_components, random_state=0).fit(X)
+    assert dico.components_.shape == (n_components, n_features)
+    assert dico.transform(X).shape == (X.shape[0], n_components)
+
+
+def test_dict_learning_overcomplete():
+    n_components = 12
+    dico = DictionaryLearning(n_components, random_state=0).fit(X)
+    assert dico.components_.shape == (n_components, n_features)
+
+
+def test_max_iter():
+    def ricker_function(resolution, center, width):
+        """Discrete sub-sampled Ricker (Mexican hat) wavelet"""
+        x = np.linspace(0, resolution - 1, resolution)
+        x = ((2 / (np.sqrt(3 * width) * np.pi ** .25))
+             * (1 - (x - center) ** 2 / width ** 2)
+             * np.exp(-(x - center) ** 2 / (2 * width ** 2)))
+        return x
+
+    def ricker_matrix(width, resolution, n_components):
+        """Dictionary of Ricker (Mexican hat) wavelets"""
+        centers = np.linspace(0, resolution - 1, n_components)
+        D = np.empty((n_components, resolution))
+        for i, center in enumerate(centers):
+            D[i] = ricker_function(resolution, center, width)
+        D /= np.sqrt(np.sum(D ** 2, axis=1))[:, np.newaxis]
+        return D
+
+    transform_algorithm = 'lasso_cd'
+    resolution = 1024
+    subsampling = 3  # subsampling factor
+    n_components = resolution // subsampling
+
+    # Compute a wavelet dictionary
+    D_multi = np.r_[tuple(ricker_matrix(width=w, resolution=resolution,
+                          n_components=n_components // 5)
+                          for w in (10, 50, 100, 500, 1000))]
+
+    X = np.linspace(0, resolution - 1, resolution)
+    first_quarter = X < resolution / 4
+    X[first_quarter] = 3.
+    X[np.logical_not(first_quarter)] = -1.
+    X = X.reshape(1, -1)
+
+    # check that the underlying model fails to converge
+    with pytest.warns(ConvergenceWarning):
+        model = SparseCoder(D_multi, transform_algorithm=transform_algorithm,
+                            transform_max_iter=1)
+        model.fit_transform(X)
+
+    # check that the underlying model converges w/o warnings
+    with pytest.warns(None) as record:
+        model = SparseCoder(D_multi, transform_algorithm=transform_algorithm,
+                            transform_max_iter=2000)
+        model.fit_transform(X)
+    assert not record.list
+
+
+def test_dict_learning_lars_positive_parameter():
+    n_components = 5
+    alpha = 1
+    err_msg = "Positive constraint not supported for 'lars' coding method."
+    with pytest.raises(ValueError, match=err_msg):
+        dict_learning(X, n_components, alpha=alpha, positive_code=True)
+
+
+@pytest.mark.parametrize("transform_algorithm", [
+    "lasso_lars",
+    "lasso_cd",
+    "threshold",
+])
+@pytest.mark.parametrize("positive_code", [False, True])
+@pytest.mark.parametrize("positive_dict", [False, True])
+def test_dict_learning_positivity(transform_algorithm,
+                                  positive_code,
+                                  positive_dict):
+    n_components = 5
+    dico = DictionaryLearning(
+        n_components, transform_algorithm=transform_algorithm, random_state=0,
+        positive_code=positive_code, positive_dict=positive_dict,
+        fit_algorithm="cd").fit(X)
+
+    code = dico.transform(X)
+    if positive_dict:
+        assert (dico.components_ >= 0).all()
+    else:
+        assert (dico.components_ < 0).any()
+    if positive_code:
+        assert (code >= 0).all()
+    else:
+        assert (code < 0).any()
+
+
+@pytest.mark.parametrize("positive_dict", [False, True])
+def test_dict_learning_lars_dict_positivity(positive_dict):
+    n_components = 5
+    dico = DictionaryLearning(
+        n_components, transform_algorithm="lars", random_state=0,
+        positive_dict=positive_dict, fit_algorithm="cd").fit(X)
+
+    if positive_dict:
+        assert (dico.components_ >= 0).all()
+    else:
+        assert (dico.components_ < 0).any()
+
+
+def test_dict_learning_lars_code_positivity():
+    n_components = 5
+    dico = DictionaryLearning(
+        n_components, transform_algorithm="lars", random_state=0,
+        positive_code=True, fit_algorithm="cd").fit(X)
+
+    err_msg = "Positive constraint not supported for '{}' coding method."
+    err_msg = err_msg.format("lars")
+    with pytest.raises(ValueError, match=err_msg):
+        dico.transform(X)
+
+
+def test_dict_learning_reconstruction():
+    n_components = 12
+    dico = DictionaryLearning(n_components, transform_algorithm='omp',
+                              transform_alpha=0.001, random_state=0)
+    code = dico.fit(X).transform(X)
+    assert_array_almost_equal(np.dot(code, dico.components_), X)
+
+    dico.set_params(transform_algorithm='lasso_lars')
+    code = dico.transform(X)
+    assert_array_almost_equal(np.dot(code, dico.components_), X, decimal=2)
+
+    # used to test lars here too, but there's no guarantee the number of
+    # nonzero atoms is right.
+
+
+def test_dict_learning_reconstruction_parallel():
+    # regression test that parallel reconstruction works with n_jobs>1
+    n_components = 12
+    dico = DictionaryLearning(n_components, transform_algorithm='omp',
+                              transform_alpha=0.001, random_state=0, n_jobs=4)
+    code = dico.fit(X).transform(X)
+    assert_array_almost_equal(np.dot(code, dico.components_), X)
+
+    dico.set_params(transform_algorithm='lasso_lars')
+    code = dico.transform(X)
+    assert_array_almost_equal(np.dot(code, dico.components_), X, decimal=2)
+
+
+def test_dict_learning_lassocd_readonly_data():
+    n_components = 12
+    with TempMemmap(X) as X_read_only:
+        dico = DictionaryLearning(n_components, transform_algorithm='lasso_cd',
+                                  transform_alpha=0.001, random_state=0,
+                                  n_jobs=4)
+        with ignore_warnings(category=ConvergenceWarning):
+            code = dico.fit(X_read_only).transform(X_read_only)
+        assert_array_almost_equal(np.dot(code, dico.components_), X_read_only,
+                                  decimal=2)
+
+
+def test_dict_learning_nonzero_coefs():
+    n_components = 4
+    dico = DictionaryLearning(n_components, transform_algorithm='lars',
+                              transform_n_nonzero_coefs=3, random_state=0)
+    code = dico.fit(X).transform(X[np.newaxis, 1])
+    assert len(np.flatnonzero(code)) == 3
+
+    dico.set_params(transform_algorithm='omp')
+    code = dico.transform(X[np.newaxis, 1])
+    assert len(np.flatnonzero(code)) == 3
+
+
+def test_dict_learning_unknown_fit_algorithm():
+    n_components = 5
+    dico = DictionaryLearning(n_components, fit_algorithm='<unknown>')
+    with pytest.raises(ValueError):
+        dico.fit(X)
+
+
+def test_dict_learning_split():
+    n_components = 5
+    dico = DictionaryLearning(n_components, transform_algorithm='threshold',
+                              random_state=0)
+    code = dico.fit(X).transform(X)
+    dico.split_sign = True
+    split_code = dico.transform(X)
+
+    assert_array_almost_equal(split_code[:, :n_components] -
+                              split_code[:, n_components:], code)
+
+
+def test_dict_learning_online_shapes():
+    rng = np.random.RandomState(0)
+    n_components = 8
+    code, dictionary = dict_learning_online(X, n_components=n_components,
+                                            alpha=1, random_state=rng)
+    assert code.shape == (n_samples, n_components)
+    assert dictionary.shape == (n_components, n_features)
+    assert np.dot(code, dictionary).shape == X.shape
+
+
+def test_dict_learning_online_lars_positive_parameter():
+    alpha = 1
+    err_msg = "Positive constraint not supported for 'lars' coding method."
+    with pytest.raises(ValueError, match=err_msg):
+        dict_learning_online(X, alpha=alpha, positive_code=True)
+
+
+@pytest.mark.parametrize("transform_algorithm", [
+    "lasso_lars",
+    "lasso_cd",
+    "threshold",
+])
+@pytest.mark.parametrize("positive_code", [False, True])
+@pytest.mark.parametrize("positive_dict", [False, True])
+def test_minibatch_dictionary_learning_positivity(transform_algorithm,
+                                                  positive_code,
+                                                  positive_dict):
+    n_components = 8
+    dico = MiniBatchDictionaryLearning(
+        n_components, transform_algorithm=transform_algorithm, random_state=0,
+        positive_code=positive_code, positive_dict=positive_dict,
+        fit_algorithm='cd').fit(X)
+
+    code = dico.transform(X)
+    if positive_dict:
+        assert (dico.components_ >= 0).all()
+    else:
+        assert (dico.components_ < 0).any()
+    if positive_code:
+        assert (code >= 0).all()
+    else:
+        assert (code < 0).any()
+
+
+@pytest.mark.parametrize("positive_dict", [False, True])
+def test_minibatch_dictionary_learning_lars(positive_dict):
+    n_components = 8
+
+    dico = MiniBatchDictionaryLearning(
+        n_components, transform_algorithm="lars", random_state=0,
+        positive_dict=positive_dict, fit_algorithm='cd').fit(X)
+
+    if positive_dict:
+        assert (dico.components_ >= 0).all()
+    else:
+        assert (dico.components_ < 0).any()
+
+
+@pytest.mark.parametrize("positive_code", [False, True])
+@pytest.mark.parametrize("positive_dict", [False, True])
+def test_dict_learning_online_positivity(positive_code,
+                                         positive_dict):
+    rng = np.random.RandomState(0)
+    n_components = 8
+
+    code, dictionary = dict_learning_online(X, n_components=n_components,
+                                            method="cd",
+                                            alpha=1, random_state=rng,
+                                            positive_dict=positive_dict,
+                                            positive_code=positive_code)
+    if positive_dict:
+        assert (dictionary >= 0).all()
+    else:
+        assert (dictionary < 0).any()
+    if positive_code:
+        assert (code >= 0).all()
+    else:
+        assert (code < 0).any()
+
+
+def test_dict_learning_online_verbosity():
+    n_components = 5
+    # test verbosity
+    from io import StringIO
+    import sys
+
+    old_stdout = sys.stdout
+    try:
+        sys.stdout = StringIO()
+        dico = MiniBatchDictionaryLearning(n_components, n_iter=20, verbose=1,
+                                           random_state=0)
+        dico.fit(X)
+        dico = MiniBatchDictionaryLearning(n_components, n_iter=20, verbose=2,
+                                           random_state=0)
+        dico.fit(X)
+        dict_learning_online(X, n_components=n_components, alpha=1, verbose=1,
+                             random_state=0)
+        dict_learning_online(X, n_components=n_components, alpha=1, verbose=2,
+                             random_state=0)
+    finally:
+        sys.stdout = old_stdout
+
+    assert dico.components_.shape == (n_components, n_features)
+
+
+def test_dict_learning_online_estimator_shapes():
+    n_components = 5
+    dico = MiniBatchDictionaryLearning(n_components, n_iter=20, random_state=0)
+    dico.fit(X)
+    assert dico.components_.shape == (n_components, n_features)
+
+
+def test_dict_learning_online_overcomplete():
+    n_components = 12
+    dico = MiniBatchDictionaryLearning(n_components, n_iter=20,
+                                       random_state=0).fit(X)
+    assert dico.components_.shape == (n_components, n_features)
+
+
+def test_dict_learning_online_initialization():
+    n_components = 12
+    rng = np.random.RandomState(0)
+    V = rng.randn(n_components, n_features)
+    dico = MiniBatchDictionaryLearning(n_components, n_iter=0,
+                                       dict_init=V, random_state=0).fit(X)
+    assert_array_equal(dico.components_, V)
+
+
+def test_dict_learning_online_readonly_initialization():
+    n_components = 12
+    rng = np.random.RandomState(0)
+    V = rng.randn(n_components, n_features)
+    V.setflags(write=False)
+    MiniBatchDictionaryLearning(n_components, n_iter=1, dict_init=V,
+                                random_state=0, shuffle=False).fit(X)
+
+
+def test_dict_learning_online_partial_fit():
+    n_components = 12
+    rng = np.random.RandomState(0)
+    V = rng.randn(n_components, n_features)  # random init
+    V /= np.sum(V ** 2, axis=1)[:, np.newaxis]
+    dict1 = MiniBatchDictionaryLearning(n_components, n_iter=10 * len(X),
+                                        batch_size=1,
+                                        alpha=1, shuffle=False, dict_init=V,
+                                        random_state=0).fit(X)
+    dict2 = MiniBatchDictionaryLearning(n_components, alpha=1,
+                                        n_iter=1, dict_init=V,
+                                        random_state=0)
+    for i in range(10):
+        for sample in X:
+            dict2.partial_fit(sample[np.newaxis, :])
+
+    assert not np.all(sparse_encode(X, dict1.components_, alpha=1) == 0)
+    assert_array_almost_equal(dict1.components_, dict2.components_,
+                              decimal=2)
+
+
+def test_dict_learning_iter_offset():
+    n_components = 12
+    rng = np.random.RandomState(0)
+    V = rng.randn(n_components, n_features)
+    dict1 = MiniBatchDictionaryLearning(n_components, n_iter=10,
+                                        dict_init=V, random_state=0,
+                                        shuffle=False)
+    dict2 = MiniBatchDictionaryLearning(n_components, n_iter=10,
+                                        dict_init=V, random_state=0,
+                                        shuffle=False)
+    dict1.fit(X)
+    for sample in X:
+        dict2.partial_fit(sample[np.newaxis, :])
+
+    assert dict1.iter_offset_ == dict2.iter_offset_
+
+
+def test_sparse_encode_shapes():
+    n_components = 12
+    rng = np.random.RandomState(0)
+    V = rng.randn(n_components, n_features)  # random init
+    V /= np.sum(V ** 2, axis=1)[:, np.newaxis]
+    for algo in ('lasso_lars', 'lasso_cd', 'lars', 'omp', 'threshold'):
+        code = sparse_encode(X, V, algorithm=algo)
+        assert code.shape == (n_samples, n_components)
+
+
+@pytest.mark.parametrize("algo", [
+    'lasso_lars',
+    'lasso_cd',
+    'threshold'
+])
+@pytest.mark.parametrize("positive", [False, True])
+def test_sparse_encode_positivity(algo, positive):
+    n_components = 12
+    rng = np.random.RandomState(0)
+    V = rng.randn(n_components, n_features)  # random init
+    V /= np.sum(V ** 2, axis=1)[:, np.newaxis]
+    code = sparse_encode(X, V, algorithm=algo, positive=positive)
+    if positive:
+        assert (code >= 0).all()
+    else:
+        assert (code < 0).any()
+
+
+@pytest.mark.parametrize("algo", ['lars', 'omp'])
+def test_sparse_encode_unavailable_positivity(algo):
+    n_components = 12
+    rng = np.random.RandomState(0)
+    V = rng.randn(n_components, n_features)  # random init
+    V /= np.sum(V ** 2, axis=1)[:, np.newaxis]
+    err_msg = "Positive constraint not supported for '{}' coding method."
+    err_msg = err_msg.format(algo)
+    with pytest.raises(ValueError, match=err_msg):
+        sparse_encode(X, V, algorithm=algo, positive=True)
+
+
+def test_sparse_encode_input():
+    n_components = 100
+    rng = np.random.RandomState(0)
+    V = rng.randn(n_components, n_features)  # random init
+    V /= np.sum(V ** 2, axis=1)[:, np.newaxis]
+    Xf = check_array(X, order='F')
+    for algo in ('lasso_lars', 'lasso_cd', 'lars', 'omp', 'threshold'):
+        a = sparse_encode(X, V, algorithm=algo)
+        b = sparse_encode(Xf, V, algorithm=algo)
+        assert_array_almost_equal(a, b)
+
+
+def test_sparse_encode_error():
+    n_components = 12
+    rng = np.random.RandomState(0)
+    V = rng.randn(n_components, n_features)  # random init
+    V /= np.sum(V ** 2, axis=1)[:, np.newaxis]
+    code = sparse_encode(X, V, alpha=0.001)
+    assert not np.all(code == 0)
+    assert np.sqrt(np.sum((np.dot(code, V) - X) ** 2)) < 0.1
+
+
+def test_sparse_encode_error_default_sparsity():
+    rng = np.random.RandomState(0)
+    X = rng.randn(100, 64)
+    D = rng.randn(2, 64)
+    code = ignore_warnings(sparse_encode)(X, D, algorithm='omp',
+                                          n_nonzero_coefs=None)
+    assert code.shape == (100, 2)
+
+
+def test_unknown_method():
+    n_components = 12
+    rng = np.random.RandomState(0)
+    V = rng.randn(n_components, n_features)  # random init
+    with pytest.raises(ValueError):
+        sparse_encode(X, V, algorithm="<unknown>")
+
+
+def test_sparse_coder_estimator():
+    n_components = 12
+    rng = np.random.RandomState(0)
+    V = rng.randn(n_components, n_features)  # random init
+    V /= np.sum(V ** 2, axis=1)[:, np.newaxis]
+    code = SparseCoder(dictionary=V, transform_algorithm='lasso_lars',
+                       transform_alpha=0.001).transform(X)
+    assert not np.all(code == 0)
+    assert np.sqrt(np.sum((np.dot(code, V) - X) ** 2)) < 0.1
+
+
+def test_sparse_coder_parallel_mmap():
+    # Non-regression test for:
+    # https://github.com/scikit-learn/scikit-learn/issues/5956
+    # Test that SparseCoder does not error by passing reading only
+    # arrays to child processes
+
+    rng = np.random.RandomState(777)
+    n_components, n_features = 40, 64
+    init_dict = rng.rand(n_components, n_features)
+    # Ensure that `data` is >2M. Joblib memory maps arrays
+    # if they are larger than 1MB. The 4 accounts for float32
+    # data type
+    n_samples = int(2e6) // (4 * n_features)
+    data = np.random.rand(n_samples, n_features).astype(np.float32)
+
+    sc = SparseCoder(init_dict, transform_algorithm='omp', n_jobs=2)
+    sc.fit_transform(data)
+
+
+def test_sparse_coder_n_features_in():
+    d = np.array([[1, 2, 3], [1, 2, 3]])
+    sc = SparseCoder(d)
+    assert sc.n_features_in_ == d.shape[1]

