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llmeval-env/lib/python3.10/site-packages/sklearn/cross_decomposition/tests/test_pls.py

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+import warnings
+
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose, assert_array_almost_equal, assert_array_equal
+
+from sklearn.cross_decomposition import CCA, PLSSVD, PLSCanonical, PLSRegression
+from sklearn.cross_decomposition._pls import (
+    _center_scale_xy,
+    _get_first_singular_vectors_power_method,
+    _get_first_singular_vectors_svd,
+    _svd_flip_1d,
+)
+from sklearn.datasets import load_linnerud, make_regression
+from sklearn.ensemble import VotingRegressor
+from sklearn.exceptions import ConvergenceWarning
+from sklearn.linear_model import LinearRegression
+from sklearn.utils import check_random_state
+from sklearn.utils.extmath import svd_flip
+
+
+def assert_matrix_orthogonal(M):
+    K = np.dot(M.T, M)
+    assert_array_almost_equal(K, np.diag(np.diag(K)))
+
+
+def test_pls_canonical_basics():
+    # Basic checks for PLSCanonical
+    d = load_linnerud()
+    X = d.data
+    Y = d.target
+
+    pls = PLSCanonical(n_components=X.shape[1])
+    pls.fit(X, Y)
+
+    assert_matrix_orthogonal(pls.x_weights_)
+    assert_matrix_orthogonal(pls.y_weights_)
+    assert_matrix_orthogonal(pls._x_scores)
+    assert_matrix_orthogonal(pls._y_scores)
+
+    # Check X = TP' and Y = UQ'
+    T = pls._x_scores
+    P = pls.x_loadings_
+    U = pls._y_scores
+    Q = pls.y_loadings_
+    # Need to scale first
+    Xc, Yc, x_mean, y_mean, x_std, y_std = _center_scale_xy(
+        X.copy(), Y.copy(), scale=True
+    )
+    assert_array_almost_equal(Xc, np.dot(T, P.T))
+    assert_array_almost_equal(Yc, np.dot(U, Q.T))
+
+    # Check that rotations on training data lead to scores
+    Xt = pls.transform(X)
+    assert_array_almost_equal(Xt, pls._x_scores)
+    Xt, Yt = pls.transform(X, Y)
+    assert_array_almost_equal(Xt, pls._x_scores)
+    assert_array_almost_equal(Yt, pls._y_scores)
+
+    # Check that inverse_transform works
+    X_back = pls.inverse_transform(Xt)
+    assert_array_almost_equal(X_back, X)
+    _, Y_back = pls.inverse_transform(Xt, Yt)
+    assert_array_almost_equal(Y_back, Y)
+
+
+def test_sanity_check_pls_regression():
+    # Sanity check for PLSRegression
+    # The results were checked against the R-packages plspm, misOmics and pls
+
+    d = load_linnerud()
+    X = d.data
+    Y = d.target
+
+    pls = PLSRegression(n_components=X.shape[1])
+    X_trans, _ = pls.fit_transform(X, Y)
+
+    # FIXME: one would expect y_trans == pls.y_scores_ but this is not
+    # the case.
+    # xref: https://github.com/scikit-learn/scikit-learn/issues/22420
+    assert_allclose(X_trans, pls.x_scores_)
+
+    expected_x_weights = np.array(
+        [
+            [-0.61330704, -0.00443647, 0.78983213],
+            [-0.74697144, -0.32172099, -0.58183269],
+            [-0.25668686, 0.94682413, -0.19399983],
+        ]
+    )
+
+    expected_x_loadings = np.array(
+        [
+            [-0.61470416, -0.24574278, 0.78983213],
+            [-0.65625755, -0.14396183, -0.58183269],
+            [-0.51733059, 1.00609417, -0.19399983],
+        ]
+    )
+
+    expected_y_weights = np.array(
+        [
+            [+0.32456184, 0.29892183, 0.20316322],
+            [+0.42439636, 0.61970543, 0.19320542],
+            [-0.13143144, -0.26348971, -0.17092916],
+        ]
+    )
+
+    expected_y_loadings = np.array(
+        [
+            [+0.32456184, 0.29892183, 0.20316322],
+            [+0.42439636, 0.61970543, 0.19320542],
+            [-0.13143144, -0.26348971, -0.17092916],
+        ]
+    )
+
+    assert_array_almost_equal(np.abs(pls.x_loadings_), np.abs(expected_x_loadings))
+    assert_array_almost_equal(np.abs(pls.x_weights_), np.abs(expected_x_weights))
+    assert_array_almost_equal(np.abs(pls.y_loadings_), np.abs(expected_y_loadings))
+    assert_array_almost_equal(np.abs(pls.y_weights_), np.abs(expected_y_weights))
+
+    # The R / Python difference in the signs should be consistent across
+    # loadings, weights, etc.
+    x_loadings_sign_flip = np.sign(pls.x_loadings_ / expected_x_loadings)
+    x_weights_sign_flip = np.sign(pls.x_weights_ / expected_x_weights)
+    y_weights_sign_flip = np.sign(pls.y_weights_ / expected_y_weights)
+    y_loadings_sign_flip = np.sign(pls.y_loadings_ / expected_y_loadings)
+    assert_array_almost_equal(x_loadings_sign_flip, x_weights_sign_flip)
+    assert_array_almost_equal(y_loadings_sign_flip, y_weights_sign_flip)
+
+
+def test_sanity_check_pls_regression_constant_column_Y():
+    # Check behavior when the first column of Y is constant
+    # The results are checked against a modified version of plsreg2
+    # from the R-package plsdepot
+    d = load_linnerud()
+    X = d.data
+    Y = d.target
+    Y[:, 0] = 1
+    pls = PLSRegression(n_components=X.shape[1])
+    pls.fit(X, Y)
+
+    expected_x_weights = np.array(
+        [
+            [-0.6273573, 0.007081799, 0.7786994],
+            [-0.7493417, -0.277612681, -0.6011807],
+            [-0.2119194, 0.960666981, -0.1794690],
+        ]
+    )
+
+    expected_x_loadings = np.array(
+        [
+            [-0.6273512, -0.22464538, 0.7786994],
+            [-0.6643156, -0.09871193, -0.6011807],
+            [-0.5125877, 1.01407380, -0.1794690],
+        ]
+    )
+
+    expected_y_loadings = np.array(
+        [
+            [0.0000000, 0.0000000, 0.0000000],
+            [0.4357300, 0.5828479, 0.2174802],
+            [-0.1353739, -0.2486423, -0.1810386],
+        ]
+    )
+
+    assert_array_almost_equal(np.abs(expected_x_weights), np.abs(pls.x_weights_))
+    assert_array_almost_equal(np.abs(expected_x_loadings), np.abs(pls.x_loadings_))
+    # For the PLSRegression with default parameters, y_loadings == y_weights
+    assert_array_almost_equal(np.abs(pls.y_loadings_), np.abs(expected_y_loadings))
+    assert_array_almost_equal(np.abs(pls.y_weights_), np.abs(expected_y_loadings))
+
+    x_loadings_sign_flip = np.sign(expected_x_loadings / pls.x_loadings_)
+    x_weights_sign_flip = np.sign(expected_x_weights / pls.x_weights_)
+    # we ignore the first full-zeros row for y
+    y_loadings_sign_flip = np.sign(expected_y_loadings[1:] / pls.y_loadings_[1:])
+
+    assert_array_equal(x_loadings_sign_flip, x_weights_sign_flip)
+    assert_array_equal(x_loadings_sign_flip[1:], y_loadings_sign_flip)
+
+
+def test_sanity_check_pls_canonical():
+    # Sanity check for PLSCanonical
+    # The results were checked against the R-package plspm
+
+    d = load_linnerud()
+    X = d.data
+    Y = d.target
+
+    pls = PLSCanonical(n_components=X.shape[1])
+    pls.fit(X, Y)
+
+    expected_x_weights = np.array(
+        [
+            [-0.61330704, 0.25616119, -0.74715187],
+            [-0.74697144, 0.11930791, 0.65406368],
+            [-0.25668686, -0.95924297, -0.11817271],
+        ]
+    )
+
+    expected_x_rotations = np.array(
+        [
+            [-0.61330704, 0.41591889, -0.62297525],
+            [-0.74697144, 0.31388326, 0.77368233],
+            [-0.25668686, -0.89237972, -0.24121788],
+        ]
+    )
+
+    expected_y_weights = np.array(
+        [
+            [+0.58989127, 0.7890047, 0.1717553],
+            [+0.77134053, -0.61351791, 0.16920272],
+            [-0.23887670, -0.03267062, 0.97050016],
+        ]
+    )
+
+    expected_y_rotations = np.array(
+        [
+            [+0.58989127, 0.7168115, 0.30665872],
+            [+0.77134053, -0.70791757, 0.19786539],
+            [-0.23887670, -0.00343595, 0.94162826],
+        ]
+    )
+
+    assert_array_almost_equal(np.abs(pls.x_rotations_), np.abs(expected_x_rotations))
+    assert_array_almost_equal(np.abs(pls.x_weights_), np.abs(expected_x_weights))
+    assert_array_almost_equal(np.abs(pls.y_rotations_), np.abs(expected_y_rotations))
+    assert_array_almost_equal(np.abs(pls.y_weights_), np.abs(expected_y_weights))
+
+    x_rotations_sign_flip = np.sign(pls.x_rotations_ / expected_x_rotations)
+    x_weights_sign_flip = np.sign(pls.x_weights_ / expected_x_weights)
+    y_rotations_sign_flip = np.sign(pls.y_rotations_ / expected_y_rotations)
+    y_weights_sign_flip = np.sign(pls.y_weights_ / expected_y_weights)
+    assert_array_almost_equal(x_rotations_sign_flip, x_weights_sign_flip)
+    assert_array_almost_equal(y_rotations_sign_flip, y_weights_sign_flip)
+
+    assert_matrix_orthogonal(pls.x_weights_)
+    assert_matrix_orthogonal(pls.y_weights_)
+
+    assert_matrix_orthogonal(pls._x_scores)
+    assert_matrix_orthogonal(pls._y_scores)
+
+
+def test_sanity_check_pls_canonical_random():
+    # Sanity check for PLSCanonical on random data
+    # The results were checked against the R-package plspm
+    n = 500
+    p_noise = 10
+    q_noise = 5
+    # 2 latents vars:
+    rng = check_random_state(11)
+    l1 = rng.normal(size=n)
+    l2 = rng.normal(size=n)
+    latents = np.array([l1, l1, l2, l2]).T
+    X = latents + rng.normal(size=4 * n).reshape((n, 4))
+    Y = latents + rng.normal(size=4 * n).reshape((n, 4))
+    X = np.concatenate((X, rng.normal(size=p_noise * n).reshape(n, p_noise)), axis=1)
+    Y = np.concatenate((Y, rng.normal(size=q_noise * n).reshape(n, q_noise)), axis=1)
+
+    pls = PLSCanonical(n_components=3)
+    pls.fit(X, Y)
+
+    expected_x_weights = np.array(
+        [
+            [0.65803719, 0.19197924, 0.21769083],
+            [0.7009113, 0.13303969, -0.15376699],
+            [0.13528197, -0.68636408, 0.13856546],
+            [0.16854574, -0.66788088, -0.12485304],
+            [-0.03232333, -0.04189855, 0.40690153],
+            [0.1148816, -0.09643158, 0.1613305],
+            [0.04792138, -0.02384992, 0.17175319],
+            [-0.06781, -0.01666137, -0.18556747],
+            [-0.00266945, -0.00160224, 0.11893098],
+            [-0.00849528, -0.07706095, 0.1570547],
+            [-0.00949471, -0.02964127, 0.34657036],
+            [-0.03572177, 0.0945091, 0.3414855],
+            [0.05584937, -0.02028961, -0.57682568],
+            [0.05744254, -0.01482333, -0.17431274],
+        ]
+    )
+
+    expected_x_loadings = np.array(
+        [
+            [0.65649254, 0.1847647, 0.15270699],
+            [0.67554234, 0.15237508, -0.09182247],
+            [0.19219925, -0.67750975, 0.08673128],
+            [0.2133631, -0.67034809, -0.08835483],
+            [-0.03178912, -0.06668336, 0.43395268],
+            [0.15684588, -0.13350241, 0.20578984],
+            [0.03337736, -0.03807306, 0.09871553],
+            [-0.06199844, 0.01559854, -0.1881785],
+            [0.00406146, -0.00587025, 0.16413253],
+            [-0.00374239, -0.05848466, 0.19140336],
+            [0.00139214, -0.01033161, 0.32239136],
+            [-0.05292828, 0.0953533, 0.31916881],
+            [0.04031924, -0.01961045, -0.65174036],
+            [0.06172484, -0.06597366, -0.1244497],
+        ]
+    )
+
+    expected_y_weights = np.array(
+        [
+            [0.66101097, 0.18672553, 0.22826092],
+            [0.69347861, 0.18463471, -0.23995597],
+            [0.14462724, -0.66504085, 0.17082434],
+            [0.22247955, -0.6932605, -0.09832993],
+            [0.07035859, 0.00714283, 0.67810124],
+            [0.07765351, -0.0105204, -0.44108074],
+            [-0.00917056, 0.04322147, 0.10062478],
+            [-0.01909512, 0.06182718, 0.28830475],
+            [0.01756709, 0.04797666, 0.32225745],
+        ]
+    )
+
+    expected_y_loadings = np.array(
+        [
+            [0.68568625, 0.1674376, 0.0969508],
+            [0.68782064, 0.20375837, -0.1164448],
+            [0.11712173, -0.68046903, 0.12001505],
+            [0.17860457, -0.6798319, -0.05089681],
+            [0.06265739, -0.0277703, 0.74729584],
+            [0.0914178, 0.00403751, -0.5135078],
+            [-0.02196918, -0.01377169, 0.09564505],
+            [-0.03288952, 0.09039729, 0.31858973],
+            [0.04287624, 0.05254676, 0.27836841],
+        ]
+    )
+
+    assert_array_almost_equal(np.abs(pls.x_loadings_), np.abs(expected_x_loadings))
+    assert_array_almost_equal(np.abs(pls.x_weights_), np.abs(expected_x_weights))
+    assert_array_almost_equal(np.abs(pls.y_loadings_), np.abs(expected_y_loadings))
+    assert_array_almost_equal(np.abs(pls.y_weights_), np.abs(expected_y_weights))
+
+    x_loadings_sign_flip = np.sign(pls.x_loadings_ / expected_x_loadings)
+    x_weights_sign_flip = np.sign(pls.x_weights_ / expected_x_weights)
+    y_weights_sign_flip = np.sign(pls.y_weights_ / expected_y_weights)
+    y_loadings_sign_flip = np.sign(pls.y_loadings_ / expected_y_loadings)
+    assert_array_almost_equal(x_loadings_sign_flip, x_weights_sign_flip)
+    assert_array_almost_equal(y_loadings_sign_flip, y_weights_sign_flip)
+
+    assert_matrix_orthogonal(pls.x_weights_)
+    assert_matrix_orthogonal(pls.y_weights_)
+
+    assert_matrix_orthogonal(pls._x_scores)
+    assert_matrix_orthogonal(pls._y_scores)
+
+
+def test_convergence_fail():
+    # Make sure ConvergenceWarning is raised if max_iter is too small
+    d = load_linnerud()
+    X = d.data
+    Y = d.target
+    pls_nipals = PLSCanonical(n_components=X.shape[1], max_iter=2)
+    with pytest.warns(ConvergenceWarning):
+        pls_nipals.fit(X, Y)
+
+
+@pytest.mark.parametrize("Est", (PLSSVD, PLSRegression, PLSCanonical))
+def test_attibutes_shapes(Est):
+    # Make sure attributes are of the correct shape depending on n_components
+    d = load_linnerud()
+    X = d.data
+    Y = d.target
+    n_components = 2
+    pls = Est(n_components=n_components)
+    pls.fit(X, Y)
+    assert all(
+        attr.shape[1] == n_components for attr in (pls.x_weights_, pls.y_weights_)
+    )
+
+
+@pytest.mark.parametrize("Est", (PLSRegression, PLSCanonical, CCA))
+def test_univariate_equivalence(Est):
+    # Ensure 2D Y with 1 column is equivalent to 1D Y
+    d = load_linnerud()
+    X = d.data
+    Y = d.target
+
+    est = Est(n_components=1)
+    one_d_coeff = est.fit(X, Y[:, 0]).coef_
+    two_d_coeff = est.fit(X, Y[:, :1]).coef_
+
+    assert one_d_coeff.shape == two_d_coeff.shape
+    assert_array_almost_equal(one_d_coeff, two_d_coeff)
+
+
+@pytest.mark.parametrize("Est", (PLSRegression, PLSCanonical, CCA, PLSSVD))
+def test_copy(Est):
+    # check that the "copy" keyword works
+    d = load_linnerud()
+    X = d.data
+    Y = d.target
+    X_orig = X.copy()
+
+    # copy=True won't modify inplace
+    pls = Est(copy=True).fit(X, Y)
+    assert_array_equal(X, X_orig)
+
+    # copy=False will modify inplace
+    with pytest.raises(AssertionError):
+        Est(copy=False).fit(X, Y)
+        assert_array_almost_equal(X, X_orig)
+
+    if Est is PLSSVD:
+        return  # PLSSVD does not support copy param in predict or transform
+
+    X_orig = X.copy()
+    with pytest.raises(AssertionError):
+        pls.transform(X, Y, copy=False),
+        assert_array_almost_equal(X, X_orig)
+
+    X_orig = X.copy()
+    with pytest.raises(AssertionError):
+        pls.predict(X, copy=False),
+        assert_array_almost_equal(X, X_orig)
+
+    # Make sure copy=True gives same transform and predictions as predict=False
+    assert_array_almost_equal(
+        pls.transform(X, Y, copy=True), pls.transform(X.copy(), Y.copy(), copy=False)
+    )
+    assert_array_almost_equal(
+        pls.predict(X, copy=True), pls.predict(X.copy(), copy=False)
+    )
+
+
+def _generate_test_scale_and_stability_datasets():
+    """Generate dataset for test_scale_and_stability"""
+    # dataset for non-regression 7818
+    rng = np.random.RandomState(0)
+    n_samples = 1000
+    n_targets = 5
+    n_features = 10
+    Q = rng.randn(n_targets, n_features)
+    Y = rng.randn(n_samples, n_targets)
+    X = np.dot(Y, Q) + 2 * rng.randn(n_samples, n_features) + 1
+    X *= 1000
+    yield X, Y
+
+    # Data set where one of the features is constraint
+    X, Y = load_linnerud(return_X_y=True)
+    # causes X[:, -1].std() to be zero
+    X[:, -1] = 1.0
+    yield X, Y
+
+    X = np.array([[0.0, 0.0, 1.0], [1.0, 0.0, 0.0], [2.0, 2.0, 2.0], [3.0, 5.0, 4.0]])
+    Y = np.array([[0.1, -0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]])
+    yield X, Y
+
+    # Seeds that provide a non-regression test for #18746, where CCA fails
+    seeds = [530, 741]
+    for seed in seeds:
+        rng = np.random.RandomState(seed)
+        X = rng.randn(4, 3)
+        Y = rng.randn(4, 2)
+        yield X, Y
+
+
+@pytest.mark.parametrize("Est", (CCA, PLSCanonical, PLSRegression, PLSSVD))
+@pytest.mark.parametrize("X, Y", _generate_test_scale_and_stability_datasets())
+def test_scale_and_stability(Est, X, Y):
+    """scale=True is equivalent to scale=False on centered/scaled data
+    This allows to check numerical stability over platforms as well"""
+
+    X_s, Y_s, *_ = _center_scale_xy(X, Y)
+
+    X_score, Y_score = Est(scale=True).fit_transform(X, Y)
+    X_s_score, Y_s_score = Est(scale=False).fit_transform(X_s, Y_s)
+
+    assert_allclose(X_s_score, X_score, atol=1e-4)
+    assert_allclose(Y_s_score, Y_score, atol=1e-4)
+
+
+@pytest.mark.parametrize("Estimator", (PLSSVD, PLSRegression, PLSCanonical, CCA))
+def test_n_components_upper_bounds(Estimator):
+    """Check the validation of `n_components` upper bounds for `PLS` regressors."""
+    rng = np.random.RandomState(0)
+    X = rng.randn(10, 5)
+    Y = rng.randn(10, 3)
+    est = Estimator(n_components=10)
+    err_msg = "`n_components` upper bound is .*. Got 10 instead. Reduce `n_components`."
+    with pytest.raises(ValueError, match=err_msg):
+        est.fit(X, Y)
+
+
+@pytest.mark.parametrize("n_samples, n_features", [(100, 10), (100, 200)])
+def test_singular_value_helpers(n_samples, n_features, global_random_seed):
+    # Make sure SVD and power method give approximately the same results
+    X, Y = make_regression(
+        n_samples, n_features, n_targets=5, random_state=global_random_seed
+    )
+    u1, v1, _ = _get_first_singular_vectors_power_method(X, Y, norm_y_weights=True)
+    u2, v2 = _get_first_singular_vectors_svd(X, Y)
+
+    _svd_flip_1d(u1, v1)
+    _svd_flip_1d(u2, v2)
+
+    rtol = 1e-3
+    # Setting atol because some coordinates are very close to zero
+    assert_allclose(u1, u2, atol=u2.max() * rtol)
+    assert_allclose(v1, v2, atol=v2.max() * rtol)
+
+
+def test_one_component_equivalence(global_random_seed):
+    # PLSSVD, PLSRegression and PLSCanonical should all be equivalent when
+    # n_components is 1
+    X, Y = make_regression(100, 10, n_targets=5, random_state=global_random_seed)
+    svd = PLSSVD(n_components=1).fit(X, Y).transform(X)
+    reg = PLSRegression(n_components=1).fit(X, Y).transform(X)
+    canonical = PLSCanonical(n_components=1).fit(X, Y).transform(X)
+
+    rtol = 1e-3
+    # Setting atol because some entries are very close to zero
+    assert_allclose(svd, reg, atol=reg.max() * rtol)
+    assert_allclose(svd, canonical, atol=canonical.max() * rtol)
+
+
+def test_svd_flip_1d():
+    # Make sure svd_flip_1d is equivalent to svd_flip
+    u = np.array([1, -4, 2])
+    v = np.array([1, 2, 3])
+
+    u_expected, v_expected = svd_flip(u.reshape(-1, 1), v.reshape(1, -1))
+    _svd_flip_1d(u, v)  # inplace
+
+    assert_allclose(u, u_expected.ravel())
+    assert_allclose(u, [-1, 4, -2])
+
+    assert_allclose(v, v_expected.ravel())
+    assert_allclose(v, [-1, -2, -3])
+
+
+def test_loadings_converges(global_random_seed):
+    """Test that CCA converges. Non-regression test for #19549."""
+    X, y = make_regression(
+        n_samples=200, n_features=20, n_targets=20, random_state=global_random_seed
+    )
+
+    cca = CCA(n_components=10, max_iter=500)
+
+    with warnings.catch_warnings():
+        warnings.simplefilter("error", ConvergenceWarning)
+
+        cca.fit(X, y)
+
+    # Loadings converges to reasonable values
+    assert np.all(np.abs(cca.x_loadings_) < 1)
+
+
+def test_pls_constant_y():
+    """Checks warning when y is constant. Non-regression test for #19831"""
+    rng = np.random.RandomState(42)
+    x = rng.rand(100, 3)
+    y = np.zeros(100)
+
+    pls = PLSRegression()
+
+    msg = "Y residual is constant at iteration"
+    with pytest.warns(UserWarning, match=msg):
+        pls.fit(x, y)
+
+    assert_allclose(pls.x_rotations_, 0)
+
+
+@pytest.mark.parametrize("PLSEstimator", [PLSRegression, PLSCanonical, CCA])
+def test_pls_coef_shape(PLSEstimator):
+    """Check the shape of `coef_` attribute.
+
+    Non-regression test for:
+    https://github.com/scikit-learn/scikit-learn/issues/12410
+    """
+    d = load_linnerud()
+    X = d.data
+    Y = d.target
+
+    pls = PLSEstimator(copy=True).fit(X, Y)
+
+    n_targets, n_features = Y.shape[1], X.shape[1]
+    assert pls.coef_.shape == (n_targets, n_features)
+
+
+@pytest.mark.parametrize("scale", [True, False])
+@pytest.mark.parametrize("PLSEstimator", [PLSRegression, PLSCanonical, CCA])
+def test_pls_prediction(PLSEstimator, scale):
+    """Check the behaviour of the prediction function."""
+    d = load_linnerud()
+    X = d.data
+    Y = d.target
+
+    pls = PLSEstimator(copy=True, scale=scale).fit(X, Y)
+    Y_pred = pls.predict(X, copy=True)
+
+    y_mean = Y.mean(axis=0)
+    X_trans = X - X.mean(axis=0)
+    if scale:
+        X_trans /= X.std(axis=0, ddof=1)
+
+    assert_allclose(pls.intercept_, y_mean)
+    assert_allclose(Y_pred, X_trans @ pls.coef_.T + pls.intercept_)
+
+
+@pytest.mark.parametrize("Klass", [CCA, PLSSVD, PLSRegression, PLSCanonical])
+def test_pls_feature_names_out(Klass):
+    """Check `get_feature_names_out` cross_decomposition module."""
+    X, Y = load_linnerud(return_X_y=True)
+
+    est = Klass().fit(X, Y)
+    names_out = est.get_feature_names_out()
+
+    class_name_lower = Klass.__name__.lower()
+    expected_names_out = np.array(
+        [f"{class_name_lower}{i}" for i in range(est.x_weights_.shape[1])],
+        dtype=object,
+    )
+    assert_array_equal(names_out, expected_names_out)
+
+
+@pytest.mark.parametrize("Klass", [CCA, PLSSVD, PLSRegression, PLSCanonical])
+def test_pls_set_output(Klass):
+    """Check `set_output` in cross_decomposition module."""
+    pd = pytest.importorskip("pandas")
+    X, Y = load_linnerud(return_X_y=True, as_frame=True)
+
+    est = Klass().set_output(transform="pandas").fit(X, Y)
+    X_trans, y_trans = est.transform(X, Y)
+    assert isinstance(y_trans, np.ndarray)
+    assert isinstance(X_trans, pd.DataFrame)
+    assert_array_equal(X_trans.columns, est.get_feature_names_out())
+
+
+def test_pls_regression_fit_1d_y():
+    """Check that when fitting with 1d `y`, prediction should also be 1d.
+
+    Non-regression test for Issue #26549.
+    """
+    X = np.array([[1, 1], [2, 4], [3, 9], [4, 16], [5, 25], [6, 36]])
+    y = np.array([2, 6, 12, 20, 30, 42])
+    expected = y.copy()
+
+    plsr = PLSRegression().fit(X, y)
+    y_pred = plsr.predict(X)
+    assert y_pred.shape == expected.shape
+
+    # Check that it works in VotingRegressor
+    lr = LinearRegression().fit(X, y)
+    vr = VotingRegressor([("lr", lr), ("plsr", plsr)])
+    y_pred = vr.fit(X, y).predict(X)
+    assert y_pred.shape == expected.shape
+    assert_allclose(y_pred, expected)

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/__init__.py

@@ -0,0 +1,52 @@
+"""
+The :mod:`sklearn.decomposition` module includes matrix decomposition
+algorithms, including among others PCA, NMF or ICA. Most of the algorithms of
+this module can be regarded as dimensionality reduction techniques.
+"""
+
+
+from ..utils.extmath import randomized_svd
+from ._dict_learning import (
+    DictionaryLearning,
+    MiniBatchDictionaryLearning,
+    SparseCoder,
+    dict_learning,
+    dict_learning_online,
+    sparse_encode,
+)
+from ._factor_analysis import FactorAnalysis
+from ._fastica import FastICA, fastica
+from ._incremental_pca import IncrementalPCA
+from ._kernel_pca import KernelPCA
+from ._lda import LatentDirichletAllocation
+from ._nmf import (
+    NMF,
+    MiniBatchNMF,
+    non_negative_factorization,
+)
+from ._pca import PCA
+from ._sparse_pca import MiniBatchSparsePCA, SparsePCA
+from ._truncated_svd import TruncatedSVD
+
+__all__ = [
+    "DictionaryLearning",
+    "FastICA",
+    "IncrementalPCA",
+    "KernelPCA",
+    "MiniBatchDictionaryLearning",
+    "MiniBatchNMF",
+    "MiniBatchSparsePCA",
+    "NMF",
+    "PCA",
+    "SparseCoder",
+    "SparsePCA",
+    "dict_learning",
+    "dict_learning_online",
+    "fastica",
+    "non_negative_factorization",
+    "randomized_svd",
+    "sparse_encode",
+    "FactorAnalysis",
+    "TruncatedSVD",
+    "LatentDirichletAllocation",
+]