venv/Lib/site-packages/sklearn/decomposition/tests/test_factor_analysis.py

@@ -0,0 +1,85 @@
+# Author: Christian Osendorfer <osendorf@gmail.com>
+#         Alexandre Gramfort <alexandre.gramfort@inria.fr>
+# License: BSD3
+
+import numpy as np
+import pytest
+
+from sklearn.utils._testing import assert_warns
+from sklearn.utils._testing import assert_almost_equal
+from sklearn.utils._testing import assert_array_almost_equal
+from sklearn.exceptions import ConvergenceWarning
+from sklearn.decomposition import FactorAnalysis
+from sklearn.utils._testing import ignore_warnings
+
+
+# Ignore warnings from switching to more power iterations in randomized_svd
+@ignore_warnings
+def test_factor_analysis():
+    # Test FactorAnalysis ability to recover the data covariance structure
+    rng = np.random.RandomState(0)
+    n_samples, n_features, n_components = 20, 5, 3
+
+    # Some random settings for the generative model
+    W = rng.randn(n_components, n_features)
+    # latent variable of dim 3, 20 of it
+    h = rng.randn(n_samples, n_components)
+    # using gamma to model different noise variance
+    # per component
+    noise = rng.gamma(1, size=n_features) * rng.randn(n_samples, n_features)
+
+    # generate observations
+    # wlog, mean is 0
+    X = np.dot(h, W) + noise
+
+    with pytest.raises(ValueError):
+        FactorAnalysis(svd_method='foo')
+    fa_fail = FactorAnalysis()
+    fa_fail.svd_method = 'foo'
+    with pytest.raises(ValueError):
+        fa_fail.fit(X)
+    fas = []
+    for method in ['randomized', 'lapack']:
+        fa = FactorAnalysis(n_components=n_components, svd_method=method)
+        fa.fit(X)
+        fas.append(fa)
+
+        X_t = fa.transform(X)
+        assert X_t.shape == (n_samples, n_components)
+
+        assert_almost_equal(fa.loglike_[-1], fa.score_samples(X).sum())
+        assert_almost_equal(fa.score_samples(X).mean(), fa.score(X))
+
+        diff = np.all(np.diff(fa.loglike_))
+        assert diff > 0., 'Log likelihood dif not increase'
+
+        # Sample Covariance
+        scov = np.cov(X, rowvar=0., bias=1.)
+
+        # Model Covariance
+        mcov = fa.get_covariance()
+        diff = np.sum(np.abs(scov - mcov)) / W.size
+        assert diff < 0.1, "Mean absolute difference is %f" % diff
+        fa = FactorAnalysis(n_components=n_components,
+                            noise_variance_init=np.ones(n_features))
+        with pytest.raises(ValueError):
+            fa.fit(X[:, :2])
+
+    f = lambda x, y: np.abs(getattr(x, y))  # sign will not be equal
+    fa1, fa2 = fas
+    for attr in ['loglike_', 'components_', 'noise_variance_']:
+        assert_almost_equal(f(fa1, attr), f(fa2, attr))
+
+    fa1.max_iter = 1
+    fa1.verbose = True
+    assert_warns(ConvergenceWarning, fa1.fit, X)
+
+    # Test get_covariance and get_precision with n_components == n_features
+    # with n_components < n_features and with n_components == 0
+    for n_components in [0, 2, X.shape[1]]:
+        fa.n_components = n_components
+        fa.fit(X)
+        cov = fa.get_covariance()
+        precision = fa.get_precision()
+        assert_array_almost_equal(np.dot(cov, precision),
+                                  np.eye(X.shape[1]), 12)

venv/Lib/site-packages/sklearn/decomposition/tests/test_fastica.py

@@ -0,0 +1,301 @@
+"""
+Test the fastica algorithm.
+"""
+import itertools
+import warnings
+import pytest
+
+import numpy as np
+from scipy import stats
+
+from sklearn.utils._testing import assert_almost_equal
+from sklearn.utils._testing import assert_array_almost_equal
+from sklearn.utils._testing import assert_warns
+
+from sklearn.decomposition import FastICA, fastica, PCA
+from sklearn.decomposition._fastica import _gs_decorrelation
+from sklearn.exceptions import ConvergenceWarning
+
+
+def center_and_norm(x, axis=-1):
+    """ Centers and norms x **in place**
+
+        Parameters
+        -----------
+        x: ndarray
+            Array with an axis of observations (statistical units) measured on
+            random variables.
+        axis: int, optional
+            Axis along which the mean and variance are calculated.
+    """
+    x = np.rollaxis(x, axis)
+    x -= x.mean(axis=0)
+    x /= x.std(axis=0)
+
+
+def test_gs():
+    # Test gram schmidt orthonormalization
+    # generate a random orthogonal  matrix
+    rng = np.random.RandomState(0)
+    W, _, _ = np.linalg.svd(rng.randn(10, 10))
+    w = rng.randn(10)
+    _gs_decorrelation(w, W, 10)
+    assert (w ** 2).sum() < 1.e-10
+    w = rng.randn(10)
+    u = _gs_decorrelation(w, W, 5)
+    tmp = np.dot(u, W.T)
+    assert (tmp[:5] ** 2).sum() < 1.e-10
+
+
+@pytest.mark.parametrize("add_noise", [True, False])
+@pytest.mark.parametrize("seed", range(1))
+def test_fastica_simple(add_noise, seed):
+    # Test the FastICA algorithm on very simple data.
+    rng = np.random.RandomState(seed)
+    # scipy.stats uses the global RNG:
+    n_samples = 1000
+    # Generate two sources:
+    s1 = (2 * np.sin(np.linspace(0, 100, n_samples)) > 0) - 1
+    s2 = stats.t.rvs(1, size=n_samples)
+    s = np.c_[s1, s2].T
+    center_and_norm(s)
+    s1, s2 = s
+
+    # Mixing angle
+    phi = 0.6
+    mixing = np.array([[np.cos(phi), np.sin(phi)],
+                       [np.sin(phi), -np.cos(phi)]])
+    m = np.dot(mixing, s)
+
+    if add_noise:
+        m += 0.1 * rng.randn(2, 1000)
+
+    center_and_norm(m)
+
+    # function as fun arg
+    def g_test(x):
+        return x ** 3, (3 * x ** 2).mean(axis=-1)
+
+    algos = ['parallel', 'deflation']
+    nls = ['logcosh', 'exp', 'cube', g_test]
+    whitening = [True, False]
+    for algo, nl, whiten in itertools.product(algos, nls, whitening):
+        if whiten:
+            k_, mixing_, s_ = fastica(m.T, fun=nl, algorithm=algo,
+                                      random_state=rng)
+            with pytest.raises(ValueError):
+                fastica(m.T, fun=np.tanh, algorithm=algo)
+        else:
+            pca = PCA(n_components=2, whiten=True, random_state=rng)
+            X = pca.fit_transform(m.T)
+            k_, mixing_, s_ = fastica(X, fun=nl, algorithm=algo, whiten=False,
+                                      random_state=rng)
+            with pytest.raises(ValueError):
+                fastica(X, fun=np.tanh, algorithm=algo)
+        s_ = s_.T
+        # Check that the mixing model described in the docstring holds:
+        if whiten:
+            assert_almost_equal(s_, np.dot(np.dot(mixing_, k_), m))
+
+        center_and_norm(s_)
+        s1_, s2_ = s_
+        # Check to see if the sources have been estimated
+        # in the wrong order
+        if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
+            s2_, s1_ = s_
+        s1_ *= np.sign(np.dot(s1_, s1))
+        s2_ *= np.sign(np.dot(s2_, s2))
+
+        # Check that we have estimated the original sources
+        if not add_noise:
+            assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=2)
+            assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=2)
+        else:
+            assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=1)
+            assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=1)
+
+    # Test FastICA class
+    _, _, sources_fun = fastica(m.T, fun=nl, algorithm=algo,
+                                random_state=seed)
+    ica = FastICA(fun=nl, algorithm=algo, random_state=seed)
+    sources = ica.fit_transform(m.T)
+    assert ica.components_.shape == (2, 2)
+    assert sources.shape == (1000, 2)
+
+    assert_array_almost_equal(sources_fun, sources)
+    assert_array_almost_equal(sources, ica.transform(m.T))
+
+    assert ica.mixing_.shape == (2, 2)
+
+    for fn in [np.tanh, "exp(-.5(x^2))"]:
+        ica = FastICA(fun=fn, algorithm=algo)
+        with pytest.raises(ValueError):
+            ica.fit(m.T)
+
+    with pytest.raises(TypeError):
+        FastICA(fun=range(10)).fit(m.T)
+
+
+def test_fastica_nowhiten():
+    m = [[0, 1], [1, 0]]
+
+    # test for issue #697
+    ica = FastICA(n_components=1, whiten=False, random_state=0)
+    assert_warns(UserWarning, ica.fit, m)
+    assert hasattr(ica, 'mixing_')
+
+
+def test_fastica_convergence_fail():
+    # Test the FastICA algorithm on very simple data
+    # (see test_non_square_fastica).
+    # Ensure a ConvergenceWarning raised if the tolerance is sufficiently low.
+    rng = np.random.RandomState(0)
+
+    n_samples = 1000
+    # Generate two sources:
+    t = np.linspace(0, 100, n_samples)
+    s1 = np.sin(t)
+    s2 = np.ceil(np.sin(np.pi * t))
+    s = np.c_[s1, s2].T
+    center_and_norm(s)
+
+    # Mixing matrix
+    mixing = rng.randn(6, 2)
+    m = np.dot(mixing, s)
+
+    # Do fastICA with tolerance 0. to ensure failing convergence
+    ica = FastICA(algorithm="parallel", n_components=2, random_state=rng,
+                  max_iter=2, tol=0.)
+    assert_warns(ConvergenceWarning, ica.fit, m.T)
+
+
+@pytest.mark.parametrize('add_noise', [True, False])
+def test_non_square_fastica(add_noise):
+    # Test the FastICA algorithm on very simple data.
+    rng = np.random.RandomState(0)
+
+    n_samples = 1000
+    # Generate two sources:
+    t = np.linspace(0, 100, n_samples)
+    s1 = np.sin(t)
+    s2 = np.ceil(np.sin(np.pi * t))
+    s = np.c_[s1, s2].T
+    center_and_norm(s)
+    s1, s2 = s
+
+    # Mixing matrix
+    mixing = rng.randn(6, 2)
+    m = np.dot(mixing, s)
+
+    if add_noise:
+        m += 0.1 * rng.randn(6, n_samples)
+
+    center_and_norm(m)
+
+    k_, mixing_, s_ = fastica(m.T, n_components=2, random_state=rng)
+    s_ = s_.T
+
+    # Check that the mixing model described in the docstring holds:
+    assert_almost_equal(s_, np.dot(np.dot(mixing_, k_), m))
+
+    center_and_norm(s_)
+    s1_, s2_ = s_
+    # Check to see if the sources have been estimated
+    # in the wrong order
+    if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
+        s2_, s1_ = s_
+    s1_ *= np.sign(np.dot(s1_, s1))
+    s2_ *= np.sign(np.dot(s2_, s2))
+
+    # Check that we have estimated the original sources
+    if not add_noise:
+        assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=3)
+        assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=3)
+
+
+def test_fit_transform():
+    # Test FastICA.fit_transform
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((100, 10))
+    for whiten, n_components in [[True, 5], [False, None]]:
+        n_components_ = (n_components if n_components is not None else
+                         X.shape[1])
+
+        ica = FastICA(n_components=n_components, whiten=whiten, random_state=0)
+        Xt = ica.fit_transform(X)
+        assert ica.components_.shape == (n_components_, 10)
+        assert Xt.shape == (100, n_components_)
+
+        ica = FastICA(n_components=n_components, whiten=whiten, random_state=0)
+        ica.fit(X)
+        assert ica.components_.shape == (n_components_, 10)
+        Xt2 = ica.transform(X)
+
+        assert_array_almost_equal(Xt, Xt2)
+
+
+def test_inverse_transform():
+    # Test FastICA.inverse_transform
+    n_features = 10
+    n_samples = 100
+    n1, n2 = 5, 10
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((n_samples, n_features))
+    expected = {(True, n1): (n_features, n1),
+                (True, n2): (n_features, n2),
+                (False, n1): (n_features, n2),
+                (False, n2): (n_features, n2)}
+    for whiten in [True, False]:
+        for n_components in [n1, n2]:
+            n_components_ = (n_components if n_components is not None else
+                             X.shape[1])
+            ica = FastICA(n_components=n_components, random_state=rng,
+                          whiten=whiten)
+            with warnings.catch_warnings(record=True):
+                # catch "n_components ignored" warning
+                Xt = ica.fit_transform(X)
+            expected_shape = expected[(whiten, n_components_)]
+            assert ica.mixing_.shape == expected_shape
+            X2 = ica.inverse_transform(Xt)
+            assert X.shape == X2.shape
+
+            # reversibility test in non-reduction case
+            if n_components == X.shape[1]:
+                assert_array_almost_equal(X, X2)
+
+
+def test_fastica_errors():
+    n_features = 3
+    n_samples = 10
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((n_samples, n_features))
+    w_init = rng.randn(n_features + 1, n_features + 1)
+    with pytest.raises(ValueError, match='max_iter should be greater than 1'):
+        FastICA(max_iter=0)
+    with pytest.raises(ValueError, match=r'alpha must be in \[1,2\]'):
+        fastica(X, fun_args={'alpha': 0})
+    with pytest.raises(ValueError, match='w_init has invalid shape.+'
+                       r'should be \(3L?, 3L?\)'):
+        fastica(X, w_init=w_init)
+    with pytest.raises(ValueError, match='Invalid algorithm.+must '
+                       'be.+parallel.+or.+deflation'):
+        fastica(X, algorithm='pizza')
+
+
+@pytest.mark.parametrize('whiten', [True, False])
+@pytest.mark.parametrize('return_X_mean', [True, False])
+@pytest.mark.parametrize('return_n_iter', [True, False])
+def test_fastica_output_shape(whiten, return_X_mean, return_n_iter):
+    n_features = 3
+    n_samples = 10
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((n_samples, n_features))
+
+    expected_len = 3 + return_X_mean + return_n_iter
+
+    out = fastica(X, whiten=whiten, return_n_iter=return_n_iter,
+                  return_X_mean=return_X_mean)
+
+    assert len(out) == expected_len
+    if not whiten:
+        assert out[0] is None