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/_base.py

@@ -0,0 +1,193 @@
+"""Principal Component Analysis Base Classes"""
+
+# Author: Alexandre Gramfort <[email protected]>
+#         Olivier Grisel <[email protected]>
+#         Mathieu Blondel <[email protected]>
+#         Denis A. Engemann <[email protected]>
+#         Kyle Kastner <[email protected]>
+#
+# License: BSD 3 clause
+
+from abc import ABCMeta, abstractmethod
+
+import numpy as np
+from scipy import linalg
+from scipy.sparse import issparse
+
+from ..base import BaseEstimator, ClassNamePrefixFeaturesOutMixin, TransformerMixin
+from ..utils._array_api import _add_to_diagonal, device, get_namespace
+from ..utils.sparsefuncs import _implicit_column_offset
+from ..utils.validation import check_is_fitted
+
+
+class _BasePCA(
+    ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator, metaclass=ABCMeta
+):
+    """Base class for PCA methods.
+
+    Warning: This class should not be used directly.
+    Use derived classes instead.
+    """
+
+    def get_covariance(self):
+        """Compute data covariance with the generative model.
+
+        ``cov = components_.T * S**2 * components_ + sigma2 * eye(n_features)``
+        where S**2 contains the explained variances, and sigma2 contains the
+        noise variances.
+
+        Returns
+        -------
+        cov : array of shape=(n_features, n_features)
+            Estimated covariance of data.
+        """
+        xp, _ = get_namespace(self.components_)
+
+        components_ = self.components_
+        exp_var = self.explained_variance_
+        if self.whiten:
+            components_ = components_ * xp.sqrt(exp_var[:, np.newaxis])
+        exp_var_diff = exp_var - self.noise_variance_
+        exp_var_diff = xp.where(
+            exp_var > self.noise_variance_,
+            exp_var_diff,
+            xp.asarray(0.0, device=device(exp_var)),
+        )
+        cov = (components_.T * exp_var_diff) @ components_
+        _add_to_diagonal(cov, self.noise_variance_, xp)
+        return cov
+
+    def get_precision(self):
+        """Compute data precision matrix with the generative model.
+
+        Equals the inverse of the covariance but computed with
+        the matrix inversion lemma for efficiency.
+
+        Returns
+        -------
+        precision : array, shape=(n_features, n_features)
+            Estimated precision of data.
+        """
+        xp, is_array_api_compliant = get_namespace(self.components_)
+
+        n_features = self.components_.shape[1]
+
+        # handle corner cases first
+        if self.n_components_ == 0:
+            return xp.eye(n_features) / self.noise_variance_
+
+        if is_array_api_compliant:
+            linalg_inv = xp.linalg.inv
+        else:
+            linalg_inv = linalg.inv
+
+        if self.noise_variance_ == 0.0:
+            return linalg_inv(self.get_covariance())
+
+        # Get precision using matrix inversion lemma
+        components_ = self.components_
+        exp_var = self.explained_variance_
+        if self.whiten:
+            components_ = components_ * xp.sqrt(exp_var[:, np.newaxis])
+        exp_var_diff = exp_var - self.noise_variance_
+        exp_var_diff = xp.where(
+            exp_var > self.noise_variance_,
+            exp_var_diff,
+            xp.asarray(0.0, device=device(exp_var)),
+        )
+        precision = components_ @ components_.T / self.noise_variance_
+        _add_to_diagonal(precision, 1.0 / exp_var_diff, xp)
+        precision = components_.T @ linalg_inv(precision) @ components_
+        precision /= -(self.noise_variance_**2)
+        _add_to_diagonal(precision, 1.0 / self.noise_variance_, xp)
+        return precision
+
+    @abstractmethod
+    def fit(self, X, y=None):
+        """Placeholder for fit. Subclasses should implement this method!
+
+        Fit the model with X.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            Training data, where `n_samples` is the number of samples and
+            `n_features` is the number of features.
+
+        Returns
+        -------
+        self : object
+            Returns the instance itself.
+        """
+
+    def transform(self, X):
+        """Apply dimensionality reduction to X.
+
+        X is projected on the first principal components previously extracted
+        from a training set.
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            New data, where `n_samples` is the number of samples
+            and `n_features` is the number of features.
+
+        Returns
+        -------
+        X_new : array-like of shape (n_samples, n_components)
+            Projection of X in the first principal components, where `n_samples`
+            is the number of samples and `n_components` is the number of the components.
+        """
+        xp, _ = get_namespace(X)
+
+        check_is_fitted(self)
+
+        X = self._validate_data(
+            X, accept_sparse=("csr", "csc"), dtype=[xp.float64, xp.float32], reset=False
+        )
+        if self.mean_ is not None:
+            if issparse(X):
+                X = _implicit_column_offset(X, self.mean_)
+            else:
+                X = X - self.mean_
+        X_transformed = X @ self.components_.T
+        if self.whiten:
+            X_transformed /= xp.sqrt(self.explained_variance_)
+        return X_transformed
+
+    def inverse_transform(self, X):
+        """Transform data back to its original space.
+
+        In other words, return an input `X_original` whose transform would be X.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_components)
+            New data, where `n_samples` is the number of samples
+            and `n_components` is the number of components.
+
+        Returns
+        -------
+        X_original array-like of shape (n_samples, n_features)
+            Original data, where `n_samples` is the number of samples
+            and `n_features` is the number of features.
+
+        Notes
+        -----
+        If whitening is enabled, inverse_transform will compute the
+        exact inverse operation, which includes reversing whitening.
+        """
+        xp, _ = get_namespace(X)
+
+        if self.whiten:
+            scaled_components = (
+                xp.sqrt(self.explained_variance_[:, np.newaxis]) * self.components_
+            )
+            return X @ scaled_components + self.mean_
+        else:
+            return X @ self.components_ + self.mean_
+
+    @property
+    def _n_features_out(self):
+        """Number of transformed output features."""
+        return self.components_.shape[0]

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/_factor_analysis.py

@@ -0,0 +1,458 @@
+"""Factor Analysis.
+
+A latent linear variable model.
+
+FactorAnalysis is similar to probabilistic PCA implemented by PCA.score
+While PCA assumes Gaussian noise with the same variance for each
+feature, the FactorAnalysis model assumes different variances for
+each of them.
+
+This implementation is based on David Barber's Book,
+Bayesian Reasoning and Machine Learning,
+http://www.cs.ucl.ac.uk/staff/d.barber/brml,
+Algorithm 21.1
+"""
+
+# Author: Christian Osendorfer <[email protected]>
+#         Alexandre Gramfort <[email protected]>
+#         Denis A. Engemann <[email protected]>
+
+# License: BSD3
+
+import warnings
+from math import log, sqrt
+from numbers import Integral, Real
+
+import numpy as np
+from scipy import linalg
+
+from ..base import (
+    BaseEstimator,
+    ClassNamePrefixFeaturesOutMixin,
+    TransformerMixin,
+    _fit_context,
+)
+from ..exceptions import ConvergenceWarning
+from ..utils import check_random_state
+from ..utils._param_validation import Interval, StrOptions
+from ..utils.extmath import fast_logdet, randomized_svd, squared_norm
+from ..utils.validation import check_is_fitted
+
+
+class FactorAnalysis(ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator):
+    """Factor Analysis (FA).
+
+    A simple linear generative model with Gaussian latent variables.
+
+    The observations are assumed to be caused by a linear transformation of
+    lower dimensional latent factors and added Gaussian noise.
+    Without loss of generality the factors are distributed according to a
+    Gaussian with zero mean and unit covariance. The noise is also zero mean
+    and has an arbitrary diagonal covariance matrix.
+
+    If we would restrict the model further, by assuming that the Gaussian
+    noise is even isotropic (all diagonal entries are the same) we would obtain
+    :class:`PCA`.
+
+    FactorAnalysis performs a maximum likelihood estimate of the so-called
+    `loading` matrix, the transformation of the latent variables to the
+    observed ones, using SVD based approach.
+
+    Read more in the :ref:`User Guide <FA>`.
+
+    .. versionadded:: 0.13
+
+    Parameters
+    ----------
+    n_components : int, default=None
+        Dimensionality of latent space, the number of components
+        of ``X`` that are obtained after ``transform``.
+        If None, n_components is set to the number of features.
+
+    tol : float, default=1e-2
+        Stopping tolerance for log-likelihood increase.
+
+    copy : bool, default=True
+        Whether to make a copy of X. If ``False``, the input X gets overwritten
+        during fitting.
+
+    max_iter : int, default=1000
+        Maximum number of iterations.
+
+    noise_variance_init : array-like of shape (n_features,), default=None
+        The initial guess of the noise variance for each feature.
+        If None, it defaults to np.ones(n_features).
+
+    svd_method : {'lapack', 'randomized'}, default='randomized'
+        Which SVD method to use. If 'lapack' use standard SVD from
+        scipy.linalg, if 'randomized' use fast ``randomized_svd`` function.
+        Defaults to 'randomized'. For most applications 'randomized' will
+        be sufficiently precise while providing significant speed gains.
+        Accuracy can also be improved by setting higher values for
+        `iterated_power`. If this is not sufficient, for maximum precision
+        you should choose 'lapack'.
+
+    iterated_power : int, default=3
+        Number of iterations for the power method. 3 by default. Only used
+        if ``svd_method`` equals 'randomized'.
+
+    rotation : {'varimax', 'quartimax'}, default=None
+        If not None, apply the indicated rotation. Currently, varimax and
+        quartimax are implemented. See
+        `"The varimax criterion for analytic rotation in factor analysis"
+        <https://link.springer.com/article/10.1007%2FBF02289233>`_
+        H. F. Kaiser, 1958.
+
+        .. versionadded:: 0.24
+
+    random_state : int or RandomState instance, default=0
+        Only used when ``svd_method`` equals 'randomized'. Pass an int for
+        reproducible results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+    Attributes
+    ----------
+    components_ : ndarray of shape (n_components, n_features)
+        Components with maximum variance.
+
+    loglike_ : list of shape (n_iterations,)
+        The log likelihood at each iteration.
+
+    noise_variance_ : ndarray of shape (n_features,)
+        The estimated noise variance for each feature.
+
+    n_iter_ : int
+        Number of iterations run.
+
+    mean_ : ndarray of shape (n_features,)
+        Per-feature empirical mean, estimated from the training set.
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+        .. versionadded:: 0.24
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
+    See Also
+    --------
+    PCA: Principal component analysis is also a latent linear variable model
+        which however assumes equal noise variance for each feature.
+        This extra assumption makes probabilistic PCA faster as it can be
+        computed in closed form.
+    FastICA: Independent component analysis, a latent variable model with
+        non-Gaussian latent variables.
+
+    References
+    ----------
+    - David Barber, Bayesian Reasoning and Machine Learning,
+      Algorithm 21.1.
+
+    - Christopher M. Bishop: Pattern Recognition and Machine Learning,
+      Chapter 12.2.4.
+
+    Examples
+    --------
+    >>> from sklearn.datasets import load_digits
+    >>> from sklearn.decomposition import FactorAnalysis
+    >>> X, _ = load_digits(return_X_y=True)
+    >>> transformer = FactorAnalysis(n_components=7, random_state=0)
+    >>> X_transformed = transformer.fit_transform(X)
+    >>> X_transformed.shape
+    (1797, 7)
+    """
+
+    _parameter_constraints: dict = {
+        "n_components": [Interval(Integral, 0, None, closed="left"), None],
+        "tol": [Interval(Real, 0.0, None, closed="left")],
+        "copy": ["boolean"],
+        "max_iter": [Interval(Integral, 1, None, closed="left")],
+        "noise_variance_init": ["array-like", None],
+        "svd_method": [StrOptions({"randomized", "lapack"})],
+        "iterated_power": [Interval(Integral, 0, None, closed="left")],
+        "rotation": [StrOptions({"varimax", "quartimax"}), None],
+        "random_state": ["random_state"],
+    }
+
+    def __init__(
+        self,
+        n_components=None,
+        *,
+        tol=1e-2,
+        copy=True,
+        max_iter=1000,
+        noise_variance_init=None,
+        svd_method="randomized",
+        iterated_power=3,
+        rotation=None,
+        random_state=0,
+    ):
+        self.n_components = n_components
+        self.copy = copy
+        self.tol = tol
+        self.max_iter = max_iter
+        self.svd_method = svd_method
+
+        self.noise_variance_init = noise_variance_init
+        self.iterated_power = iterated_power
+        self.random_state = random_state
+        self.rotation = rotation
+
+    @_fit_context(prefer_skip_nested_validation=True)
+    def fit(self, X, y=None):
+        """Fit the FactorAnalysis model to X using SVD based approach.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            Training data.
+
+        y : Ignored
+            Ignored parameter.
+
+        Returns
+        -------
+        self : object
+            FactorAnalysis class instance.
+        """
+        X = self._validate_data(X, copy=self.copy, dtype=np.float64)
+
+        n_samples, n_features = X.shape
+        n_components = self.n_components
+        if n_components is None:
+            n_components = n_features
+
+        self.mean_ = np.mean(X, axis=0)
+        X -= self.mean_
+
+        # some constant terms
+        nsqrt = sqrt(n_samples)
+        llconst = n_features * log(2.0 * np.pi) + n_components
+        var = np.var(X, axis=0)
+
+        if self.noise_variance_init is None:
+            psi = np.ones(n_features, dtype=X.dtype)
+        else:
+            if len(self.noise_variance_init) != n_features:
+                raise ValueError(
+                    "noise_variance_init dimension does not "
+                    "with number of features : %d != %d"
+                    % (len(self.noise_variance_init), n_features)
+                )
+            psi = np.array(self.noise_variance_init)
+
+        loglike = []
+        old_ll = -np.inf
+        SMALL = 1e-12
+
+        # we'll modify svd outputs to return unexplained variance
+        # to allow for unified computation of loglikelihood
+        if self.svd_method == "lapack":
+
+            def my_svd(X):
+                _, s, Vt = linalg.svd(X, full_matrices=False, check_finite=False)
+                return (
+                    s[:n_components],
+                    Vt[:n_components],
+                    squared_norm(s[n_components:]),
+                )
+
+        else:  # svd_method == "randomized"
+            random_state = check_random_state(self.random_state)
+
+            def my_svd(X):
+                _, s, Vt = randomized_svd(
+                    X,
+                    n_components,
+                    random_state=random_state,
+                    n_iter=self.iterated_power,
+                )
+                return s, Vt, squared_norm(X) - squared_norm(s)
+
+        for i in range(self.max_iter):
+            # SMALL helps numerics
+            sqrt_psi = np.sqrt(psi) + SMALL
+            s, Vt, unexp_var = my_svd(X / (sqrt_psi * nsqrt))
+            s **= 2
+            # Use 'maximum' here to avoid sqrt problems.
+            W = np.sqrt(np.maximum(s - 1.0, 0.0))[:, np.newaxis] * Vt
+            del Vt
+            W *= sqrt_psi
+
+            # loglikelihood
+            ll = llconst + np.sum(np.log(s))
+            ll += unexp_var + np.sum(np.log(psi))
+            ll *= -n_samples / 2.0
+            loglike.append(ll)
+            if (ll - old_ll) < self.tol:
+                break
+            old_ll = ll
+
+            psi = np.maximum(var - np.sum(W**2, axis=0), SMALL)
+        else:
+            warnings.warn(
+                "FactorAnalysis did not converge."
+                + " You might want"
+                + " to increase the number of iterations.",
+                ConvergenceWarning,
+            )
+
+        self.components_ = W
+        if self.rotation is not None:
+            self.components_ = self._rotate(W)
+        self.noise_variance_ = psi
+        self.loglike_ = loglike
+        self.n_iter_ = i + 1
+        return self
+
+    def transform(self, X):
+        """Apply dimensionality reduction to X using the model.
+
+        Compute the expected mean of the latent variables.
+        See Barber, 21.2.33 (or Bishop, 12.66).
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            Training data.
+
+        Returns
+        -------
+        X_new : ndarray of shape (n_samples, n_components)
+            The latent variables of X.
+        """
+        check_is_fitted(self)
+
+        X = self._validate_data(X, reset=False)
+        Ih = np.eye(len(self.components_))
+
+        X_transformed = X - self.mean_
+
+        Wpsi = self.components_ / self.noise_variance_
+        cov_z = linalg.inv(Ih + np.dot(Wpsi, self.components_.T))
+        tmp = np.dot(X_transformed, Wpsi.T)
+        X_transformed = np.dot(tmp, cov_z)
+
+        return X_transformed
+
+    def get_covariance(self):
+        """Compute data covariance with the FactorAnalysis model.
+
+        ``cov = components_.T * components_ + diag(noise_variance)``
+
+        Returns
+        -------
+        cov : ndarray of shape (n_features, n_features)
+            Estimated covariance of data.
+        """
+        check_is_fitted(self)
+
+        cov = np.dot(self.components_.T, self.components_)
+        cov.flat[:: len(cov) + 1] += self.noise_variance_  # modify diag inplace
+        return cov
+
+    def get_precision(self):
+        """Compute data precision matrix with the FactorAnalysis model.
+
+        Returns
+        -------
+        precision : ndarray of shape (n_features, n_features)
+            Estimated precision of data.
+        """
+        check_is_fitted(self)
+
+        n_features = self.components_.shape[1]
+
+        # handle corner cases first
+        if self.n_components == 0:
+            return np.diag(1.0 / self.noise_variance_)
+        if self.n_components == n_features:
+            return linalg.inv(self.get_covariance())
+
+        # Get precision using matrix inversion lemma
+        components_ = self.components_
+        precision = np.dot(components_ / self.noise_variance_, components_.T)
+        precision.flat[:: len(precision) + 1] += 1.0
+        precision = np.dot(components_.T, np.dot(linalg.inv(precision), components_))
+        precision /= self.noise_variance_[:, np.newaxis]
+        precision /= -self.noise_variance_[np.newaxis, :]
+        precision.flat[:: len(precision) + 1] += 1.0 / self.noise_variance_
+        return precision
+
+    def score_samples(self, X):
+        """Compute the log-likelihood of each sample.
+
+        Parameters
+        ----------
+        X : ndarray of shape (n_samples, n_features)
+            The data.
+
+        Returns
+        -------
+        ll : ndarray of shape (n_samples,)
+            Log-likelihood of each sample under the current model.
+        """
+        check_is_fitted(self)
+        X = self._validate_data(X, reset=False)
+        Xr = X - self.mean_
+        precision = self.get_precision()
+        n_features = X.shape[1]
+        log_like = -0.5 * (Xr * (np.dot(Xr, precision))).sum(axis=1)
+        log_like -= 0.5 * (n_features * log(2.0 * np.pi) - fast_logdet(precision))
+        return log_like
+
+    def score(self, X, y=None):
+        """Compute the average log-likelihood of the samples.
+
+        Parameters
+        ----------
+        X : ndarray of shape (n_samples, n_features)
+            The data.
+
+        y : Ignored
+            Ignored parameter.
+
+        Returns
+        -------
+        ll : float
+            Average log-likelihood of the samples under the current model.
+        """
+        return np.mean(self.score_samples(X))
+
+    def _rotate(self, components, n_components=None, tol=1e-6):
+        "Rotate the factor analysis solution."
+        # note that tol is not exposed
+        return _ortho_rotation(components.T, method=self.rotation, tol=tol)[
+            : self.n_components
+        ]
+
+    @property
+    def _n_features_out(self):
+        """Number of transformed output features."""
+        return self.components_.shape[0]
+
+
+def _ortho_rotation(components, method="varimax", tol=1e-6, max_iter=100):
+    """Return rotated components."""
+    nrow, ncol = components.shape
+    rotation_matrix = np.eye(ncol)
+    var = 0
+
+    for _ in range(max_iter):
+        comp_rot = np.dot(components, rotation_matrix)
+        if method == "varimax":
+            tmp = comp_rot * np.transpose((comp_rot**2).sum(axis=0) / nrow)
+        elif method == "quartimax":
+            tmp = 0
+        u, s, v = np.linalg.svd(np.dot(components.T, comp_rot**3 - tmp))
+        rotation_matrix = np.dot(u, v)
+        var_new = np.sum(s)
+        if var != 0 and var_new < var * (1 + tol):
+            break
+        var = var_new
+
+    return np.dot(components, rotation_matrix).T

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/_incremental_pca.py

@@ -0,0 +1,409 @@
+"""Incremental Principal Components Analysis."""
+
+# Author: Kyle Kastner <[email protected]>
+#         Giorgio Patrini
+# License: BSD 3 clause
+
+from numbers import Integral
+
+import numpy as np
+from scipy import linalg, sparse
+
+from ..base import _fit_context
+from ..utils import gen_batches
+from ..utils._param_validation import Interval
+from ..utils.extmath import _incremental_mean_and_var, svd_flip
+from ._base import _BasePCA
+
+
+class IncrementalPCA(_BasePCA):
+    """Incremental principal components analysis (IPCA).
+
+    Linear dimensionality reduction using Singular Value Decomposition of
+    the data, keeping only the most significant singular vectors to
+    project the data to a lower dimensional space. The input data is centered
+    but not scaled for each feature before applying the SVD.
+
+    Depending on the size of the input data, this algorithm can be much more
+    memory efficient than a PCA, and allows sparse input.
+
+    This algorithm has constant memory complexity, on the order
+    of ``batch_size * n_features``, enabling use of np.memmap files without
+    loading the entire file into memory. For sparse matrices, the input
+    is converted to dense in batches (in order to be able to subtract the
+    mean) which avoids storing the entire dense matrix at any one time.
+
+    The computational overhead of each SVD is
+    ``O(batch_size * n_features ** 2)``, but only 2 * batch_size samples
+    remain in memory at a time. There will be ``n_samples / batch_size`` SVD
+    computations to get the principal components, versus 1 large SVD of
+    complexity ``O(n_samples * n_features ** 2)`` for PCA.
+
+    For a usage example, see
+    :ref:`sphx_glr_auto_examples_decomposition_plot_incremental_pca.py`.
+
+    Read more in the :ref:`User Guide <IncrementalPCA>`.
+
+    .. versionadded:: 0.16
+
+    Parameters
+    ----------
+    n_components : int, default=None
+        Number of components to keep. If ``n_components`` is ``None``,
+        then ``n_components`` is set to ``min(n_samples, n_features)``.
+
+    whiten : bool, default=False
+        When True (False by default) the ``components_`` vectors are divided
+        by ``n_samples`` times ``components_`` to ensure uncorrelated outputs
+        with unit component-wise variances.
+
+        Whitening will remove some information from the transformed signal
+        (the relative variance scales of the components) but can sometimes
+        improve the predictive accuracy of the downstream estimators by
+        making data respect some hard-wired assumptions.
+
+    copy : bool, default=True
+        If False, X will be overwritten. ``copy=False`` can be used to
+        save memory but is unsafe for general use.
+
+    batch_size : int, default=None
+        The number of samples to use for each batch. Only used when calling
+        ``fit``. If ``batch_size`` is ``None``, then ``batch_size``
+        is inferred from the data and set to ``5 * n_features``, to provide a
+        balance between approximation accuracy and memory consumption.
+
+    Attributes
+    ----------
+    components_ : ndarray of shape (n_components, n_features)
+        Principal axes in feature space, representing the directions of
+        maximum variance in the data. Equivalently, the right singular
+        vectors of the centered input data, parallel to its eigenvectors.
+        The components are sorted by decreasing ``explained_variance_``.
+
+    explained_variance_ : ndarray of shape (n_components,)
+        Variance explained by each of the selected components.
+
+    explained_variance_ratio_ : ndarray of shape (n_components,)
+        Percentage of variance explained by each of the selected components.
+        If all components are stored, the sum of explained variances is equal
+        to 1.0.
+
+    singular_values_ : ndarray of shape (n_components,)
+        The singular values corresponding to each of the selected components.
+        The singular values are equal to the 2-norms of the ``n_components``
+        variables in the lower-dimensional space.
+
+    mean_ : ndarray of shape (n_features,)
+        Per-feature empirical mean, aggregate over calls to ``partial_fit``.
+
+    var_ : ndarray of shape (n_features,)
+        Per-feature empirical variance, aggregate over calls to
+        ``partial_fit``.
+
+    noise_variance_ : float
+        The estimated noise covariance following the Probabilistic PCA model
+        from Tipping and Bishop 1999. See "Pattern Recognition and
+        Machine Learning" by C. Bishop, 12.2.1 p. 574 or
+        http://www.miketipping.com/papers/met-mppca.pdf.
+
+    n_components_ : int
+        The estimated number of components. Relevant when
+        ``n_components=None``.
+
+    n_samples_seen_ : int
+        The number of samples processed by the estimator. Will be reset on
+        new calls to fit, but increments across ``partial_fit`` calls.
+
+    batch_size_ : int
+        Inferred batch size from ``batch_size``.
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+        .. versionadded:: 0.24
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
+    See Also
+    --------
+    PCA : Principal component analysis (PCA).
+    KernelPCA : Kernel Principal component analysis (KPCA).
+    SparsePCA : Sparse Principal Components Analysis (SparsePCA).
+    TruncatedSVD : Dimensionality reduction using truncated SVD.
+
+    Notes
+    -----
+    Implements the incremental PCA model from:
+    *D. Ross, J. Lim, R. Lin, M. Yang, Incremental Learning for Robust Visual
+    Tracking, International Journal of Computer Vision, Volume 77, Issue 1-3,
+    pp. 125-141, May 2008.*
+    See https://www.cs.toronto.edu/~dross/ivt/RossLimLinYang_ijcv.pdf
+
+    This model is an extension of the Sequential Karhunen-Loeve Transform from:
+    :doi:`A. Levy and M. Lindenbaum, Sequential Karhunen-Loeve Basis Extraction and
+    its Application to Images, IEEE Transactions on Image Processing, Volume 9,
+    Number 8, pp. 1371-1374, August 2000. <10.1109/83.855432>`
+
+    We have specifically abstained from an optimization used by authors of both
+    papers, a QR decomposition used in specific situations to reduce the
+    algorithmic complexity of the SVD. The source for this technique is
+    *Matrix Computations, Third Edition, G. Holub and C. Van Loan, Chapter 5,
+    section 5.4.4, pp 252-253.*. This technique has been omitted because it is
+    advantageous only when decomposing a matrix with ``n_samples`` (rows)
+    >= 5/3 * ``n_features`` (columns), and hurts the readability of the
+    implemented algorithm. This would be a good opportunity for future
+    optimization, if it is deemed necessary.
+
+    References
+    ----------
+    D. Ross, J. Lim, R. Lin, M. Yang. Incremental Learning for Robust Visual
+    Tracking, International Journal of Computer Vision, Volume 77,
+    Issue 1-3, pp. 125-141, May 2008.
+
+    G. Golub and C. Van Loan. Matrix Computations, Third Edition, Chapter 5,
+    Section 5.4.4, pp. 252-253.
+
+    Examples
+    --------
+    >>> from sklearn.datasets import load_digits
+    >>> from sklearn.decomposition import IncrementalPCA
+    >>> from scipy import sparse
+    >>> X, _ = load_digits(return_X_y=True)
+    >>> transformer = IncrementalPCA(n_components=7, batch_size=200)
+    >>> # either partially fit on smaller batches of data
+    >>> transformer.partial_fit(X[:100, :])
+    IncrementalPCA(batch_size=200, n_components=7)
+    >>> # or let the fit function itself divide the data into batches
+    >>> X_sparse = sparse.csr_matrix(X)
+    >>> X_transformed = transformer.fit_transform(X_sparse)
+    >>> X_transformed.shape
+    (1797, 7)
+    """
+
+    _parameter_constraints: dict = {
+        "n_components": [Interval(Integral, 1, None, closed="left"), None],
+        "whiten": ["boolean"],
+        "copy": ["boolean"],
+        "batch_size": [Interval(Integral, 1, None, closed="left"), None],
+    }
+
+    def __init__(self, n_components=None, *, whiten=False, copy=True, batch_size=None):
+        self.n_components = n_components
+        self.whiten = whiten
+        self.copy = copy
+        self.batch_size = batch_size
+
+    @_fit_context(prefer_skip_nested_validation=True)
+    def fit(self, X, y=None):
+        """Fit the model with X, using minibatches of size batch_size.
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            Training data, where `n_samples` is the number of samples and
+            `n_features` is the number of features.
+
+        y : Ignored
+            Not used, present for API consistency by convention.
+
+        Returns
+        -------
+        self : object
+            Returns the instance itself.
+        """
+        self.components_ = None
+        self.n_samples_seen_ = 0
+        self.mean_ = 0.0
+        self.var_ = 0.0
+        self.singular_values_ = None
+        self.explained_variance_ = None
+        self.explained_variance_ratio_ = None
+        self.noise_variance_ = None
+
+        X = self._validate_data(
+            X,
+            accept_sparse=["csr", "csc", "lil"],
+            copy=self.copy,
+            dtype=[np.float64, np.float32],
+        )
+        n_samples, n_features = X.shape
+
+        if self.batch_size is None:
+            self.batch_size_ = 5 * n_features
+        else:
+            self.batch_size_ = self.batch_size
+
+        for batch in gen_batches(
+            n_samples, self.batch_size_, min_batch_size=self.n_components or 0
+        ):
+            X_batch = X[batch]
+            if sparse.issparse(X_batch):
+                X_batch = X_batch.toarray()
+            self.partial_fit(X_batch, check_input=False)
+
+        return self
+
+    @_fit_context(prefer_skip_nested_validation=True)
+    def partial_fit(self, X, y=None, check_input=True):
+        """Incremental fit with X. All of X is processed as a single batch.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            Training data, where `n_samples` is the number of samples and
+            `n_features` is the number of features.
+
+        y : Ignored
+            Not used, present for API consistency by convention.
+
+        check_input : bool, default=True
+            Run check_array on X.
+
+        Returns
+        -------
+        self : object
+            Returns the instance itself.
+        """
+        first_pass = not hasattr(self, "components_")
+
+        if check_input:
+            if sparse.issparse(X):
+                raise TypeError(
+                    "IncrementalPCA.partial_fit does not support "
+                    "sparse input. Either convert data to dense "
+                    "or use IncrementalPCA.fit to do so in batches."
+                )
+            X = self._validate_data(
+                X, copy=self.copy, dtype=[np.float64, np.float32], reset=first_pass
+            )
+        n_samples, n_features = X.shape
+        if first_pass:
+            self.components_ = None
+
+        if self.n_components is None:
+            if self.components_ is None:
+                self.n_components_ = min(n_samples, n_features)
+            else:
+                self.n_components_ = self.components_.shape[0]
+        elif not self.n_components <= n_features:
+            raise ValueError(
+                "n_components=%r invalid for n_features=%d, need "
+                "more rows than columns for IncrementalPCA "
+                "processing" % (self.n_components, n_features)
+            )
+        elif not self.n_components <= n_samples:
+            raise ValueError(
+                "n_components=%r must be less or equal to "
+                "the batch number of samples "
+                "%d." % (self.n_components, n_samples)
+            )
+        else:
+            self.n_components_ = self.n_components
+
+        if (self.components_ is not None) and (
+            self.components_.shape[0] != self.n_components_
+        ):
+            raise ValueError(
+                "Number of input features has changed from %i "
+                "to %i between calls to partial_fit! Try "
+                "setting n_components to a fixed value."
+                % (self.components_.shape[0], self.n_components_)
+            )
+
+        # This is the first partial_fit
+        if not hasattr(self, "n_samples_seen_"):
+            self.n_samples_seen_ = 0
+            self.mean_ = 0.0
+            self.var_ = 0.0
+
+        # Update stats - they are 0 if this is the first step
+        col_mean, col_var, n_total_samples = _incremental_mean_and_var(
+            X,
+            last_mean=self.mean_,
+            last_variance=self.var_,
+            last_sample_count=np.repeat(self.n_samples_seen_, X.shape[1]),
+        )
+        n_total_samples = n_total_samples[0]
+
+        # Whitening
+        if self.n_samples_seen_ == 0:
+            # If it is the first step, simply whiten X
+            X -= col_mean
+        else:
+            col_batch_mean = np.mean(X, axis=0)
+            X -= col_batch_mean
+            # Build matrix of combined previous basis and new data
+            mean_correction = np.sqrt(
+                (self.n_samples_seen_ / n_total_samples) * n_samples
+            ) * (self.mean_ - col_batch_mean)
+            X = np.vstack(
+                (
+                    self.singular_values_.reshape((-1, 1)) * self.components_,
+                    X,
+                    mean_correction,
+                )
+            )
+
+        U, S, Vt = linalg.svd(X, full_matrices=False, check_finite=False)
+        U, Vt = svd_flip(U, Vt, u_based_decision=False)
+        explained_variance = S**2 / (n_total_samples - 1)
+        explained_variance_ratio = S**2 / np.sum(col_var * n_total_samples)
+
+        self.n_samples_seen_ = n_total_samples
+        self.components_ = Vt[: self.n_components_]
+        self.singular_values_ = S[: self.n_components_]
+        self.mean_ = col_mean
+        self.var_ = col_var
+        self.explained_variance_ = explained_variance[: self.n_components_]
+        self.explained_variance_ratio_ = explained_variance_ratio[: self.n_components_]
+        # we already checked `self.n_components <= n_samples` above
+        if self.n_components_ not in (n_samples, n_features):
+            self.noise_variance_ = explained_variance[self.n_components_ :].mean()
+        else:
+            self.noise_variance_ = 0.0
+        return self
+
+    def transform(self, X):
+        """Apply dimensionality reduction to X.
+
+        X is projected on the first principal components previously extracted
+        from a training set, using minibatches of size batch_size if X is
+        sparse.
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            New data, where `n_samples` is the number of samples
+            and `n_features` is the number of features.
+
+        Returns
+        -------
+        X_new : ndarray of shape (n_samples, n_components)
+            Projection of X in the first principal components.
+
+        Examples
+        --------
+
+        >>> import numpy as np
+        >>> from sklearn.decomposition import IncrementalPCA
+        >>> X = np.array([[-1, -1], [-2, -1], [-3, -2],
+        ...               [1, 1], [2, 1], [3, 2]])
+        >>> ipca = IncrementalPCA(n_components=2, batch_size=3)
+        >>> ipca.fit(X)
+        IncrementalPCA(batch_size=3, n_components=2)
+        >>> ipca.transform(X) # doctest: +SKIP
+        """
+        if sparse.issparse(X):
+            n_samples = X.shape[0]
+            output = []
+            for batch in gen_batches(
+                n_samples, self.batch_size_, min_batch_size=self.n_components or 0
+            ):
+                output.append(super().transform(X[batch].toarray()))
+            return np.vstack(output)
+        else:
+            return super().transform(X)