venv/Lib/site-packages/sklearn/decomposition/tests/test_incremental_pca.py

@@ -0,0 +1,401 @@
+"""Tests for Incremental PCA."""
+import numpy as np
+import pytest
+
+from sklearn.utils._testing import assert_almost_equal
+from sklearn.utils._testing import assert_array_almost_equal
+from sklearn.utils._testing import assert_allclose_dense_sparse
+
+from sklearn import datasets
+from sklearn.decomposition import PCA, IncrementalPCA
+
+from scipy import sparse
+
+iris = datasets.load_iris()
+
+
+def test_incremental_pca():
+    # Incremental PCA on dense arrays.
+    X = iris.data
+    batch_size = X.shape[0] // 3
+    ipca = IncrementalPCA(n_components=2, batch_size=batch_size)
+    pca = PCA(n_components=2)
+    pca.fit_transform(X)
+
+    X_transformed = ipca.fit_transform(X)
+
+    assert X_transformed.shape == (X.shape[0], 2)
+    np.testing.assert_allclose(ipca.explained_variance_ratio_.sum(),
+                               pca.explained_variance_ratio_.sum(), rtol=1e-3)
+
+    for n_components in [1, 2, X.shape[1]]:
+        ipca = IncrementalPCA(n_components, batch_size=batch_size)
+        ipca.fit(X)
+        cov = ipca.get_covariance()
+        precision = ipca.get_precision()
+        np.testing.assert_allclose(np.dot(cov, precision),
+                                   np.eye(X.shape[1]), atol=1e-13)
+
+
+@pytest.mark.parametrize(
+    "matrix_class",
+    [sparse.csc_matrix, sparse.csr_matrix, sparse.lil_matrix])
+def test_incremental_pca_sparse(matrix_class):
+    # Incremental PCA on sparse arrays.
+    X = iris.data
+    pca = PCA(n_components=2)
+    pca.fit_transform(X)
+    X_sparse = matrix_class(X)
+    batch_size = X_sparse.shape[0] // 3
+    ipca = IncrementalPCA(n_components=2, batch_size=batch_size)
+
+    X_transformed = ipca.fit_transform(X_sparse)
+
+    assert X_transformed.shape == (X_sparse.shape[0], 2)
+    np.testing.assert_allclose(ipca.explained_variance_ratio_.sum(),
+                               pca.explained_variance_ratio_.sum(), rtol=1e-3)
+
+    for n_components in [1, 2, X.shape[1]]:
+        ipca = IncrementalPCA(n_components, batch_size=batch_size)
+        ipca.fit(X_sparse)
+        cov = ipca.get_covariance()
+        precision = ipca.get_precision()
+        np.testing.assert_allclose(np.dot(cov, precision),
+                                   np.eye(X_sparse.shape[1]), atol=1e-13)
+
+    with pytest.raises(
+            TypeError,
+            match="IncrementalPCA.partial_fit does not support "
+            "sparse input. Either convert data to dense "
+            "or use IncrementalPCA.fit to do so in batches."):
+        ipca.partial_fit(X_sparse)
+
+
+def test_incremental_pca_check_projection():
+    # Test that the projection of data is correct.
+    rng = np.random.RandomState(1999)
+    n, p = 100, 3
+    X = rng.randn(n, p) * .1
+    X[:10] += np.array([3, 4, 5])
+    Xt = 0.1 * rng.randn(1, p) + np.array([3, 4, 5])
+
+    # Get the reconstruction of the generated data X
+    # Note that Xt has the same "components" as X, just separated
+    # This is what we want to ensure is recreated correctly
+    Yt = IncrementalPCA(n_components=2).fit(X).transform(Xt)
+
+    # Normalize
+    Yt /= np.sqrt((Yt ** 2).sum())
+
+    # Make sure that the first element of Yt is ~1, this means
+    # the reconstruction worked as expected
+    assert_almost_equal(np.abs(Yt[0][0]), 1., 1)
+
+
+def test_incremental_pca_inverse():
+    # Test that the projection of data can be inverted.
+    rng = np.random.RandomState(1999)
+    n, p = 50, 3
+    X = rng.randn(n, p)  # spherical data
+    X[:, 1] *= .00001  # make middle component relatively small
+    X += [5, 4, 3]  # make a large mean
+
+    # same check that we can find the original data from the transformed
+    # signal (since the data is almost of rank n_components)
+    ipca = IncrementalPCA(n_components=2, batch_size=10).fit(X)
+    Y = ipca.transform(X)
+    Y_inverse = ipca.inverse_transform(Y)
+    assert_almost_equal(X, Y_inverse, decimal=3)
+
+
+def test_incremental_pca_validation():
+    # Test that n_components is >=1 and <= n_features.
+    X = np.array([[0, 1, 0], [1, 0, 0]])
+    n_samples, n_features = X.shape
+    for n_components in [-1, 0, .99, 4]:
+        with pytest.raises(ValueError, match="n_components={} invalid"
+                           " for n_features={}, need more rows than"
+                           " columns for IncrementalPCA"
+                           " processing".format(n_components,
+                                                n_features)):
+            IncrementalPCA(n_components, batch_size=10).fit(X)
+
+    # Tests that n_components is also <= n_samples.
+    n_components = 3
+    with pytest.raises(ValueError, match="n_components={} must be"
+                       " less or equal to the batch number of"
+                       " samples {}".format(n_components, n_samples)):
+        IncrementalPCA(n_components=n_components).partial_fit(X)
+
+
+def test_n_components_none():
+    # Ensures that n_components == None is handled correctly
+    rng = np.random.RandomState(1999)
+    for n_samples, n_features in [(50, 10), (10, 50)]:
+        X = rng.rand(n_samples, n_features)
+        ipca = IncrementalPCA(n_components=None)
+
+        # First partial_fit call, ipca.n_components_ is inferred from
+        # min(X.shape)
+        ipca.partial_fit(X)
+        assert ipca.n_components_ == min(X.shape)
+
+        # Second partial_fit call, ipca.n_components_ is inferred from
+        # ipca.components_ computed from the first partial_fit call
+        ipca.partial_fit(X)
+        assert ipca.n_components_ == ipca.components_.shape[0]
+
+
+def test_incremental_pca_set_params():
+    # Test that components_ sign is stable over batch sizes.
+    rng = np.random.RandomState(1999)
+    n_samples = 100
+    n_features = 20
+    X = rng.randn(n_samples, n_features)
+    X2 = rng.randn(n_samples, n_features)
+    X3 = rng.randn(n_samples, n_features)
+    ipca = IncrementalPCA(n_components=20)
+    ipca.fit(X)
+    # Decreasing number of components
+    ipca.set_params(n_components=10)
+    with pytest.raises(ValueError):
+        ipca.partial_fit(X2)
+    # Increasing number of components
+    ipca.set_params(n_components=15)
+    with pytest.raises(ValueError):
+        ipca.partial_fit(X3)
+    # Returning to original setting
+    ipca.set_params(n_components=20)
+    ipca.partial_fit(X)
+
+
+def test_incremental_pca_num_features_change():
+    # Test that changing n_components will raise an error.
+    rng = np.random.RandomState(1999)
+    n_samples = 100
+    X = rng.randn(n_samples, 20)
+    X2 = rng.randn(n_samples, 50)
+    ipca = IncrementalPCA(n_components=None)
+    ipca.fit(X)
+    with pytest.raises(ValueError):
+        ipca.partial_fit(X2)
+
+
+def test_incremental_pca_batch_signs():
+    # Test that components_ sign is stable over batch sizes.
+    rng = np.random.RandomState(1999)
+    n_samples = 100
+    n_features = 3
+    X = rng.randn(n_samples, n_features)
+    all_components = []
+    batch_sizes = np.arange(10, 20)
+    for batch_size in batch_sizes:
+        ipca = IncrementalPCA(n_components=None, batch_size=batch_size).fit(X)
+        all_components.append(ipca.components_)
+
+    for i, j in zip(all_components[:-1], all_components[1:]):
+        assert_almost_equal(np.sign(i), np.sign(j), decimal=6)
+
+
+def test_incremental_pca_batch_values():
+    # Test that components_ values are stable over batch sizes.
+    rng = np.random.RandomState(1999)
+    n_samples = 100
+    n_features = 3
+    X = rng.randn(n_samples, n_features)
+    all_components = []
+    batch_sizes = np.arange(20, 40, 3)
+    for batch_size in batch_sizes:
+        ipca = IncrementalPCA(n_components=None, batch_size=batch_size).fit(X)
+        all_components.append(ipca.components_)
+
+    for i, j in zip(all_components[:-1], all_components[1:]):
+        assert_almost_equal(i, j, decimal=1)
+
+
+def test_incremental_pca_batch_rank():
+    # Test sample size in each batch is always larger or equal to n_components
+    rng = np.random.RandomState(1999)
+    n_samples = 100
+    n_features = 20
+    X = rng.randn(n_samples, n_features)
+    all_components = []
+    batch_sizes = np.arange(20, 90, 3)
+    for batch_size in batch_sizes:
+        ipca = IncrementalPCA(n_components=20, batch_size=batch_size).fit(X)
+        all_components.append(ipca.components_)
+
+    for components_i, components_j in zip(all_components[:-1],
+                                          all_components[1:]):
+        assert_allclose_dense_sparse(components_i, components_j)
+
+
+def test_incremental_pca_partial_fit():
+    # Test that fit and partial_fit get equivalent results.
+    rng = np.random.RandomState(1999)
+    n, p = 50, 3
+    X = rng.randn(n, p)  # spherical data
+    X[:, 1] *= .00001  # make middle component relatively small
+    X += [5, 4, 3]  # make a large mean
+
+    # same check that we can find the original data from the transformed
+    # signal (since the data is almost of rank n_components)
+    batch_size = 10
+    ipca = IncrementalPCA(n_components=2, batch_size=batch_size).fit(X)
+    pipca = IncrementalPCA(n_components=2, batch_size=batch_size)
+    # Add one to make sure endpoint is included
+    batch_itr = np.arange(0, n + 1, batch_size)
+    for i, j in zip(batch_itr[:-1], batch_itr[1:]):
+        pipca.partial_fit(X[i:j, :])
+    assert_almost_equal(ipca.components_, pipca.components_, decimal=3)
+
+
+def test_incremental_pca_against_pca_iris():
+    # Test that IncrementalPCA and PCA are approximate (to a sign flip).
+    X = iris.data
+
+    Y_pca = PCA(n_components=2).fit_transform(X)
+    Y_ipca = IncrementalPCA(n_components=2, batch_size=25).fit_transform(X)
+
+    assert_almost_equal(np.abs(Y_pca), np.abs(Y_ipca), 1)
+
+
+def test_incremental_pca_against_pca_random_data():
+    # Test that IncrementalPCA and PCA are approximate (to a sign flip).
+    rng = np.random.RandomState(1999)
+    n_samples = 100
+    n_features = 3
+    X = rng.randn(n_samples, n_features) + 5 * rng.rand(1, n_features)
+
+    Y_pca = PCA(n_components=3).fit_transform(X)
+    Y_ipca = IncrementalPCA(n_components=3, batch_size=25).fit_transform(X)
+
+    assert_almost_equal(np.abs(Y_pca), np.abs(Y_ipca), 1)
+
+
+def test_explained_variances():
+    # Test that PCA and IncrementalPCA calculations match
+    X = datasets.make_low_rank_matrix(1000, 100, tail_strength=0.,
+                                      effective_rank=10, random_state=1999)
+    prec = 3
+    n_samples, n_features = X.shape
+    for nc in [None, 99]:
+        pca = PCA(n_components=nc).fit(X)
+        ipca = IncrementalPCA(n_components=nc, batch_size=100).fit(X)
+        assert_almost_equal(pca.explained_variance_, ipca.explained_variance_,
+                            decimal=prec)
+        assert_almost_equal(pca.explained_variance_ratio_,
+                            ipca.explained_variance_ratio_, decimal=prec)
+        assert_almost_equal(pca.noise_variance_, ipca.noise_variance_,
+                            decimal=prec)
+
+
+def test_singular_values():
+    # Check that the IncrementalPCA output has the correct singular values
+
+    rng = np.random.RandomState(0)
+    n_samples = 1000
+    n_features = 100
+
+    X = datasets.make_low_rank_matrix(n_samples, n_features, tail_strength=0.0,
+                                      effective_rank=10, random_state=rng)
+
+    pca = PCA(n_components=10, svd_solver='full', random_state=rng).fit(X)
+    ipca = IncrementalPCA(n_components=10, batch_size=100).fit(X)
+    assert_array_almost_equal(pca.singular_values_, ipca.singular_values_, 2)
+
+    # Compare to the Frobenius norm
+    X_pca = pca.transform(X)
+    X_ipca = ipca.transform(X)
+    assert_array_almost_equal(np.sum(pca.singular_values_**2.0),
+                              np.linalg.norm(X_pca, "fro")**2.0, 12)
+    assert_array_almost_equal(np.sum(ipca.singular_values_**2.0),
+                              np.linalg.norm(X_ipca, "fro")**2.0, 2)
+
+    # Compare to the 2-norms of the score vectors
+    assert_array_almost_equal(pca.singular_values_,
+                              np.sqrt(np.sum(X_pca**2.0, axis=0)), 12)
+    assert_array_almost_equal(ipca.singular_values_,
+                              np.sqrt(np.sum(X_ipca**2.0, axis=0)), 2)
+
+    # Set the singular values and see what we get back
+    rng = np.random.RandomState(0)
+    n_samples = 100
+    n_features = 110
+
+    X = datasets.make_low_rank_matrix(n_samples, n_features, tail_strength=0.0,
+                                      effective_rank=3, random_state=rng)
+
+    pca = PCA(n_components=3, svd_solver='full', random_state=rng)
+    ipca = IncrementalPCA(n_components=3, batch_size=100)
+
+    X_pca = pca.fit_transform(X)
+    X_pca /= np.sqrt(np.sum(X_pca**2.0, axis=0))
+    X_pca[:, 0] *= 3.142
+    X_pca[:, 1] *= 2.718
+
+    X_hat = np.dot(X_pca, pca.components_)
+    pca.fit(X_hat)
+    ipca.fit(X_hat)
+    assert_array_almost_equal(pca.singular_values_, [3.142, 2.718, 1.0], 14)
+    assert_array_almost_equal(ipca.singular_values_, [3.142, 2.718, 1.0], 14)
+
+
+def test_whitening():
+    # Test that PCA and IncrementalPCA transforms match to sign flip.
+    X = datasets.make_low_rank_matrix(1000, 10, tail_strength=0.,
+                                      effective_rank=2, random_state=1999)
+    prec = 3
+    n_samples, n_features = X.shape
+    for nc in [None, 9]:
+        pca = PCA(whiten=True, n_components=nc).fit(X)
+        ipca = IncrementalPCA(whiten=True, n_components=nc,
+                              batch_size=250).fit(X)
+
+        Xt_pca = pca.transform(X)
+        Xt_ipca = ipca.transform(X)
+        assert_almost_equal(np.abs(Xt_pca), np.abs(Xt_ipca), decimal=prec)
+        Xinv_ipca = ipca.inverse_transform(Xt_ipca)
+        Xinv_pca = pca.inverse_transform(Xt_pca)
+        assert_almost_equal(X, Xinv_ipca, decimal=prec)
+        assert_almost_equal(X, Xinv_pca, decimal=prec)
+        assert_almost_equal(Xinv_pca, Xinv_ipca, decimal=prec)
+
+
+def test_incremental_pca_partial_fit_float_division():
+    # Test to ensure float division is used in all versions of Python
+    # (non-regression test for issue #9489)
+
+    rng = np.random.RandomState(0)
+    A = rng.randn(5, 3) + 2
+    B = rng.randn(7, 3) + 5
+
+    pca = IncrementalPCA(n_components=2)
+    pca.partial_fit(A)
+    # Set n_samples_seen_ to be a floating point number instead of an int
+    pca.n_samples_seen_ = float(pca.n_samples_seen_)
+    pca.partial_fit(B)
+    singular_vals_float_samples_seen = pca.singular_values_
+
+    pca2 = IncrementalPCA(n_components=2)
+    pca2.partial_fit(A)
+    pca2.partial_fit(B)
+    singular_vals_int_samples_seen = pca2.singular_values_
+
+    np.testing.assert_allclose(singular_vals_float_samples_seen,
+                               singular_vals_int_samples_seen)
+
+
+def test_incremental_pca_fit_overflow_error():
+    # Test for overflow error on Windows OS
+    # (non-regression test for issue #17693)
+    rng = np.random.RandomState(0)
+    A = rng.rand(500000, 2)
+
+    ipca = IncrementalPCA(n_components=2, batch_size=10000)
+    ipca.fit(A)
+
+    pca = PCA(n_components=2)
+    pca.fit(A)
+
+    np.testing.assert_allclose(ipca.singular_values_, pca.singular_values_)

venv/Lib/site-packages/sklearn/decomposition/tests/test_kernel_pca.py

@@ -0,0 +1,297 @@
+import numpy as np
+import scipy.sparse as sp
+import pytest
+
+from sklearn.utils._testing import (assert_array_almost_equal,
+                                   assert_allclose)
+
+from sklearn.decomposition import PCA, KernelPCA
+from sklearn.datasets import make_circles
+from sklearn.datasets import make_blobs
+from sklearn.linear_model import Perceptron
+from sklearn.pipeline import Pipeline
+from sklearn.model_selection import GridSearchCV
+from sklearn.metrics.pairwise import rbf_kernel
+from sklearn.utils.validation import _check_psd_eigenvalues
+
+
+def test_kernel_pca():
+    rng = np.random.RandomState(0)
+    X_fit = rng.random_sample((5, 4))
+    X_pred = rng.random_sample((2, 4))
+
+    def histogram(x, y, **kwargs):
+        # Histogram kernel implemented as a callable.
+        assert kwargs == {}    # no kernel_params that we didn't ask for
+        return np.minimum(x, y).sum()
+
+    for eigen_solver in ("auto", "dense", "arpack"):
+        for kernel in ("linear", "rbf", "poly", histogram):
+            # histogram kernel produces singular matrix inside linalg.solve
+            # XXX use a least-squares approximation?
+            inv = not callable(kernel)
+
+            # transform fit data
+            kpca = KernelPCA(4, kernel=kernel, eigen_solver=eigen_solver,
+                             fit_inverse_transform=inv)
+            X_fit_transformed = kpca.fit_transform(X_fit)
+            X_fit_transformed2 = kpca.fit(X_fit).transform(X_fit)
+            assert_array_almost_equal(np.abs(X_fit_transformed),
+                                      np.abs(X_fit_transformed2))
+
+            # non-regression test: previously, gamma would be 0 by default,
+            # forcing all eigenvalues to 0 under the poly kernel
+            assert X_fit_transformed.size != 0
+
+            # transform new data
+            X_pred_transformed = kpca.transform(X_pred)
+            assert (X_pred_transformed.shape[1] ==
+                         X_fit_transformed.shape[1])
+
+            # inverse transform
+            if inv:
+                X_pred2 = kpca.inverse_transform(X_pred_transformed)
+                assert X_pred2.shape == X_pred.shape
+
+
+def test_kernel_pca_invalid_parameters():
+    with pytest.raises(ValueError):
+        KernelPCA(10, fit_inverse_transform=True, kernel='precomputed')
+
+
+def test_kernel_pca_consistent_transform():
+    # X_fit_ needs to retain the old, unmodified copy of X
+    state = np.random.RandomState(0)
+    X = state.rand(10, 10)
+    kpca = KernelPCA(random_state=state).fit(X)
+    transformed1 = kpca.transform(X)
+
+    X_copy = X.copy()
+    X[:, 0] = 666
+    transformed2 = kpca.transform(X_copy)
+    assert_array_almost_equal(transformed1, transformed2)
+
+
+def test_kernel_pca_deterministic_output():
+    rng = np.random.RandomState(0)
+    X = rng.rand(10, 10)
+    eigen_solver = ('arpack', 'dense')
+
+    for solver in eigen_solver:
+        transformed_X = np.zeros((20, 2))
+        for i in range(20):
+            kpca = KernelPCA(n_components=2, eigen_solver=solver,
+                             random_state=rng)
+            transformed_X[i, :] = kpca.fit_transform(X)[0]
+        assert_allclose(
+            transformed_X, np.tile(transformed_X[0, :], 20).reshape(20, 2))
+
+
+def test_kernel_pca_sparse():
+    rng = np.random.RandomState(0)
+    X_fit = sp.csr_matrix(rng.random_sample((5, 4)))
+    X_pred = sp.csr_matrix(rng.random_sample((2, 4)))
+
+    for eigen_solver in ("auto", "arpack"):
+        for kernel in ("linear", "rbf", "poly"):
+            # transform fit data
+            kpca = KernelPCA(4, kernel=kernel, eigen_solver=eigen_solver,
+                             fit_inverse_transform=False)
+            X_fit_transformed = kpca.fit_transform(X_fit)
+            X_fit_transformed2 = kpca.fit(X_fit).transform(X_fit)
+            assert_array_almost_equal(np.abs(X_fit_transformed),
+                                      np.abs(X_fit_transformed2))
+
+            # transform new data
+            X_pred_transformed = kpca.transform(X_pred)
+            assert (X_pred_transformed.shape[1] ==
+                         X_fit_transformed.shape[1])
+
+            # inverse transform
+            # X_pred2 = kpca.inverse_transform(X_pred_transformed)
+            # assert X_pred2.shape == X_pred.shape)
+
+
+def test_kernel_pca_linear_kernel():
+    rng = np.random.RandomState(0)
+    X_fit = rng.random_sample((5, 4))
+    X_pred = rng.random_sample((2, 4))
+
+    # for a linear kernel, kernel PCA should find the same projection as PCA
+    # modulo the sign (direction)
+    # fit only the first four components: fifth is near zero eigenvalue, so
+    # can be trimmed due to roundoff error
+    assert_array_almost_equal(
+        np.abs(KernelPCA(4).fit(X_fit).transform(X_pred)),
+        np.abs(PCA(4).fit(X_fit).transform(X_pred)))
+
+
+def test_kernel_pca_n_components():
+    rng = np.random.RandomState(0)
+    X_fit = rng.random_sample((5, 4))
+    X_pred = rng.random_sample((2, 4))
+
+    for eigen_solver in ("dense", "arpack"):
+        for c in [1, 2, 4]:
+            kpca = KernelPCA(n_components=c, eigen_solver=eigen_solver)
+            shape = kpca.fit(X_fit).transform(X_pred).shape
+
+            assert shape == (2, c)
+
+
+def test_remove_zero_eig():
+    X = np.array([[1 - 1e-30, 1], [1, 1], [1, 1 - 1e-20]])
+
+    # n_components=None (default) => remove_zero_eig is True
+    kpca = KernelPCA()
+    Xt = kpca.fit_transform(X)
+    assert Xt.shape == (3, 0)
+
+    kpca = KernelPCA(n_components=2)
+    Xt = kpca.fit_transform(X)
+    assert Xt.shape == (3, 2)
+
+    kpca = KernelPCA(n_components=2, remove_zero_eig=True)
+    Xt = kpca.fit_transform(X)
+    assert Xt.shape == (3, 0)
+
+
+def test_leave_zero_eig():
+    """This test checks that fit().transform() returns the same result as
+    fit_transform() in case of non-removed zero eigenvalue.
+    Non-regression test for issue #12141 (PR #12143)"""
+    X_fit = np.array([[1, 1], [0, 0]])
+
+    # Assert that even with all np warnings on, there is no div by zero warning
+    with pytest.warns(None) as record:
+        with np.errstate(all='warn'):
+            k = KernelPCA(n_components=2, remove_zero_eig=False,
+                          eigen_solver="dense")
+            # Fit, then transform
+            A = k.fit(X_fit).transform(X_fit)
+            # Do both at once
+            B = k.fit_transform(X_fit)
+            # Compare
+            assert_array_almost_equal(np.abs(A), np.abs(B))
+
+    for w in record:
+        # There might be warnings about the kernel being badly conditioned,
+        # but there should not be warnings about division by zero.
+        # (Numpy division by zero warning can have many message variants, but
+        # at least we know that it is a RuntimeWarning so lets check only this)
+        assert not issubclass(w.category, RuntimeWarning)
+
+
+def test_kernel_pca_precomputed():
+    rng = np.random.RandomState(0)
+    X_fit = rng.random_sample((5, 4))
+    X_pred = rng.random_sample((2, 4))
+
+    for eigen_solver in ("dense", "arpack"):
+        X_kpca = KernelPCA(4, eigen_solver=eigen_solver).\
+            fit(X_fit).transform(X_pred)
+        X_kpca2 = KernelPCA(
+            4, eigen_solver=eigen_solver, kernel='precomputed').fit(
+                np.dot(X_fit, X_fit.T)).transform(np.dot(X_pred, X_fit.T))
+
+        X_kpca_train = KernelPCA(
+            4, eigen_solver=eigen_solver,
+            kernel='precomputed').fit_transform(np.dot(X_fit, X_fit.T))
+        X_kpca_train2 = KernelPCA(
+            4, eigen_solver=eigen_solver, kernel='precomputed').fit(
+                np.dot(X_fit, X_fit.T)).transform(np.dot(X_fit, X_fit.T))
+
+        assert_array_almost_equal(np.abs(X_kpca),
+                                  np.abs(X_kpca2))
+
+        assert_array_almost_equal(np.abs(X_kpca_train),
+                                  np.abs(X_kpca_train2))
+
+
+def test_kernel_pca_invalid_kernel():
+    rng = np.random.RandomState(0)
+    X_fit = rng.random_sample((2, 4))
+    kpca = KernelPCA(kernel="tototiti")
+    with pytest.raises(ValueError):
+        kpca.fit(X_fit)
+
+
+def test_gridsearch_pipeline():
+    # Test if we can do a grid-search to find parameters to separate
+    # circles with a perceptron model.
+    X, y = make_circles(n_samples=400, factor=.3, noise=.05,
+                        random_state=0)
+    kpca = KernelPCA(kernel="rbf", n_components=2)
+    pipeline = Pipeline([("kernel_pca", kpca),
+                         ("Perceptron", Perceptron(max_iter=5))])
+    param_grid = dict(kernel_pca__gamma=2. ** np.arange(-2, 2))
+    grid_search = GridSearchCV(pipeline, cv=3, param_grid=param_grid)
+    grid_search.fit(X, y)
+    assert grid_search.best_score_ == 1
+
+
+def test_gridsearch_pipeline_precomputed():
+    # Test if we can do a grid-search to find parameters to separate
+    # circles with a perceptron model using a precomputed kernel.
+    X, y = make_circles(n_samples=400, factor=.3, noise=.05,
+                        random_state=0)
+    kpca = KernelPCA(kernel="precomputed", n_components=2)
+    pipeline = Pipeline([("kernel_pca", kpca),
+                         ("Perceptron", Perceptron(max_iter=5))])
+    param_grid = dict(Perceptron__max_iter=np.arange(1, 5))
+    grid_search = GridSearchCV(pipeline, cv=3, param_grid=param_grid)
+    X_kernel = rbf_kernel(X, gamma=2.)
+    grid_search.fit(X_kernel, y)
+    assert grid_search.best_score_ == 1
+
+
+def test_nested_circles():
+    # Test the linear separability of the first 2D KPCA transform
+    X, y = make_circles(n_samples=400, factor=.3, noise=.05,
+                        random_state=0)
+
+    # 2D nested circles are not linearly separable
+    train_score = Perceptron(max_iter=5).fit(X, y).score(X, y)
+    assert train_score < 0.8
+
+    # Project the circles data into the first 2 components of a RBF Kernel
+    # PCA model.
+    # Note that the gamma value is data dependent. If this test breaks
+    # and the gamma value has to be updated, the Kernel PCA example will
+    # have to be updated too.
+    kpca = KernelPCA(kernel="rbf", n_components=2,
+                     fit_inverse_transform=True, gamma=2.)
+    X_kpca = kpca.fit_transform(X)
+
+    # The data is perfectly linearly separable in that space
+    train_score = Perceptron(max_iter=5).fit(X_kpca, y).score(X_kpca, y)
+    assert train_score == 1.0
+
+
+def test_kernel_conditioning():
+    """ Test that ``_check_psd_eigenvalues`` is correctly called
+    Non-regression test for issue #12140 (PR #12145)"""
+
+    # create a pathological X leading to small non-zero eigenvalue
+    X = [[5, 1],
+         [5+1e-8, 1e-8],
+         [5+1e-8, 0]]
+    kpca = KernelPCA(kernel="linear", n_components=2,
+                     fit_inverse_transform=True)
+    kpca.fit(X)
+
+    # check that the small non-zero eigenvalue was correctly set to zero
+    assert kpca.lambdas_.min() == 0
+    assert np.all(kpca.lambdas_ == _check_psd_eigenvalues(kpca.lambdas_))
+
+
+@pytest.mark.parametrize("kernel",
+                         ["linear", "poly", "rbf", "sigmoid", "cosine"])
+def test_kernel_pca_inverse_transform(kernel):
+    X, *_ = make_blobs(n_samples=100, n_features=4, centers=[[1, 1, 1, 1]],
+                       random_state=0)
+
+    kp = KernelPCA(n_components=2, kernel=kernel, fit_inverse_transform=True)
+    X_trans = kp.fit_transform(X)
+    X_inv = kp.inverse_transform(X_trans)
+    assert_allclose(X, X_inv)