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/_nmf.py

@@ -0,0 +1,2443 @@
+""" Non-negative matrix factorization.
+"""
+# Author: Vlad Niculae
+#         Lars Buitinck
+#         Mathieu Blondel <[email protected]>
+#         Tom Dupre la Tour
+# License: BSD 3 clause
+
+import itertools
+import time
+import warnings
+from abc import ABC
+from math import sqrt
+from numbers import Integral, Real
+
+import numpy as np
+import scipy.sparse as sp
+from scipy import linalg
+
+from .._config import config_context
+from ..base import (
+    BaseEstimator,
+    ClassNamePrefixFeaturesOutMixin,
+    TransformerMixin,
+    _fit_context,
+)
+from ..exceptions import ConvergenceWarning
+from ..utils import check_array, check_random_state, gen_batches, metadata_routing
+from ..utils._param_validation import (
+    Hidden,
+    Interval,
+    StrOptions,
+    validate_params,
+)
+from ..utils.extmath import randomized_svd, safe_sparse_dot, squared_norm
+from ..utils.validation import (
+    check_is_fitted,
+    check_non_negative,
+)
+from ._cdnmf_fast import _update_cdnmf_fast
+
+EPSILON = np.finfo(np.float32).eps
+
+
+def norm(x):
+    """Dot product-based Euclidean norm implementation.
+
+    See: http://fa.bianp.net/blog/2011/computing-the-vector-norm/
+
+    Parameters
+    ----------
+    x : array-like
+        Vector for which to compute the norm.
+    """
+    return sqrt(squared_norm(x))
+
+
+def trace_dot(X, Y):
+    """Trace of np.dot(X, Y.T).
+
+    Parameters
+    ----------
+    X : array-like
+        First matrix.
+    Y : array-like
+        Second matrix.
+    """
+    return np.dot(X.ravel(), Y.ravel())
+
+
+def _check_init(A, shape, whom):
+    A = check_array(A)
+    if shape[0] != "auto" and A.shape[0] != shape[0]:
+        raise ValueError(
+            f"Array with wrong first dimension passed to {whom}. Expected {shape[0]}, "
+            f"but got {A.shape[0]}."
+        )
+    if shape[1] != "auto" and A.shape[1] != shape[1]:
+        raise ValueError(
+            f"Array with wrong second dimension passed to {whom}. Expected {shape[1]}, "
+            f"but got {A.shape[1]}."
+        )
+    check_non_negative(A, whom)
+    if np.max(A) == 0:
+        raise ValueError(f"Array passed to {whom} is full of zeros.")
+
+
+def _beta_divergence(X, W, H, beta, square_root=False):
+    """Compute the beta-divergence of X and dot(W, H).
+
+    Parameters
+    ----------
+    X : float or array-like of shape (n_samples, n_features)
+
+    W : float or array-like of shape (n_samples, n_components)
+
+    H : float or array-like of shape (n_components, n_features)
+
+    beta : float or {'frobenius', 'kullback-leibler', 'itakura-saito'}
+        Parameter of the beta-divergence.
+        If beta == 2, this is half the Frobenius *squared* norm.
+        If beta == 1, this is the generalized Kullback-Leibler divergence.
+        If beta == 0, this is the Itakura-Saito divergence.
+        Else, this is the general beta-divergence.
+
+    square_root : bool, default=False
+        If True, return np.sqrt(2 * res)
+        For beta == 2, it corresponds to the Frobenius norm.
+
+    Returns
+    -------
+        res : float
+            Beta divergence of X and np.dot(X, H).
+    """
+    beta = _beta_loss_to_float(beta)
+
+    # The method can be called with scalars
+    if not sp.issparse(X):
+        X = np.atleast_2d(X)
+    W = np.atleast_2d(W)
+    H = np.atleast_2d(H)
+
+    # Frobenius norm
+    if beta == 2:
+        # Avoid the creation of the dense np.dot(W, H) if X is sparse.
+        if sp.issparse(X):
+            norm_X = np.dot(X.data, X.data)
+            norm_WH = trace_dot(np.linalg.multi_dot([W.T, W, H]), H)
+            cross_prod = trace_dot((X @ H.T), W)
+            res = (norm_X + norm_WH - 2.0 * cross_prod) / 2.0
+        else:
+            res = squared_norm(X - np.dot(W, H)) / 2.0
+
+        if square_root:
+            return np.sqrt(res * 2)
+        else:
+            return res
+
+    if sp.issparse(X):
+        # compute np.dot(W, H) only where X is nonzero
+        WH_data = _special_sparse_dot(W, H, X).data
+        X_data = X.data
+    else:
+        WH = np.dot(W, H)
+        WH_data = WH.ravel()
+        X_data = X.ravel()
+
+    # do not affect the zeros: here 0 ** (-1) = 0 and not infinity
+    indices = X_data > EPSILON
+    WH_data = WH_data[indices]
+    X_data = X_data[indices]
+
+    # used to avoid division by zero
+    WH_data[WH_data < EPSILON] = EPSILON
+
+    # generalized Kullback-Leibler divergence
+    if beta == 1:
+        # fast and memory efficient computation of np.sum(np.dot(W, H))
+        sum_WH = np.dot(np.sum(W, axis=0), np.sum(H, axis=1))
+        # computes np.sum(X * log(X / WH)) only where X is nonzero
+        div = X_data / WH_data
+        res = np.dot(X_data, np.log(div))
+        # add full np.sum(np.dot(W, H)) - np.sum(X)
+        res += sum_WH - X_data.sum()
+
+    # Itakura-Saito divergence
+    elif beta == 0:
+        div = X_data / WH_data
+        res = np.sum(div) - np.prod(X.shape) - np.sum(np.log(div))
+
+    # beta-divergence, beta not in (0, 1, 2)
+    else:
+        if sp.issparse(X):
+            # slow loop, but memory efficient computation of :
+            # np.sum(np.dot(W, H) ** beta)
+            sum_WH_beta = 0
+            for i in range(X.shape[1]):
+                sum_WH_beta += np.sum(np.dot(W, H[:, i]) ** beta)
+
+        else:
+            sum_WH_beta = np.sum(WH**beta)
+
+        sum_X_WH = np.dot(X_data, WH_data ** (beta - 1))
+        res = (X_data**beta).sum() - beta * sum_X_WH
+        res += sum_WH_beta * (beta - 1)
+        res /= beta * (beta - 1)
+
+    if square_root:
+        res = max(res, 0)  # avoid negative number due to rounding errors
+        return np.sqrt(2 * res)
+    else:
+        return res
+
+
+def _special_sparse_dot(W, H, X):
+    """Computes np.dot(W, H), only where X is non zero."""
+    if sp.issparse(X):
+        ii, jj = X.nonzero()
+        n_vals = ii.shape[0]
+        dot_vals = np.empty(n_vals)
+        n_components = W.shape[1]
+
+        batch_size = max(n_components, n_vals // n_components)
+        for start in range(0, n_vals, batch_size):
+            batch = slice(start, start + batch_size)
+            dot_vals[batch] = np.multiply(W[ii[batch], :], H.T[jj[batch], :]).sum(
+                axis=1
+            )
+
+        WH = sp.coo_matrix((dot_vals, (ii, jj)), shape=X.shape)
+        return WH.tocsr()
+    else:
+        return np.dot(W, H)
+
+
+def _beta_loss_to_float(beta_loss):
+    """Convert string beta_loss to float."""
+    beta_loss_map = {"frobenius": 2, "kullback-leibler": 1, "itakura-saito": 0}
+    if isinstance(beta_loss, str):
+        beta_loss = beta_loss_map[beta_loss]
+    return beta_loss
+
+
+def _initialize_nmf(X, n_components, init=None, eps=1e-6, random_state=None):
+    """Algorithms for NMF initialization.
+
+    Computes an initial guess for the non-negative
+    rank k matrix approximation for X: X = WH.
+
+    Parameters
+    ----------
+    X : array-like of shape (n_samples, n_features)
+        The data matrix to be decomposed.
+
+    n_components : int
+        The number of components desired in the approximation.
+
+    init :  {'random', 'nndsvd', 'nndsvda', 'nndsvdar'}, default=None
+        Method used to initialize the procedure.
+        Valid options:
+
+        - None: 'nndsvda' if n_components <= min(n_samples, n_features),
+            otherwise 'random'.
+
+        - 'random': non-negative random matrices, scaled with:
+            sqrt(X.mean() / n_components)
+
+        - 'nndsvd': Nonnegative Double Singular Value Decomposition (NNDSVD)
+            initialization (better for sparseness)
+
+        - 'nndsvda': NNDSVD with zeros filled with the average of X
+            (better when sparsity is not desired)
+
+        - 'nndsvdar': NNDSVD with zeros filled with small random values
+            (generally faster, less accurate alternative to NNDSVDa
+            for when sparsity is not desired)
+
+        - 'custom': use custom matrices W and H
+
+        .. versionchanged:: 1.1
+            When `init=None` and n_components is less than n_samples and n_features
+            defaults to `nndsvda` instead of `nndsvd`.
+
+    eps : float, default=1e-6
+        Truncate all values less then this in output to zero.
+
+    random_state : int, RandomState instance or None, default=None
+        Used when ``init`` == 'nndsvdar' or 'random'. Pass an int for
+        reproducible results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+    Returns
+    -------
+    W : array-like of shape (n_samples, n_components)
+        Initial guesses for solving X ~= WH.
+
+    H : array-like of shape (n_components, n_features)
+        Initial guesses for solving X ~= WH.
+
+    References
+    ----------
+    C. Boutsidis, E. Gallopoulos: SVD based initialization: A head start for
+    nonnegative matrix factorization - Pattern Recognition, 2008
+    http://tinyurl.com/nndsvd
+    """
+    check_non_negative(X, "NMF initialization")
+    n_samples, n_features = X.shape
+
+    if (
+        init is not None
+        and init != "random"
+        and n_components > min(n_samples, n_features)
+    ):
+        raise ValueError(
+            "init = '{}' can only be used when "
+            "n_components <= min(n_samples, n_features)".format(init)
+        )
+
+    if init is None:
+        if n_components <= min(n_samples, n_features):
+            init = "nndsvda"
+        else:
+            init = "random"
+
+    # Random initialization
+    if init == "random":
+        avg = np.sqrt(X.mean() / n_components)
+        rng = check_random_state(random_state)
+        H = avg * rng.standard_normal(size=(n_components, n_features)).astype(
+            X.dtype, copy=False
+        )
+        W = avg * rng.standard_normal(size=(n_samples, n_components)).astype(
+            X.dtype, copy=False
+        )
+        np.abs(H, out=H)
+        np.abs(W, out=W)
+        return W, H
+
+    # NNDSVD initialization
+    U, S, V = randomized_svd(X, n_components, random_state=random_state)
+    W = np.zeros_like(U)
+    H = np.zeros_like(V)
+
+    # The leading singular triplet is non-negative
+    # so it can be used as is for initialization.
+    W[:, 0] = np.sqrt(S[0]) * np.abs(U[:, 0])
+    H[0, :] = np.sqrt(S[0]) * np.abs(V[0, :])
+
+    for j in range(1, n_components):
+        x, y = U[:, j], V[j, :]
+
+        # extract positive and negative parts of column vectors
+        x_p, y_p = np.maximum(x, 0), np.maximum(y, 0)
+        x_n, y_n = np.abs(np.minimum(x, 0)), np.abs(np.minimum(y, 0))
+
+        # and their norms
+        x_p_nrm, y_p_nrm = norm(x_p), norm(y_p)
+        x_n_nrm, y_n_nrm = norm(x_n), norm(y_n)
+
+        m_p, m_n = x_p_nrm * y_p_nrm, x_n_nrm * y_n_nrm
+
+        # choose update
+        if m_p > m_n:
+            u = x_p / x_p_nrm
+            v = y_p / y_p_nrm
+            sigma = m_p
+        else:
+            u = x_n / x_n_nrm
+            v = y_n / y_n_nrm
+            sigma = m_n
+
+        lbd = np.sqrt(S[j] * sigma)
+        W[:, j] = lbd * u
+        H[j, :] = lbd * v
+
+    W[W < eps] = 0
+    H[H < eps] = 0
+
+    if init == "nndsvd":
+        pass
+    elif init == "nndsvda":
+        avg = X.mean()
+        W[W == 0] = avg
+        H[H == 0] = avg
+    elif init == "nndsvdar":
+        rng = check_random_state(random_state)
+        avg = X.mean()
+        W[W == 0] = abs(avg * rng.standard_normal(size=len(W[W == 0])) / 100)
+        H[H == 0] = abs(avg * rng.standard_normal(size=len(H[H == 0])) / 100)
+    else:
+        raise ValueError(
+            "Invalid init parameter: got %r instead of one of %r"
+            % (init, (None, "random", "nndsvd", "nndsvda", "nndsvdar"))
+        )
+
+    return W, H
+
+
+def _update_coordinate_descent(X, W, Ht, l1_reg, l2_reg, shuffle, random_state):
+    """Helper function for _fit_coordinate_descent.
+
+    Update W to minimize the objective function, iterating once over all
+    coordinates. By symmetry, to update H, one can call
+    _update_coordinate_descent(X.T, Ht, W, ...).
+
+    """
+    n_components = Ht.shape[1]
+
+    HHt = np.dot(Ht.T, Ht)
+    XHt = safe_sparse_dot(X, Ht)
+
+    # L2 regularization corresponds to increase of the diagonal of HHt
+    if l2_reg != 0.0:
+        # adds l2_reg only on the diagonal
+        HHt.flat[:: n_components + 1] += l2_reg
+    # L1 regularization corresponds to decrease of each element of XHt
+    if l1_reg != 0.0:
+        XHt -= l1_reg
+
+    if shuffle:
+        permutation = random_state.permutation(n_components)
+    else:
+        permutation = np.arange(n_components)
+    # The following seems to be required on 64-bit Windows w/ Python 3.5.
+    permutation = np.asarray(permutation, dtype=np.intp)
+    return _update_cdnmf_fast(W, HHt, XHt, permutation)
+
+
+def _fit_coordinate_descent(
+    X,
+    W,
+    H,
+    tol=1e-4,
+    max_iter=200,
+    l1_reg_W=0,
+    l1_reg_H=0,
+    l2_reg_W=0,
+    l2_reg_H=0,
+    update_H=True,
+    verbose=0,
+    shuffle=False,
+    random_state=None,
+):
+    """Compute Non-negative Matrix Factorization (NMF) with Coordinate Descent
+
+    The objective function is minimized with an alternating minimization of W
+    and H. Each minimization is done with a cyclic (up to a permutation of the
+    features) Coordinate Descent.
+
+    Parameters
+    ----------
+    X : array-like of shape (n_samples, n_features)
+        Constant matrix.
+
+    W : array-like of shape (n_samples, n_components)
+        Initial guess for the solution.
+
+    H : array-like of shape (n_components, n_features)
+        Initial guess for the solution.
+
+    tol : float, default=1e-4
+        Tolerance of the stopping condition.
+
+    max_iter : int, default=200
+        Maximum number of iterations before timing out.
+
+    l1_reg_W : float, default=0.
+        L1 regularization parameter for W.
+
+    l1_reg_H : float, default=0.
+        L1 regularization parameter for H.
+
+    l2_reg_W : float, default=0.
+        L2 regularization parameter for W.
+
+    l2_reg_H : float, default=0.
+        L2 regularization parameter for H.
+
+    update_H : bool, default=True
+        Set to True, both W and H will be estimated from initial guesses.
+        Set to False, only W will be estimated.
+
+    verbose : int, default=0
+        The verbosity level.
+
+    shuffle : bool, default=False
+        If true, randomize the order of coordinates in the CD solver.
+
+    random_state : int, RandomState instance or None, default=None
+        Used to randomize the coordinates in the CD solver, when
+        ``shuffle`` is set to ``True``. Pass an int for reproducible
+        results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+    Returns
+    -------
+    W : ndarray of shape (n_samples, n_components)
+        Solution to the non-negative least squares problem.
+
+    H : ndarray of shape (n_components, n_features)
+        Solution to the non-negative least squares problem.
+
+    n_iter : int
+        The number of iterations done by the algorithm.
+
+    References
+    ----------
+    .. [1] :doi:`"Fast local algorithms for large scale nonnegative matrix and tensor
+       factorizations" <10.1587/transfun.E92.A.708>`
+       Cichocki, Andrzej, and P. H. A. N. Anh-Huy. IEICE transactions on fundamentals
+       of electronics, communications and computer sciences 92.3: 708-721, 2009.
+    """
+    # so W and Ht are both in C order in memory
+    Ht = check_array(H.T, order="C")
+    X = check_array(X, accept_sparse="csr")
+
+    rng = check_random_state(random_state)
+
+    for n_iter in range(1, max_iter + 1):
+        violation = 0.0
+
+        # Update W
+        violation += _update_coordinate_descent(
+            X, W, Ht, l1_reg_W, l2_reg_W, shuffle, rng
+        )
+        # Update H
+        if update_H:
+            violation += _update_coordinate_descent(
+                X.T, Ht, W, l1_reg_H, l2_reg_H, shuffle, rng
+            )
+
+        if n_iter == 1:
+            violation_init = violation
+
+        if violation_init == 0:
+            break
+
+        if verbose:
+            print("violation:", violation / violation_init)
+
+        if violation / violation_init <= tol:
+            if verbose:
+                print("Converged at iteration", n_iter + 1)
+            break
+
+    return W, Ht.T, n_iter
+
+
+def _multiplicative_update_w(
+    X,
+    W,
+    H,
+    beta_loss,
+    l1_reg_W,
+    l2_reg_W,
+    gamma,
+    H_sum=None,
+    HHt=None,
+    XHt=None,
+    update_H=True,
+):
+    """Update W in Multiplicative Update NMF."""
+    if beta_loss == 2:
+        # Numerator
+        if XHt is None:
+            XHt = safe_sparse_dot(X, H.T)
+        if update_H:
+            # avoid a copy of XHt, which will be re-computed (update_H=True)
+            numerator = XHt
+        else:
+            # preserve the XHt, which is not re-computed (update_H=False)
+            numerator = XHt.copy()
+
+        # Denominator
+        if HHt is None:
+            HHt = np.dot(H, H.T)
+        denominator = np.dot(W, HHt)
+
+    else:
+        # Numerator
+        # if X is sparse, compute WH only where X is non zero
+        WH_safe_X = _special_sparse_dot(W, H, X)
+        if sp.issparse(X):
+            WH_safe_X_data = WH_safe_X.data
+            X_data = X.data
+        else:
+            WH_safe_X_data = WH_safe_X
+            X_data = X
+            # copy used in the Denominator
+            WH = WH_safe_X.copy()
+            if beta_loss - 1.0 < 0:
+                WH[WH < EPSILON] = EPSILON
+
+        # to avoid taking a negative power of zero
+        if beta_loss - 2.0 < 0:
+            WH_safe_X_data[WH_safe_X_data < EPSILON] = EPSILON
+
+        if beta_loss == 1:
+            np.divide(X_data, WH_safe_X_data, out=WH_safe_X_data)
+        elif beta_loss == 0:
+            # speeds up computation time
+            # refer to /numpy/numpy/issues/9363
+            WH_safe_X_data **= -1
+            WH_safe_X_data **= 2
+            # element-wise multiplication
+            WH_safe_X_data *= X_data
+        else:
+            WH_safe_X_data **= beta_loss - 2
+            # element-wise multiplication
+            WH_safe_X_data *= X_data
+
+        # here numerator = dot(X * (dot(W, H) ** (beta_loss - 2)), H.T)
+        numerator = safe_sparse_dot(WH_safe_X, H.T)
+
+        # Denominator
+        if beta_loss == 1:
+            if H_sum is None:
+                H_sum = np.sum(H, axis=1)  # shape(n_components, )
+            denominator = H_sum[np.newaxis, :]
+
+        else:
+            # computation of WHHt = dot(dot(W, H) ** beta_loss - 1, H.T)
+            if sp.issparse(X):
+                # memory efficient computation
+                # (compute row by row, avoiding the dense matrix WH)
+                WHHt = np.empty(W.shape)
+                for i in range(X.shape[0]):
+                    WHi = np.dot(W[i, :], H)
+                    if beta_loss - 1 < 0:
+                        WHi[WHi < EPSILON] = EPSILON
+                    WHi **= beta_loss - 1
+                    WHHt[i, :] = np.dot(WHi, H.T)
+            else:
+                WH **= beta_loss - 1
+                WHHt = np.dot(WH, H.T)
+            denominator = WHHt
+
+    # Add L1 and L2 regularization
+    if l1_reg_W > 0:
+        denominator += l1_reg_W
+    if l2_reg_W > 0:
+        denominator = denominator + l2_reg_W * W
+    denominator[denominator == 0] = EPSILON
+
+    numerator /= denominator
+    delta_W = numerator
+
+    # gamma is in ]0, 1]
+    if gamma != 1:
+        delta_W **= gamma
+
+    W *= delta_W
+
+    return W, H_sum, HHt, XHt
+
+
+def _multiplicative_update_h(
+    X, W, H, beta_loss, l1_reg_H, l2_reg_H, gamma, A=None, B=None, rho=None
+):
+    """update H in Multiplicative Update NMF."""
+    if beta_loss == 2:
+        numerator = safe_sparse_dot(W.T, X)
+        denominator = np.linalg.multi_dot([W.T, W, H])
+
+    else:
+        # Numerator
+        WH_safe_X = _special_sparse_dot(W, H, X)
+        if sp.issparse(X):
+            WH_safe_X_data = WH_safe_X.data
+            X_data = X.data
+        else:
+            WH_safe_X_data = WH_safe_X
+            X_data = X
+            # copy used in the Denominator
+            WH = WH_safe_X.copy()
+            if beta_loss - 1.0 < 0:
+                WH[WH < EPSILON] = EPSILON
+
+        # to avoid division by zero
+        if beta_loss - 2.0 < 0:
+            WH_safe_X_data[WH_safe_X_data < EPSILON] = EPSILON
+
+        if beta_loss == 1:
+            np.divide(X_data, WH_safe_X_data, out=WH_safe_X_data)
+        elif beta_loss == 0:
+            # speeds up computation time
+            # refer to /numpy/numpy/issues/9363
+            WH_safe_X_data **= -1
+            WH_safe_X_data **= 2
+            # element-wise multiplication
+            WH_safe_X_data *= X_data
+        else:
+            WH_safe_X_data **= beta_loss - 2
+            # element-wise multiplication
+            WH_safe_X_data *= X_data
+
+        # here numerator = dot(W.T, (dot(W, H) ** (beta_loss - 2)) * X)
+        numerator = safe_sparse_dot(W.T, WH_safe_X)
+
+        # Denominator
+        if beta_loss == 1:
+            W_sum = np.sum(W, axis=0)  # shape(n_components, )
+            W_sum[W_sum == 0] = 1.0
+            denominator = W_sum[:, np.newaxis]
+
+        # beta_loss not in (1, 2)
+        else:
+            # computation of WtWH = dot(W.T, dot(W, H) ** beta_loss - 1)
+            if sp.issparse(X):
+                # memory efficient computation
+                # (compute column by column, avoiding the dense matrix WH)
+                WtWH = np.empty(H.shape)
+                for i in range(X.shape[1]):
+                    WHi = np.dot(W, H[:, i])
+                    if beta_loss - 1 < 0:
+                        WHi[WHi < EPSILON] = EPSILON
+                    WHi **= beta_loss - 1
+                    WtWH[:, i] = np.dot(W.T, WHi)
+            else:
+                WH **= beta_loss - 1
+                WtWH = np.dot(W.T, WH)
+            denominator = WtWH
+
+    # Add L1 and L2 regularization
+    if l1_reg_H > 0:
+        denominator += l1_reg_H
+    if l2_reg_H > 0:
+        denominator = denominator + l2_reg_H * H
+    denominator[denominator == 0] = EPSILON
+
+    if A is not None and B is not None:
+        # Updates for the online nmf
+        if gamma != 1:
+            H **= 1 / gamma
+        numerator *= H
+        A *= rho
+        B *= rho
+        A += numerator
+        B += denominator
+        H = A / B
+
+        if gamma != 1:
+            H **= gamma
+    else:
+        delta_H = numerator
+        delta_H /= denominator
+        if gamma != 1:
+            delta_H **= gamma
+        H *= delta_H
+
+    return H
+
+
+def _fit_multiplicative_update(
+    X,
+    W,
+    H,
+    beta_loss="frobenius",
+    max_iter=200,
+    tol=1e-4,
+    l1_reg_W=0,
+    l1_reg_H=0,
+    l2_reg_W=0,
+    l2_reg_H=0,
+    update_H=True,
+    verbose=0,
+):
+    """Compute Non-negative Matrix Factorization with Multiplicative Update.
+
+    The objective function is _beta_divergence(X, WH) and is minimized with an
+    alternating minimization of W and H. Each minimization is done with a
+    Multiplicative Update.
+
+    Parameters
+    ----------
+    X : array-like of shape (n_samples, n_features)
+        Constant input matrix.
+
+    W : array-like of shape (n_samples, n_components)
+        Initial guess for the solution.
+
+    H : array-like of shape (n_components, n_features)
+        Initial guess for the solution.
+
+    beta_loss : float or {'frobenius', 'kullback-leibler', \
+            'itakura-saito'}, default='frobenius'
+        String must be in {'frobenius', 'kullback-leibler', 'itakura-saito'}.
+        Beta divergence to be minimized, measuring the distance between X
+        and the dot product WH. Note that values different from 'frobenius'
+        (or 2) and 'kullback-leibler' (or 1) lead to significantly slower
+        fits. Note that for beta_loss <= 0 (or 'itakura-saito'), the input
+        matrix X cannot contain zeros.
+
+    max_iter : int, default=200
+        Number of iterations.
+
+    tol : float, default=1e-4
+        Tolerance of the stopping condition.
+
+    l1_reg_W : float, default=0.
+        L1 regularization parameter for W.
+
+    l1_reg_H : float, default=0.
+        L1 regularization parameter for H.
+
+    l2_reg_W : float, default=0.
+        L2 regularization parameter for W.
+
+    l2_reg_H : float, default=0.
+        L2 regularization parameter for H.
+
+    update_H : bool, default=True
+        Set to True, both W and H will be estimated from initial guesses.
+        Set to False, only W will be estimated.
+
+    verbose : int, default=0
+        The verbosity level.
+
+    Returns
+    -------
+    W : ndarray of shape (n_samples, n_components)
+        Solution to the non-negative least squares problem.
+
+    H : ndarray of shape (n_components, n_features)
+        Solution to the non-negative least squares problem.
+
+    n_iter : int
+        The number of iterations done by the algorithm.
+
+    References
+    ----------
+    Lee, D. D., & Seung, H., S. (2001). Algorithms for Non-negative Matrix
+    Factorization. Adv. Neural Inform. Process. Syst.. 13.
+    Fevotte, C., & Idier, J. (2011). Algorithms for nonnegative matrix
+    factorization with the beta-divergence. Neural Computation, 23(9).
+    """
+    start_time = time.time()
+
+    beta_loss = _beta_loss_to_float(beta_loss)
+
+    # gamma for Maximization-Minimization (MM) algorithm [Fevotte 2011]
+    if beta_loss < 1:
+        gamma = 1.0 / (2.0 - beta_loss)
+    elif beta_loss > 2:
+        gamma = 1.0 / (beta_loss - 1.0)
+    else:
+        gamma = 1.0
+
+    # used for the convergence criterion
+    error_at_init = _beta_divergence(X, W, H, beta_loss, square_root=True)
+    previous_error = error_at_init
+
+    H_sum, HHt, XHt = None, None, None
+    for n_iter in range(1, max_iter + 1):
+        # update W
+        # H_sum, HHt and XHt are saved and reused if not update_H
+        W, H_sum, HHt, XHt = _multiplicative_update_w(
+            X,
+            W,
+            H,
+            beta_loss=beta_loss,
+            l1_reg_W=l1_reg_W,
+            l2_reg_W=l2_reg_W,
+            gamma=gamma,
+            H_sum=H_sum,
+            HHt=HHt,
+            XHt=XHt,
+            update_H=update_H,
+        )
+
+        # necessary for stability with beta_loss < 1
+        if beta_loss < 1:
+            W[W < np.finfo(np.float64).eps] = 0.0
+
+        # update H (only at fit or fit_transform)
+        if update_H:
+            H = _multiplicative_update_h(
+                X,
+                W,
+                H,
+                beta_loss=beta_loss,
+                l1_reg_H=l1_reg_H,
+                l2_reg_H=l2_reg_H,
+                gamma=gamma,
+            )
+
+            # These values will be recomputed since H changed
+            H_sum, HHt, XHt = None, None, None
+
+            # necessary for stability with beta_loss < 1
+            if beta_loss <= 1:
+                H[H < np.finfo(np.float64).eps] = 0.0
+
+        # test convergence criterion every 10 iterations
+        if tol > 0 and n_iter % 10 == 0:
+            error = _beta_divergence(X, W, H, beta_loss, square_root=True)
+
+            if verbose:
+                iter_time = time.time()
+                print(
+                    "Epoch %02d reached after %.3f seconds, error: %f"
+                    % (n_iter, iter_time - start_time, error)
+                )
+
+            if (previous_error - error) / error_at_init < tol:
+                break
+            previous_error = error
+