venv/Lib/site-packages/sklearn/decomposition/tests/test_nmf.py

@@ -0,0 +1,554 @@
+import numpy as np
+import scipy.sparse as sp
+
+from scipy import linalg
+from sklearn.decomposition import NMF, non_negative_factorization
+from sklearn.decomposition import _nmf as nmf  # For testing internals
+from scipy.sparse import csc_matrix
+
+import pytest
+
+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_almost_equal
+from sklearn.utils._testing import assert_allclose
+from sklearn.utils._testing import ignore_warnings
+from sklearn.utils.extmath import squared_norm
+from sklearn.base import clone
+from sklearn.exceptions import ConvergenceWarning
+
+
+@pytest.mark.parametrize('solver', ['cd', 'mu'])
+def test_convergence_warning(solver):
+    convergence_warning = ("Maximum number of iterations 1 reached. "
+                           "Increase it to improve convergence.")
+    A = np.ones((2, 2))
+    with pytest.warns(ConvergenceWarning, match=convergence_warning):
+        NMF(solver=solver, max_iter=1).fit(A)
+
+
+def test_initialize_nn_output():
+    # Test that initialization does not return negative values
+    rng = np.random.mtrand.RandomState(42)
+    data = np.abs(rng.randn(10, 10))
+    for init in ('random', 'nndsvd', 'nndsvda', 'nndsvdar'):
+        W, H = nmf._initialize_nmf(data, 10, init=init, random_state=0)
+        assert not ((W < 0).any() or (H < 0).any())
+
+
+def test_parameter_checking():
+    A = np.ones((2, 2))
+    name = 'spam'
+    msg = "Invalid solver parameter: got 'spam' instead of one of"
+    assert_raise_message(ValueError, msg, NMF(solver=name).fit, A)
+    msg = "Invalid init parameter: got 'spam' instead of one of"
+    assert_raise_message(ValueError, msg, NMF(init=name).fit, A)
+    msg = "Invalid beta_loss parameter: got 'spam' instead of one"
+    assert_raise_message(ValueError, msg, NMF(solver='mu',
+                                              beta_loss=name).fit, A)
+    msg = "Invalid beta_loss parameter: solver 'cd' does not handle "
+    msg += "beta_loss = 1.0"
+    assert_raise_message(ValueError, msg, NMF(solver='cd',
+                                              beta_loss=1.0).fit, A)
+
+    msg = "Negative values in data passed to"
+    assert_raise_message(ValueError, msg, NMF().fit, -A)
+    assert_raise_message(ValueError, msg, nmf._initialize_nmf, -A,
+                         2, 'nndsvd')
+    clf = NMF(2, tol=0.1).fit(A)
+    assert_raise_message(ValueError, msg, clf.transform, -A)
+
+    for init in ['nndsvd', 'nndsvda', 'nndsvdar']:
+        msg = ("init = '{}' can only be used when "
+               "n_components <= min(n_samples, n_features)"
+               .format(init))
+        assert_raise_message(ValueError, msg, NMF(3, init=init).fit, A)
+        assert_raise_message(ValueError, msg, nmf._initialize_nmf, A,
+                             3, init)
+
+
+def test_initialize_close():
+    # Test NNDSVD error
+    # Test that _initialize_nmf error is less than the standard deviation of
+    # the entries in the matrix.
+    rng = np.random.mtrand.RandomState(42)
+    A = np.abs(rng.randn(10, 10))
+    W, H = nmf._initialize_nmf(A, 10, init='nndsvd')
+    error = linalg.norm(np.dot(W, H) - A)
+    sdev = linalg.norm(A - A.mean())
+    assert error <= sdev
+
+
+def test_initialize_variants():
+    # Test NNDSVD variants correctness
+    # Test that the variants 'nndsvda' and 'nndsvdar' differ from basic
+    # 'nndsvd' only where the basic version has zeros.
+    rng = np.random.mtrand.RandomState(42)
+    data = np.abs(rng.randn(10, 10))
+    W0, H0 = nmf._initialize_nmf(data, 10, init='nndsvd')
+    Wa, Ha = nmf._initialize_nmf(data, 10, init='nndsvda')
+    War, Har = nmf._initialize_nmf(data, 10, init='nndsvdar',
+                                   random_state=0)
+
+    for ref, evl in ((W0, Wa), (W0, War), (H0, Ha), (H0, Har)):
+        assert_almost_equal(evl[ref != 0], ref[ref != 0])
+
+
+# ignore UserWarning raised when both solver='mu' and init='nndsvd'
+@ignore_warnings(category=UserWarning)
+def test_nmf_fit_nn_output():
+    # Test that the decomposition does not contain negative values
+    A = np.c_[5. - np.arange(1, 6),
+              5. + np.arange(1, 6)]
+    for solver in ('cd', 'mu'):
+        for init in (None, 'nndsvd', 'nndsvda', 'nndsvdar', 'random'):
+            model = NMF(n_components=2, solver=solver, init=init,
+                        random_state=0)
+            transf = model.fit_transform(A)
+            assert not((model.components_ < 0).any() or
+                       (transf < 0).any())
+
+
+@pytest.mark.parametrize('solver', ('cd', 'mu'))
+def test_nmf_fit_close(solver):
+    rng = np.random.mtrand.RandomState(42)
+    # Test that the fit is not too far away
+    pnmf = NMF(5, solver=solver, init='nndsvdar', random_state=0,
+               max_iter=600)
+    X = np.abs(rng.randn(6, 5))
+    assert pnmf.fit(X).reconstruction_err_ < 0.1
+
+
+@pytest.mark.parametrize('solver', ('cd', 'mu'))
+def test_nmf_transform(solver):
+    # Test that NMF.transform returns close values
+    rng = np.random.mtrand.RandomState(42)
+    A = np.abs(rng.randn(6, 5))
+    m = NMF(solver=solver, n_components=3, init='random',
+            random_state=0, tol=1e-5)
+    ft = m.fit_transform(A)
+    t = m.transform(A)
+    assert_array_almost_equal(ft, t, decimal=2)
+
+
+def test_nmf_transform_custom_init():
+    # Smoke test that checks if NMF.transform works with custom initialization
+    random_state = np.random.RandomState(0)
+    A = np.abs(random_state.randn(6, 5))
+    n_components = 4
+    avg = np.sqrt(A.mean() / n_components)
+    H_init = np.abs(avg * random_state.randn(n_components, 5))
+    W_init = np.abs(avg * random_state.randn(6, n_components))
+
+    m = NMF(solver='cd', n_components=n_components, init='custom',
+            random_state=0)
+    m.fit_transform(A, W=W_init, H=H_init)
+    m.transform(A)
+
+
+@pytest.mark.parametrize('solver', ('cd', 'mu'))
+def test_nmf_inverse_transform(solver):
+    # Test that NMF.inverse_transform returns close values
+    random_state = np.random.RandomState(0)
+    A = np.abs(random_state.randn(6, 4))
+    m = NMF(solver=solver, n_components=4, init='random', random_state=0,
+            max_iter=1000)
+    ft = m.fit_transform(A)
+    A_new = m.inverse_transform(ft)
+    assert_array_almost_equal(A, A_new, decimal=2)
+
+
+def test_n_components_greater_n_features():
+    # Smoke test for the case of more components than features.
+    rng = np.random.mtrand.RandomState(42)
+    A = np.abs(rng.randn(30, 10))
+    NMF(n_components=15, random_state=0, tol=1e-2).fit(A)
+
+
+def test_nmf_sparse_input():
+    # Test that sparse matrices are accepted as input
+    from scipy.sparse import csc_matrix
+
+    rng = np.random.mtrand.RandomState(42)
+    A = np.abs(rng.randn(10, 10))
+    A[:, 2 * np.arange(5)] = 0
+    A_sparse = csc_matrix(A)
+
+    for solver in ('cd', 'mu'):
+        est1 = NMF(solver=solver, n_components=5, init='random',
+                   random_state=0, tol=1e-2)
+        est2 = clone(est1)
+
+    W1 = est1.fit_transform(A)
+    W2 = est2.fit_transform(A_sparse)
+    H1 = est1.components_
+    H2 = est2.components_
+
+    assert_array_almost_equal(W1, W2)
+    assert_array_almost_equal(H1, H2)
+
+
+def test_nmf_sparse_transform():
+    # Test that transform works on sparse data.  Issue #2124
+    rng = np.random.mtrand.RandomState(42)
+    A = np.abs(rng.randn(3, 2))
+    A[1, 1] = 0
+    A = csc_matrix(A)
+
+    for solver in ('cd', 'mu'):
+        model = NMF(solver=solver, random_state=0, n_components=2,
+                    max_iter=400)
+        A_fit_tr = model.fit_transform(A)
+        A_tr = model.transform(A)
+        assert_array_almost_equal(A_fit_tr, A_tr, decimal=1)
+
+
+def test_non_negative_factorization_consistency():
+    # Test that the function is called in the same way, either directly
+    # or through the NMF class
+    rng = np.random.mtrand.RandomState(42)
+    A = np.abs(rng.randn(10, 10))
+    A[:, 2 * np.arange(5)] = 0
+
+    for init in ['random', 'nndsvd']:
+        for solver in ('cd', 'mu'):
+            W_nmf, H, _ = non_negative_factorization(
+                A, init=init, solver=solver, random_state=1, tol=1e-2)
+            W_nmf_2, _, _ = non_negative_factorization(
+                A, H=H, update_H=False, init=init, solver=solver,
+                random_state=1, tol=1e-2)
+
+            model_class = NMF(init=init, solver=solver, random_state=1,
+                              tol=1e-2)
+            W_cls = model_class.fit_transform(A)
+            W_cls_2 = model_class.transform(A)
+
+            assert_array_almost_equal(W_nmf, W_cls, decimal=10)
+            assert_array_almost_equal(W_nmf_2, W_cls_2, decimal=10)
+
+
+def test_non_negative_factorization_checking():
+    A = np.ones((2, 2))
+    # Test parameters checking is public function
+    nnmf = non_negative_factorization
+    msg = ("Number of components must be a positive integer; "
+           "got (n_components=1.5)")
+    assert_raise_message(ValueError, msg, nnmf, A, A, A, 1.5, init='random')
+    msg = ("Number of components must be a positive integer; "
+           "got (n_components='2')")
+    assert_raise_message(ValueError, msg, nnmf, A, A, A, '2', init='random')
+    msg = "Negative values in data passed to NMF (input H)"
+    assert_raise_message(ValueError, msg, nnmf, A, A, -A, 2, init='custom')
+    msg = "Negative values in data passed to NMF (input W)"
+    assert_raise_message(ValueError, msg, nnmf, A, -A, A, 2, init='custom')
+    msg = "Array passed to NMF (input H) is full of zeros"
+    assert_raise_message(ValueError, msg, nnmf, A, A, 0 * A, 2, init='custom')
+    msg = "Invalid regularization parameter: got 'spam' instead of one of"
+    assert_raise_message(ValueError, msg, nnmf, A, A, 0 * A, 2, init='custom',
+                         regularization='spam')
+
+
+def _beta_divergence_dense(X, W, H, beta):
+    """Compute the beta-divergence of X and W.H for dense array only.
+
+    Used as a reference for testing nmf._beta_divergence.
+    """
+    WH = np.dot(W, H)
+
+    if beta == 2:
+        return squared_norm(X - WH) / 2
+
+    WH_Xnonzero = WH[X != 0]
+    X_nonzero = X[X != 0]
+    np.maximum(WH_Xnonzero, 1e-9, out=WH_Xnonzero)
+
+    if beta == 1:
+        res = np.sum(X_nonzero * np.log(X_nonzero / WH_Xnonzero))
+        res += WH.sum() - X.sum()
+
+    elif beta == 0:
+        div = X_nonzero / WH_Xnonzero
+        res = np.sum(div) - X.size - np.sum(np.log(div))
+    else:
+        res = (X_nonzero ** beta).sum()
+        res += (beta - 1) * (WH ** beta).sum()
+        res -= beta * (X_nonzero * (WH_Xnonzero ** (beta - 1))).sum()
+        res /= beta * (beta - 1)
+
+    return res
+
+
+def test_beta_divergence():
+    # Compare _beta_divergence with the reference _beta_divergence_dense
+    n_samples = 20
+    n_features = 10
+    n_components = 5
+    beta_losses = [0., 0.5, 1., 1.5, 2.]
+
+    # initialization
+    rng = np.random.mtrand.RandomState(42)
+    X = rng.randn(n_samples, n_features)
+    np.clip(X, 0, None, out=X)
+    X_csr = sp.csr_matrix(X)
+    W, H = nmf._initialize_nmf(X, n_components, init='random', random_state=42)
+
+    for beta in beta_losses:
+        ref = _beta_divergence_dense(X, W, H, beta)
+        loss = nmf._beta_divergence(X, W, H, beta)
+        loss_csr = nmf._beta_divergence(X_csr, W, H, beta)
+
+        assert_almost_equal(ref, loss, decimal=7)
+        assert_almost_equal(ref, loss_csr, decimal=7)
+
+
+def test_special_sparse_dot():
+    # Test the function that computes np.dot(W, H), only where X is non zero.
+    n_samples = 10
+    n_features = 5
+    n_components = 3
+    rng = np.random.mtrand.RandomState(42)
+    X = rng.randn(n_samples, n_features)
+    np.clip(X, 0, None, out=X)
+    X_csr = sp.csr_matrix(X)
+
+    W = np.abs(rng.randn(n_samples, n_components))
+    H = np.abs(rng.randn(n_components, n_features))
+
+    WH_safe = nmf._special_sparse_dot(W, H, X_csr)
+    WH = nmf._special_sparse_dot(W, H, X)
+
+    # test that both results have same values, in X_csr nonzero elements
+    ii, jj = X_csr.nonzero()
+    WH_safe_data = np.asarray(WH_safe[ii, jj]).ravel()
+    assert_array_almost_equal(WH_safe_data, WH[ii, jj], decimal=10)
+
+    # test that WH_safe and X_csr have the same sparse structure
+    assert_array_equal(WH_safe.indices, X_csr.indices)
+    assert_array_equal(WH_safe.indptr, X_csr.indptr)
+    assert_array_equal(WH_safe.shape, X_csr.shape)
+
+
+@ignore_warnings(category=ConvergenceWarning)
+def test_nmf_multiplicative_update_sparse():
+    # Compare sparse and dense input in multiplicative update NMF
+    # Also test continuity of the results with respect to beta_loss parameter
+    n_samples = 20
+    n_features = 10
+    n_components = 5
+    alpha = 0.1
+    l1_ratio = 0.5
+    n_iter = 20
+
+    # initialization
+    rng = np.random.mtrand.RandomState(1337)
+    X = rng.randn(n_samples, n_features)
+    X = np.abs(X)
+    X_csr = sp.csr_matrix(X)
+    W0, H0 = nmf._initialize_nmf(X, n_components, init='random',
+                                 random_state=42)
+
+    for beta_loss in (-1.2, 0, 0.2, 1., 2., 2.5):
+        # Reference with dense array X
+        W, H = W0.copy(), H0.copy()
+        W1, H1, _ = non_negative_factorization(
+            X, W, H, n_components, init='custom', update_H=True,
+            solver='mu', beta_loss=beta_loss, max_iter=n_iter, alpha=alpha,
+            l1_ratio=l1_ratio, regularization='both', random_state=42)
+
+        # Compare with sparse X
+        W, H = W0.copy(), H0.copy()
+        W2, H2, _ = non_negative_factorization(
+            X_csr, W, H, n_components, init='custom', update_H=True,
+            solver='mu', beta_loss=beta_loss, max_iter=n_iter, alpha=alpha,
+            l1_ratio=l1_ratio, regularization='both', random_state=42)
+
+        assert_array_almost_equal(W1, W2, decimal=7)
+        assert_array_almost_equal(H1, H2, decimal=7)
+
+        # Compare with almost same beta_loss, since some values have a specific
+        # behavior, but the results should be continuous w.r.t beta_loss
+        beta_loss -= 1.e-5
+        W, H = W0.copy(), H0.copy()
+        W3, H3, _ = non_negative_factorization(
+            X_csr, W, H, n_components, init='custom', update_H=True,
+            solver='mu', beta_loss=beta_loss, max_iter=n_iter, alpha=alpha,
+            l1_ratio=l1_ratio, regularization='both', random_state=42)
+
+        assert_array_almost_equal(W1, W3, decimal=4)
+        assert_array_almost_equal(H1, H3, decimal=4)
+
+
+def test_nmf_negative_beta_loss():
+    # Test that an error is raised if beta_loss < 0 and X contains zeros.
+    # Test that the output has not NaN values when the input contains zeros.
+    n_samples = 6
+    n_features = 5
+    n_components = 3
+
+    rng = np.random.mtrand.RandomState(42)
+    X = rng.randn(n_samples, n_features)
+    np.clip(X, 0, None, out=X)
+    X_csr = sp.csr_matrix(X)
+
+    def _assert_nmf_no_nan(X, beta_loss):
+        W, H, _ = non_negative_factorization(
+            X, init='random', n_components=n_components, solver='mu',
+            beta_loss=beta_loss, random_state=0, max_iter=1000)
+        assert not np.any(np.isnan(W))
+        assert not np.any(np.isnan(H))
+
+    msg = "When beta_loss <= 0 and X contains zeros, the solver may diverge."
+    for beta_loss in (-0.6, 0.):
+        assert_raise_message(ValueError, msg, _assert_nmf_no_nan, X, beta_loss)
+        _assert_nmf_no_nan(X + 1e-9, beta_loss)
+
+    for beta_loss in (0.2, 1., 1.2, 2., 2.5):
+        _assert_nmf_no_nan(X, beta_loss)
+        _assert_nmf_no_nan(X_csr, beta_loss)
+
+
+def test_nmf_regularization():
+    # Test the effect of L1 and L2 regularizations
+    n_samples = 6
+    n_features = 5
+    n_components = 3
+    rng = np.random.mtrand.RandomState(42)
+    X = np.abs(rng.randn(n_samples, n_features))
+
+    # L1 regularization should increase the number of zeros
+    l1_ratio = 1.
+    for solver in ['cd', 'mu']:
+        regul = nmf.NMF(n_components=n_components, solver=solver,
+                        alpha=0.5, l1_ratio=l1_ratio, random_state=42)
+        model = nmf.NMF(n_components=n_components, solver=solver,
+                        alpha=0., l1_ratio=l1_ratio, random_state=42)
+
+        W_regul = regul.fit_transform(X)
+        W_model = model.fit_transform(X)
+
+        H_regul = regul.components_
+        H_model = model.components_
+
+        W_regul_n_zeros = W_regul[W_regul == 0].size
+        W_model_n_zeros = W_model[W_model == 0].size
+        H_regul_n_zeros = H_regul[H_regul == 0].size
+        H_model_n_zeros = H_model[H_model == 0].size
+
+        assert W_regul_n_zeros > W_model_n_zeros
+        assert H_regul_n_zeros > H_model_n_zeros
+
+    # L2 regularization should decrease the mean of the coefficients
+    l1_ratio = 0.
+    for solver in ['cd', 'mu']:
+        regul = nmf.NMF(n_components=n_components, solver=solver,
+                        alpha=0.5, l1_ratio=l1_ratio, random_state=42)
+        model = nmf.NMF(n_components=n_components, solver=solver,
+                        alpha=0., l1_ratio=l1_ratio, random_state=42)
+
+        W_regul = regul.fit_transform(X)
+        W_model = model.fit_transform(X)
+
+        H_regul = regul.components_
+        H_model = model.components_
+
+        assert W_model.mean() > W_regul.mean()
+        assert H_model.mean() > H_regul.mean()
+
+
+@ignore_warnings(category=ConvergenceWarning)
+def test_nmf_decreasing():
+    # test that the objective function is decreasing at each iteration
+    n_samples = 20
+    n_features = 15
+    n_components = 10
+    alpha = 0.1
+    l1_ratio = 0.5
+    tol = 0.
+
+    # initialization
+    rng = np.random.mtrand.RandomState(42)
+    X = rng.randn(n_samples, n_features)
+    np.abs(X, X)
+    W0, H0 = nmf._initialize_nmf(X, n_components, init='random',
+                                 random_state=42)
+
+    for beta_loss in (-1.2, 0, 0.2, 1., 2., 2.5):
+        for solver in ('cd', 'mu'):
+            if solver != 'mu' and beta_loss != 2:
+                # not implemented
+                continue
+            W, H = W0.copy(), H0.copy()
+            previous_loss = None
+            for _ in range(30):
+                # one more iteration starting from the previous results
+                W, H, _ = non_negative_factorization(
+                    X, W, H, beta_loss=beta_loss, init='custom',
+                    n_components=n_components, max_iter=1, alpha=alpha,
+                    solver=solver, tol=tol, l1_ratio=l1_ratio, verbose=0,
+                    regularization='both', random_state=0, update_H=True)
+
+                loss = nmf._beta_divergence(X, W, H, beta_loss)
+                if previous_loss is not None:
+                    assert previous_loss > loss
+                previous_loss = loss
+
+
+def test_nmf_underflow():
+    # Regression test for an underflow issue in _beta_divergence
+    rng = np.random.RandomState(0)
+    n_samples, n_features, n_components = 10, 2, 2
+    X = np.abs(rng.randn(n_samples, n_features)) * 10
+    W = np.abs(rng.randn(n_samples, n_components)) * 10
+    H = np.abs(rng.randn(n_components, n_features))
+
+    X[0, 0] = 0
+    ref = nmf._beta_divergence(X, W, H, beta=1.0)
+    X[0, 0] = 1e-323
+    res = nmf._beta_divergence(X, W, H, beta=1.0)
+    assert_almost_equal(res, ref)
+
+
+@pytest.mark.parametrize("dtype_in, dtype_out", [
+    (np.float32, np.float32),
+    (np.float64, np.float64),
+    (np.int32, np.float64),
+    (np.int64, np.float64)])
+@pytest.mark.parametrize("solver", ["cd", "mu"])
+def test_nmf_dtype_match(dtype_in, dtype_out, solver):
+    # Check that NMF preserves dtype (float32 and float64)
+    X = np.random.RandomState(0).randn(20, 15).astype(dtype_in, copy=False)
+    np.abs(X, out=X)
+    nmf = NMF(solver=solver)
+
+    assert nmf.fit(X).transform(X).dtype == dtype_out
+    assert nmf.fit_transform(X).dtype == dtype_out
+    assert nmf.components_.dtype == dtype_out
+
+
+@pytest.mark.parametrize("solver", ["cd", "mu"])
+def test_nmf_float32_float64_consistency(solver):
+    # Check that the result of NMF is the same between float32 and float64
+    X = np.random.RandomState(0).randn(50, 7)
+    np.abs(X, out=X)
+    nmf32 = NMF(solver=solver, random_state=0)
+    W32 = nmf32.fit_transform(X.astype(np.float32))
+    nmf64 = NMF(solver=solver, random_state=0)
+    W64 = nmf64.fit_transform(X)
+
+    assert_allclose(W32, W64, rtol=1e-6, atol=1e-5)
+
+
+def test_nmf_custom_init_dtype_error():
+    # Check that an error is raise if custom H and/or W don't have the same
+    # dtype as X.
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((20, 15))
+    H = rng.random_sample((15, 15)).astype(np.float32)
+    W = rng.random_sample((20, 15))
+
+    with pytest.raises(TypeError, match="should have the same dtype as X"):
+        NMF(init='custom').fit(X, H=H, W=W)
+
+    with pytest.raises(TypeError, match="should have the same dtype as X"):
+        non_negative_factorization(X, H=H, update_H=False)

venv/Lib/site-packages/sklearn/decomposition/tests/test_online_lda.py

@@ -0,0 +1,401 @@
+import sys
+
+import numpy as np
+from scipy.linalg import block_diag
+from scipy.sparse import csr_matrix
+from scipy.special import psi
+
+import pytest
+
+from sklearn.decomposition import LatentDirichletAllocation
+from sklearn.decomposition._lda import (_dirichlet_expectation_1d,
+                                        _dirichlet_expectation_2d)
+
+from sklearn.utils._testing import assert_allclose
+from sklearn.utils._testing import assert_array_almost_equal
+from sklearn.utils._testing import assert_almost_equal
+from sklearn.utils._testing import if_safe_multiprocessing_with_blas
+
+from sklearn.exceptions import NotFittedError
+from io import StringIO
+
+
+def _build_sparse_mtx():
+    # Create 3 topics and each topic has 3 distinct words.
+    # (Each word only belongs to a single topic.)
+    n_components = 3
+    block = np.full((3, 3), n_components, dtype=np.int)
+    blocks = [block] * n_components
+    X = block_diag(*blocks)
+    X = csr_matrix(X)
+    return (n_components, X)
+
+
+def test_lda_default_prior_params():
+    # default prior parameter should be `1 / topics`
+    # and verbose params should not affect result
+    n_components, X = _build_sparse_mtx()
+    prior = 1. / n_components
+    lda_1 = LatentDirichletAllocation(n_components=n_components,
+                                      doc_topic_prior=prior,
+                                      topic_word_prior=prior, random_state=0)
+    lda_2 = LatentDirichletAllocation(n_components=n_components,
+                                      random_state=0)
+    topic_distr_1 = lda_1.fit_transform(X)
+    topic_distr_2 = lda_2.fit_transform(X)
+    assert_almost_equal(topic_distr_1, topic_distr_2)
+
+
+def test_lda_fit_batch():
+    # Test LDA batch learning_offset (`fit` method with 'batch' learning)
+    rng = np.random.RandomState(0)
+    n_components, X = _build_sparse_mtx()
+    lda = LatentDirichletAllocation(n_components=n_components,
+                                    evaluate_every=1, learning_method='batch',
+                                    random_state=rng)
+    lda.fit(X)
+
+    correct_idx_grps = [(0, 1, 2), (3, 4, 5), (6, 7, 8)]
+    for component in lda.components_:
+        # Find top 3 words in each LDA component
+        top_idx = set(component.argsort()[-3:][::-1])
+        assert tuple(sorted(top_idx)) in correct_idx_grps
+
+
+def test_lda_fit_online():
+    # Test LDA online learning (`fit` method with 'online' learning)
+    rng = np.random.RandomState(0)
+    n_components, X = _build_sparse_mtx()
+    lda = LatentDirichletAllocation(n_components=n_components,
+                                    learning_offset=10., evaluate_every=1,
+                                    learning_method='online', random_state=rng)
+    lda.fit(X)
+
+    correct_idx_grps = [(0, 1, 2), (3, 4, 5), (6, 7, 8)]
+    for component in lda.components_:
+        # Find top 3 words in each LDA component
+        top_idx = set(component.argsort()[-3:][::-1])
+        assert tuple(sorted(top_idx)) in correct_idx_grps
+
+
+def test_lda_partial_fit():
+    # Test LDA online learning (`partial_fit` method)
+    # (same as test_lda_batch)
+    rng = np.random.RandomState(0)
+    n_components, X = _build_sparse_mtx()
+    lda = LatentDirichletAllocation(n_components=n_components,
+                                    learning_offset=10., total_samples=100,
+                                    random_state=rng)
+    for i in range(3):
+        lda.partial_fit(X)
+
+    correct_idx_grps = [(0, 1, 2), (3, 4, 5), (6, 7, 8)]
+    for c in lda.components_:
+        top_idx = set(c.argsort()[-3:][::-1])
+        assert tuple(sorted(top_idx)) in correct_idx_grps
+
+
+def test_lda_dense_input():
+    # Test LDA with dense input.
+    rng = np.random.RandomState(0)
+    n_components, X = _build_sparse_mtx()
+    lda = LatentDirichletAllocation(n_components=n_components,
+                                    learning_method='batch', random_state=rng)
+    lda.fit(X.toarray())
+
+    correct_idx_grps = [(0, 1, 2), (3, 4, 5), (6, 7, 8)]
+    for component in lda.components_:
+        # Find top 3 words in each LDA component
+        top_idx = set(component.argsort()[-3:][::-1])
+        assert tuple(sorted(top_idx)) in correct_idx_grps
+
+
+def test_lda_transform():
+    # Test LDA transform.
+    # Transform result cannot be negative and should be normalized
+    rng = np.random.RandomState(0)
+    X = rng.randint(5, size=(20, 10))
+    n_components = 3
+    lda = LatentDirichletAllocation(n_components=n_components,
+                                    random_state=rng)
+    X_trans = lda.fit_transform(X)
+    assert (X_trans > 0.0).any()
+    assert_array_almost_equal(np.sum(X_trans, axis=1),
+                              np.ones(X_trans.shape[0]))
+
+
+@pytest.mark.parametrize('method', ('online', 'batch'))
+def test_lda_fit_transform(method):
+    # Test LDA fit_transform & transform
+    # fit_transform and transform result should be the same
+    rng = np.random.RandomState(0)
+    X = rng.randint(10, size=(50, 20))
+    lda = LatentDirichletAllocation(n_components=5, learning_method=method,
+                                    random_state=rng)
+    X_fit = lda.fit_transform(X)
+    X_trans = lda.transform(X)
+    assert_array_almost_equal(X_fit, X_trans, 4)
+
+
+def test_lda_partial_fit_dim_mismatch():
+    # test `n_features` mismatch in `partial_fit`
+    rng = np.random.RandomState(0)
+    n_components = rng.randint(3, 6)
+    n_col = rng.randint(6, 10)
+    X_1 = np.random.randint(4, size=(10, n_col))
+    X_2 = np.random.randint(4, size=(10, n_col + 1))
+    lda = LatentDirichletAllocation(n_components=n_components,
+                                    learning_offset=5., total_samples=20,
+                                    random_state=rng)
+    lda.partial_fit(X_1)
+    with pytest.raises(ValueError, match=r"^The provided data has"):
+        lda.partial_fit(X_2)
+
+
+def test_invalid_params():
+    # test `_check_params` method
+    X = np.ones((5, 10))
+
+    invalid_models = (
+        ('n_components', LatentDirichletAllocation(n_components=0)),
+        ('learning_method',
+         LatentDirichletAllocation(learning_method='unknown')),
+        ('total_samples', LatentDirichletAllocation(total_samples=0)),
+        ('learning_offset', LatentDirichletAllocation(learning_offset=-1)),
+    )
+    for param, model in invalid_models:
+        regex = r"^Invalid %r parameter" % param
+        with pytest.raises(ValueError, match=regex):
+            model.fit(X)
+
+
+def test_lda_negative_input():
+    # test pass dense matrix with sparse negative input.
+    X = np.full((5, 10), -1.)
+    lda = LatentDirichletAllocation()
+    regex = r"^Negative values in data passed"
+    with pytest.raises(ValueError, match=regex):
+        lda.fit(X)
+
+
+def test_lda_no_component_error():
+    # test `perplexity` before `fit`
+    rng = np.random.RandomState(0)
+    X = rng.randint(4, size=(20, 10))
+    lda = LatentDirichletAllocation()
+    regex = ("This LatentDirichletAllocation instance is not fitted yet. "
+             "Call 'fit' with appropriate arguments before using this "
+             "estimator.")
+    with pytest.raises(NotFittedError, match=regex):
+        lda.perplexity(X)
+
+
+def test_lda_transform_mismatch():
+    # test `n_features` mismatch in partial_fit and transform
+    rng = np.random.RandomState(0)
+    X = rng.randint(4, size=(20, 10))
+    X_2 = rng.randint(4, size=(10, 8))
+
+    n_components = rng.randint(3, 6)
+    lda = LatentDirichletAllocation(n_components=n_components,
+                                    random_state=rng)
+    lda.partial_fit(X)
+    with pytest.raises(ValueError, match=r"^The provided data has"):
+        lda.partial_fit(X_2)
+
+
+@if_safe_multiprocessing_with_blas
+@pytest.mark.parametrize('method', ('online', 'batch'))
+def test_lda_multi_jobs(method):
+    n_components, X = _build_sparse_mtx()
+    # Test LDA batch training with multi CPU
+    rng = np.random.RandomState(0)
+    lda = LatentDirichletAllocation(n_components=n_components, n_jobs=2,
+                                    learning_method=method,
+                                    evaluate_every=1, random_state=rng)
+    lda.fit(X)
+
+    correct_idx_grps = [(0, 1, 2), (3, 4, 5), (6, 7, 8)]
+    for c in lda.components_:
+        top_idx = set(c.argsort()[-3:][::-1])
+        assert tuple(sorted(top_idx)) in correct_idx_grps
+
+
+@if_safe_multiprocessing_with_blas
+def test_lda_partial_fit_multi_jobs():
+    # Test LDA online training with multi CPU
+    rng = np.random.RandomState(0)
+    n_components, X = _build_sparse_mtx()
+    lda = LatentDirichletAllocation(n_components=n_components, n_jobs=2,
+                                    learning_offset=5., total_samples=30,
+                                    random_state=rng)
+    for i in range(2):
+        lda.partial_fit(X)
+
+    correct_idx_grps = [(0, 1, 2), (3, 4, 5), (6, 7, 8)]
+    for c in lda.components_:
+        top_idx = set(c.argsort()[-3:][::-1])
+        assert tuple(sorted(top_idx)) in correct_idx_grps
+
+
+def test_lda_preplexity_mismatch():
+    # test dimension mismatch in `perplexity` method
+    rng = np.random.RandomState(0)
+    n_components = rng.randint(3, 6)
+    n_samples = rng.randint(6, 10)
+    X = np.random.randint(4, size=(n_samples, 10))
+    lda = LatentDirichletAllocation(n_components=n_components,
+                                    learning_offset=5., total_samples=20,
+                                    random_state=rng)
+    lda.fit(X)
+    # invalid samples
+    invalid_n_samples = rng.randint(4, size=(n_samples + 1, n_components))
+    with pytest.raises(ValueError, match=r'Number of samples'):
+        lda._perplexity_precomp_distr(X, invalid_n_samples)
+    # invalid topic number
+    invalid_n_components = rng.randint(4, size=(n_samples, n_components + 1))
+    with pytest.raises(ValueError, match=r'Number of topics'):
+        lda._perplexity_precomp_distr(X, invalid_n_components)
+
+
+@pytest.mark.parametrize('method', ('online', 'batch'))
+def test_lda_perplexity(method):
+    # Test LDA perplexity for batch training
+    # perplexity should be lower after each iteration
+    n_components, X = _build_sparse_mtx()
+    lda_1 = LatentDirichletAllocation(n_components=n_components,
+                                      max_iter=1, learning_method=method,
+                                      total_samples=100, random_state=0)
+    lda_2 = LatentDirichletAllocation(n_components=n_components,
+                                      max_iter=10, learning_method=method,
+                                      total_samples=100, random_state=0)
+    lda_1.fit(X)
+    perp_1 = lda_1.perplexity(X, sub_sampling=False)
+
+    lda_2.fit(X)
+    perp_2 = lda_2.perplexity(X, sub_sampling=False)
+    assert perp_1 >= perp_2
+
+    perp_1_subsampling = lda_1.perplexity(X, sub_sampling=True)
+    perp_2_subsampling = lda_2.perplexity(X, sub_sampling=True)
+    assert perp_1_subsampling >= perp_2_subsampling
+
+
+@pytest.mark.parametrize('method', ('online', 'batch'))
+def test_lda_score(method):
+    # Test LDA score for batch training
+    # score should be higher after each iteration
+    n_components, X = _build_sparse_mtx()
+    lda_1 = LatentDirichletAllocation(n_components=n_components,
+                                      max_iter=1, learning_method=method,
+                                      total_samples=100, random_state=0)
+    lda_2 = LatentDirichletAllocation(n_components=n_components,
+                                      max_iter=10, learning_method=method,
+                                      total_samples=100, random_state=0)
+    lda_1.fit_transform(X)
+    score_1 = lda_1.score(X)
+
+    lda_2.fit_transform(X)
+    score_2 = lda_2.score(X)
+    assert score_2 >= score_1
+
+
+def test_perplexity_input_format():
+    # Test LDA perplexity for sparse and dense input
+    # score should be the same for both dense and sparse input
+    n_components, X = _build_sparse_mtx()
+    lda = LatentDirichletAllocation(n_components=n_components, max_iter=1,
+                                    learning_method='batch',
+                                    total_samples=100, random_state=0)
+    lda.fit(X)
+    perp_1 = lda.perplexity(X)
+    perp_2 = lda.perplexity(X.toarray())
+    assert_almost_equal(perp_1, perp_2)
+
+
+def test_lda_score_perplexity():
+    # Test the relationship between LDA score and perplexity
+    n_components, X = _build_sparse_mtx()
+    lda = LatentDirichletAllocation(n_components=n_components, max_iter=10,
+                                    random_state=0)
+    lda.fit(X)
+    perplexity_1 = lda.perplexity(X, sub_sampling=False)
+
+    score = lda.score(X)
+    perplexity_2 = np.exp(-1. * (score / np.sum(X.data)))
+    assert_almost_equal(perplexity_1, perplexity_2)
+
+
+def test_lda_fit_perplexity():
+    # Test that the perplexity computed during fit is consistent with what is
+    # returned by the perplexity method
+    n_components, X = _build_sparse_mtx()
+    lda = LatentDirichletAllocation(n_components=n_components, max_iter=1,
+                                    learning_method='batch', random_state=0,
+                                    evaluate_every=1)
+    lda.fit(X)
+
+    # Perplexity computed at end of fit method
+    perplexity1 = lda.bound_
+
+    # Result of perplexity method on the train set
+    perplexity2 = lda.perplexity(X)
+
+    assert_almost_equal(perplexity1, perplexity2)
+
+
+def test_lda_empty_docs():
+    """Test LDA on empty document (all-zero rows)."""
+    Z = np.zeros((5, 4))
+    for X in [Z, csr_matrix(Z)]:
+        lda = LatentDirichletAllocation(max_iter=750).fit(X)
+        assert_almost_equal(lda.components_.sum(axis=0),
+                            np.ones(lda.components_.shape[1]))
+
+
+def test_dirichlet_expectation():
+    """Test Cython version of Dirichlet expectation calculation."""
+    x = np.logspace(-100, 10, 10000)
+    expectation = np.empty_like(x)
+    _dirichlet_expectation_1d(x, 0, expectation)
+    assert_allclose(expectation, np.exp(psi(x) - psi(np.sum(x))),
+                    atol=1e-19)
+
+    x = x.reshape(100, 100)
+    assert_allclose(_dirichlet_expectation_2d(x),
+                    psi(x) - psi(np.sum(x, axis=1)[:, np.newaxis]),
+                    rtol=1e-11, atol=3e-9)
+
+
+def check_verbosity(verbose, evaluate_every, expected_lines,
+                    expected_perplexities):
+    n_components, X = _build_sparse_mtx()
+    lda = LatentDirichletAllocation(n_components=n_components, max_iter=3,
+                                    learning_method='batch',
+                                    verbose=verbose,
+                                    evaluate_every=evaluate_every,
+                                    random_state=0)
+    out = StringIO()
+    old_out, sys.stdout = sys.stdout, out
+    try:
+        lda.fit(X)
+    finally:
+        sys.stdout = old_out
+
+    n_lines = out.getvalue().count('\n')
+    n_perplexity = out.getvalue().count('perplexity')
+    assert expected_lines == n_lines
+    assert expected_perplexities == n_perplexity
+
+
+@pytest.mark.parametrize(
+        'verbose,evaluate_every,expected_lines,expected_perplexities',
+        [(False, 1, 0, 0),
+         (False, 0, 0, 0),
+         (True, 0, 3, 0),
+         (True, 1, 3, 3),
+         (True, 2, 3, 1)])
+def test_verbosity(verbose, evaluate_every, expected_lines,
+                   expected_perplexities):
+    check_verbosity(verbose, evaluate_every, expected_lines,
+                    expected_perplexities)