+    # do not print if we have already printed in the convergence test
+    if verbose and (tol == 0 or n_iter % 10 != 0):
+        end_time = time.time()
+        print(
+            "Epoch %02d reached after %.3f seconds." % (n_iter, end_time - start_time)
+        )
+
+    return W, H, n_iter
+
+
+@validate_params(
+    {
+        "X": ["array-like", "sparse matrix"],
+        "W": ["array-like", None],
+        "H": ["array-like", None],
+        "update_H": ["boolean"],
+    },
+    prefer_skip_nested_validation=False,
+)
+def non_negative_factorization(
+    X,
+    W=None,
+    H=None,
+    n_components="warn",
+    *,
+    init=None,
+    update_H=True,
+    solver="cd",
+    beta_loss="frobenius",
+    tol=1e-4,
+    max_iter=200,
+    alpha_W=0.0,
+    alpha_H="same",
+    l1_ratio=0.0,
+    random_state=None,
+    verbose=0,
+    shuffle=False,
+):
+    """Compute Non-negative Matrix Factorization (NMF).
+
+    Find two non-negative matrices (W, H) whose product approximates the non-
+    negative matrix X. This factorization can be used for example for
+    dimensionality reduction, source separation or topic extraction.
+
+    The objective function is:
+
+        .. math::
+
+            L(W, H) &= 0.5 * ||X - WH||_{loss}^2
+
+            &+ alpha\\_W * l1\\_ratio * n\\_features * ||vec(W)||_1
+
+            &+ alpha\\_H * l1\\_ratio * n\\_samples * ||vec(H)||_1
+
+            &+ 0.5 * alpha\\_W * (1 - l1\\_ratio) * n\\_features * ||W||_{Fro}^2
+
+            &+ 0.5 * alpha\\_H * (1 - l1\\_ratio) * n\\_samples * ||H||_{Fro}^2
+
+    Where:
+
+    :math:`||A||_{Fro}^2 = \\sum_{i,j} A_{ij}^2` (Frobenius norm)
+
+    :math:`||vec(A)||_1 = \\sum_{i,j} abs(A_{ij})` (Elementwise L1 norm)
+
+    The generic norm :math:`||X - WH||_{loss}^2` may represent
+    the Frobenius norm or another supported beta-divergence loss.
+    The choice between options is controlled by the `beta_loss` parameter.
+
+    The regularization terms are scaled by `n_features` for `W` and by `n_samples` for
+    `H` to keep their impact balanced with respect to one another and to the data fit
+    term as independent as possible of the size `n_samples` of the training set.
+
+    The objective function is minimized with an alternating minimization of W
+    and H. If H is given and update_H=False, it solves for W only.
+
+    Note that the transformed data is named W and the components matrix is named H. In
+    the NMF literature, the naming convention is usually the opposite since the data
+    matrix X is transposed.
+
+    Parameters
+    ----------
+    X : {array-like, sparse matrix} of shape (n_samples, n_features)
+        Constant matrix.
+
+    W : array-like of shape (n_samples, n_components), default=None
+        If `init='custom'`, it is used as initial guess for the solution.
+        If `update_H=False`, it is initialised as an array of zeros, unless
+        `solver='mu'`, then it is filled with values calculated by
+        `np.sqrt(X.mean() / self._n_components)`.
+        If `None`, uses the initialisation method specified in `init`.
+
+    H : array-like of shape (n_components, n_features), default=None
+        If `init='custom'`, it is used as initial guess for the solution.
+        If `update_H=False`, it is used as a constant, to solve for W only.
+        If `None`, uses the initialisation method specified in `init`.
+
+    n_components : int or {'auto'} or None, default=None
+        Number of components, if n_components is not set all features
+        are kept.
+        If `n_components='auto'`, the number of components is automatically inferred
+        from `W` or `H` shapes.
+
+        .. versionchanged:: 1.4
+            Added `'auto'` value.
+
+    init : {'random', 'nndsvd', 'nndsvda', 'nndsvdar', 'custom'}, default=None
+        Method used to initialize the procedure.
+
+        Valid options:
+
+        - None: 'nndsvda' if n_components < n_features, otherwise 'random'.
+        - 'random': non-negative random matrices, scaled with:
+          `sqrt(X.mean() / n_components)`
+        - 'nndsvd': Nonnegative Double Singular Value Decomposition (NNDSVD)
+          initialization (better for sparseness)
+        - 'nndsvda': NNDSVD with zeros filled with the average of X
+          (better when sparsity is not desired)
+        - 'nndsvdar': NNDSVD with zeros filled with small random values
+          (generally faster, less accurate alternative to NNDSVDa
+          for when sparsity is not desired)
+        - 'custom': If `update_H=True`, use custom matrices W and H which must both
+          be provided. If `update_H=False`, then only custom matrix H is used.
+
+        .. versionchanged:: 0.23
+            The default value of `init` changed from 'random' to None in 0.23.
+
+        .. versionchanged:: 1.1
+            When `init=None` and n_components is less than n_samples and n_features
+            defaults to `nndsvda` instead of `nndsvd`.
+
+    update_H : bool, default=True
+        Set to True, both W and H will be estimated from initial guesses.
+        Set to False, only W will be estimated.
+
+    solver : {'cd', 'mu'}, default='cd'
+        Numerical solver to use:
+
+        - 'cd' is a Coordinate Descent solver that uses Fast Hierarchical
+          Alternating Least Squares (Fast HALS).
+        - 'mu' is a Multiplicative Update solver.
+
+        .. versionadded:: 0.17
+           Coordinate Descent solver.
+
+        .. versionadded:: 0.19
+           Multiplicative Update solver.
+
+    beta_loss : float or {'frobenius', 'kullback-leibler', \
+            'itakura-saito'}, default='frobenius'
+        Beta divergence to be minimized, measuring the distance between X
+        and the dot product WH. Note that values different from 'frobenius'
+        (or 2) and 'kullback-leibler' (or 1) lead to significantly slower
+        fits. Note that for beta_loss <= 0 (or 'itakura-saito'), the input
+        matrix X cannot contain zeros. Used only in 'mu' solver.
+
+        .. versionadded:: 0.19
+
+    tol : float, default=1e-4
+        Tolerance of the stopping condition.
+
+    max_iter : int, default=200
+        Maximum number of iterations before timing out.
+
+    alpha_W : float, default=0.0
+        Constant that multiplies the regularization terms of `W`. Set it to zero
+        (default) to have no regularization on `W`.
+
+        .. versionadded:: 1.0
+
+    alpha_H : float or "same", default="same"
+        Constant that multiplies the regularization terms of `H`. Set it to zero to
+        have no regularization on `H`. If "same" (default), it takes the same value as
+        `alpha_W`.
+
+        .. versionadded:: 1.0
+
+    l1_ratio : float, default=0.0
+        The regularization mixing parameter, with 0 <= l1_ratio <= 1.
+        For l1_ratio = 0 the penalty is an elementwise L2 penalty
+        (aka Frobenius Norm).
+        For l1_ratio = 1 it is an elementwise L1 penalty.
+        For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2.
+
+    random_state : int, RandomState instance or None, default=None
+        Used for NMF initialisation (when ``init`` == 'nndsvdar' or
+        'random'), and in Coordinate Descent. Pass an int for reproducible
+        results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+    verbose : int, default=0
+        The verbosity level.
+
+    shuffle : bool, default=False
+        If true, randomize the order of coordinates in the CD solver.
+
+    Returns
+    -------
+    W : ndarray of shape (n_samples, n_components)
+        Solution to the non-negative least squares problem.
+
+    H : ndarray of shape (n_components, n_features)
+        Solution to the non-negative least squares problem.
+
+    n_iter : int
+        Actual number of iterations.
+
+    References
+    ----------
+    .. [1] :doi:`"Fast local algorithms for large scale nonnegative matrix and tensor
+       factorizations" <10.1587/transfun.E92.A.708>`
+       Cichocki, Andrzej, and P. H. A. N. Anh-Huy. IEICE transactions on fundamentals
+       of electronics, communications and computer sciences 92.3: 708-721, 2009.
+
+    .. [2] :doi:`"Algorithms for nonnegative matrix factorization with the
+       beta-divergence" <10.1162/NECO_a_00168>`
+       Fevotte, C., & Idier, J. (2011). Neural Computation, 23(9).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> X = np.array([[1,1], [2, 1], [3, 1.2], [4, 1], [5, 0.8], [6, 1]])
+    >>> from sklearn.decomposition import non_negative_factorization
+    >>> W, H, n_iter = non_negative_factorization(
+    ...     X, n_components=2, init='random', random_state=0)
+    """
+    est = NMF(
+        n_components=n_components,
+        init=init,
+        solver=solver,
+        beta_loss=beta_loss,
+        tol=tol,
+        max_iter=max_iter,
+        random_state=random_state,
+        alpha_W=alpha_W,
+        alpha_H=alpha_H,
+        l1_ratio=l1_ratio,
+        verbose=verbose,
+        shuffle=shuffle,
+    )
+    est._validate_params()
+
+    X = check_array(X, accept_sparse=("csr", "csc"), dtype=[np.float64, np.float32])
+
+    with config_context(assume_finite=True):
+        W, H, n_iter = est._fit_transform(X, W=W, H=H, update_H=update_H)
+
+    return W, H, n_iter
+
+
+class _BaseNMF(ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator, ABC):
+    """Base class for NMF and MiniBatchNMF."""
+
+    # This prevents ``set_split_inverse_transform`` to be generated for the
+    # non-standard ``W`` arg on ``inverse_transform``.
+    # TODO: remove when W is removed in v1.5 for inverse_transform
+    __metadata_request__inverse_transform = {"W": metadata_routing.UNUSED}
+
+    _parameter_constraints: dict = {
+        "n_components": [
+            Interval(Integral, 1, None, closed="left"),
+            None,
+            StrOptions({"auto"}),
+            Hidden(StrOptions({"warn"})),
+        ],
+        "init": [
+            StrOptions({"random", "nndsvd", "nndsvda", "nndsvdar", "custom"}),
+            None,
+        ],
+        "beta_loss": [
+            StrOptions({"frobenius", "kullback-leibler", "itakura-saito"}),
+            Real,
+        ],
+        "tol": [Interval(Real, 0, None, closed="left")],
+        "max_iter": [Interval(Integral, 1, None, closed="left")],
+        "random_state": ["random_state"],
+        "alpha_W": [Interval(Real, 0, None, closed="left")],
+        "alpha_H": [Interval(Real, 0, None, closed="left"), StrOptions({"same"})],
+        "l1_ratio": [Interval(Real, 0, 1, closed="both")],
+        "verbose": ["verbose"],
+    }
+
+    def __init__(
+        self,
+        n_components="warn",
+        *,
+        init=None,
+        beta_loss="frobenius",
+        tol=1e-4,
+        max_iter=200,
+        random_state=None,
+        alpha_W=0.0,
+        alpha_H="same",
+        l1_ratio=0.0,
+        verbose=0,
+    ):
+        self.n_components = n_components
+        self.init = init
+        self.beta_loss = beta_loss
+        self.tol = tol
+        self.max_iter = max_iter
+        self.random_state = random_state
+        self.alpha_W = alpha_W
+        self.alpha_H = alpha_H
+        self.l1_ratio = l1_ratio
+        self.verbose = verbose
+
+    def _check_params(self, X):
+        # n_components
+        self._n_components = self.n_components
+        if self.n_components == "warn":
+            warnings.warn(
+                (
+                    "The default value of `n_components` will change from `None` to"
+                    " `'auto'` in 1.6. Set the value of `n_components` to `None`"
+                    " explicitly to suppress the warning."
+                ),
+                FutureWarning,
+            )
+            self._n_components = None  # Keeping the old default value
+        if self._n_components is None:
+            self._n_components = X.shape[1]
+
+        # beta_loss
+        self._beta_loss = _beta_loss_to_float(self.beta_loss)
+
+    def _check_w_h(self, X, W, H, update_H):
+        """Check W and H, or initialize them."""
+        n_samples, n_features = X.shape
+
+        if self.init == "custom" and update_H:
+            _check_init(H, (self._n_components, n_features), "NMF (input H)")
+            _check_init(W, (n_samples, self._n_components), "NMF (input W)")
+            if self._n_components == "auto":
+                self._n_components = H.shape[0]
+
+            if H.dtype != X.dtype or W.dtype != X.dtype:
+                raise TypeError(
+                    "H and W should have the same dtype as X. Got "
+                    "H.dtype = {} and W.dtype = {}.".format(H.dtype, W.dtype)
+                )
+
+        elif not update_H:
+            if W is not None:
+                warnings.warn(
+                    "When update_H=False, the provided initial W is not used.",
+                    RuntimeWarning,
+                )
+
+            _check_init(H, (self._n_components, n_features), "NMF (input H)")
+            if self._n_components == "auto":
+                self._n_components = H.shape[0]
+
+            if H.dtype != X.dtype:
+                raise TypeError(
+                    "H should have the same dtype as X. Got H.dtype = {}.".format(
+                        H.dtype
+                    )
+                )
+
+            # 'mu' solver should not be initialized by zeros
+            if self.solver == "mu":
+                avg = np.sqrt(X.mean() / self._n_components)
+                W = np.full((n_samples, self._n_components), avg, dtype=X.dtype)
+            else:
+                W = np.zeros((n_samples, self._n_components), dtype=X.dtype)
+
+        else:
+            if W is not None or H is not None:
+                warnings.warn(
+                    (
+                        "When init!='custom', provided W or H are ignored. Set "
+                        " init='custom' to use them as initialization."
+                    ),
+                    RuntimeWarning,
+                )
+
+            if self._n_components == "auto":
+                self._n_components = X.shape[1]
+
+            W, H = _initialize_nmf(
+                X, self._n_components, init=self.init, random_state=self.random_state
+            )
+
+        return W, H
+
+    def _compute_regularization(self, X):
+        """Compute scaled regularization terms."""
+        n_samples, n_features = X.shape
+        alpha_W = self.alpha_W
+        alpha_H = self.alpha_W if self.alpha_H == "same" else self.alpha_H
+
+        l1_reg_W = n_features * alpha_W * self.l1_ratio
+        l1_reg_H = n_samples * alpha_H * self.l1_ratio
+        l2_reg_W = n_features * alpha_W * (1.0 - self.l1_ratio)
+        l2_reg_H = n_samples * alpha_H * (1.0 - self.l1_ratio)
+
+        return l1_reg_W, l1_reg_H, l2_reg_W, l2_reg_H
+
+    def fit(self, X, y=None, **params):
+        """Learn a NMF model for the data X.
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            Training vector, where `n_samples` is the number of samples
+            and `n_features` is the number of features.
+
+        y : Ignored
+            Not used, present for API consistency by convention.
+
+        **params : kwargs
+            Parameters (keyword arguments) and values passed to
+            the fit_transform instance.
+
+        Returns
+        -------
+        self : object
+            Returns the instance itself.
+        """
+        # param validation is done in fit_transform
+
+        self.fit_transform(X, **params)
+        return self
+
+    def inverse_transform(self, Xt=None, W=None):
+        """Transform data back to its original space.
+
+        .. versionadded:: 0.18
+
+        Parameters
+        ----------
+        Xt : {ndarray, sparse matrix} of shape (n_samples, n_components)
+            Transformed data matrix.
+
+        W : deprecated
+            Use `Xt` instead.
+
+            .. deprecated:: 1.3
+
+        Returns
+        -------
+        X : ndarray of shape (n_samples, n_features)
+            Returns a data matrix of the original shape.
+        """
+        if Xt is None and W is None:
+            raise TypeError("Missing required positional argument: Xt")
+
+        if W is not None and Xt is not None:
+            raise ValueError("Please provide only `Xt`, and not `W`.")
+
+        if W is not None:
+            warnings.warn(
+                (
+                    "Input argument `W` was renamed to `Xt` in v1.3 and will be removed"
+                    " in v1.5."
+                ),
+                FutureWarning,
+            )
+            Xt = W
+
+        check_is_fitted(self)
+        return Xt @ self.components_
+
+    @property
+    def _n_features_out(self):
+        """Number of transformed output features."""
+        return self.components_.shape[0]
+
+    def _more_tags(self):
+        return {
+            "requires_positive_X": True,
+            "preserves_dtype": [np.float64, np.float32],
+        }
+
+
+class NMF(_BaseNMF):
+    """Non-Negative Matrix Factorization (NMF).
+
+    Find two non-negative matrices, i.e. matrices with all non-negative elements, (W, H)
+    whose product approximates the non-negative matrix X. This factorization can be used
+    for example for dimensionality reduction, source separation or topic extraction.
+
+    The objective function is:
+
+        .. math::
+
+            L(W, H) &= 0.5 * ||X - WH||_{loss}^2
+
+            &+ alpha\\_W * l1\\_ratio * n\\_features * ||vec(W)||_1
+
+            &+ alpha\\_H * l1\\_ratio * n\\_samples * ||vec(H)||_1
+
+            &+ 0.5 * alpha\\_W * (1 - l1\\_ratio) * n\\_features * ||W||_{Fro}^2
+
+            &+ 0.5 * alpha\\_H * (1 - l1\\_ratio) * n\\_samples * ||H||_{Fro}^2
+
+    Where:
+
+    :math:`||A||_{Fro}^2 = \\sum_{i,j} A_{ij}^2` (Frobenius norm)
+
+    :math:`||vec(A)||_1 = \\sum_{i,j} abs(A_{ij})` (Elementwise L1 norm)
+
+    The generic norm :math:`||X - WH||_{loss}` may represent
+    the Frobenius norm or another supported beta-divergence loss.
+    The choice between options is controlled by the `beta_loss` parameter.
+
+    The regularization terms are scaled by `n_features` for `W` and by `n_samples` for
+    `H` to keep their impact balanced with respect to one another and to the data fit
+    term as independent as possible of the size `n_samples` of the training set.
+
+    The objective function is minimized with an alternating minimization of W
+    and H.
+
+    Note that the transformed data is named W and the components matrix is named H. In
+    the NMF literature, the naming convention is usually the opposite since the data
+    matrix X is transposed.
+
+    Read more in the :ref:`User Guide <NMF>`.
+
+    Parameters
+    ----------
+    n_components : int or {'auto'} or None, default=None
+        Number of components, if n_components is not set all features
+        are kept.
+        If `n_components='auto'`, the number of components is automatically inferred
+        from W or H shapes.
+
+        .. versionchanged:: 1.4
+            Added `'auto'` value.
+
+    init : {'random', 'nndsvd', 'nndsvda', 'nndsvdar', 'custom'}, default=None
+        Method used to initialize the procedure.
+        Valid options:
+
+        - `None`: 'nndsvda' if n_components <= min(n_samples, n_features),
+          otherwise random.
+
+        - `'random'`: non-negative random matrices, scaled with:
+          `sqrt(X.mean() / n_components)`
+
+        - `'nndsvd'`: Nonnegative Double Singular Value Decomposition (NNDSVD)
+          initialization (better for sparseness)
+
+        - `'nndsvda'`: NNDSVD with zeros filled with the average of X
+          (better when sparsity is not desired)
+
+        - `'nndsvdar'` NNDSVD with zeros filled with small random values
+          (generally faster, less accurate alternative to NNDSVDa
+          for when sparsity is not desired)
+
+        - `'custom'`: Use custom matrices `W` and `H` which must both be provided.
+
+        .. versionchanged:: 1.1
+            When `init=None` and n_components is less than n_samples and n_features
+            defaults to `nndsvda` instead of `nndsvd`.
+
+    solver : {'cd', 'mu'}, default='cd'
+        Numerical solver to use:
+
+        - 'cd' is a Coordinate Descent solver.
+        - 'mu' is a Multiplicative Update solver.
+
+        .. versionadded:: 0.17
+           Coordinate Descent solver.
+
+        .. versionadded:: 0.19
+           Multiplicative Update solver.
+
+    beta_loss : float or {'frobenius', 'kullback-leibler', \
+            'itakura-saito'}, default='frobenius'
+        Beta divergence to be minimized, measuring the distance between X
+        and the dot product WH. Note that values different from 'frobenius'
+        (or 2) and 'kullback-leibler' (or 1) lead to significantly slower
+        fits. Note that for beta_loss <= 0 (or 'itakura-saito'), the input
+        matrix X cannot contain zeros. Used only in 'mu' solver.
+
+        .. versionadded:: 0.19
+
+    tol : float, default=1e-4
+        Tolerance of the stopping condition.
+
+    max_iter : int, default=200
+        Maximum number of iterations before timing out.
+
+    random_state : int, RandomState instance or None, default=None
+        Used for initialisation (when ``init`` == 'nndsvdar' or
+        'random'), and in Coordinate Descent. Pass an int for reproducible
+        results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+    alpha_W : float, default=0.0
+        Constant that multiplies the regularization terms of `W`. Set it to zero
+        (default) to have no regularization on `W`.
+
+        .. versionadded:: 1.0
+
+    alpha_H : float or "same", default="same"
+        Constant that multiplies the regularization terms of `H`. Set it to zero to
+        have no regularization on `H`. If "same" (default), it takes the same value as
+        `alpha_W`.
+
+        .. versionadded:: 1.0
+
+    l1_ratio : float, default=0.0
+        The regularization mixing parameter, with 0 <= l1_ratio <= 1.
+        For l1_ratio = 0 the penalty is an elementwise L2 penalty
+        (aka Frobenius Norm).
+        For l1_ratio = 1 it is an elementwise L1 penalty.
+        For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2.
+
+        .. versionadded:: 0.17
+           Regularization parameter *l1_ratio* used in the Coordinate Descent
+           solver.
+
+    verbose : int, default=0
+        Whether to be verbose.
+
+    shuffle : bool, default=False
+        If true, randomize the order of coordinates in the CD solver.
+
+        .. versionadded:: 0.17
+           *shuffle* parameter used in the Coordinate Descent solver.
+
+    Attributes
+    ----------
+    components_ : ndarray of shape (n_components, n_features)
+        Factorization matrix, sometimes called 'dictionary'.
+
+    n_components_ : int
+        The number of components. It is same as the `n_components` parameter
+        if it was given. Otherwise, it will be same as the number of
+        features.
+
+    reconstruction_err_ : float
+        Frobenius norm of the matrix difference, or beta-divergence, between
+        the training data ``X`` and the reconstructed data ``WH`` from
+        the fitted model.
+
+    n_iter_ : int
+        Actual number of iterations.
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+        .. versionadded:: 0.24
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
+    See Also
+    --------
+    DictionaryLearning : Find a dictionary that sparsely encodes data.
+    MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis.
+    PCA : Principal component analysis.
+    SparseCoder : Find a sparse representation of data from a fixed,
+        precomputed dictionary.
+    SparsePCA : Sparse Principal Components Analysis.
+    TruncatedSVD : Dimensionality reduction using truncated SVD.
+
+    References
+    ----------
+    .. [1] :doi:`"Fast local algorithms for large scale nonnegative matrix and tensor
+       factorizations" <10.1587/transfun.E92.A.708>`
+       Cichocki, Andrzej, and P. H. A. N. Anh-Huy. IEICE transactions on fundamentals
+       of electronics, communications and computer sciences 92.3: 708-721, 2009.
+
+    .. [2] :doi:`"Algorithms for nonnegative matrix factorization with the
+       beta-divergence" <10.1162/NECO_a_00168>`
+       Fevotte, C., & Idier, J. (2011). Neural Computation, 23(9).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> X = np.array([[1, 1], [2, 1], [3, 1.2], [4, 1], [5, 0.8], [6, 1]])
+    >>> from sklearn.decomposition import NMF
+    >>> model = NMF(n_components=2, init='random', random_state=0)
+    >>> W = model.fit_transform(X)
+    >>> H = model.components_
+    """
+
+    _parameter_constraints: dict = {
+        **_BaseNMF._parameter_constraints,
+        "solver": [StrOptions({"mu", "cd"})],
+        "shuffle": ["boolean"],
+    }
+
+    def __init__(
+        self,
+        n_components="warn",
+        *,
+        init=None,
+        solver="cd",
+        beta_loss="frobenius",
+        tol=1e-4,
+        max_iter=200,
+        random_state=None,
+        alpha_W=0.0,
+        alpha_H="same",
+        l1_ratio=0.0,
+        verbose=0,
+        shuffle=False,
+    ):
+        super().__init__(
+            n_components=n_components,
+            init=init,
+            beta_loss=beta_loss,
+            tol=tol,
+            max_iter=max_iter,
+            random_state=random_state,
+            alpha_W=alpha_W,
+            alpha_H=alpha_H,
+            l1_ratio=l1_ratio,
+            verbose=verbose,
+        )
+
+        self.solver = solver
+        self.shuffle = shuffle
+
+    def _check_params(self, X):
+        super()._check_params(X)
+
+        # solver
+        if self.solver != "mu" and self.beta_loss not in (2, "frobenius"):
+            # 'mu' is the only solver that handles other beta losses than 'frobenius'
+            raise ValueError(
+                f"Invalid beta_loss parameter: solver {self.solver!r} does not handle "
+                f"beta_loss = {self.beta_loss!r}"
+            )
+        if self.solver == "mu" and self.init == "nndsvd":
+            warnings.warn(
+                (
+                    "The multiplicative update ('mu') solver cannot update "
+                    "zeros present in the initialization, and so leads to "
+                    "poorer results when used jointly with init='nndsvd'. "
+                    "You may try init='nndsvda' or init='nndsvdar' instead."
+                ),
+                UserWarning,
+            )
+
+        return self
+
+    @_fit_context(prefer_skip_nested_validation=True)
+    def fit_transform(self, X, y=None, W=None, H=None):
+        """Learn a NMF model for the data X and returns the transformed data.
+
+        This is more efficient than calling fit followed by transform.
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            Training vector, where `n_samples` is the number of samples
+            and `n_features` is the number of features.
+
+        y : Ignored
+            Not used, present for API consistency by convention.
+
+        W : array-like of shape (n_samples, n_components), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+            If `None`, uses the initialisation method specified in `init`.
+
+        H : array-like of shape (n_components, n_features), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+            If `None`, uses the initialisation method specified in `init`.
+
+        Returns
+        -------
+        W : ndarray of shape (n_samples, n_components)
+            Transformed data.
+        """
+        X = self._validate_data(
+            X, accept_sparse=("csr", "csc"), dtype=[np.float64, np.float32]
+        )
+
+        with config_context(assume_finite=True):
+            W, H, n_iter = self._fit_transform(X, W=W, H=H)
+
+        self.reconstruction_err_ = _beta_divergence(
+            X, W, H, self._beta_loss, square_root=True
+        )
+
+        self.n_components_ = H.shape[0]
+        self.components_ = H
+        self.n_iter_ = n_iter
+
+        return W
+
+    def _fit_transform(self, X, y=None, W=None, H=None, update_H=True):
+        """Learn a NMF model for the data X and returns the transformed data.
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            Data matrix to be decomposed
+
+        y : Ignored
+
+        W : array-like of shape (n_samples, n_components), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+            If `update_H=False`, it is initialised as an array of zeros, unless
+            `solver='mu'`, then it is filled with values calculated by
+            `np.sqrt(X.mean() / self._n_components)`.
+            If `None`, uses the initialisation method specified in `init`.
+
+        H : array-like of shape (n_components, n_features), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+            If `update_H=False`, it is used as a constant, to solve for W only.
+            If `None`, uses the initialisation method specified in `init`.
+
+        update_H : bool, default=True
+            If True, both W and H will be estimated from initial guesses,
+            this corresponds to a call to the 'fit_transform' method.
+            If False, only W will be estimated, this corresponds to a call
+            to the 'transform' method.
+
+        Returns
+        -------
+        W : ndarray of shape (n_samples, n_components)
+            Transformed data.
+
+        H : ndarray of shape (n_components, n_features)
+            Factorization matrix, sometimes called 'dictionary'.
+
+        n_iter_ : int
+            Actual number of iterations.
+        """
+        check_non_negative(X, "NMF (input X)")
+
+        # check parameters
+        self._check_params(X)
+
+        if X.min() == 0 and self._beta_loss <= 0:
+            raise ValueError(
+                "When beta_loss <= 0 and X contains zeros, "
+                "the solver may diverge. Please add small values "
+                "to X, or use a positive beta_loss."
+            )
+
+        # initialize or check W and H
+        W, H = self._check_w_h(X, W, H, update_H)
+
+        # scale the regularization terms
+        l1_reg_W, l1_reg_H, l2_reg_W, l2_reg_H = self._compute_regularization(X)
+
+        if self.solver == "cd":
+            W, H, n_iter = _fit_coordinate_descent(
+                X,
+                W,
+                H,
+                self.tol,
+                self.max_iter,
+                l1_reg_W,
+                l1_reg_H,
+                l2_reg_W,
+                l2_reg_H,
+                update_H=update_H,
+                verbose=self.verbose,
+                shuffle=self.shuffle,
+                random_state=self.random_state,
+            )
+        elif self.solver == "mu":
+            W, H, n_iter, *_ = _fit_multiplicative_update(
+                X,
+                W,
+                H,
+                self._beta_loss,
+                self.max_iter,
+                self.tol,
+                l1_reg_W,
+                l1_reg_H,
+                l2_reg_W,
+                l2_reg_H,
+                update_H,
+                self.verbose,
+            )
+        else:
+            raise ValueError("Invalid solver parameter '%s'." % self.solver)
+
+        if n_iter == self.max_iter and self.tol > 0:
+            warnings.warn(
+                "Maximum number of iterations %d reached. Increase "
+                "it to improve convergence."
+                % self.max_iter,
+                ConvergenceWarning,
+            )
+
+        return W, H, n_iter
+
+    def transform(self, X):
+        """Transform the data X according to the fitted NMF model.
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            Training vector, where `n_samples` is the number of samples
+            and `n_features` is the number of features.
+
+        Returns
+        -------
+        W : ndarray of shape (n_samples, n_components)
+            Transformed data.
+        """
+        check_is_fitted(self)
+        X = self._validate_data(
+            X, accept_sparse=("csr", "csc"), dtype=[np.float64, np.float32], reset=False
+        )
+
+        with config_context(assume_finite=True):
+            W, *_ = self._fit_transform(X, H=self.components_, update_H=False)
+
+        return W
+
+
+class MiniBatchNMF(_BaseNMF):
+    """Mini-Batch Non-Negative Matrix Factorization (NMF).
+
+    .. versionadded:: 1.1
+
+    Find two non-negative matrices, i.e. matrices with all non-negative elements,
+    (`W`, `H`) whose product approximates the non-negative matrix `X`. This
+    factorization can be used for example for dimensionality reduction, source
+    separation or topic extraction.
+
+    The objective function is:
+
+        .. math::
+
+            L(W, H) &= 0.5 * ||X - WH||_{loss}^2
+
+            &+ alpha\\_W * l1\\_ratio * n\\_features * ||vec(W)||_1
+
+            &+ alpha\\_H * l1\\_ratio * n\\_samples * ||vec(H)||_1
+
+            &+ 0.5 * alpha\\_W * (1 - l1\\_ratio) * n\\_features * ||W||_{Fro}^2
+
+            &+ 0.5 * alpha\\_H * (1 - l1\\_ratio) * n\\_samples * ||H||_{Fro}^2
+
+    Where:
+
+    :math:`||A||_{Fro}^2 = \\sum_{i,j} A_{ij}^2` (Frobenius norm)
+
+    :math:`||vec(A)||_1 = \\sum_{i,j} abs(A_{ij})` (Elementwise L1 norm)
+
+    The generic norm :math:`||X - WH||_{loss}^2` may represent
+    the Frobenius norm or another supported beta-divergence loss.
+    The choice between options is controlled by the `beta_loss` parameter.
+
+    The objective function is minimized with an alternating minimization of `W`
+    and `H`.
+
+    Note that the transformed data is named `W` and the components matrix is
+    named `H`. In the NMF literature, the naming convention is usually the opposite
+    since the data matrix `X` is transposed.
+
+    Read more in the :ref:`User Guide <MiniBatchNMF>`.
+
+    Parameters
+    ----------
+    n_components : int or {'auto'} or None, default=None
+        Number of components, if `n_components` is not set all features
+        are kept.
+        If `n_components='auto'`, the number of components is automatically inferred
+        from W or H shapes.
+
+        .. versionchanged:: 1.4
+            Added `'auto'` value.
+
+    init : {'random', 'nndsvd', 'nndsvda', 'nndsvdar', 'custom'}, default=None
+        Method used to initialize the procedure.
+        Valid options:
+
+        - `None`: 'nndsvda' if `n_components <= min(n_samples, n_features)`,
+          otherwise random.
+
+        - `'random'`: non-negative random matrices, scaled with:
+          `sqrt(X.mean() / n_components)`
+
+        - `'nndsvd'`: Nonnegative Double Singular Value Decomposition (NNDSVD)
+          initialization (better for sparseness).
+
+        - `'nndsvda'`: NNDSVD with zeros filled with the average of X
+          (better when sparsity is not desired).
+
+        - `'nndsvdar'` NNDSVD with zeros filled with small random values
+          (generally faster, less accurate alternative to NNDSVDa
+          for when sparsity is not desired).
+
+        - `'custom'`: Use custom matrices `W` and `H` which must both be provided.
+
+    batch_size : int, default=1024
+        Number of samples in each mini-batch. Large batch sizes
+        give better long-term convergence at the cost of a slower start.
+
+    beta_loss : float or {'frobenius', 'kullback-leibler', \
+            'itakura-saito'}, default='frobenius'
+        Beta divergence to be minimized, measuring the distance between `X`
+        and the dot product `WH`. Note that values different from 'frobenius'
+        (or 2) and 'kullback-leibler' (or 1) lead to significantly slower
+        fits. Note that for `beta_loss <= 0` (or 'itakura-saito'), the input
+        matrix `X` cannot contain zeros.
+
+    tol : float, default=1e-4
+        Control early stopping based on the norm of the differences in `H`
+        between 2 steps. To disable early stopping based on changes in `H`, set
+        `tol` to 0.0.
+
+    max_no_improvement : int, default=10
+        Control early stopping based on the consecutive number of mini batches
+        that does not yield an improvement on the smoothed cost function.
+        To disable convergence detection based on cost function, set
+        `max_no_improvement` to None.
+
+    max_iter : int, default=200
+        Maximum number of iterations over the complete dataset before
+        timing out.
+
+    alpha_W : float, default=0.0
+        Constant that multiplies the regularization terms of `W`. Set it to zero
+        (default) to have no regularization on `W`.
+
+    alpha_H : float or "same", default="same"
+        Constant that multiplies the regularization terms of `H`. Set it to zero to
+        have no regularization on `H`. If "same" (default), it takes the same value as
+        `alpha_W`.
+
+    l1_ratio : float, default=0.0
+        The regularization mixing parameter, with 0 <= l1_ratio <= 1.
+        For l1_ratio = 0 the penalty is an elementwise L2 penalty
+        (aka Frobenius Norm).
+        For l1_ratio = 1 it is an elementwise L1 penalty.
+        For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2.
+
+    forget_factor : float, default=0.7
+        Amount of rescaling of past information. Its value could be 1 with
+        finite datasets. Choosing values < 1 is recommended with online
+        learning as more recent batches will weight more than past batches.
+
+    fresh_restarts : bool, default=False
+        Whether to completely solve for W at each step. Doing fresh restarts will likely
+        lead to a better solution for a same number of iterations but it is much slower.
+
+    fresh_restarts_max_iter : int, default=30
+        Maximum number of iterations when solving for W at each step. Only used when
+        doing fresh restarts. These iterations may be stopped early based on a small
+        change of W controlled by `tol`.
+
+    transform_max_iter : int, default=None
+        Maximum number of iterations when solving for W at transform time.
+        If None, it defaults to `max_iter`.
+
+    random_state : int, RandomState instance or None, default=None
+        Used for initialisation (when ``init`` == 'nndsvdar' or
+        'random'), and in Coordinate Descent. Pass an int for reproducible
+        results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+    verbose : bool, default=False
+        Whether to be verbose.
+
+    Attributes
+    ----------
+    components_ : ndarray of shape (n_components, n_features)
+        Factorization matrix, sometimes called 'dictionary'.
+
+    n_components_ : int
+        The number of components. It is same as the `n_components` parameter
+        if it was given. Otherwise, it will be same as the number of
+        features.
+
+    reconstruction_err_ : float
+        Frobenius norm of the matrix difference, or beta-divergence, between
+        the training data `X` and the reconstructed data `WH` from
+        the fitted model.
+
+    n_iter_ : int
+        Actual number of started iterations over the whole dataset.
+
+    n_steps_ : int
+        Number of mini-batches processed.
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+    See Also
+    --------
+    NMF : Non-negative matrix factorization.
+    MiniBatchDictionaryLearning : Finds a dictionary that can best be used to represent
+        data using a sparse code.
+
+    References
+    ----------
+    .. [1] :doi:`"Fast local algorithms for large scale nonnegative matrix and tensor
+       factorizations" <10.1587/transfun.E92.A.708>`
+       Cichocki, Andrzej, and P. H. A. N. Anh-Huy. IEICE transactions on fundamentals
+       of electronics, communications and computer sciences 92.3: 708-721, 2009.
+
+    .. [2] :doi:`"Algorithms for nonnegative matrix factorization with the
+       beta-divergence" <10.1162/NECO_a_00168>`
+       Fevotte, C., & Idier, J. (2011). Neural Computation, 23(9).
+
+    .. [3] :doi:`"Online algorithms for nonnegative matrix factorization with the
+       Itakura-Saito divergence" <10.1109/ASPAA.2011.6082314>`
+       Lefevre, A., Bach, F., Fevotte, C. (2011). WASPA.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> X = np.array([[1, 1], [2, 1], [3, 1.2], [4, 1], [5, 0.8], [6, 1]])
+    >>> from sklearn.decomposition import MiniBatchNMF
+    >>> model = MiniBatchNMF(n_components=2, init='random', random_state=0)
+    >>> W = model.fit_transform(X)
+    >>> H = model.components_
+    """
+
+    _parameter_constraints: dict = {
+        **_BaseNMF._parameter_constraints,
+        "max_no_improvement": [Interval(Integral, 1, None, closed="left"), None],
+        "batch_size": [Interval(Integral, 1, None, closed="left")],
+        "forget_factor": [Interval(Real, 0, 1, closed="both")],
+        "fresh_restarts": ["boolean"],
+        "fresh_restarts_max_iter": [Interval(Integral, 1, None, closed="left")],
+        "transform_max_iter": [Interval(Integral, 1, None, closed="left"), None],
+    }
+
+    def __init__(
+        self,
+        n_components="warn",
+        *,
+        init=None,
+        batch_size=1024,
+        beta_loss="frobenius",
+        tol=1e-4,
+        max_no_improvement=10,
+        max_iter=200,
+        alpha_W=0.0,
+        alpha_H="same",
+        l1_ratio=0.0,
+        forget_factor=0.7,
+        fresh_restarts=False,
+        fresh_restarts_max_iter=30,
+        transform_max_iter=None,
+        random_state=None,
+        verbose=0,
+    ):
+        super().__init__(
+            n_components=n_components,
+            init=init,
+            beta_loss=beta_loss,
+            tol=tol,
+            max_iter=max_iter,
+            random_state=random_state,
+            alpha_W=alpha_W,
+            alpha_H=alpha_H,
+            l1_ratio=l1_ratio,
+            verbose=verbose,
+        )
+
+        self.max_no_improvement = max_no_improvement
+        self.batch_size = batch_size
+        self.forget_factor = forget_factor
+        self.fresh_restarts = fresh_restarts
+        self.fresh_restarts_max_iter = fresh_restarts_max_iter
+        self.transform_max_iter = transform_max_iter
+
+    def _check_params(self, X):
+        super()._check_params(X)
+
+        # batch_size
+        self._batch_size = min(self.batch_size, X.shape[0])
+
+        # forget_factor
+        self._rho = self.forget_factor ** (self._batch_size / X.shape[0])
+
+        # gamma for Maximization-Minimization (MM) algorithm [Fevotte 2011]
+        if self._beta_loss < 1:
+            self._gamma = 1.0 / (2.0 - self._beta_loss)
+        elif self._beta_loss > 2:
+            self._gamma = 1.0 / (self._beta_loss - 1.0)
+        else:
+            self._gamma = 1.0
+
+        # transform_max_iter
+        self._transform_max_iter = (
+            self.max_iter
+            if self.transform_max_iter is None
+            else self.transform_max_iter
+        )
+
+        return self
+
+    def _solve_W(self, X, H, max_iter):
+        """Minimize the objective function w.r.t W.
+
+        Update W with H being fixed, until convergence. This is the heart
+        of `transform` but it's also used during `fit` when doing fresh restarts.
+        """
+        avg = np.sqrt(X.mean() / self._n_components)
+        W = np.full((X.shape[0], self._n_components), avg, dtype=X.dtype)
+        W_buffer = W.copy()
+
+        # Get scaled regularization terms. Done for each minibatch to take into account
+        # variable sizes of minibatches.
+        l1_reg_W, _, l2_reg_W, _ = self._compute_regularization(X)
+
+        for _ in range(max_iter):
+            W, *_ = _multiplicative_update_w(
+                X, W, H, self._beta_loss, l1_reg_W, l2_reg_W, self._gamma
+            )
+
+            W_diff = linalg.norm(W - W_buffer) / linalg.norm(W)
+            if self.tol > 0 and W_diff <= self.tol:
+                break
+
+            W_buffer[:] = W
+
+        return W
+
+    def _minibatch_step(self, X, W, H, update_H):
+        """Perform the update of W and H for one minibatch."""
+        batch_size = X.shape[0]
+
+        # get scaled regularization terms. Done for each minibatch to take into account
+        # variable sizes of minibatches.
+        l1_reg_W, l1_reg_H, l2_reg_W, l2_reg_H = self._compute_regularization(X)
+
+        # update W
+        if self.fresh_restarts or W is None:
+            W = self._solve_W(X, H, self.fresh_restarts_max_iter)
+        else:
+            W, *_ = _multiplicative_update_w(
+                X, W, H, self._beta_loss, l1_reg_W, l2_reg_W, self._gamma
+            )
+
+        # necessary for stability with beta_loss < 1
+        if self._beta_loss < 1:
+            W[W < np.finfo(np.float64).eps] = 0.0
+
+        batch_cost = (
+            _beta_divergence(X, W, H, self._beta_loss)
+            + l1_reg_W * W.sum()
+            + l1_reg_H * H.sum()
+            + l2_reg_W * (W**2).sum()
+            + l2_reg_H * (H**2).sum()
+        ) / batch_size
+
+        # update H (only at fit or fit_transform)
+        if update_H:
+            H[:] = _multiplicative_update_h(
+                X,
+                W,
+                H,
+                beta_loss=self._beta_loss,
+                l1_reg_H=l1_reg_H,
+                l2_reg_H=l2_reg_H,
+                gamma=self._gamma,
+                A=self._components_numerator,
+                B=self._components_denominator,
+                rho=self._rho,
+            )
+
+            # necessary for stability with beta_loss < 1
+            if self._beta_loss <= 1:
+                H[H < np.finfo(np.float64).eps] = 0.0
+
+        return batch_cost
+
+    def _minibatch_convergence(
+        self, X, batch_cost, H, H_buffer, n_samples, step, n_steps
+    ):
+        """Helper function to encapsulate the early stopping logic"""
+        batch_size = X.shape[0]
+
+        # counts steps starting from 1 for user friendly verbose mode.
+        step = step + 1
+
+        # Ignore first iteration because H is not updated yet.
+        if step == 1:
+            if self.verbose:
+                print(f"Minibatch step {step}/{n_steps}: mean batch cost: {batch_cost}")
+            return False
+
+        # Compute an Exponentially Weighted Average of the cost function to
+        # monitor the convergence while discarding minibatch-local stochastic
+        # variability: https://en.wikipedia.org/wiki/Moving_average
+        if self._ewa_cost is None:
+            self._ewa_cost = batch_cost
+        else:
+            alpha = batch_size / (n_samples + 1)
+            alpha = min(alpha, 1)
+            self._ewa_cost = self._ewa_cost * (1 - alpha) + batch_cost * alpha
+
+        # Log progress to be able to monitor convergence
+        if self.verbose:
+            print(
+                f"Minibatch step {step}/{n_steps}: mean batch cost: "
+                f"{batch_cost}, ewa cost: {self._ewa_cost}"
+            )
+
+        # Early stopping based on change of H
+        H_diff = linalg.norm(H - H_buffer) / linalg.norm(H)
+        if self.tol > 0 and H_diff <= self.tol:
+            if self.verbose:
+                print(f"Converged (small H change) at step {step}/{n_steps}")
+            return True
+
+        # Early stopping heuristic due to lack of improvement on smoothed
+        # cost function
+        if self._ewa_cost_min is None or self._ewa_cost < self._ewa_cost_min:
+            self._no_improvement = 0
+            self._ewa_cost_min = self._ewa_cost
+        else:
+            self._no_improvement += 1
+
+        if (
+            self.max_no_improvement is not None
+            and self._no_improvement >= self.max_no_improvement
+        ):
+            if self.verbose:
+                print(
+                    "Converged (lack of improvement in objective function) "
+                    f"at step {step}/{n_steps}"
+                )
+            return True
+
+        return False
+
+    @_fit_context(prefer_skip_nested_validation=True)
+    def fit_transform(self, X, y=None, W=None, H=None):
+        """Learn a NMF model for the data X and returns the transformed data.
+
+        This is more efficient than calling fit followed by transform.
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            Data matrix to be decomposed.
+
+        y : Ignored
+            Not used, present here for API consistency by convention.
+
+        W : array-like of shape (n_samples, n_components), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+            If `None`, uses the initialisation method specified in `init`.
+
+        H : array-like of shape (n_components, n_features), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+            If `None`, uses the initialisation method specified in `init`.
+
+        Returns
+        -------
+        W : ndarray of shape (n_samples, n_components)
+            Transformed data.
+        """
+        X = self._validate_data(
+            X, accept_sparse=("csr", "csc"), dtype=[np.float64, np.float32]
+        )
+
+        with config_context(assume_finite=True):
+            W, H, n_iter, n_steps = self._fit_transform(X, W=W, H=H)
+
+        self.reconstruction_err_ = _beta_divergence(
+            X, W, H, self._beta_loss, square_root=True
+        )
+
+        self.n_components_ = H.shape[0]
+        self.components_ = H
+        self.n_iter_ = n_iter
+        self.n_steps_ = n_steps
+
+        return W
+
+    def _fit_transform(self, X, W=None, H=None, update_H=True):
+        """Learn a NMF model for the data X and returns the transformed data.
+
+        Parameters
+        ----------
+        X : {ndarray, sparse matrix} of shape (n_samples, n_features)
+            Data matrix to be decomposed.
+
+        W : array-like of shape (n_samples, n_components), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+            If `update_H=False`, it is initialised as an array of zeros, unless
+            `solver='mu'`, then it is filled with values calculated by
+            `np.sqrt(X.mean() / self._n_components)`.
+            If `None`, uses the initialisation method specified in `init`.
+
+        H : array-like of shape (n_components, n_features), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+            If `update_H=False`, it is used as a constant, to solve for W only.
+            If `None`, uses the initialisation method specified in `init`.
+
+        update_H : bool, default=True
+            If True, both W and H will be estimated from initial guesses,
+            this corresponds to a call to the `fit_transform` method.
+            If False, only W will be estimated, this corresponds to a call
+            to the `transform` method.
+
+        Returns
+        -------
+        W : ndarray of shape (n_samples, n_components)
+            Transformed data.
+
+        H : ndarray of shape (n_components, n_features)
+            Factorization matrix, sometimes called 'dictionary'.
+
+        n_iter : int
+            Actual number of started iterations over the whole dataset.
+
+        n_steps : int
+            Number of mini-batches processed.
+        """
+        check_non_negative(X, "MiniBatchNMF (input X)")
+        self._check_params(X)
+
+        if X.min() == 0 and self._beta_loss <= 0:
+            raise ValueError(
+                "When beta_loss <= 0 and X contains zeros, "
+                "the solver may diverge. Please add small values "
+                "to X, or use a positive beta_loss."
+            )
+
+        n_samples = X.shape[0]
+
+        # initialize or check W and H
+        W, H = self._check_w_h(X, W, H, update_H)
+        H_buffer = H.copy()
+
+        # Initialize auxiliary matrices
+        self._components_numerator = H.copy()
+        self._components_denominator = np.ones(H.shape, dtype=H.dtype)
+
+        # Attributes to monitor the convergence
+        self._ewa_cost = None
+        self._ewa_cost_min = None
+        self._no_improvement = 0
+
+        batches = gen_batches(n_samples, self._batch_size)
+        batches = itertools.cycle(batches)
+        n_steps_per_iter = int(np.ceil(n_samples / self._batch_size))
+        n_steps = self.max_iter * n_steps_per_iter
+
+        for i, batch in zip(range(n_steps), batches):
+            batch_cost = self._minibatch_step(X[batch], W[batch], H, update_H)
+
+            if update_H and self._minibatch_convergence(
+                X[batch], batch_cost, H, H_buffer, n_samples, i, n_steps
+            ):
+                break
+
+            H_buffer[:] = H
+
+        if self.fresh_restarts:
+            W = self._solve_W(X, H, self._transform_max_iter)
+
+        n_steps = i + 1
+        n_iter = int(np.ceil(n_steps / n_steps_per_iter))
+
+        if n_iter == self.max_iter and self.tol > 0:
+            warnings.warn(
+                (
+                    f"Maximum number of iterations {self.max_iter} reached. "
+                    "Increase it to improve convergence."
+                ),
+                ConvergenceWarning,
+            )
+
+        return W, H, n_iter, n_steps
+
+    def transform(self, X):
+        """Transform the data X according to the fitted MiniBatchNMF model.
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            Data matrix to be transformed by the model.
+
+        Returns
+        -------
+        W : ndarray of shape (n_samples, n_components)
+            Transformed data.
+        """
+        check_is_fitted(self)
+        X = self._validate_data(
+            X, accept_sparse=("csr", "csc"), dtype=[np.float64, np.float32], reset=False
+        )
+
+        W = self._solve_W(X, self.components_, self._transform_max_iter)
+
+        return W
+
+    @_fit_context(prefer_skip_nested_validation=True)
+    def partial_fit(self, X, y=None, W=None, H=None):
+        """Update the model using the data in `X` as a mini-batch.
+
+        This method is expected to be called several times consecutively
+        on different chunks of a dataset so as to implement out-of-core
+        or online learning.
+
+        This is especially useful when the whole dataset is too big to fit in
+        memory at once (see :ref:`scaling_strategies`).
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            Data matrix to be decomposed.
+
+        y : Ignored
+            Not used, present here for API consistency by convention.
+
+        W : array-like of shape (n_samples, n_components), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+            Only used for the first call to `partial_fit`.
+
+        H : array-like of shape (n_components, n_features), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+            Only used for the first call to `partial_fit`.
+
+        Returns
+        -------
+        self
+            Returns the instance itself.
+        """
+        has_components = hasattr(self, "components_")
+
+        X = self._validate_data(
+            X,
+            accept_sparse=("csr", "csc"),
+            dtype=[np.float64, np.float32],
+            reset=not has_components,
+        )
+
+        if not has_components:
+            # This instance has not been fitted yet (fit or partial_fit)
+            self._check_params(X)
+            _, H = self._check_w_h(X, W=W, H=H, update_H=True)
+
+            self._components_numerator = H.copy()
+            self._components_denominator = np.ones(H.shape, dtype=H.dtype)
+            self.n_steps_ = 0
+        else:
+            H = self.components_
+
+        self._minibatch_step(X, None, H, update_H=True)
+
+        self.n_components_ = H.shape[0]
+        self.components_ = H
+        self.n_steps_ += 1
+
+        return self