venv/Lib/site-packages/sklearn/decomposition/tests/test_pca.py

@@ -0,0 +1,640 @@
+import numpy as np
+import scipy as sp
+
+import pytest
+
+from sklearn.utils._testing import assert_allclose
+
+from sklearn import datasets
+from sklearn.decomposition import PCA
+from sklearn.datasets import load_iris
+from sklearn.decomposition._pca import _assess_dimension
+from sklearn.decomposition._pca import _infer_dimension
+
+iris = datasets.load_iris()
+PCA_SOLVERS = ['full', 'arpack', 'randomized', 'auto']
+
+
+@pytest.mark.parametrize('svd_solver', PCA_SOLVERS)
+@pytest.mark.parametrize('n_components', range(1, iris.data.shape[1]))
+def test_pca(svd_solver, n_components):
+    X = iris.data
+    pca = PCA(n_components=n_components, svd_solver=svd_solver)
+
+    # check the shape of fit.transform
+    X_r = pca.fit(X).transform(X)
+    assert X_r.shape[1] == n_components
+
+    # check the equivalence of fit.transform and fit_transform
+    X_r2 = pca.fit_transform(X)
+    assert_allclose(X_r, X_r2)
+    X_r = pca.transform(X)
+    assert_allclose(X_r, X_r2)
+
+    # Test get_covariance and get_precision
+    cov = pca.get_covariance()
+    precision = pca.get_precision()
+    assert_allclose(np.dot(cov, precision), np.eye(X.shape[1]), atol=1e-12)
+
+
+def test_no_empty_slice_warning():
+    # test if we avoid numpy warnings for computing over empty arrays
+    n_components = 10
+    n_features = n_components + 2  # anything > n_comps triggered it in 0.16
+    X = np.random.uniform(-1, 1, size=(n_components, n_features))
+    pca = PCA(n_components=n_components)
+    with pytest.warns(None) as record:
+        pca.fit(X)
+    assert not record.list
+
+
+@pytest.mark.parametrize('copy', [True, False])
+@pytest.mark.parametrize('solver', PCA_SOLVERS)
+def test_whitening(solver, copy):
+    # Check that PCA output has unit-variance
+    rng = np.random.RandomState(0)
+    n_samples = 100
+    n_features = 80
+    n_components = 30
+    rank = 50
+
+    # some low rank data with correlated features
+    X = np.dot(rng.randn(n_samples, rank),
+               np.dot(np.diag(np.linspace(10.0, 1.0, rank)),
+                      rng.randn(rank, n_features)))
+    # the component-wise variance of the first 50 features is 3 times the
+    # mean component-wise variance of the remaining 30 features
+    X[:, :50] *= 3
+
+    assert X.shape == (n_samples, n_features)
+
+    # the component-wise variance is thus highly varying:
+    assert X.std(axis=0).std() > 43.8
+
+    # whiten the data while projecting to the lower dim subspace
+    X_ = X.copy()  # make sure we keep an original across iterations.
+    pca = PCA(n_components=n_components, whiten=True, copy=copy,
+              svd_solver=solver, random_state=0, iterated_power=7)
+    # test fit_transform
+    X_whitened = pca.fit_transform(X_.copy())
+    assert X_whitened.shape == (n_samples, n_components)
+    X_whitened2 = pca.transform(X_)
+    assert_allclose(X_whitened, X_whitened2, rtol=5e-4)
+
+    assert_allclose(X_whitened.std(ddof=1, axis=0), np.ones(n_components))
+    assert_allclose(
+        X_whitened.mean(axis=0), np.zeros(n_components), atol=1e-12
+    )
+
+    X_ = X.copy()
+    pca = PCA(n_components=n_components, whiten=False, copy=copy,
+              svd_solver=solver).fit(X_)
+    X_unwhitened = pca.transform(X_)
+    assert X_unwhitened.shape == (n_samples, n_components)
+
+    # in that case the output components still have varying variances
+    assert X_unwhitened.std(axis=0).std() == pytest.approx(74.1, rel=1e-1)
+    # we always center, so no test for non-centering.
+
+
+@pytest.mark.parametrize('svd_solver', ['arpack', 'randomized'])
+def test_pca_explained_variance_equivalence_solver(svd_solver):
+    rng = np.random.RandomState(0)
+    n_samples, n_features = 100, 80
+    X = rng.randn(n_samples, n_features)
+
+    pca_full = PCA(n_components=2, svd_solver='full')
+    pca_other = PCA(n_components=2, svd_solver=svd_solver, random_state=0)
+
+    pca_full.fit(X)
+    pca_other.fit(X)
+
+    assert_allclose(
+        pca_full.explained_variance_,
+        pca_other.explained_variance_,
+        rtol=5e-2
+    )
+    assert_allclose(
+        pca_full.explained_variance_ratio_,
+        pca_other.explained_variance_ratio_,
+        rtol=5e-2
+    )
+
+
+@pytest.mark.parametrize(
+    'X',
+    [np.random.RandomState(0).randn(100, 80),
+     datasets.make_classification(100, 80, n_informative=78,
+                                  random_state=0)[0]],
+    ids=['random-data', 'correlated-data']
+)
+@pytest.mark.parametrize('svd_solver', PCA_SOLVERS)
+def test_pca_explained_variance_empirical(X, svd_solver):
+    pca = PCA(n_components=2, svd_solver=svd_solver, random_state=0)
+    X_pca = pca.fit_transform(X)
+    assert_allclose(pca.explained_variance_, np.var(X_pca, ddof=1, axis=0))
+
+    expected_result = np.linalg.eig(np.cov(X, rowvar=False))[0]
+    expected_result = sorted(expected_result, reverse=True)[:2]
+    assert_allclose(pca.explained_variance_, expected_result, rtol=5e-3)
+
+
+@pytest.mark.parametrize("svd_solver", ['arpack', 'randomized'])
+def test_pca_singular_values_consistency(svd_solver):
+    rng = np.random.RandomState(0)
+    n_samples, n_features = 100, 80
+    X = rng.randn(n_samples, n_features)
+
+    pca_full = PCA(n_components=2, svd_solver='full', random_state=rng)
+    pca_other = PCA(n_components=2, svd_solver=svd_solver, random_state=rng)
+
+    pca_full.fit(X)
+    pca_other.fit(X)
+
+    assert_allclose(
+        pca_full.singular_values_, pca_other.singular_values_, rtol=5e-3
+    )
+
+
+@pytest.mark.parametrize("svd_solver", PCA_SOLVERS)
+def test_pca_singular_values(svd_solver):
+    rng = np.random.RandomState(0)
+    n_samples, n_features = 100, 80
+    X = rng.randn(n_samples, n_features)
+
+    pca = PCA(n_components=2, svd_solver=svd_solver, random_state=rng)
+    X_trans = pca.fit_transform(X)
+
+    # compare to the Frobenius norm
+    assert_allclose(
+        np.sum(pca.singular_values_ ** 2), np.linalg.norm(X_trans, "fro") ** 2
+    )
+    # Compare to the 2-norms of the score vectors
+    assert_allclose(
+        pca.singular_values_, np.sqrt(np.sum(X_trans ** 2, axis=0))
+    )
+
+    # set the singular values and see what er get back
+    n_samples, n_features = 100, 110
+    X = rng.randn(n_samples, n_features)
+
+    pca = PCA(n_components=3, svd_solver=svd_solver, random_state=rng)
+    X_trans = pca.fit_transform(X)
+    X_trans /= np.sqrt(np.sum(X_trans ** 2, axis=0))
+    X_trans[:, 0] *= 3.142
+    X_trans[:, 1] *= 2.718
+    X_hat = np.dot(X_trans, pca.components_)
+    pca.fit(X_hat)
+    assert_allclose(pca.singular_values_, [3.142, 2.718, 1.0])
+
+
+@pytest.mark.parametrize("svd_solver", PCA_SOLVERS)
+def test_pca_check_projection(svd_solver):
+    # Test that the projection of data is correct
+    rng = np.random.RandomState(0)
+    n, p = 100, 3
+    X = rng.randn(n, p) * .1
+    X[:10] += np.array([3, 4, 5])
+    Xt = 0.1 * rng.randn(1, p) + np.array([3, 4, 5])
+
+    Yt = PCA(n_components=2, svd_solver=svd_solver).fit(X).transform(Xt)
+    Yt /= np.sqrt((Yt ** 2).sum())
+
+    assert_allclose(np.abs(Yt[0][0]), 1., rtol=5e-3)
+
+
+@pytest.mark.parametrize("svd_solver", PCA_SOLVERS)
+def test_pca_check_projection_list(svd_solver):
+    # Test that the projection of data is correct
+    X = [[1.0, 0.0], [0.0, 1.0]]
+    pca = PCA(n_components=1, svd_solver=svd_solver, random_state=0)
+    X_trans = pca.fit_transform(X)
+    assert X_trans.shape, (2, 1)
+    assert_allclose(X_trans.mean(), 0.00, atol=1e-12)
+    assert_allclose(X_trans.std(), 0.71, rtol=5e-3)
+
+
+@pytest.mark.parametrize("svd_solver", ['full', 'arpack', 'randomized'])
+@pytest.mark.parametrize("whiten", [False, True])
+def test_pca_inverse(svd_solver, whiten):
+    # Test that the projection of data can be inverted
+    rng = np.random.RandomState(0)
+    n, p = 50, 3
+    X = rng.randn(n, p)  # spherical data
+    X[:, 1] *= .00001  # make middle component relatively small
+    X += [5, 4, 3]  # make a large mean
+
+    # same check that we can find the original data from the transformed
+    # signal (since the data is almost of rank n_components)
+    pca = PCA(n_components=2, svd_solver=svd_solver, whiten=whiten).fit(X)
+    Y = pca.transform(X)
+    Y_inverse = pca.inverse_transform(Y)
+    assert_allclose(X, Y_inverse, rtol=5e-6)
+
+
+@pytest.mark.parametrize(
+    'data',
+    [np.array([[0, 1, 0], [1, 0, 0]]), np.array([[0, 1, 0], [1, 0, 0]]).T]
+)
+@pytest.mark.parametrize(
+    "svd_solver, n_components, err_msg",
+    [('arpack', 0, r'must be between 1 and min\(n_samples, n_features\)'),
+     ('randomized', 0, r'must be between 1 and min\(n_samples, n_features\)'),
+     ('arpack', 2, r'must be strictly less than min'),
+     ('auto', -1, (r"n_components={}L? must be between {}L? and "
+                   r"min\(n_samples, n_features\)={}L? with "
+                   r"svd_solver=\'{}\'")),
+     ('auto', 3, (r"n_components={}L? must be between {}L? and "
+                  r"min\(n_samples, n_features\)={}L? with "
+                  r"svd_solver=\'{}\'")),
+     ('auto', 1.0, "must be of type int")]
+)
+def test_pca_validation(svd_solver, data, n_components, err_msg):
+    # Ensures that solver-specific extreme inputs for the n_components
+    # parameter raise errors
+    smallest_d = 2  # The smallest dimension
+    lower_limit = {'randomized': 1, 'arpack': 1, 'full': 0, 'auto': 0}
+    pca_fitted = PCA(n_components, svd_solver=svd_solver)
+
+    solver_reported = 'full' if svd_solver == 'auto' else svd_solver
+    err_msg = err_msg.format(
+        n_components, lower_limit[svd_solver], smallest_d, solver_reported
+    )
+    with pytest.raises(ValueError, match=err_msg):
+        pca_fitted.fit(data)
+
+    # Additional case for arpack
+    if svd_solver == 'arpack':
+        n_components = smallest_d
+
+        err_msg = ("n_components={}L? must be strictly less than "
+                   r"min\(n_samples, n_features\)={}L? with "
+                   "svd_solver=\'arpack\'".format(n_components, smallest_d))
+        with pytest.raises(ValueError, match=err_msg):
+            PCA(n_components, svd_solver=svd_solver).fit(data)
+
+
+@pytest.mark.parametrize(
+    'solver, n_components_',
+    [('full', min(iris.data.shape)),
+     ('arpack', min(iris.data.shape) - 1),
+     ('randomized', min(iris.data.shape))]
+)
+@pytest.mark.parametrize("data", [iris.data, iris.data.T])
+def test_n_components_none(data, solver, n_components_):
+    pca = PCA(svd_solver=solver)
+    pca.fit(data)
+    assert pca.n_components_ == n_components_
+
+
+@pytest.mark.parametrize("svd_solver", ['auto', 'full'])
+def test_n_components_mle(svd_solver):
+    # Ensure that n_components == 'mle' doesn't raise error for auto/full
+    rng = np.random.RandomState(0)
+    n_samples, n_features = 600, 10
+    X = rng.randn(n_samples, n_features)
+    pca = PCA(n_components='mle', svd_solver=svd_solver)
+    pca.fit(X)
+    assert pca.n_components_ == 1
+
+
+@pytest.mark.parametrize("svd_solver", ["arpack", "randomized"])
+def test_n_components_mle_error(svd_solver):
+    # Ensure that n_components == 'mle' will raise an error for unsupported
+    # solvers
+    rng = np.random.RandomState(0)
+    n_samples, n_features = 600, 10
+    X = rng.randn(n_samples, n_features)
+    pca = PCA(n_components='mle', svd_solver=svd_solver)
+    err_msg = ("n_components='mle' cannot be a string with svd_solver='{}'"
+               .format(svd_solver))
+    with pytest.raises(ValueError, match=err_msg):
+        pca.fit(X)
+
+
+def test_pca_dim():
+    # Check automated dimensionality setting
+    rng = np.random.RandomState(0)
+    n, p = 100, 5
+    X = rng.randn(n, p) * .1
+    X[:10] += np.array([3, 4, 5, 1, 2])
+    pca = PCA(n_components='mle', svd_solver='full').fit(X)
+    assert pca.n_components == 'mle'
+    assert pca.n_components_ == 1
+
+
+def test_infer_dim_1():
+    # TODO: explain what this is testing
+    # Or at least use explicit variable names...
+    n, p = 1000, 5
+    rng = np.random.RandomState(0)
+    X = (rng.randn(n, p) * .1 + rng.randn(n, 1) * np.array([3, 4, 5, 1, 2]) +
+         np.array([1, 0, 7, 4, 6]))
+    pca = PCA(n_components=p, svd_solver='full')
+    pca.fit(X)
+    spect = pca.explained_variance_
+    ll = np.array([_assess_dimension(spect, k, n) for k in range(1, p)])
+    assert ll[1] > ll.max() - .01 * n
+
+
+def test_infer_dim_2():
+    # TODO: explain what this is testing
+    # Or at least use explicit variable names...
+    n, p = 1000, 5
+    rng = np.random.RandomState(0)
+    X = rng.randn(n, p) * .1
+    X[:10] += np.array([3, 4, 5, 1, 2])
+    X[10:20] += np.array([6, 0, 7, 2, -1])
+    pca = PCA(n_components=p, svd_solver='full')
+    pca.fit(X)
+    spect = pca.explained_variance_
+    assert _infer_dimension(spect, n) > 1
+
+
+def test_infer_dim_3():
+    n, p = 100, 5
+    rng = np.random.RandomState(0)
+    X = rng.randn(n, p) * .1
+    X[:10] += np.array([3, 4, 5, 1, 2])
+    X[10:20] += np.array([6, 0, 7, 2, -1])
+    X[30:40] += 2 * np.array([-1, 1, -1, 1, -1])
+    pca = PCA(n_components=p, svd_solver='full')
+    pca.fit(X)
+    spect = pca.explained_variance_
+    assert _infer_dimension(spect, n) > 2
+
+
+@pytest.mark.parametrize(
+    "X, n_components, n_components_validated",
+    [(iris.data, 0.95, 2),  # row > col
+     (iris.data, 0.01, 1),  # row > col
+     (np.random.RandomState(0).rand(5, 20), 0.5, 2)]  # row < col
+)
+def test_infer_dim_by_explained_variance(X, n_components,
+                                         n_components_validated):
+    pca = PCA(n_components=n_components, svd_solver='full')
+    pca.fit(X)
+    assert pca.n_components == pytest.approx(n_components)
+    assert pca.n_components_ == n_components_validated
+
+
+@pytest.mark.parametrize("svd_solver", PCA_SOLVERS)
+def test_pca_score(svd_solver):
+    # Test that probabilistic PCA scoring yields a reasonable score
+    n, p = 1000, 3
+    rng = np.random.RandomState(0)
+    X = rng.randn(n, p) * .1 + np.array([3, 4, 5])
+    pca = PCA(n_components=2, svd_solver=svd_solver)
+    pca.fit(X)
+
+    ll1 = pca.score(X)
+    h = -0.5 * np.log(2 * np.pi * np.exp(1) * 0.1 ** 2) * p
+    assert_allclose(ll1 / h, 1, rtol=5e-2)
+
+    ll2 = pca.score(rng.randn(n, p) * .2 + np.array([3, 4, 5]))
+    assert ll1 > ll2
+
+    pca = PCA(n_components=2, whiten=True, svd_solver=svd_solver)
+    pca.fit(X)
+    ll2 = pca.score(X)
+    assert ll1 > ll2
+
+
+def test_pca_score3():
+    # Check that probabilistic PCA selects the right model
+    n, p = 200, 3
+    rng = np.random.RandomState(0)
+    Xl = (rng.randn(n, p) + rng.randn(n, 1) * np.array([3, 4, 5]) +
+          np.array([1, 0, 7]))
+    Xt = (rng.randn(n, p) + rng.randn(n, 1) * np.array([3, 4, 5]) +
+          np.array([1, 0, 7]))
+    ll = np.zeros(p)
+    for k in range(p):
+        pca = PCA(n_components=k, svd_solver='full')
+        pca.fit(Xl)
+        ll[k] = pca.score(Xt)
+
+    assert ll.argmax() == 1
+
+
+@pytest.mark.parametrize("svd_solver", PCA_SOLVERS)
+def test_pca_sanity_noise_variance(svd_solver):
+    # Sanity check for the noise_variance_. For more details see
+    # https://github.com/scikit-learn/scikit-learn/issues/7568
+    # https://github.com/scikit-learn/scikit-learn/issues/8541
+    # https://github.com/scikit-learn/scikit-learn/issues/8544
+    X, _ = datasets.load_digits(return_X_y=True)
+    pca = PCA(n_components=30, svd_solver=svd_solver, random_state=0)
+    pca.fit(X)
+    assert np.all((pca.explained_variance_ - pca.noise_variance_) >= 0)
+
+
+@pytest.mark.parametrize("svd_solver", ["arpack", "randomized"])
+def test_pca_score_consistency_solvers(svd_solver):
+    # Check the consistency of score between solvers
+    X, _ = datasets.load_digits(return_X_y=True)
+    pca_full = PCA(n_components=30, svd_solver='full', random_state=0)
+    pca_other = PCA(n_components=30, svd_solver=svd_solver, random_state=0)
+    pca_full.fit(X)
+    pca_other.fit(X)
+    assert_allclose(pca_full.score(X), pca_other.score(X), rtol=5e-6)
+
+
+# arpack raises ValueError for n_components == min(n_samples,  n_features)
+@pytest.mark.parametrize("svd_solver", ["full", "randomized"])
+def test_pca_zero_noise_variance_edge_cases(svd_solver):
+    # ensure that noise_variance_ is 0 in edge cases
+    # when n_components == min(n_samples, n_features)
+    n, p = 100, 3
+    rng = np.random.RandomState(0)
+    X = rng.randn(n, p) * .1 + np.array([3, 4, 5])
+
+    pca = PCA(n_components=p, svd_solver=svd_solver)
+    pca.fit(X)
+    assert pca.noise_variance_ == 0
+
+    pca.fit(X.T)
+    assert pca.noise_variance_ == 0
+
+
+@pytest.mark.parametrize(
+    'data, n_components, expected_solver',
+    [   # case: n_components in (0,1) => 'full'
+        (np.random.RandomState(0).uniform(size=(1000, 50)), 0.5, 'full'),
+        # case: max(X.shape) <= 500 => 'full'
+        (np.random.RandomState(0).uniform(size=(10, 50)), 5, 'full'),
+        # case: n_components >= .8 * min(X.shape) => 'full'
+        (np.random.RandomState(0).uniform(size=(1000, 50)), 50, 'full'),
+        # n_components >= 1 and n_components < .8*min(X.shape) => 'randomized'
+        (np.random.RandomState(0).uniform(size=(1000, 50)), 10, 'randomized')
+    ]
+)
+def test_pca_svd_solver_auto(data, n_components, expected_solver):
+    pca_auto = PCA(n_components=n_components, random_state=0)
+    pca_test = PCA(
+        n_components=n_components, svd_solver=expected_solver, random_state=0
+    )
+    pca_auto.fit(data)
+    pca_test.fit(data)
+    assert_allclose(pca_auto.components_, pca_test.components_)
+
+
+@pytest.mark.parametrize('svd_solver', PCA_SOLVERS)
+def test_pca_sparse_input(svd_solver):
+    X = np.random.RandomState(0).rand(5, 4)
+    X = sp.sparse.csr_matrix(X)
+    assert sp.sparse.issparse(X)
+
+    pca = PCA(n_components=3, svd_solver=svd_solver)
+    with pytest.raises(TypeError):
+        pca.fit(X)
+
+
+def test_pca_bad_solver():
+    X = np.random.RandomState(0).rand(5, 4)
+    pca = PCA(n_components=3, svd_solver='bad_argument')
+    with pytest.raises(ValueError):
+        pca.fit(X)
+
+
+@pytest.mark.parametrize("svd_solver", PCA_SOLVERS)
+def test_pca_deterministic_output(svd_solver):
+    rng = np.random.RandomState(0)
+    X = rng.rand(10, 10)
+
+    transformed_X = np.zeros((20, 2))
+    for i in range(20):
+        pca = PCA(n_components=2, svd_solver=svd_solver, random_state=rng)
+        transformed_X[i, :] = pca.fit_transform(X)[0]
+    assert_allclose(
+        transformed_X, np.tile(transformed_X[0, :], 20).reshape(20, 2)
+    )
+
+
+@pytest.mark.parametrize('svd_solver', PCA_SOLVERS)
+def test_pca_dtype_preservation(svd_solver):
+    check_pca_float_dtype_preservation(svd_solver)
+    check_pca_int_dtype_upcast_to_double(svd_solver)
+
+
+def check_pca_float_dtype_preservation(svd_solver):
+    # Ensure that PCA does not upscale the dtype when input is float32
+    X_64 = np.random.RandomState(0).rand(1000, 4).astype(np.float64,
+                                                         copy=False)
+    X_32 = X_64.astype(np.float32)
+
+    pca_64 = PCA(n_components=3, svd_solver=svd_solver,
+                 random_state=0).fit(X_64)
+    pca_32 = PCA(n_components=3, svd_solver=svd_solver,
+                 random_state=0).fit(X_32)
+
+    assert pca_64.components_.dtype == np.float64
+    assert pca_32.components_.dtype == np.float32
+    assert pca_64.transform(X_64).dtype == np.float64
+    assert pca_32.transform(X_32).dtype == np.float32
+
+    # the rtol is set such that the test passes on all platforms tested on
+    # conda-forge: PR#15775
+    # see: https://github.com/conda-forge/scikit-learn-feedstock/pull/113
+    assert_allclose(pca_64.components_, pca_32.components_, rtol=2e-4)
+
+
+def check_pca_int_dtype_upcast_to_double(svd_solver):
+    # Ensure that all int types will be upcast to float64
+    X_i64 = np.random.RandomState(0).randint(0, 1000, (1000, 4))
+    X_i64 = X_i64.astype(np.int64, copy=False)
+    X_i32 = X_i64.astype(np.int32, copy=False)
+
+    pca_64 = PCA(n_components=3, svd_solver=svd_solver,
+                 random_state=0).fit(X_i64)
+    pca_32 = PCA(n_components=3, svd_solver=svd_solver,
+                 random_state=0).fit(X_i32)
+
+    assert pca_64.components_.dtype == np.float64
+    assert pca_32.components_.dtype == np.float64
+    assert pca_64.transform(X_i64).dtype == np.float64
+    assert pca_32.transform(X_i32).dtype == np.float64
+
+    assert_allclose(pca_64.components_, pca_32.components_, rtol=1e-4)
+
+
+def test_pca_n_components_mostly_explained_variance_ratio():
+    # when n_components is the second highest cumulative sum of the
+    # explained_variance_ratio_, then n_components_ should equal the
+    # number of features in the dataset #15669
+    X, y = load_iris(return_X_y=True)
+    pca1 = PCA().fit(X, y)
+
+    n_components = pca1.explained_variance_ratio_.cumsum()[-2]
+    pca2 = PCA(n_components=n_components).fit(X, y)
+    assert pca2.n_components_ == X.shape[1]
+
+
+def test_assess_dimension_bad_rank():
+    # Test error when tested rank not in [1, n_features - 1]
+    spectrum = np.array([1, 1e-30, 1e-30, 1e-30])
+    n_samples = 10
+    for rank in (0, 5):
+        with pytest.raises(ValueError,
+                           match=r"should be in \[1, n_features - 1\]"):
+            _assess_dimension(spectrum, rank, n_samples)
+
+
+def test_small_eigenvalues_mle():
+    # Test rank associated with tiny eigenvalues are given a log-likelihood of
+    # -inf. The inferred rank will be 1
+    spectrum = np.array([1, 1e-30, 1e-30, 1e-30])
+
+    assert _assess_dimension(spectrum, rank=1, n_samples=10) > -np.inf
+
+    for rank in (2, 3):
+        assert _assess_dimension(spectrum, rank, 10) == -np.inf
+
+    assert _infer_dimension(spectrum, 10) == 1
+
+
+def test_mle_redundant_data():
+    # Test 'mle' with pathological X: only one relevant feature should give a
+    # rank of 1
+    X, _ = datasets.make_classification(n_features=20,
+                                        n_informative=1, n_repeated=18,
+                                        n_redundant=1, n_clusters_per_class=1,
+                                        random_state=42)
+    pca = PCA(n_components='mle').fit(X)
+    assert pca.n_components_ == 1
+
+
+def test_fit_mle_too_few_samples():
+    # Tests that an error is raised when the number of samples is smaller
+    # than the number of features during an mle fit
+    X, _ = datasets.make_classification(n_samples=20, n_features=21,
+                                        random_state=42)
+
+    pca = PCA(n_components='mle', svd_solver='full')
+    with pytest.raises(ValueError, match="n_components='mle' is only "
+                                         "supported if "
+                                         "n_samples >= n_features"):
+        pca.fit(X)
+
+
+def test_mle_simple_case():
+    # non-regression test for issue
+    # https://github.com/scikit-learn/scikit-learn/issues/16730
+    n_samples, n_dim = 1000, 10
+    X = np.random.RandomState(0).randn(n_samples, n_dim)
+    X[:, -1] = np.mean(X[:, :-1], axis=-1)  # true X dim is ndim - 1
+    pca_skl = PCA('mle', svd_solver='full')
+    pca_skl.fit(X)
+    assert pca_skl.n_components_ == n_dim - 1
+
+
+def test_assess_dimesion_rank_one():
+    # Make sure assess_dimension works properly on a matrix of rank 1
+    n_samples, n_features = 9, 6
+    X = np.ones((n_samples, n_features))  # rank 1 matrix
+    _, s, _ = np.linalg.svd(X, full_matrices=True)
+    assert sum(s[1:]) == 0  # except for rank 1, all eigenvalues are 0
+
+    assert np.isfinite(_assess_dimension(s, rank=1, n_samples=n_samples))
+    for rank in range(2, n_features):
+        assert _assess_dimension(s, rank, n_samples) == -np.inf