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/_pca.py

@@ -0,0 +1,747 @@
+""" Principal Component Analysis.
+"""
+
+# Author: Alexandre Gramfort <[email protected]>
+#         Olivier Grisel <[email protected]>
+#         Mathieu Blondel <[email protected]>
+#         Denis A. Engemann <[email protected]>
+#         Michael Eickenberg <[email protected]>
+#         Giorgio Patrini <[email protected]>
+#
+# License: BSD 3 clause
+
+from math import log, sqrt
+from numbers import Integral, Real
+
+import numpy as np
+from scipy import linalg
+from scipy.sparse import issparse
+from scipy.sparse.linalg import svds
+from scipy.special import gammaln
+
+from ..base import _fit_context
+from ..utils import check_random_state
+from ..utils._arpack import _init_arpack_v0
+from ..utils._array_api import _convert_to_numpy, get_namespace
+from ..utils._param_validation import Interval, RealNotInt, StrOptions
+from ..utils.extmath import fast_logdet, randomized_svd, stable_cumsum, svd_flip
+from ..utils.sparsefuncs import _implicit_column_offset, mean_variance_axis
+from ..utils.validation import check_is_fitted
+from ._base import _BasePCA
+
+
+def _assess_dimension(spectrum, rank, n_samples):
+    """Compute the log-likelihood of a rank ``rank`` dataset.
+
+    The dataset is assumed to be embedded in gaussian noise of shape(n,
+    dimf) having spectrum ``spectrum``. This implements the method of
+    T. P. Minka.
+
+    Parameters
+    ----------
+    spectrum : ndarray of shape (n_features,)
+        Data spectrum.
+    rank : int
+        Tested rank value. It should be strictly lower than n_features,
+        otherwise the method isn't specified (division by zero in equation
+        (31) from the paper).
+    n_samples : int
+        Number of samples.
+
+    Returns
+    -------
+    ll : float
+        The log-likelihood.
+
+    References
+    ----------
+    This implements the method of `Thomas P. Minka:
+    Automatic Choice of Dimensionality for PCA. NIPS 2000: 598-604
+    <https://proceedings.neurips.cc/paper/2000/file/7503cfacd12053d309b6bed5c89de212-Paper.pdf>`_
+    """
+    xp, _ = get_namespace(spectrum)
+
+    n_features = spectrum.shape[0]
+    if not 1 <= rank < n_features:
+        raise ValueError("the tested rank should be in [1, n_features - 1]")
+
+    eps = 1e-15
+
+    if spectrum[rank - 1] < eps:
+        # When the tested rank is associated with a small eigenvalue, there's
+        # no point in computing the log-likelihood: it's going to be very
+        # small and won't be the max anyway. Also, it can lead to numerical
+        # issues below when computing pa, in particular in log((spectrum[i] -
+        # spectrum[j]) because this will take the log of something very small.
+        return -xp.inf
+
+    pu = -rank * log(2.0)
+    for i in range(1, rank + 1):
+        pu += (
+            gammaln((n_features - i + 1) / 2.0)
+            - log(xp.pi) * (n_features - i + 1) / 2.0
+        )
+
+    pl = xp.sum(xp.log(spectrum[:rank]))
+    pl = -pl * n_samples / 2.0
+
+    v = max(eps, xp.sum(spectrum[rank:]) / (n_features - rank))
+    pv = -log(v) * n_samples * (n_features - rank) / 2.0
+
+    m = n_features * rank - rank * (rank + 1.0) / 2.0
+    pp = log(2.0 * xp.pi) * (m + rank) / 2.0
+
+    pa = 0.0
+    spectrum_ = xp.asarray(spectrum, copy=True)
+    spectrum_[rank:n_features] = v
+    for i in range(rank):
+        for j in range(i + 1, spectrum.shape[0]):
+            pa += log(
+                (spectrum[i] - spectrum[j]) * (1.0 / spectrum_[j] - 1.0 / spectrum_[i])
+            ) + log(n_samples)
+
+    ll = pu + pl + pv + pp - pa / 2.0 - rank * log(n_samples) / 2.0
+
+    return ll
+
+
+def _infer_dimension(spectrum, n_samples):
+    """Infers the dimension of a dataset with a given spectrum.
+
+    The returned value will be in [1, n_features - 1].
+    """
+    xp, _ = get_namespace(spectrum)
+
+    ll = xp.empty_like(spectrum)
+    ll[0] = -xp.inf  # we don't want to return n_components = 0
+    for rank in range(1, spectrum.shape[0]):
+        ll[rank] = _assess_dimension(spectrum, rank, n_samples)
+    return xp.argmax(ll)
+
+
+class PCA(_BasePCA):
+    """Principal component analysis (PCA).
+
+    Linear dimensionality reduction using Singular Value Decomposition of the
+    data to project it to a lower dimensional space. The input data is centered
+    but not scaled for each feature before applying the SVD.
+
+    It uses the LAPACK implementation of the full SVD or a randomized truncated
+    SVD by the method of Halko et al. 2009, depending on the shape of the input
+    data and the number of components to extract.
+
+    It can also use the scipy.sparse.linalg ARPACK implementation of the
+    truncated SVD.
+
+    Notice that this class does not support sparse input. See
+    :class:`TruncatedSVD` for an alternative with sparse data.
+
+    For a usage example, see
+    :ref:`sphx_glr_auto_examples_decomposition_plot_pca_iris.py`
+
+    Read more in the :ref:`User Guide <PCA>`.
+
+    Parameters
+    ----------
+    n_components : int, float or 'mle', default=None
+        Number of components to keep.
+        if n_components is not set all components are kept::
+
+            n_components == min(n_samples, n_features)
+
+        If ``n_components == 'mle'`` and ``svd_solver == 'full'``, Minka's
+        MLE is used to guess the dimension. Use of ``n_components == 'mle'``
+        will interpret ``svd_solver == 'auto'`` as ``svd_solver == 'full'``.
+
+        If ``0 < n_components < 1`` and ``svd_solver == 'full'``, select the
+        number of components such that the amount of variance that needs to be
+        explained is greater than the percentage specified by n_components.
+
+        If ``svd_solver == 'arpack'``, the number of components must be
+        strictly less than the minimum of n_features and n_samples.
+
+        Hence, the None case results in::
+
+            n_components == min(n_samples, n_features) - 1
+
+    copy : bool, default=True
+        If False, data passed to fit are overwritten and running
+        fit(X).transform(X) will not yield the expected results,
+        use fit_transform(X) instead.
+
+    whiten : bool, default=False
+        When True (False by default) the `components_` vectors are multiplied
+        by the square root of n_samples and then divided by the singular values
+        to ensure uncorrelated outputs with unit component-wise variances.
+
+        Whitening will remove some information from the transformed signal
+        (the relative variance scales of the components) but can sometime
+        improve the predictive accuracy of the downstream estimators by
+        making their data respect some hard-wired assumptions.
+
+    svd_solver : {'auto', 'full', 'arpack', 'randomized'}, default='auto'
+        If auto :
+            The solver is selected by a default policy based on `X.shape` and
+            `n_components`: if the input data is larger than 500x500 and the
+            number of components to extract is lower than 80% of the smallest
+            dimension of the data, then the more efficient 'randomized'
+            method is enabled. Otherwise the exact full SVD is computed and
+            optionally truncated afterwards.
+        If full :
+            run exact full SVD calling the standard LAPACK solver via
+            `scipy.linalg.svd` and select the components by postprocessing
+        If arpack :
+            run SVD truncated to n_components calling ARPACK solver via
+            `scipy.sparse.linalg.svds`. It requires strictly
+            0 < n_components < min(X.shape)
+        If randomized :
+            run randomized SVD by the method of Halko et al.
+
+        .. versionadded:: 0.18.0
+
+    tol : float, default=0.0
+        Tolerance for singular values computed by svd_solver == 'arpack'.
+        Must be of range [0.0, infinity).
+
+        .. versionadded:: 0.18.0
+
+    iterated_power : int or 'auto', default='auto'
+        Number of iterations for the power method computed by
+        svd_solver == 'randomized'.
+        Must be of range [0, infinity).
+
+        .. versionadded:: 0.18.0
+
+    n_oversamples : int, default=10
+        This parameter is only relevant when `svd_solver="randomized"`.
+        It corresponds to the additional number of random vectors to sample the
+        range of `X` so as to ensure proper conditioning. See
+        :func:`~sklearn.utils.extmath.randomized_svd` for more details.
+
+        .. versionadded:: 1.1
+
+    power_iteration_normalizer : {'auto', 'QR', 'LU', 'none'}, default='auto'
+        Power iteration normalizer for randomized SVD solver.
+        Not used by ARPACK. See :func:`~sklearn.utils.extmath.randomized_svd`
+        for more details.
+
+        .. versionadded:: 1.1
+
+    random_state : int, RandomState instance or None, default=None
+        Used when the 'arpack' or 'randomized' solvers are used. Pass an int
+        for reproducible results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+        .. versionadded:: 0.18.0
+
+    Attributes
+    ----------
+    components_ : ndarray of shape (n_components, n_features)
+        Principal axes in feature space, representing the directions of
+        maximum variance in the data. Equivalently, the right singular
+        vectors of the centered input data, parallel to its eigenvectors.
+        The components are sorted by decreasing ``explained_variance_``.
+
+    explained_variance_ : ndarray of shape (n_components,)
+        The amount of variance explained by each of the selected components.
+        The variance estimation uses `n_samples - 1` degrees of freedom.
+
+        Equal to n_components largest eigenvalues
+        of the covariance matrix of X.
+
+        .. versionadded:: 0.18
+
+    explained_variance_ratio_ : ndarray of shape (n_components,)
+        Percentage of variance explained by each of the selected components.
+
+        If ``n_components`` is not set then all components are stored and the
+        sum of the ratios is equal to 1.0.
+
+    singular_values_ : ndarray of shape (n_components,)
+        The singular values corresponding to each of the selected components.
+        The singular values are equal to the 2-norms of the ``n_components``
+        variables in the lower-dimensional space.
+
+        .. versionadded:: 0.19
+
+    mean_ : ndarray of shape (n_features,)
+        Per-feature empirical mean, estimated from the training set.
+
+        Equal to `X.mean(axis=0)`.
+
+    n_components_ : int
+        The estimated number of components. When n_components is set
+        to 'mle' or a number between 0 and 1 (with svd_solver == 'full') this
+        number is estimated from input data. Otherwise it equals the parameter
+        n_components, or the lesser value of n_features and n_samples
+        if n_components is None.
+
+    n_samples_ : int
+        Number of samples in the training data.
+
+    noise_variance_ : float
+        The estimated noise covariance following the Probabilistic PCA model
+        from Tipping and Bishop 1999. See "Pattern Recognition and
+        Machine Learning" by C. Bishop, 12.2.1 p. 574 or
+        http://www.miketipping.com/papers/met-mppca.pdf. It is required to
+        compute the estimated data covariance and score samples.
+
+        Equal to the average of (min(n_features, n_samples) - n_components)
+        smallest eigenvalues of the covariance matrix of X.
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+        .. versionadded:: 0.24
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
+    See Also
+    --------
+    KernelPCA : Kernel Principal Component Analysis.
+    SparsePCA : Sparse Principal Component Analysis.
+    TruncatedSVD : Dimensionality reduction using truncated SVD.
+    IncrementalPCA : Incremental Principal Component Analysis.
+
+    References
+    ----------
+    For n_components == 'mle', this class uses the method from:
+    `Minka, T. P.. "Automatic choice of dimensionality for PCA".
+    In NIPS, pp. 598-604 <https://tminka.github.io/papers/pca/minka-pca.pdf>`_
+
+    Implements the probabilistic PCA model from:
+    `Tipping, M. E., and Bishop, C. M. (1999). "Probabilistic principal
+    component analysis". Journal of the Royal Statistical Society:
+    Series B (Statistical Methodology), 61(3), 611-622.
+    <http://www.miketipping.com/papers/met-mppca.pdf>`_
+    via the score and score_samples methods.
+
+    For svd_solver == 'arpack', refer to `scipy.sparse.linalg.svds`.
+
+    For svd_solver == 'randomized', see:
+    :doi:`Halko, N., Martinsson, P. G., and Tropp, J. A. (2011).
+    "Finding structure with randomness: Probabilistic algorithms for
+    constructing approximate matrix decompositions".
+    SIAM review, 53(2), 217-288.
+    <10.1137/090771806>`
+    and also
+    :doi:`Martinsson, P. G., Rokhlin, V., and Tygert, M. (2011).
+    "A randomized algorithm for the decomposition of matrices".
+    Applied and Computational Harmonic Analysis, 30(1), 47-68.
+    <10.1016/j.acha.2010.02.003>`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from sklearn.decomposition import PCA
+    >>> X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
+    >>> pca = PCA(n_components=2)
+    >>> pca.fit(X)
+    PCA(n_components=2)
+    >>> print(pca.explained_variance_ratio_)
+    [0.9924... 0.0075...]
+    >>> print(pca.singular_values_)
+    [6.30061... 0.54980...]
+
+    >>> pca = PCA(n_components=2, svd_solver='full')
+    >>> pca.fit(X)
+    PCA(n_components=2, svd_solver='full')
+    >>> print(pca.explained_variance_ratio_)
+    [0.9924... 0.00755...]
+    >>> print(pca.singular_values_)
+    [6.30061... 0.54980...]
+
+    >>> pca = PCA(n_components=1, svd_solver='arpack')
+    >>> pca.fit(X)
+    PCA(n_components=1, svd_solver='arpack')
+    >>> print(pca.explained_variance_ratio_)
+    [0.99244...]
+    >>> print(pca.singular_values_)
+    [6.30061...]
+    """
+
+    _parameter_constraints: dict = {
+        "n_components": [
+            Interval(Integral, 0, None, closed="left"),
+            Interval(RealNotInt, 0, 1, closed="neither"),
+            StrOptions({"mle"}),
+            None,
+        ],
+        "copy": ["boolean"],
+        "whiten": ["boolean"],
+        "svd_solver": [StrOptions({"auto", "full", "arpack", "randomized"})],
+        "tol": [Interval(Real, 0, None, closed="left")],
+        "iterated_power": [
+            StrOptions({"auto"}),
+            Interval(Integral, 0, None, closed="left"),
+        ],
+        "n_oversamples": [Interval(Integral, 1, None, closed="left")],
+        "power_iteration_normalizer": [StrOptions({"auto", "QR", "LU", "none"})],
+        "random_state": ["random_state"],
+    }
+
+    def __init__(
+        self,
+        n_components=None,
+        *,
+        copy=True,
+        whiten=False,
+        svd_solver="auto",
+        tol=0.0,
+        iterated_power="auto",
+        n_oversamples=10,
+        power_iteration_normalizer="auto",
+        random_state=None,
+    ):
+        self.n_components = n_components
+        self.copy = copy
+        self.whiten = whiten
+        self.svd_solver = svd_solver
+        self.tol = tol
+        self.iterated_power = iterated_power
+        self.n_oversamples = n_oversamples
+        self.power_iteration_normalizer = power_iteration_normalizer
+        self.random_state = random_state
+
+    @_fit_context(prefer_skip_nested_validation=True)
+    def fit(self, X, y=None):
+        """Fit the model with X.
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            Training data, where `n_samples` is the number of samples
+            and `n_features` is the number of features.
+
+        y : Ignored
+            Ignored.
+
+        Returns
+        -------
+        self : object
+            Returns the instance itself.
+        """
+        self._fit(X)
+        return self
+
+    @_fit_context(prefer_skip_nested_validation=True)
+    def fit_transform(self, X, y=None):
+        """Fit the model with X and apply the dimensionality reduction on X.
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            Training data, where `n_samples` is the number of samples
+            and `n_features` is the number of features.
+
+        y : Ignored
+            Ignored.
+
+        Returns
+        -------
+        X_new : ndarray of shape (n_samples, n_components)
+            Transformed values.
+
+        Notes
+        -----
+        This method returns a Fortran-ordered array. To convert it to a
+        C-ordered array, use 'np.ascontiguousarray'.
+        """
+        U, S, Vt = self._fit(X)
+        U = U[:, : self.n_components_]
+
+        if self.whiten:
+            # X_new = X * V / S * sqrt(n_samples) = U * sqrt(n_samples)
+            U *= sqrt(X.shape[0] - 1)
+        else:
+            # X_new = X * V = U * S * Vt * V = U * S
+            U *= S[: self.n_components_]
+
+        return U
+
+    def _fit(self, X):
+        """Dispatch to the right submethod depending on the chosen solver."""
+        xp, is_array_api_compliant = get_namespace(X)
+
+        # Raise an error for sparse input and unsupported svd_solver
+        if issparse(X) and self.svd_solver != "arpack":
+            raise TypeError(
+                'PCA only support sparse inputs with the "arpack" solver, while '
+                f'"{self.svd_solver}" was passed. See TruncatedSVD for a possible'
+                " alternative."
+            )
+        # Raise an error for non-Numpy input and arpack solver.
+        if self.svd_solver == "arpack" and is_array_api_compliant:
+            raise ValueError(
+                "PCA with svd_solver='arpack' is not supported for Array API inputs."
+            )
+
+        X = self._validate_data(
+            X,
+            dtype=[xp.float64, xp.float32],
+            accept_sparse=("csr", "csc"),
+            ensure_2d=True,
+            copy=self.copy,
+        )
+
+        # Handle n_components==None
+        if self.n_components is None:
+            if self.svd_solver != "arpack":
+                n_components = min(X.shape)
+            else:
+                n_components = min(X.shape) - 1
+        else:
+            n_components = self.n_components
+
+        # Handle svd_solver
+        self._fit_svd_solver = self.svd_solver
+        if self._fit_svd_solver == "auto":
+            # Small problem or n_components == 'mle', just call full PCA
+            if max(X.shape) <= 500 or n_components == "mle":
+                self._fit_svd_solver = "full"
+            elif 1 <= n_components < 0.8 * min(X.shape):
+                self._fit_svd_solver = "randomized"
+            # This is also the case of n_components in (0,1)
+            else:
+                self._fit_svd_solver = "full"
+
+        # Call different fits for either full or truncated SVD
+        if self._fit_svd_solver == "full":
+            return self._fit_full(X, n_components)
+        elif self._fit_svd_solver in ["arpack", "randomized"]:
+            return self._fit_truncated(X, n_components, self._fit_svd_solver)
+
+    def _fit_full(self, X, n_components):
+        """Fit the model by computing full SVD on X."""
+        xp, is_array_api_compliant = get_namespace(X)
+
+        n_samples, n_features = X.shape
+
+        if n_components == "mle":
+            if n_samples < n_features:
+                raise ValueError(
+                    "n_components='mle' is only supported if n_samples >= n_features"
+                )
+        elif not 0 <= n_components <= min(n_samples, n_features):
+            raise ValueError(
+                "n_components=%r must be between 0 and "
+                "min(n_samples, n_features)=%r with "
+                "svd_solver='full'" % (n_components, min(n_samples, n_features))
+            )
+
+        # Center data
+        self.mean_ = xp.mean(X, axis=0)
+        X -= self.mean_
+
+        if not is_array_api_compliant:
+            # Use scipy.linalg with NumPy/SciPy inputs for the sake of not
+            # introducing unanticipated behavior changes. In the long run we
+            # could instead decide to always use xp.linalg.svd for all inputs,
+            # but that would make this code rely on numpy's SVD instead of
+            # scipy's. It's not 100% clear whether they use the same LAPACK
+            # solver by default though (assuming both are built against the
+            # same BLAS).
+            U, S, Vt = linalg.svd(X, full_matrices=False)
+        else:
+            U, S, Vt = xp.linalg.svd(X, full_matrices=False)
+        # flip eigenvectors' sign to enforce deterministic output
+        U, Vt = svd_flip(U, Vt)
+
+        components_ = Vt
+
+        # Get variance explained by singular values
+        explained_variance_ = (S**2) / (n_samples - 1)
+        total_var = xp.sum(explained_variance_)
+        explained_variance_ratio_ = explained_variance_ / total_var
+        singular_values_ = xp.asarray(S, copy=True)  # Store the singular values.
+
+        # Postprocess the number of components required
+        if n_components == "mle":
+            n_components = _infer_dimension(explained_variance_, n_samples)
+        elif 0 < n_components < 1.0:
+            # number of components for which the cumulated explained
+            # variance percentage is superior to the desired threshold
+            # side='right' ensures that number of features selected
+            # their variance is always greater than n_components float
+            # passed. More discussion in issue: #15669
+            if is_array_api_compliant:
+                # Convert to numpy as xp.cumsum and xp.searchsorted are not
+                # part of the Array API standard yet:
+                #
+                # https://github.com/data-apis/array-api/issues/597
+                # https://github.com/data-apis/array-api/issues/688
+                #
+                # Furthermore, it's not always safe to call them for namespaces
+                # that already implement them: for instance as
+                # cupy.searchsorted does not accept a float as second argument.
+                explained_variance_ratio_np = _convert_to_numpy(
+                    explained_variance_ratio_, xp=xp
+                )
+            else:
+                explained_variance_ratio_np = explained_variance_ratio_
+            ratio_cumsum = stable_cumsum(explained_variance_ratio_np)
+            n_components = np.searchsorted(ratio_cumsum, n_components, side="right") + 1
+
+        # Compute noise covariance using Probabilistic PCA model
+        # The sigma2 maximum likelihood (cf. eq. 12.46)
+        if n_components < min(n_features, n_samples):
+            self.noise_variance_ = xp.mean(explained_variance_[n_components:])
+        else:
+            self.noise_variance_ = 0.0
+
+        self.n_samples_ = n_samples
+        self.components_ = components_[:n_components, :]
+        self.n_components_ = n_components
+        self.explained_variance_ = explained_variance_[:n_components]
+        self.explained_variance_ratio_ = explained_variance_ratio_[:n_components]
+        self.singular_values_ = singular_values_[:n_components]
+
+        return U, S, Vt
+
+    def _fit_truncated(self, X, n_components, svd_solver):
+        """Fit the model by computing truncated SVD (by ARPACK or randomized)
+        on X.
+        """
+        xp, _ = get_namespace(X)
+
+        n_samples, n_features = X.shape
+
+        if isinstance(n_components, str):
+            raise ValueError(
+                "n_components=%r cannot be a string with svd_solver='%s'"
+                % (n_components, svd_solver)
+            )
+        elif not 1 <= n_components <= min(n_samples, n_features):
+            raise ValueError(
+                "n_components=%r must be between 1 and "
+                "min(n_samples, n_features)=%r with "
+                "svd_solver='%s'"
+                % (n_components, min(n_samples, n_features), svd_solver)
+            )
+        elif svd_solver == "arpack" and n_components == min(n_samples, n_features):
+            raise ValueError(
+                "n_components=%r must be strictly less than "
+                "min(n_samples, n_features)=%r with "
+                "svd_solver='%s'"
+                % (n_components, min(n_samples, n_features), svd_solver)
+            )
+
+        random_state = check_random_state(self.random_state)
+
+        # Center data
+        total_var = None
+        if issparse(X):
+            self.mean_, var = mean_variance_axis(X, axis=0)
+            total_var = var.sum() * n_samples / (n_samples - 1)  # ddof=1
+            X = _implicit_column_offset(X, self.mean_)
+        else:
+            self.mean_ = xp.mean(X, axis=0)
+            X -= self.mean_
+
+        if svd_solver == "arpack":
+            v0 = _init_arpack_v0(min(X.shape), random_state)
+            U, S, Vt = svds(X, k=n_components, tol=self.tol, v0=v0)
+            # svds doesn't abide by scipy.linalg.svd/randomized_svd
+            # conventions, so reverse its outputs.
+            S = S[::-1]
+            # flip eigenvectors' sign to enforce deterministic output
+            U, Vt = svd_flip(U[:, ::-1], Vt[::-1])
+
+        elif svd_solver == "randomized":
+            # sign flipping is done inside
+            U, S, Vt = randomized_svd(
+                X,
+                n_components=n_components,
+                n_oversamples=self.n_oversamples,
+                n_iter=self.iterated_power,
+                power_iteration_normalizer=self.power_iteration_normalizer,
+                flip_sign=True,
+                random_state=random_state,
+            )
+
+        self.n_samples_ = n_samples
+        self.components_ = Vt
+        self.n_components_ = n_components
+
+        # Get variance explained by singular values
+        self.explained_variance_ = (S**2) / (n_samples - 1)
+
+        # Workaround in-place variance calculation since at the time numpy
+        # did not have a way to calculate variance in-place.
+        #
+        # TODO: update this code to either:
+        # * Use the array-api variance calculation, unless memory usage suffers
+        # * Update sklearn.utils.extmath._incremental_mean_and_var to support array-api
+        # See: https://github.com/scikit-learn/scikit-learn/pull/18689#discussion_r1335540991
+        if total_var is None:
+            N = X.shape[0] - 1
+            X **= 2
+            total_var = xp.sum(X) / N
+
+        self.explained_variance_ratio_ = self.explained_variance_ / total_var
+        self.singular_values_ = xp.asarray(S, copy=True)  # Store the singular values.
+
+        if self.n_components_ < min(n_features, n_samples):
+            self.noise_variance_ = total_var - xp.sum(self.explained_variance_)
+            self.noise_variance_ /= min(n_features, n_samples) - n_components
+        else:
+            self.noise_variance_ = 0.0
+
+        return U, S, Vt
+
+    def score_samples(self, X):
+        """Return the log-likelihood of each sample.
+
+        See. "Pattern Recognition and Machine Learning"
+        by C. Bishop, 12.2.1 p. 574
+        or http://www.miketipping.com/papers/met-mppca.pdf
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            The data.
+
+        Returns
+        -------
+        ll : ndarray of shape (n_samples,)
+            Log-likelihood of each sample under the current model.
+        """
+        check_is_fitted(self)
+        xp, _ = get_namespace(X)
+        X = self._validate_data(X, dtype=[xp.float64, xp.float32], reset=False)
+        Xr = X - self.mean_
+        n_features = X.shape[1]
+        precision = self.get_precision()
+        log_like = -0.5 * xp.sum(Xr * (Xr @ precision), axis=1)
+        log_like -= 0.5 * (n_features * log(2.0 * np.pi) - fast_logdet(precision))
+        return log_like
+
+    def score(self, X, y=None):
+        """Return the average log-likelihood of all samples.
+
+        See. "Pattern Recognition and Machine Learning"
+        by C. Bishop, 12.2.1 p. 574
+        or http://www.miketipping.com/papers/met-mppca.pdf
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            The data.
+
+        y : Ignored
+            Ignored.
+
+        Returns
+        -------
+        ll : float
+            Average log-likelihood of the samples under the current model.
+        """
+        xp, _ = get_namespace(X)
+        return float(xp.mean(self.score_samples(X)))
+
+    def _more_tags(self):
+        return {"preserves_dtype": [np.float64, np.float32], "array_api_support": True}

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/tests/test_dict_learning.py

@@ -0,0 +1,983 @@
+import itertools
+import warnings
+from functools import partial
+
+import numpy as np
+import pytest
+
+import sklearn
+from sklearn.base import clone
+from sklearn.decomposition import (
+    DictionaryLearning,
+    MiniBatchDictionaryLearning,
+    SparseCoder,
+    dict_learning,
+    dict_learning_online,
+    sparse_encode,
+)
+from sklearn.decomposition._dict_learning import _update_dict
+from sklearn.exceptions import ConvergenceWarning
+from sklearn.utils import check_array
+from sklearn.utils._testing import (
+    TempMemmap,
+    assert_allclose,
+    assert_array_almost_equal,
+    assert_array_equal,
+    ignore_warnings,
+)
+from sklearn.utils.estimator_checks import (
+    check_transformer_data_not_an_array,
+    check_transformer_general,
+    check_transformers_unfitted,
+)
+from sklearn.utils.parallel import Parallel
+
+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, 2]):
+            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**0.25))
+            * (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] = 3.0
+    X[np.logical_not(first_quarter)] = -1.0
+    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 warnings.catch_warnings():
+        warnings.simplefilter("error", ConvergenceWarning)
+        model = SparseCoder(
+            D_multi, transform_algorithm=transform_algorithm, transform_max_iter=2000
+        )
+        model.fit_transform(X)
+
+
+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_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,
+        batch_size=4,
+        max_iter=10,
+        method="cd",
+        random_state=rng,
+        return_code=True,
+    )
+    assert code.shape == (n_samples, n_components)
+    assert dictionary.shape == (n_components, n_features)
+    assert np.dot(code, dictionary).shape == X.shape
+
+    dictionary = dict_learning_online(
+        X,
+        n_components=n_components,
+        batch_size=4,
+        max_iter=10,
+        method="cd",
+        random_state=rng,
+        return_code=False,
+    )
+    assert dictionary.shape == (n_components, n_features)
+
+
+def test_dict_learning_online_lars_positive_parameter():
+    err_msg = "Positive constraint not supported for 'lars' coding method."
+    with pytest.raises(ValueError, match=err_msg):
+        dict_learning_online(X, batch_size=4, max_iter=10, 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,
+        batch_size=4,
+        max_iter=10,
+        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,
+        batch_size=4,
+        max_iter=10,
+        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,
+        batch_size=4,
+        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():
+    # test verbosity for better coverage
+    n_components = 5
+    import sys
+    from io import StringIO
+
+    old_stdout = sys.stdout
+    try:
+        sys.stdout = StringIO()
+
+        # convergence monitoring verbosity
+        dico = MiniBatchDictionaryLearning(
+            n_components, batch_size=4, max_iter=5, verbose=1, tol=0.1, random_state=0
+        )
+        dico.fit(X)
+        dico = MiniBatchDictionaryLearning(
+            n_components,
+            batch_size=4,
+            max_iter=5,
+            verbose=1,
+            max_no_improvement=2,
+            random_state=0,
+        )
+        dico.fit(X)
+        # higher verbosity level
+        dico = MiniBatchDictionaryLearning(
+            n_components, batch_size=4, max_iter=5, verbose=2, random_state=0
+        )
+        dico.fit(X)
+
+        # function API verbosity
+        dict_learning_online(
+            X,
+            n_components=n_components,
+            batch_size=4,
+            alpha=1,
+            verbose=1,
+            random_state=0,
+        )
+        dict_learning_online(
+            X,
+            n_components=n_components,
+            batch_size=4,
+            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, batch_size=4, max_iter=5, 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, batch_size=4, max_iter=5, 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, batch_size=4, max_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,
+        batch_size=4,
+        max_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,
+        max_iter=10,
+        batch_size=1,
+        alpha=1,
+        shuffle=False,
+        dict_init=V,
+        max_no_improvement=None,
+        tol=0.0,
+        random_state=0,
+    ).fit(X)
+    dict2 = MiniBatchDictionaryLearning(
+        n_components, alpha=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)
+
+    # partial_fit should ignore max_iter (#17433)
+    assert dict1.n_steps_ == dict2.n_steps_ == 100
+
+
+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_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]
+    coder = SparseCoder(
+        dictionary=V, transform_algorithm="lasso_lars", transform_alpha=0.001
+    ).transform(X)
+    assert not np.all(coder == 0)
+    assert np.sqrt(np.sum((np.dot(coder, V) - X) ** 2)) < 0.1
+
+
+def test_sparse_coder_estimator_clone():
+    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]
+    coder = SparseCoder(
+        dictionary=V, transform_algorithm="lasso_lars", transform_alpha=0.001
+    )
+    cloned = clone(coder)
+    assert id(cloned) != id(coder)
+    np.testing.assert_allclose(cloned.dictionary, coder.dictionary)
+    assert id(cloned.dictionary) != id(coder.dictionary)
+    assert cloned.n_components_ == coder.n_components_
+    assert cloned.n_features_in_ == coder.n_features_in_
+    data = np.random.rand(n_samples, n_features).astype(np.float32)
+    np.testing.assert_allclose(cloned.transform(data), coder.transform(data))
+
+
+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_common_transformer():
+    rng = np.random.RandomState(777)
+    n_components, n_features = 40, 3
+    init_dict = rng.rand(n_components, n_features)
+
+    sc = SparseCoder(init_dict)
+
+    check_transformer_data_not_an_array(sc.__class__.__name__, sc)
+    check_transformer_general(sc.__class__.__name__, sc)
+    check_transformer_general_memmap = partial(
+        check_transformer_general, readonly_memmap=True
+    )
+    check_transformer_general_memmap(sc.__class__.__name__, sc)
+    check_transformers_unfitted(sc.__class__.__name__, sc)
+
+
+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]
+
+
+def test_update_dict():
+    # Check the dict update in batch mode vs online mode
+    # Non-regression test for #4866
+    rng = np.random.RandomState(0)
+
+    code = np.array([[0.5, -0.5], [0.1, 0.9]])
+    dictionary = np.array([[1.0, 0.0], [0.6, 0.8]])
+
+    X = np.dot(code, dictionary) + rng.randn(2, 2)
+
+    # full batch update
+    newd_batch = dictionary.copy()
+    _update_dict(newd_batch, X, code)
+
+    # online update
+    A = np.dot(code.T, code)
+    B = np.dot(X.T, code)
+    newd_online = dictionary.copy()
+    _update_dict(newd_online, X, code, A, B)
+
+    assert_allclose(newd_batch, newd_online)
+
+
+@pytest.mark.parametrize(
+    "algorithm", ("lasso_lars", "lasso_cd", "lars", "threshold", "omp")
+)
+@pytest.mark.parametrize("data_type", (np.float32, np.float64))
+# Note: do not check integer input because `lasso_lars` and `lars` fail with
+# `ValueError` in `_lars_path_solver`
+def test_sparse_encode_dtype_match(data_type, algorithm):
+    n_components = 6
+    rng = np.random.RandomState(0)
+    dictionary = rng.randn(n_components, n_features)
+    code = sparse_encode(
+        X.astype(data_type), dictionary.astype(data_type), algorithm=algorithm
+    )
+    assert code.dtype == data_type
+
+
+@pytest.mark.parametrize(
+    "algorithm", ("lasso_lars", "lasso_cd", "lars", "threshold", "omp")
+)
+def test_sparse_encode_numerical_consistency(algorithm):
+    # verify numerical consistency among np.float32 and np.float64
+    rtol = 1e-4
+    n_components = 6
+    rng = np.random.RandomState(0)
+    dictionary = rng.randn(n_components, n_features)
+    code_32 = sparse_encode(
+        X.astype(np.float32), dictionary.astype(np.float32), algorithm=algorithm
+    )
+    code_64 = sparse_encode(
+        X.astype(np.float64), dictionary.astype(np.float64), algorithm=algorithm
+    )
+    assert_allclose(code_32, code_64, rtol=rtol)
+
+
+@pytest.mark.parametrize(
+    "transform_algorithm", ("lasso_lars", "lasso_cd", "lars", "threshold", "omp")
+)
+@pytest.mark.parametrize("data_type", (np.float32, np.float64))
+# Note: do not check integer input because `lasso_lars` and `lars` fail with
+# `ValueError` in `_lars_path_solver`
+def test_sparse_coder_dtype_match(data_type, transform_algorithm):
+    # Verify preserving dtype for transform in sparse coder
+    n_components = 6
+    rng = np.random.RandomState(0)
+    dictionary = rng.randn(n_components, n_features)
+    coder = SparseCoder(
+        dictionary.astype(data_type), transform_algorithm=transform_algorithm
+    )
+    code = coder.transform(X.astype(data_type))
+    assert code.dtype == data_type
+
+
+@pytest.mark.parametrize("fit_algorithm", ("lars", "cd"))
+@pytest.mark.parametrize(
+    "transform_algorithm", ("lasso_lars", "lasso_cd", "lars", "threshold", "omp")
+)
+@pytest.mark.parametrize(
+    "data_type, expected_type",
+    (
+        (np.float32, np.float32),
+        (np.float64, np.float64),
+        (np.int32, np.float64),
+        (np.int64, np.float64),
+    ),
+)
+def test_dictionary_learning_dtype_match(
+    data_type,
+    expected_type,
+    fit_algorithm,
+    transform_algorithm,
+):
+    # Verify preserving dtype for fit and transform in dictionary learning class
+    dict_learner = DictionaryLearning(
+        n_components=8,
+        fit_algorithm=fit_algorithm,
+        transform_algorithm=transform_algorithm,
+        random_state=0,
+    )
+    dict_learner.fit(X.astype(data_type))
+    assert dict_learner.components_.dtype == expected_type
+    assert dict_learner.transform(X.astype(data_type)).dtype == expected_type
+
+
+@pytest.mark.parametrize("fit_algorithm", ("lars", "cd"))
+@pytest.mark.parametrize(
+    "transform_algorithm", ("lasso_lars", "lasso_cd", "lars", "threshold", "omp")
+)
+@pytest.mark.parametrize(
+    "data_type, expected_type",
+    (
+        (np.float32, np.float32),
+        (np.float64, np.float64),
+        (np.int32, np.float64),
+        (np.int64, np.float64),
+    ),
+)
+def test_minibatch_dictionary_learning_dtype_match(
+    data_type,
+    expected_type,
+    fit_algorithm,
+    transform_algorithm,
+):
+    # Verify preserving dtype for fit and transform in minibatch dictionary learning
+    dict_learner = MiniBatchDictionaryLearning(
+        n_components=8,
+        batch_size=10,
+        fit_algorithm=fit_algorithm,
+        transform_algorithm=transform_algorithm,
+        max_iter=100,
+        tol=1e-1,
+        random_state=0,
+    )
+    dict_learner.fit(X.astype(data_type))
+
+    assert dict_learner.components_.dtype == expected_type
+    assert dict_learner.transform(X.astype(data_type)).dtype == expected_type
+    assert dict_learner._A.dtype == expected_type
+    assert dict_learner._B.dtype == expected_type
+
+
+@pytest.mark.parametrize("method", ("lars", "cd"))
+@pytest.mark.parametrize(
+    "data_type, expected_type",
+    (
+        (np.float32, np.float32),
+        (np.float64, np.float64),
+        (np.int32, np.float64),
+        (np.int64, np.float64),
+    ),
+)
+def test_dict_learning_dtype_match(data_type, expected_type, method):
+    # Verify output matrix dtype
+    rng = np.random.RandomState(0)
+    n_components = 8
+    code, dictionary, _ = dict_learning(
+        X.astype(data_type),
+        n_components=n_components,
+        alpha=1,
+        random_state=rng,
+        method=method,
+    )
+    assert code.dtype == expected_type
+    assert dictionary.dtype == expected_type
+
+
+@pytest.mark.parametrize("method", ("lars", "cd"))
+def test_dict_learning_numerical_consistency(method):
+    # verify numerically consistent among np.float32 and np.float64
+    rtol = 1e-6
+    n_components = 4
+    alpha = 2
+
+    U_64, V_64, _ = dict_learning(
+        X.astype(np.float64),
+        n_components=n_components,
+        alpha=alpha,
+        random_state=0,
+        method=method,
+    )
+    U_32, V_32, _ = dict_learning(
+        X.astype(np.float32),
+        n_components=n_components,
+        alpha=alpha,
+        random_state=0,
+        method=method,
+    )
+
+    # Optimal solution (U*, V*) is not unique.
+    # If (U*, V*) is optimal solution, (-U*,-V*) is also optimal,
+    # and (column permutated U*, row permutated V*) are also optional
+    # as long as holding UV.
+    # So here UV, ||U||_1,1 and sum(||V_k||_2^2) are verified
+    # instead of comparing directly U and V.
+    assert_allclose(np.matmul(U_64, V_64), np.matmul(U_32, V_32), rtol=rtol)
+    assert_allclose(np.sum(np.abs(U_64)), np.sum(np.abs(U_32)), rtol=rtol)
+    assert_allclose(np.sum(V_64**2), np.sum(V_32**2), rtol=rtol)
+    # verify an obtained solution is not degenerate
+    assert np.mean(U_64 != 0.0) > 0.05
+    assert np.count_nonzero(U_64 != 0.0) == np.count_nonzero(U_32 != 0.0)
+
+
+@pytest.mark.parametrize("method", ("lars", "cd"))
+@pytest.mark.parametrize(
+    "data_type, expected_type",
+    (
+        (np.float32, np.float32),
+        (np.float64, np.float64),
+        (np.int32, np.float64),
+        (np.int64, np.float64),
+    ),
+)
+def test_dict_learning_online_dtype_match(data_type, expected_type, method):
+    # Verify output matrix dtype
+    rng = np.random.RandomState(0)
+    n_components = 8
+    code, dictionary = dict_learning_online(
+        X.astype(data_type),
+        n_components=n_components,
+        alpha=1,
+        batch_size=10,
+        random_state=rng,
+        method=method,
+    )
+    assert code.dtype == expected_type
+    assert dictionary.dtype == expected_type
+
+
+@pytest.mark.parametrize("method", ("lars", "cd"))
+def test_dict_learning_online_numerical_consistency(method):
+    # verify numerically consistent among np.float32 and np.float64
+    rtol = 1e-4
+    n_components = 4
+    alpha = 1
+
+    U_64, V_64 = dict_learning_online(
+        X.astype(np.float64),
+        n_components=n_components,
+        max_iter=1_000,
+        alpha=alpha,
+        batch_size=10,
+        random_state=0,
+        method=method,
+        tol=0.0,
+        max_no_improvement=None,
+    )
+    U_32, V_32 = dict_learning_online(
+        X.astype(np.float32),
+        n_components=n_components,
+        max_iter=1_000,
+        alpha=alpha,
+        batch_size=10,
+        random_state=0,
+        method=method,
+        tol=0.0,
+        max_no_improvement=None,
+    )
+
+    # Optimal solution (U*, V*) is not unique.
+    # If (U*, V*) is optimal solution, (-U*,-V*) is also optimal,
+    # and (column permutated U*, row permutated V*) are also optional
+    # as long as holding UV.
+    # So here UV, ||U||_1,1 and sum(||V_k||_2) are verified
+    # instead of comparing directly U and V.
+    assert_allclose(np.matmul(U_64, V_64), np.matmul(U_32, V_32), rtol=rtol)
+    assert_allclose(np.sum(np.abs(U_64)), np.sum(np.abs(U_32)), rtol=rtol)
+    assert_allclose(np.sum(V_64**2), np.sum(V_32**2), rtol=rtol)
+    # verify an obtained solution is not degenerate
+    assert np.mean(U_64 != 0.0) > 0.05
+    assert np.count_nonzero(U_64 != 0.0) == np.count_nonzero(U_32 != 0.0)
+
+
+@pytest.mark.parametrize(
+    "estimator",
+    [
+        SparseCoder(X.T),
+        DictionaryLearning(),
+        MiniBatchDictionaryLearning(batch_size=4, max_iter=10),
+    ],
+    ids=lambda x: x.__class__.__name__,
+)
+def test_get_feature_names_out(estimator):
+    """Check feature names for dict learning estimators."""
+    estimator.fit(X)
+    n_components = X.shape[1]
+
+    feature_names_out = estimator.get_feature_names_out()
+    estimator_name = estimator.__class__.__name__.lower()
+    assert_array_equal(
+        feature_names_out,
+        [f"{estimator_name}{i}" for i in range(n_components)],
+    )
+
+
+def test_cd_work_on_joblib_memmapped_data(monkeypatch):
+    monkeypatch.setattr(
+        sklearn.decomposition._dict_learning,
+        "Parallel",
+        partial(Parallel, max_nbytes=100),
+    )
+
+    rng = np.random.RandomState(0)
+    X_train = rng.randn(10, 10)
+
+    dict_learner = DictionaryLearning(
+        n_components=5,
+        random_state=0,
+        n_jobs=2,
+        fit_algorithm="cd",
+        max_iter=50,
+        verbose=True,
+    )
+
+    # This must run and complete without error.
+    dict_learner.fit(X_train)
+
+
+# TODO(1.6): remove in 1.6
+def test_xxx():
+    warn_msg = "`max_iter=None` is deprecated in version 1.4 and will be removed"
+    with pytest.warns(FutureWarning, match=warn_msg):
+        MiniBatchDictionaryLearning(max_iter=None, random_state=0).fit(X)
+    with pytest.warns(FutureWarning, match=warn_msg):
+        dict_learning_online(X, max_iter=None, random_state=0)

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/tests/test_factor_analysis.py

@@ -0,0 +1,116 @@
+# Author: Christian Osendorfer <[email protected]>
+#         Alexandre Gramfort <[email protected]>
+# License: BSD3
+
+from itertools import combinations
+
+import numpy as np
+import pytest
+
+from sklearn.decomposition import FactorAnalysis
+from sklearn.decomposition._factor_analysis import _ortho_rotation
+from sklearn.exceptions import ConvergenceWarning
+from sklearn.utils._testing import (
+    assert_almost_equal,
+    assert_array_almost_equal,
+    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
+
+    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 > 0.0, "Log likelihood dif not increase"
+
+        # Sample Covariance
+        scov = np.cov(X, rowvar=0.0, bias=1.0)
+
+        # 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])
+
+    def f(x, y):
+        return 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
+    with pytest.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)
+
+    # test rotation
+    n_components = 2
+
+    results, projections = {}, {}
+    for method in (None, "varimax", "quartimax"):
+        fa_var = FactorAnalysis(n_components=n_components, rotation=method)
+        results[method] = fa_var.fit_transform(X)
+        projections[method] = fa_var.get_covariance()
+    for rot1, rot2 in combinations([None, "varimax", "quartimax"], 2):
+        assert not np.allclose(results[rot1], results[rot2])
+        assert np.allclose(projections[rot1], projections[rot2], atol=3)
+
+    # test against R's psych::principal with rotate="varimax"
+    # (i.e., the values below stem from rotating the components in R)
+    # R's factor analysis returns quite different values; therefore, we only
+    # test the rotation itself
+    factors = np.array(
+        [
+            [0.89421016, -0.35854928, -0.27770122, 0.03773647],
+            [-0.45081822, -0.89132754, 0.0932195, -0.01787973],
+            [0.99500666, -0.02031465, 0.05426497, -0.11539407],
+            [0.96822861, -0.06299656, 0.24411001, 0.07540887],
+        ]
+    )
+    r_solution = np.array(
+        [[0.962, 0.052], [-0.141, 0.989], [0.949, -0.300], [0.937, -0.251]]
+    )
+    rotated = _ortho_rotation(factors[:, :n_components], method="varimax").T
+    assert_array_almost_equal(np.abs(rotated), np.abs(r_solution), decimal=3)

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/tests/test_fastica.py

@@ -0,0 +1,451 @@
+"""
+Test the fastica algorithm.
+"""
+import itertools
+import os
+import warnings
+
+import numpy as np
+import pytest
+from scipy import stats
+
+from sklearn.decomposition import PCA, FastICA, fastica
+from sklearn.decomposition._fastica import _gs_decorrelation
+from sklearn.exceptions import ConvergenceWarning
+from sklearn.utils._testing import assert_allclose
+
+
+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() < 1.0e-10
+    w = rng.randn(10)
+    u = _gs_decorrelation(w, W, 5)
+    tmp = np.dot(u, W.T)
+    assert (tmp[:5] ** 2).sum() < 1.0e-10
+
+
+def test_fastica_attributes_dtypes(global_dtype):
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((100, 10)).astype(global_dtype, copy=False)
+    fica = FastICA(
+        n_components=5, max_iter=1000, whiten="unit-variance", random_state=0
+    ).fit(X)
+    assert fica.components_.dtype == global_dtype
+    assert fica.mixing_.dtype == global_dtype
+    assert fica.mean_.dtype == global_dtype
+    assert fica.whitening_.dtype == global_dtype
+
+
+def test_fastica_return_dtypes(global_dtype):
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((100, 10)).astype(global_dtype, copy=False)
+    k_, mixing_, s_ = fastica(
+        X, max_iter=1000, whiten="unit-variance", random_state=rng
+    )
+    assert k_.dtype == global_dtype
+    assert mixing_.dtype == global_dtype
+    assert s_.dtype == global_dtype
+
+
+@pytest.mark.parametrize("add_noise", [True, False])
+def test_fastica_simple(add_noise, global_random_seed, global_dtype):
+    if (
+        global_random_seed == 20
+        and global_dtype == np.float32
+        and not add_noise
+        and os.getenv("DISTRIB") == "ubuntu"
+    ):
+        pytest.xfail(
+            "FastICA instability with Ubuntu Atlas build with float32 "
+            "global_dtype. For more details, see "
+            "https://github.com/scikit-learn/scikit-learn/issues/24131#issuecomment-1208091119"  # noqa
+        )
+
+    # Test the FastICA algorithm on very simple data.
+    rng = np.random.RandomState(global_random_seed)
+    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, random_state=global_random_seed)
+    s = np.c_[s1, s2].T
+    center_and_norm(s)
+    s = s.astype(global_dtype)
+    s1, s2 = s
+
+    # Mixing angle
+    phi = 0.6
+    mixing = np.array([[np.cos(phi), np.sin(phi)], [np.sin(phi), -np.cos(phi)]])
+    mixing = mixing.astype(global_dtype)
+    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 = ["arbitrary-variance", "unit-variance", False]
+    for algo, nl, whiten in itertools.product(algos, nls, whitening):
+        if whiten:
+            k_, mixing_, s_ = fastica(
+                m.T, fun=nl, whiten=whiten, algorithm=algo, random_state=rng
+            )
+            with pytest.raises(ValueError):
+                fastica(m.T, fun=np.tanh, whiten=whiten, 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:
+            # XXX: exact reconstruction to standard relative tolerance is not
+            # possible. This is probably expected when add_noise is True but we
+            # also need a non-trivial atol in float32 when add_noise is False.
+            #
+            # Note that the 2 sources are non-Gaussian in this test.
+            atol = 1e-5 if global_dtype == np.float32 else 0
+            assert_allclose(np.dot(np.dot(mixing_, k_), m), s_, atol=atol)
+
+        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_allclose(np.dot(s1_, s1) / n_samples, 1, atol=1e-2)
+            assert_allclose(np.dot(s2_, s2) / n_samples, 1, atol=1e-2)
+        else:
+            assert_allclose(np.dot(s1_, s1) / n_samples, 1, atol=1e-1)
+            assert_allclose(np.dot(s2_, s2) / n_samples, 1, atol=1e-1)
+
+    # Test FastICA class
+    _, _, sources_fun = fastica(
+        m.T, fun=nl, algorithm=algo, random_state=global_random_seed
+    )
+    ica = FastICA(fun=nl, algorithm=algo, random_state=global_random_seed)
+    sources = ica.fit_transform(m.T)
+    assert ica.components_.shape == (2, 2)
+    assert sources.shape == (1000, 2)
+
+    assert_allclose(sources_fun, sources)
+    # Set atol to account for the different magnitudes of the elements in sources
+    # (from 1e-4 to 1e1).
+    atol = np.max(np.abs(sources)) * (1e-5 if global_dtype == np.float32 else 1e-7)
+    assert_allclose(sources, ica.transform(m.T), atol=atol)
+
+    assert ica.mixing_.shape == (2, 2)
+
+    ica = FastICA(fun=np.tanh, algorithm=algo)
+    with pytest.raises(ValueError):
+        ica.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)
+    warn_msg = "Ignoring n_components with whiten=False."
+    with pytest.warns(UserWarning, match=warn_msg):
+        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
+    warn_msg = (
+        "FastICA did not converge. Consider increasing tolerance "
+        "or the maximum number of iterations."
+    )
+    with pytest.warns(ConvergenceWarning, match=warn_msg):
+        ica = FastICA(
+            algorithm="parallel", n_components=2, random_state=rng, max_iter=2, tol=0.0
+        )
+        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, whiten="unit-variance", random_state=rng
+    )
+    s_ = s_.T
+
+    # Check that the mixing model described in the docstring holds:
+    assert_allclose(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_allclose(np.dot(s1_, s1) / n_samples, 1, atol=1e-3)
+        assert_allclose(np.dot(s2_, s2) / n_samples, 1, atol=1e-3)
+
+
+def test_fit_transform(global_random_seed, global_dtype):
+    """Test unit variance of transformed data using FastICA algorithm.
+
+    Check that `fit_transform` gives the same result as applying
+    `fit` and then `transform`.
+
+    Bug #13056
+    """
+    # multivariate uniform data in [0, 1]
+    rng = np.random.RandomState(global_random_seed)
+    X = rng.random_sample((100, 10)).astype(global_dtype)
+    max_iter = 300
+    for whiten, n_components in [["unit-variance", 5], [False, None]]:
+        n_components_ = n_components if n_components is not None else X.shape[1]
+
+        ica = FastICA(
+            n_components=n_components, max_iter=max_iter, whiten=whiten, random_state=0
+        )
+        with warnings.catch_warnings():
+            # make sure that numerical errors do not cause sqrt of negative
+            # values
+            warnings.simplefilter("error", RuntimeWarning)
+            # XXX: for some seeds, the model does not converge.
+            # However this is not what we test here.
+            warnings.simplefilter("ignore", ConvergenceWarning)
+            Xt = ica.fit_transform(X)
+        assert ica.components_.shape == (n_components_, 10)
+        assert Xt.shape == (X.shape[0], n_components_)
+
+        ica2 = FastICA(
+            n_components=n_components, max_iter=max_iter, whiten=whiten, random_state=0
+        )
+        with warnings.catch_warnings():
+            # make sure that numerical errors do not cause sqrt of negative
+            # values
+            warnings.simplefilter("error", RuntimeWarning)
+            warnings.simplefilter("ignore", ConvergenceWarning)
+            ica2.fit(X)
+        assert ica2.components_.shape == (n_components_, 10)
+        Xt2 = ica2.transform(X)
+
+        # XXX: we have to set atol for this test to pass for all seeds when
+        # fitting with float32 data. Is this revealing a bug?
+        if global_dtype:
+            atol = np.abs(Xt2).mean() / 1e6
+        else:
+            atol = 0.0  # the default rtol is enough for float64 data
+        assert_allclose(Xt, Xt2, atol=atol)
+
+
+@pytest.mark.filterwarnings("ignore:Ignoring n_components with whiten=False.")
+@pytest.mark.parametrize(
+    "whiten, n_components, expected_mixing_shape",
+    [
+        ("arbitrary-variance", 5, (10, 5)),
+        ("arbitrary-variance", 10, (10, 10)),
+        ("unit-variance", 5, (10, 5)),
+        ("unit-variance", 10, (10, 10)),
+        (False, 5, (10, 10)),
+        (False, 10, (10, 10)),
+    ],
+)
+def test_inverse_transform(
+    whiten, n_components, expected_mixing_shape, global_random_seed, global_dtype
+):
+    # Test FastICA.inverse_transform
+    n_samples = 100
+    rng = np.random.RandomState(global_random_seed)
+    X = rng.random_sample((n_samples, 10)).astype(global_dtype)
+
+    ica = FastICA(n_components=n_components, random_state=rng, whiten=whiten)
+    with warnings.catch_warnings():
+        # For some dataset (depending on the value of global_dtype) the model
+        # can fail to converge but this should not impact the definition of
+        # a valid inverse transform.
+        warnings.simplefilter("ignore", ConvergenceWarning)
+        Xt = ica.fit_transform(X)
+    assert ica.mixing_.shape == expected_mixing_shape
+    X2 = ica.inverse_transform(Xt)
+    assert X.shape == X2.shape
+
+    # reversibility test in non-reduction case
+    if n_components == X.shape[1]:
+        # XXX: we have to set atol for this test to pass for all seeds when
+        # fitting with float32 data. Is this revealing a bug?
+        if global_dtype:
+            # XXX: dividing by a smaller number makes
+            # tests fail for some seeds.
+            atol = np.abs(X2).mean() / 1e5
+        else:
+            atol = 0.0  # the default rtol is enough for float64 data
+        assert_allclose(X, X2, atol=atol)
+
+
+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=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)
+
+
+def test_fastica_whiten_unit_variance():
+    """Test unit variance of transformed data using FastICA algorithm.
+
+    Bug #13056
+    """
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((100, 10))
+    n_components = X.shape[1]
+    ica = FastICA(n_components=n_components, whiten="unit-variance", random_state=0)
+    Xt = ica.fit_transform(X)
+
+    assert np.var(Xt) == pytest.approx(1.0)
+
+
+@pytest.mark.parametrize("whiten", ["arbitrary-variance", "unit-variance", 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
+
+
+@pytest.mark.parametrize("add_noise", [True, False])
+def test_fastica_simple_different_solvers(add_noise, global_random_seed):
+    """Test FastICA is consistent between whiten_solvers."""
+    rng = np.random.RandomState(global_random_seed)
+    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, random_state=rng)
+    s = np.c_[s1, s2].T
+    center_and_norm(s)
+    s1, s2 = s
+
+    # Mixing angle
+    phi = rng.rand() * 2 * np.pi
+    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)
+
+    outs = {}
+    for solver in ("svd", "eigh"):
+        ica = FastICA(random_state=0, whiten="unit-variance", whiten_solver=solver)
+        sources = ica.fit_transform(m.T)
+        outs[solver] = sources
+        assert ica.components_.shape == (2, 2)
+        assert sources.shape == (1000, 2)
+
+    # compared numbers are not all on the same magnitude. Using a small atol to
+    # make the test less brittle
+    assert_allclose(outs["eigh"], outs["svd"], atol=1e-12)
+
+
+def test_fastica_eigh_low_rank_warning(global_random_seed):
+    """Test FastICA eigh solver raises warning for low-rank data."""
+    rng = np.random.RandomState(global_random_seed)
+    A = rng.randn(10, 2)
+    X = A @ A.T
+    ica = FastICA(random_state=0, whiten="unit-variance", whiten_solver="eigh")
+    msg = "There are some small singular values"
+    with pytest.warns(UserWarning, match=msg):
+        ica.fit(X)