venv/Lib/site-packages/sklearn/decomposition/tests/test_sparse_pca.py

@@ -0,0 +1,224 @@
+# Author: Vlad Niculae
+# License: BSD 3 clause
+
+import sys
+import pytest
+
+import numpy as np
+
+from sklearn.utils._testing import assert_array_almost_equal
+from sklearn.utils._testing import assert_allclose
+from sklearn.utils._testing import if_safe_multiprocessing_with_blas
+
+from sklearn.decomposition import SparsePCA, MiniBatchSparsePCA, PCA
+from sklearn.utils import check_random_state
+
+def generate_toy_data(n_components, n_samples, image_size, random_state=None):
+    n_features = image_size[0] * image_size[1]
+
+    rng = check_random_state(random_state)
+    U = rng.randn(n_samples, n_components)
+    V = rng.randn(n_components, n_features)
+
+    centers = [(3, 3), (6, 7), (8, 1)]
+    sz = [1, 2, 1]
+    for k in range(n_components):
+        img = np.zeros(image_size)
+        xmin, xmax = centers[k][0] - sz[k], centers[k][0] + sz[k]
+        ymin, ymax = centers[k][1] - sz[k], centers[k][1] + sz[k]
+        img[xmin:xmax][:, ymin:ymax] = 1.0
+        V[k, :] = img.ravel()
+
+    # Y is defined by : Y = UV + noise
+    Y = np.dot(U, V)
+    Y += 0.1 * rng.randn(Y.shape[0], Y.shape[1])  # Add noise
+    return Y, U, V
+
+# SparsePCA can be a bit slow. To avoid having test times go up, we
+# test different aspects of the code in the same test
+
+
+def test_correct_shapes():
+    rng = np.random.RandomState(0)
+    X = rng.randn(12, 10)
+    spca = SparsePCA(n_components=8, random_state=rng)
+    U = spca.fit_transform(X)
+    assert spca.components_.shape == (8, 10)
+    assert U.shape == (12, 8)
+    # test overcomplete decomposition
+    spca = SparsePCA(n_components=13, random_state=rng)
+    U = spca.fit_transform(X)
+    assert spca.components_.shape == (13, 10)
+    assert U.shape == (12, 13)
+
+
+def test_fit_transform():
+    alpha = 1
+    rng = np.random.RandomState(0)
+    Y, _, _ = generate_toy_data(3, 10, (8, 8), random_state=rng)  # wide array
+    spca_lars = SparsePCA(n_components=3, method='lars', alpha=alpha,
+                          random_state=0)
+    spca_lars.fit(Y)
+
+    # Test that CD gives similar results
+    spca_lasso = SparsePCA(n_components=3, method='cd', random_state=0,
+                           alpha=alpha)
+    spca_lasso.fit(Y)
+    assert_array_almost_equal(spca_lasso.components_, spca_lars.components_)
+
+
+@if_safe_multiprocessing_with_blas
+def test_fit_transform_parallel():
+    alpha = 1
+    rng = np.random.RandomState(0)
+    Y, _, _ = generate_toy_data(3, 10, (8, 8), random_state=rng)  # wide array
+    spca_lars = SparsePCA(n_components=3, method='lars', alpha=alpha,
+                          random_state=0)
+    spca_lars.fit(Y)
+    U1 = spca_lars.transform(Y)
+    # Test multiple CPUs
+    spca = SparsePCA(n_components=3, n_jobs=2, method='lars', alpha=alpha,
+                     random_state=0).fit(Y)
+    U2 = spca.transform(Y)
+    assert not np.all(spca_lars.components_ == 0)
+    assert_array_almost_equal(U1, U2)
+
+
+def test_transform_nan():
+    # Test that SparsePCA won't return NaN when there is 0 feature in all
+    # samples.
+    rng = np.random.RandomState(0)
+    Y, _, _ = generate_toy_data(3, 10, (8, 8), random_state=rng)  # wide array
+    Y[:, 0] = 0
+    estimator = SparsePCA(n_components=8)
+    assert not np.any(np.isnan(estimator.fit_transform(Y)))
+
+
+def test_fit_transform_tall():
+    rng = np.random.RandomState(0)
+    Y, _, _ = generate_toy_data(3, 65, (8, 8), random_state=rng)  # tall array
+    spca_lars = SparsePCA(n_components=3, method='lars', random_state=rng)
+    U1 = spca_lars.fit_transform(Y)
+    spca_lasso = SparsePCA(n_components=3, method='cd', random_state=rng)
+    U2 = spca_lasso.fit(Y).transform(Y)
+    assert_array_almost_equal(U1, U2)
+
+
+def test_initialization():
+    rng = np.random.RandomState(0)
+    U_init = rng.randn(5, 3)
+    V_init = rng.randn(3, 4)
+    model = SparsePCA(n_components=3, U_init=U_init, V_init=V_init, max_iter=0,
+                      random_state=rng)
+    model.fit(rng.randn(5, 4))
+    assert_allclose(model.components_,
+                    V_init / np.linalg.norm(V_init, axis=1)[:, None])
+
+
+def test_mini_batch_correct_shapes():
+    rng = np.random.RandomState(0)
+    X = rng.randn(12, 10)
+    pca = MiniBatchSparsePCA(n_components=8, random_state=rng)
+    U = pca.fit_transform(X)
+    assert pca.components_.shape == (8, 10)
+    assert U.shape == (12, 8)
+    # test overcomplete decomposition
+    pca = MiniBatchSparsePCA(n_components=13, random_state=rng)
+    U = pca.fit_transform(X)
+    assert pca.components_.shape == (13, 10)
+    assert U.shape == (12, 13)
+
+
+# XXX: test always skipped
+@pytest.mark.skipif(True, reason="skipping mini_batch_fit_transform.")
+def test_mini_batch_fit_transform():
+    alpha = 1
+    rng = np.random.RandomState(0)
+    Y, _, _ = generate_toy_data(3, 10, (8, 8), random_state=rng)  # wide array
+    spca_lars = MiniBatchSparsePCA(n_components=3, random_state=0,
+                                   alpha=alpha).fit(Y)
+    U1 = spca_lars.transform(Y)
+    # Test multiple CPUs
+    if sys.platform == 'win32':  # fake parallelism for win32
+        import joblib
+        _mp = joblib.parallel.multiprocessing
+        joblib.parallel.multiprocessing = None
+        try:
+            spca = MiniBatchSparsePCA(n_components=3, n_jobs=2, alpha=alpha,
+                                      random_state=0)
+            U2 = spca.fit(Y).transform(Y)
+        finally:
+            joblib.parallel.multiprocessing = _mp
+    else:  # we can efficiently use parallelism
+        spca = MiniBatchSparsePCA(n_components=3, n_jobs=2, alpha=alpha,
+                                  random_state=0)
+        U2 = spca.fit(Y).transform(Y)
+    assert not np.all(spca_lars.components_ == 0)
+    assert_array_almost_equal(U1, U2)
+    # Test that CD gives similar results
+    spca_lasso = MiniBatchSparsePCA(n_components=3, method='cd', alpha=alpha,
+                                    random_state=0).fit(Y)
+    assert_array_almost_equal(spca_lasso.components_, spca_lars.components_)
+
+
+def test_scaling_fit_transform():
+    alpha = 1
+    rng = np.random.RandomState(0)
+    Y, _, _ = generate_toy_data(3, 1000, (8, 8), random_state=rng)
+    spca_lars = SparsePCA(n_components=3, method='lars', alpha=alpha,
+                          random_state=rng)
+    results_train = spca_lars.fit_transform(Y)
+    results_test = spca_lars.transform(Y[:10])
+    assert_allclose(results_train[0], results_test[0])
+
+
+def test_pca_vs_spca():
+    rng = np.random.RandomState(0)
+    Y, _, _ = generate_toy_data(3, 1000, (8, 8), random_state=rng)
+    Z, _, _ = generate_toy_data(3, 10, (8, 8), random_state=rng)
+    spca = SparsePCA(alpha=0, ridge_alpha=0, n_components=2)
+    pca = PCA(n_components=2)
+    pca.fit(Y)
+    spca.fit(Y)
+    results_test_pca = pca.transform(Z)
+    results_test_spca = spca.transform(Z)
+    assert_allclose(np.abs(spca.components_.dot(pca.components_.T)),
+                    np.eye(2), atol=1e-5)
+    results_test_pca *= np.sign(results_test_pca[0, :])
+    results_test_spca *= np.sign(results_test_spca[0, :])
+    assert_allclose(results_test_pca, results_test_spca)
+
+
+@pytest.mark.parametrize("spca", [SparsePCA, MiniBatchSparsePCA])
+def test_spca_deprecation_warning(spca):
+    rng = np.random.RandomState(0)
+    Y, _, _ = generate_toy_data(3, 10, (8, 8), random_state=rng)
+
+    warn_msg = "'normalize_components' has been deprecated in 0.22"
+    with pytest.warns(FutureWarning, match=warn_msg):
+        spca(normalize_components=True).fit(Y)
+
+
+@pytest.mark.parametrize("spca", [SparsePCA, MiniBatchSparsePCA])
+def test_spca_error_unormalized_components(spca):
+    rng = np.random.RandomState(0)
+    Y, _, _ = generate_toy_data(3, 10, (8, 8), random_state=rng)
+
+    err_msg = "normalize_components=False is not supported starting "
+    with pytest.raises(NotImplementedError, match=err_msg):
+        spca(normalize_components=False).fit(Y)
+
+
+@pytest.mark.parametrize("SPCA", [SparsePCA, MiniBatchSparsePCA])
+@pytest.mark.parametrize("n_components", [None, 3])
+def test_spca_n_components_(SPCA, n_components):
+    rng = np.random.RandomState(0)
+    n_samples, n_features = 12, 10
+    X = rng.randn(n_samples, n_features)
+
+    model = SPCA(n_components=n_components).fit(X)
+
+    if n_components is not None:
+        assert model.n_components_ == n_components
+    else:
+        assert model.n_components_ == n_features

venv/Lib/site-packages/sklearn/decomposition/tests/test_truncated_svd.py

@@ -0,0 +1,193 @@
+"""Test truncated SVD transformer."""
+
+import numpy as np
+import scipy.sparse as sp
+
+import pytest
+
+from sklearn.decomposition import TruncatedSVD, PCA
+from sklearn.utils import check_random_state
+from sklearn.utils._testing import assert_array_less, assert_allclose
+
+SVD_SOLVERS = ['arpack', 'randomized']
+
+
+@pytest.fixture(scope='module')
+def X_sparse():
+    # Make an X that looks somewhat like a small tf-idf matrix.
+    rng = check_random_state(42)
+    X = sp.random(60, 55, density=0.2, format="csr", random_state=rng)
+    X.data[:] = 1 + np.log(X.data)
+    return X
+
+
+@pytest.mark.parametrize("solver", ['randomized'])
+@pytest.mark.parametrize('kind', ('dense', 'sparse'))
+def test_solvers(X_sparse, solver, kind):
+    X = X_sparse if kind == 'sparse' else X_sparse.toarray()
+    svd_a = TruncatedSVD(30, algorithm="arpack")
+    svd = TruncatedSVD(30, algorithm=solver, random_state=42)
+
+    Xa = svd_a.fit_transform(X)[:, :6]
+    Xr = svd.fit_transform(X)[:, :6]
+    assert_allclose(Xa, Xr, rtol=2e-3)
+
+    comp_a = np.abs(svd_a.components_)
+    comp = np.abs(svd.components_)
+    # All elements are equal, but some elements are more equal than others.
+    assert_allclose(comp_a[:9], comp[:9], rtol=1e-3)
+    assert_allclose(comp_a[9:], comp[9:], atol=1e-2)
+
+
+@pytest.mark.parametrize("n_components", (10, 25, 41))
+def test_attributes(n_components, X_sparse):
+    n_features = X_sparse.shape[1]
+    tsvd = TruncatedSVD(n_components).fit(X_sparse)
+    assert tsvd.n_components == n_components
+    assert tsvd.components_.shape == (n_components, n_features)
+
+
+@pytest.mark.parametrize('algorithm', SVD_SOLVERS)
+def test_too_many_components(algorithm, X_sparse):
+    n_features = X_sparse.shape[1]
+    for n_components in (n_features, n_features + 1):
+        tsvd = TruncatedSVD(n_components=n_components, algorithm=algorithm)
+        with pytest.raises(ValueError):
+            tsvd.fit(X_sparse)
+
+
+@pytest.mark.parametrize('fmt', ("array", "csr", "csc", "coo", "lil"))
+def test_sparse_formats(fmt, X_sparse):
+    n_samples = X_sparse.shape[0]
+    Xfmt = (X_sparse.toarray()
+            if fmt == "dense" else getattr(X_sparse, "to" + fmt)())
+    tsvd = TruncatedSVD(n_components=11)
+    Xtrans = tsvd.fit_transform(Xfmt)
+    assert Xtrans.shape == (n_samples, 11)
+    Xtrans = tsvd.transform(Xfmt)
+    assert Xtrans.shape == (n_samples, 11)
+
+
+@pytest.mark.parametrize('algo', SVD_SOLVERS)
+def test_inverse_transform(algo, X_sparse):
+    # We need a lot of components for the reconstruction to be "almost
+    # equal" in all positions. XXX Test means or sums instead?
+    tsvd = TruncatedSVD(n_components=52, random_state=42, algorithm=algo)
+    Xt = tsvd.fit_transform(X_sparse)
+    Xinv = tsvd.inverse_transform(Xt)
+    assert_allclose(Xinv, X_sparse.toarray(), rtol=1e-1, atol=2e-1)
+
+
+def test_integers(X_sparse):
+    n_samples = X_sparse.shape[0]
+    Xint = X_sparse.astype(np.int64)
+    tsvd = TruncatedSVD(n_components=6)
+    Xtrans = tsvd.fit_transform(Xint)
+    assert Xtrans.shape == (n_samples, tsvd.n_components)
+
+
+@pytest.mark.parametrize('kind', ('dense', 'sparse'))
+@pytest.mark.parametrize('n_components', [10, 20])
+@pytest.mark.parametrize('solver', SVD_SOLVERS)
+def test_explained_variance(X_sparse, kind, n_components, solver):
+    X = X_sparse if kind == 'sparse' else X_sparse.toarray()
+    svd = TruncatedSVD(n_components, algorithm=solver)
+    X_tr = svd.fit_transform(X)
+    # Assert that all the values are greater than 0
+    assert_array_less(0.0, svd.explained_variance_ratio_)
+
+    # Assert that total explained variance is less than 1
+    assert_array_less(svd.explained_variance_ratio_.sum(), 1.0)
+
+    # Test that explained_variance is correct
+    total_variance = np.var(X_sparse.toarray(), axis=0).sum()
+    variances = np.var(X_tr, axis=0)
+    true_explained_variance_ratio = variances / total_variance
+
+    assert_allclose(
+        svd.explained_variance_ratio_,
+        true_explained_variance_ratio,
+    )
+
+
+@pytest.mark.parametrize('kind', ('dense', 'sparse'))
+@pytest.mark.parametrize('solver', SVD_SOLVERS)
+def test_explained_variance_components_10_20(X_sparse, kind, solver):
+    X = X_sparse if kind == 'sparse' else X_sparse.toarray()
+    svd_10 = TruncatedSVD(10, algorithm=solver, n_iter=10).fit(X)
+    svd_20 = TruncatedSVD(20, algorithm=solver, n_iter=10).fit(X)
+
+    # Assert the 1st component is equal
+    assert_allclose(
+        svd_10.explained_variance_ratio_,
+        svd_20.explained_variance_ratio_[:10],
+        rtol=5e-3,
+    )
+
+    # Assert that 20 components has higher explained variance than 10
+    assert (
+        svd_20.explained_variance_ratio_.sum() >
+        svd_10.explained_variance_ratio_.sum()
+    )
+
+
+@pytest.mark.parametrize('solver', SVD_SOLVERS)
+def test_singular_values_consistency(solver):
+    # Check that the TruncatedSVD output has the correct singular values
+    rng = np.random.RandomState(0)
+    n_samples, n_features = 100, 80
+    X = rng.randn(n_samples, n_features)
+
+    pca = TruncatedSVD(n_components=2, algorithm=solver,
+                       random_state=rng).fit(X)
+
+    # Compare to the Frobenius norm
+    X_pca = pca.transform(X)
+    assert_allclose(np.sum(pca.singular_values_**2.0),
+                    np.linalg.norm(X_pca, "fro")**2.0, rtol=1e-2)
+
+    # Compare to the 2-norms of the score vectors
+    assert_allclose(pca.singular_values_,
+                    np.sqrt(np.sum(X_pca**2.0, axis=0)), rtol=1e-2)
+
+
+@pytest.mark.parametrize('solver', SVD_SOLVERS)
+def test_singular_values_expected(solver):
+    # Set the singular values and see what we get back
+    rng = np.random.RandomState(0)
+    n_samples = 100
+    n_features = 110
+
+    X = rng.randn(n_samples, n_features)
+
+    pca = TruncatedSVD(n_components=3, algorithm=solver,
+                       random_state=rng)
+    X_pca = pca.fit_transform(X)
+
+    X_pca /= np.sqrt(np.sum(X_pca**2.0, axis=0))
+    X_pca[:, 0] *= 3.142
+    X_pca[:, 1] *= 2.718
+
+    X_hat_pca = np.dot(X_pca, pca.components_)
+    pca.fit(X_hat_pca)
+    assert_allclose(pca.singular_values_, [3.142, 2.718, 1.0], rtol=1e-14)
+
+
+def test_truncated_svd_eq_pca(X_sparse):
+    # TruncatedSVD should be equal to PCA on centered data
+
+    X_dense = X_sparse.toarray()
+
+    X_c = X_dense - X_dense.mean(axis=0)
+
+    params = dict(n_components=10, random_state=42)
+
+    svd = TruncatedSVD(algorithm='arpack', **params)
+    pca = PCA(svd_solver='arpack', **params)
+
+    Xt_svd = svd.fit_transform(X_c)
+    Xt_pca = pca.fit_transform(X_c)
+
+    assert_allclose(Xt_svd, Xt_pca, rtol=1e-9)
+    assert_allclose(pca.mean_, 0, atol=1e-9)
+    assert_allclose(svd.components_, pca.components_)