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/tests/test_incremental_pca.py

@@ -0,0 +1,452 @@
+"""Tests for Incremental PCA."""
+import warnings
+
+import numpy as np
+import pytest
+from numpy.testing import assert_array_equal
+
+from sklearn import datasets
+from sklearn.decomposition import PCA, IncrementalPCA
+from sklearn.utils._testing import (
+    assert_allclose_dense_sparse,
+    assert_almost_equal,
+    assert_array_almost_equal,
+)
+from sklearn.utils.fixes import CSC_CONTAINERS, CSR_CONTAINERS, LIL_CONTAINERS
+
+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(
+    "sparse_container", CSC_CONTAINERS + CSR_CONTAINERS + LIL_CONTAINERS
+)
+def test_incremental_pca_sparse(sparse_container):
+    # Incremental PCA on sparse arrays.
+    X = iris.data
+    pca = PCA(n_components=2)
+    pca.fit_transform(X)
+    X_sparse = sparse_container(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) * 0.1
+    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]), 1.0, 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] *= 0.00001  # 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 <= n_features.
+    X = np.array([[0, 1, 0], [1, 0, 0]])
+    n_samples, n_features = X.shape
+    n_components = 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_samples_equal_n_components():
+    # Ensures no warning is raised when n_samples==n_components
+    # Non-regression test for gh-19050
+    ipca = IncrementalPCA(n_components=5)
+    with warnings.catch_warnings():
+        warnings.simplefilter("error", RuntimeWarning)
+        ipca.partial_fit(np.random.randn(5, 7))
+    with warnings.catch_warnings():
+        warnings.simplefilter("error", RuntimeWarning)
+        ipca.fit(np.random.randn(5, 7))
+
+
+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] *= 0.00001  # 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=0.0, 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=0.0, 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_)
+
+
+def test_incremental_pca_feature_names_out():
+    """Check feature names out for IncrementalPCA."""
+    ipca = IncrementalPCA(n_components=2).fit(iris.data)
+
+    names = ipca.get_feature_names_out()
+    assert_array_equal([f"incrementalpca{i}" for i in range(2)], names)

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/tests/test_kernel_pca.py

@@ -0,0 +1,566 @@
+import warnings
+
+import numpy as np
+import pytest
+
+import sklearn
+from sklearn.datasets import load_iris, make_blobs, make_circles
+from sklearn.decomposition import PCA, KernelPCA
+from sklearn.exceptions import NotFittedError
+from sklearn.linear_model import Perceptron
+from sklearn.metrics.pairwise import rbf_kernel
+from sklearn.model_selection import GridSearchCV
+from sklearn.pipeline import Pipeline
+from sklearn.preprocessing import StandardScaler
+from sklearn.utils._testing import (
+    assert_allclose,
+    assert_array_almost_equal,
+    assert_array_equal,
+)
+from sklearn.utils.fixes import CSR_CONTAINERS
+from sklearn.utils.validation import _check_psd_eigenvalues
+
+
+def test_kernel_pca():
+    """Nominal test for all solvers and all known kernels + a custom one
+
+    It tests
+     - that fit_transform is equivalent to fit+transform
+     - that the shapes of transforms and inverse transforms are correct
+    """
+    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", "randomized"):
+        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():
+    """Check that kPCA raises an error if the parameters are invalid
+
+    Tests fitting inverse transform with a precomputed kernel raises a
+    ValueError.
+    """
+    estimator = KernelPCA(
+        n_components=10, fit_inverse_transform=True, kernel="precomputed"
+    )
+    err_ms = "Cannot fit_inverse_transform with a precomputed kernel"
+    with pytest.raises(ValueError, match=err_ms):
+        estimator.fit(np.random.randn(10, 10))
+
+
+def test_kernel_pca_consistent_transform():
+    """Check robustness to mutations in the original training array
+
+    Test that after fitting a kPCA model, it stays independent of any
+    mutation of the values of the original data object by relying on an
+    internal copy.
+    """
+    # 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():
+    """Test that Kernel PCA produces deterministic output
+
+    Tests that the same inputs and random state produce the same 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))
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_kernel_pca_sparse(csr_container):
+    """Test that kPCA works on a sparse data input.
+
+    Same test as ``test_kernel_pca except inverse_transform`` since it's not
+    implemented for sparse matrices.
+    """
+    rng = np.random.RandomState(0)
+    X_fit = csr_container(rng.random_sample((5, 4)))
+    X_pred = csr_container(rng.random_sample((2, 4)))
+
+    for eigen_solver in ("auto", "arpack", "randomized"):
+        for kernel in ("linear", "rbf", "poly"):
+            # transform fit data
+            kpca = KernelPCA(
+                4,
+                kernel=kernel,
+                eigen_solver=eigen_solver,
+                fit_inverse_transform=False,
+                random_state=0,
+            )
+            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: not available for sparse matrices
+            # XXX: should we raise another exception type here? For instance:
+            # NotImplementedError.
+            with pytest.raises(NotFittedError):
+                kpca.inverse_transform(X_pred_transformed)
+
+
+@pytest.mark.parametrize("solver", ["auto", "dense", "arpack", "randomized"])
+@pytest.mark.parametrize("n_features", [4, 10])
+def test_kernel_pca_linear_kernel(solver, n_features):
+    """Test that kPCA with linear kernel is equivalent to PCA for all solvers.
+
+    KernelPCA with linear kernel should produce the same output as PCA.
+    """
+    rng = np.random.RandomState(0)
+    X_fit = rng.random_sample((5, n_features))
+    X_pred = rng.random_sample((2, n_features))
+
+    # 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
+    n_comps = 3 if solver == "arpack" else 4
+    assert_array_almost_equal(
+        np.abs(KernelPCA(n_comps, eigen_solver=solver).fit(X_fit).transform(X_pred)),
+        np.abs(
+            PCA(n_comps, svd_solver=solver if solver != "dense" else "full")
+            .fit(X_fit)
+            .transform(X_pred)
+        ),
+    )
+
+
+def test_kernel_pca_n_components():
+    """Test that `n_components` is correctly taken into account for projections
+
+    For all solvers this tests that the output has the correct shape depending
+    on the selected number of 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", "randomized"):
+        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():
+    """Check that the ``remove_zero_eig`` parameter works correctly.
+
+    Tests that the null-space (Zero) eigenvalues are removed when
+    remove_zero_eig=True, whereas they are not by default.
+    """
+    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():
+    """Non-regression test for issue #12141 (PR #12143)
+
+    This test checks that fit().transform() returns the same result as
+    fit_transform() in case of non-removed zero eigenvalue.
+    """
+    X_fit = np.array([[1, 1], [0, 0]])
+
+    # Assert that even with all np warnings on, there is no div by zero warning
+    with warnings.catch_warnings():
+        # 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)
+        warnings.simplefilter("error", RuntimeWarning)
+        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))
+
+
+def test_kernel_pca_precomputed():
+    """Test that kPCA works with a precomputed kernel, for all solvers"""
+    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", "randomized"):
+        X_kpca = (
+            KernelPCA(4, eigen_solver=eigen_solver, random_state=0)
+            .fit(X_fit)
+            .transform(X_pred)
+        )
+
+        X_kpca2 = (
+            KernelPCA(
+                4, eigen_solver=eigen_solver, kernel="precomputed", random_state=0
+            )
+            .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", random_state=0
+        ).fit_transform(np.dot(X_fit, X_fit.T))
+
+        X_kpca_train2 = (
+            KernelPCA(
+                4, eigen_solver=eigen_solver, kernel="precomputed", random_state=0
+            )
+            .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))
+
+
+@pytest.mark.parametrize("solver", ["auto", "dense", "arpack", "randomized"])
+def test_kernel_pca_precomputed_non_symmetric(solver):
+    """Check that the kernel centerer works.
+
+    Tests that a non symmetric precomputed kernel is actually accepted
+    because the kernel centerer does its job correctly.
+    """
+
+    # a non symmetric gram matrix
+    K = [[1, 2], [3, 40]]
+    kpca = KernelPCA(
+        kernel="precomputed", eigen_solver=solver, n_components=1, random_state=0
+    )
+    kpca.fit(K)  # no error
+
+    # same test with centered kernel
+    Kc = [[9, -9], [-9, 9]]
+    kpca_c = KernelPCA(
+        kernel="precomputed", eigen_solver=solver, n_components=1, random_state=0
+    )
+    kpca_c.fit(Kc)
+
+    # comparison between the non-centered and centered versions
+    assert_array_equal(kpca.eigenvectors_, kpca_c.eigenvectors_)
+    assert_array_equal(kpca.eigenvalues_, kpca_c.eigenvalues_)
+
+
+def test_gridsearch_pipeline():
+    """Check that kPCA works as expected in a grid search 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=0.3, noise=0.05, 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=2.0 ** 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():
+    """Check that kPCA works as expected in a grid search pipeline (2)
+
+    Test if we can do a grid-search to find parameters to separate
+    circles with a perceptron model. This test uses a precomputed kernel.
+    """
+    X, y = make_circles(n_samples=400, factor=0.3, noise=0.05, 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=2.0)
+    grid_search.fit(X_kernel, y)
+    assert grid_search.best_score_ == 1
+
+
+def test_nested_circles():
+    """Check that kPCA projects in a space where nested circles are separable
+
+    Tests that 2D nested circles become separable with a perceptron when
+    projected in the first 2 kPCA using an RBF kernel, while raw samples
+    are not directly separable in the original space.
+    """
+    X, y = make_circles(n_samples=400, factor=0.3, noise=0.05, 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=2.0
+    )
+    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():
+    """Check that ``_check_psd_eigenvalues`` is correctly called in kPCA
+
+    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.eigenvalues_.min() == 0
+    assert np.all(kpca.eigenvalues_ == _check_psd_eigenvalues(kpca.eigenvalues_))
+
+
+@pytest.mark.parametrize("solver", ["auto", "dense", "arpack", "randomized"])
+def test_precomputed_kernel_not_psd(solver):
+    """Check how KernelPCA works with non-PSD kernels depending on n_components
+
+    Tests for all methods what happens with a non PSD gram matrix (this
+    can happen in an isomap scenario, or with custom kernel functions, or
+    maybe with ill-posed datasets).
+
+    When ``n_component`` is large enough to capture a negative eigenvalue, an
+    error should be raised. Otherwise, KernelPCA should run without error
+    since the negative eigenvalues are not selected.
+    """
+
+    # a non PSD kernel with large eigenvalues, already centered
+    # it was captured from an isomap call and multiplied by 100 for compacity
+    K = [
+        [4.48, -1.0, 8.07, 2.33, 2.33, 2.33, -5.76, -12.78],
+        [-1.0, -6.48, 4.5, -1.24, -1.24, -1.24, -0.81, 7.49],
+        [8.07, 4.5, 15.48, 2.09, 2.09, 2.09, -11.1, -23.23],
+        [2.33, -1.24, 2.09, 4.0, -3.65, -3.65, 1.02, -0.9],
+        [2.33, -1.24, 2.09, -3.65, 4.0, -3.65, 1.02, -0.9],
+        [2.33, -1.24, 2.09, -3.65, -3.65, 4.0, 1.02, -0.9],
+        [-5.76, -0.81, -11.1, 1.02, 1.02, 1.02, 4.86, 9.75],
+        [-12.78, 7.49, -23.23, -0.9, -0.9, -0.9, 9.75, 21.46],
+    ]
+    # this gram matrix has 5 positive eigenvalues and 3 negative ones
+    # [ 52.72,   7.65,   7.65,   5.02,   0.  ,  -0.  ,  -6.13, -15.11]
+
+    # 1. ask for enough components to get a significant negative one
+    kpca = KernelPCA(kernel="precomputed", eigen_solver=solver, n_components=7)
+    # make sure that the appropriate error is raised
+    with pytest.raises(ValueError, match="There are significant negative eigenvalues"):
+        kpca.fit(K)
+
+    # 2. ask for a small enough n_components to get only positive ones
+    kpca = KernelPCA(kernel="precomputed", eigen_solver=solver, n_components=2)
+    if solver == "randomized":
+        # the randomized method is still inconsistent with the others on this
+        # since it selects the eigenvalues based on the largest 2 modules, not
+        # on the largest 2 values.
+        #
+        # At least we can ensure that we return an error instead of returning
+        # the wrong eigenvalues
+        with pytest.raises(
+            ValueError, match="There are significant negative eigenvalues"
+        ):
+            kpca.fit(K)
+    else:
+        # general case: make sure that it works
+        kpca.fit(K)
+
+
+@pytest.mark.parametrize("n_components", [4, 10, 20])
+def test_kernel_pca_solvers_equivalence(n_components):
+    """Check that 'dense' 'arpack' & 'randomized' solvers give similar results"""
+
+    # Generate random data
+    n_train, n_test = 1_000, 100
+    X, _ = make_circles(
+        n_samples=(n_train + n_test), factor=0.3, noise=0.05, random_state=0
+    )
+    X_fit, X_pred = X[:n_train, :], X[n_train:, :]
+
+    # reference (full)
+    ref_pred = (
+        KernelPCA(n_components, eigen_solver="dense", random_state=0)
+        .fit(X_fit)
+        .transform(X_pred)
+    )
+
+    # arpack
+    a_pred = (
+        KernelPCA(n_components, eigen_solver="arpack", random_state=0)
+        .fit(X_fit)
+        .transform(X_pred)
+    )
+    # check that the result is still correct despite the approx
+    assert_array_almost_equal(np.abs(a_pred), np.abs(ref_pred))
+
+    # randomized
+    r_pred = (
+        KernelPCA(n_components, eigen_solver="randomized", random_state=0)
+        .fit(X_fit)
+        .transform(X_pred)
+    )
+    # check that the result is still correct despite the approximation
+    assert_array_almost_equal(np.abs(r_pred), np.abs(ref_pred))
+
+
+def test_kernel_pca_inverse_transform_reconstruction():
+    """Test if the reconstruction is a good approximation.
+
+    Note that in general it is not possible to get an arbitrarily good
+    reconstruction because of kernel centering that does not
+    preserve all the information of the original data.
+    """
+    X, *_ = make_blobs(n_samples=100, n_features=4, random_state=0)
+
+    kpca = KernelPCA(
+        n_components=20, kernel="rbf", fit_inverse_transform=True, alpha=1e-3
+    )
+    X_trans = kpca.fit_transform(X)
+    X_reconst = kpca.inverse_transform(X_trans)
+    assert np.linalg.norm(X - X_reconst) / np.linalg.norm(X) < 1e-1
+
+
+def test_kernel_pca_raise_not_fitted_error():
+    X = np.random.randn(15).reshape(5, 3)
+    kpca = KernelPCA()
+    kpca.fit(X)
+    with pytest.raises(NotFittedError):
+        kpca.inverse_transform(X)
+
+
+def test_32_64_decomposition_shape():
+    """Test that the decomposition is similar for 32 and 64 bits data
+
+    Non regression test for
+    https://github.com/scikit-learn/scikit-learn/issues/18146
+    """
+    X, y = make_blobs(
+        n_samples=30, centers=[[0, 0, 0], [1, 1, 1]], random_state=0, cluster_std=0.1
+    )
+    X = StandardScaler().fit_transform(X)
+    X -= X.min()
+
+    # Compare the shapes (corresponds to the number of non-zero eigenvalues)
+    kpca = KernelPCA()
+    assert kpca.fit_transform(X).shape == kpca.fit_transform(X.astype(np.float32)).shape
+
+
+def test_kernel_pca_feature_names_out():
+    """Check feature names out for KernelPCA."""
+    X, *_ = make_blobs(n_samples=100, n_features=4, random_state=0)
+    kpca = KernelPCA(n_components=2).fit(X)
+
+    names = kpca.get_feature_names_out()
+    assert_array_equal([f"kernelpca{i}" for i in range(2)], names)
+
+
+def test_kernel_pca_inverse_correct_gamma():
+    """Check that gamma is set correctly when not provided.
+
+    Non-regression test for #26280
+    """
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((5, 4))
+
+    kwargs = {
+        "n_components": 2,
+        "random_state": rng,
+        "fit_inverse_transform": True,
+        "kernel": "rbf",
+    }
+
+    expected_gamma = 1 / X.shape[1]
+    kpca1 = KernelPCA(gamma=None, **kwargs).fit(X)
+    kpca2 = KernelPCA(gamma=expected_gamma, **kwargs).fit(X)
+
+    assert kpca1.gamma_ == expected_gamma
+    assert kpca2.gamma_ == expected_gamma
+
+    X1_recon = kpca1.inverse_transform(kpca1.transform(X))
+    X2_recon = kpca2.inverse_transform(kpca1.transform(X))
+
+    assert_allclose(X1_recon, X2_recon)
+
+
+def test_kernel_pca_pandas_output():
+    """Check that KernelPCA works with pandas output when the solver is arpack.
+
+    Non-regression test for:
+    https://github.com/scikit-learn/scikit-learn/issues/27579
+    """
+    pytest.importorskip("pandas")
+    X, _ = load_iris(as_frame=True, return_X_y=True)
+    with sklearn.config_context(transform_output="pandas"):
+        KernelPCA(n_components=2, eigen_solver="arpack").fit_transform(X)

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/tests/test_nmf.py

@@ -0,0 +1,1062 @@
+import re
+import sys
+import warnings
+from io import StringIO
+
+import numpy as np
+import pytest
+from scipy import linalg
+
+from sklearn.base import clone
+from sklearn.decomposition import NMF, MiniBatchNMF, non_negative_factorization
+from sklearn.decomposition import _nmf as nmf  # For testing internals
+from sklearn.exceptions import ConvergenceWarning
+from sklearn.utils._testing import (
+    assert_allclose,
+    assert_almost_equal,
+    assert_array_almost_equal,
+    assert_array_equal,
+    ignore_warnings,
+)
+from sklearn.utils.extmath import squared_norm
+from sklearn.utils.fixes import CSC_CONTAINERS, CSR_CONTAINERS
+
+
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+def test_convergence_warning(Estimator, 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):
+        Estimator(max_iter=1, n_components="auto", **solver).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())
+
+
+# TODO(1.6): remove the warning filter for `n_components`
+@pytest.mark.filterwarnings(
+    r"ignore:The multiplicative update \('mu'\) solver cannot update zeros present in"
+    r" the initialization",
+    "ignore:The default value of `n_components` will change",
+)
+def test_parameter_checking():
+    # Here we only check for invalid parameter values that are not already
+    # automatically tested in the common tests.
+
+    A = np.ones((2, 2))
+
+    msg = "Invalid beta_loss parameter: solver 'cd' does not handle beta_loss = 1.0"
+    with pytest.raises(ValueError, match=msg):
+        NMF(solver="cd", beta_loss=1.0).fit(A)
+    msg = "Negative values in data passed to"
+    with pytest.raises(ValueError, match=msg):
+        NMF().fit(-A)
+    clf = NMF(2, tol=0.1).fit(A)
+    with pytest.raises(ValueError, match=msg):
+        clf.transform(-A)
+    with pytest.raises(ValueError, match=msg):
+        nmf._initialize_nmf(-A, 2, "nndsvd")
+
+    for init in ["nndsvd", "nndsvda", "nndsvdar"]:
+        msg = re.escape(
+            "init = '{}' can only be used when "
+            "n_components <= min(n_samples, n_features)".format(init)
+        )
+        with pytest.raises(ValueError, match=msg):
+            NMF(3, init=init).fit(A)
+        with pytest.raises(ValueError, match=msg):
+            MiniBatchNMF(3, init=init).fit(A)
+        with pytest.raises(ValueError, match=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)
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+@pytest.mark.parametrize("init", (None, "nndsvd", "nndsvda", "nndsvdar", "random"))
+@pytest.mark.parametrize("alpha_W", (0.0, 1.0))
+@pytest.mark.parametrize("alpha_H", (0.0, 1.0, "same"))
+def test_nmf_fit_nn_output(Estimator, solver, init, alpha_W, alpha_H):
+    # Test that the decomposition does not contain negative values
+    A = np.c_[5.0 - np.arange(1, 6), 5.0 + np.arange(1, 6)]
+    model = Estimator(
+        n_components=2,
+        init=init,
+        alpha_W=alpha_W,
+        alpha_H=alpha_H,
+        random_state=0,
+        **solver,
+    )
+    transf = model.fit_transform(A)
+    assert not ((model.components_ < 0).any() or (transf < 0).any())
+
+
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+def test_nmf_fit_close(Estimator, solver):
+    rng = np.random.mtrand.RandomState(42)
+    # Test that the fit is not too far away
+    pnmf = Estimator(
+        5,
+        init="nndsvdar",
+        random_state=0,
+        max_iter=600,
+        **solver,
+    )
+    X = np.abs(rng.randn(6, 5))
+    assert pnmf.fit(X).reconstruction_err_ < 0.1
+
+
+def test_nmf_true_reconstruction():
+    # Test that the fit is not too far away from an exact solution
+    # (by construction)
+    n_samples = 15
+    n_features = 10
+    n_components = 5
+    beta_loss = 1
+    batch_size = 3
+    max_iter = 1000
+
+    rng = np.random.mtrand.RandomState(42)
+    W_true = np.zeros([n_samples, n_components])
+    W_array = np.abs(rng.randn(n_samples))
+    for j in range(n_components):
+        W_true[j % n_samples, j] = W_array[j % n_samples]
+    H_true = np.zeros([n_components, n_features])
+    H_array = np.abs(rng.randn(n_components))
+    for j in range(n_features):
+        H_true[j % n_components, j] = H_array[j % n_components]
+    X = np.dot(W_true, H_true)
+
+    model = NMF(
+        n_components=n_components,
+        solver="mu",
+        beta_loss=beta_loss,
+        max_iter=max_iter,
+        random_state=0,
+    )
+    transf = model.fit_transform(X)
+    X_calc = np.dot(transf, model.components_)
+
+    assert model.reconstruction_err_ < 0.1
+    assert_allclose(X, X_calc)
+
+    mbmodel = MiniBatchNMF(
+        n_components=n_components,
+        beta_loss=beta_loss,
+        batch_size=batch_size,
+        random_state=0,
+        max_iter=max_iter,
+    )
+    transf = mbmodel.fit_transform(X)
+    X_calc = np.dot(transf, mbmodel.components_)
+
+    assert mbmodel.reconstruction_err_ < 0.1
+    assert_allclose(X, X_calc, atol=1)
+
+
+@pytest.mark.parametrize("solver", ["cd", "mu"])
+def test_nmf_transform(solver):
+    # Test that fit_transform is equivalent to fit.transform for NMF
+    # 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-6,
+    )
+    ft = m.fit_transform(A)
+    t = m.transform(A)
+    assert_allclose(ft, t, atol=1e-1)
+
+
+def test_minibatch_nmf_transform():
+    # Test that fit_transform is equivalent to fit.transform for MiniBatchNMF
+    # Only guaranteed with fresh restarts
+    rng = np.random.mtrand.RandomState(42)
+    A = np.abs(rng.randn(6, 5))
+    m = MiniBatchNMF(
+        n_components=3,
+        random_state=0,
+        tol=1e-3,
+        fresh_restarts=True,
+    )
+    ft = m.fit_transform(A)
+    t = m.transform(A)
+    assert_allclose(ft, t)
+
+
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+def test_nmf_transform_custom_init(Estimator, solver):
+    # 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 = Estimator(
+        n_components=n_components, init="custom", random_state=0, tol=1e-3, **solver
+    )
+    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)
+
+
+# TODO(1.6): remove the warning filter
+@pytest.mark.filterwarnings("ignore:The default value of `n_components` will change")
+def test_mbnmf_inverse_transform():
+    # Test that MiniBatchNMF.transform followed by MiniBatchNMF.inverse_transform
+    # is close to the identity
+    rng = np.random.RandomState(0)
+    A = np.abs(rng.randn(6, 4))
+    nmf = MiniBatchNMF(
+        random_state=rng,
+        max_iter=500,
+        init="nndsvdar",
+        fresh_restarts=True,
+    )
+    ft = nmf.fit_transform(A)
+    A_new = nmf.inverse_transform(ft)
+    assert_allclose(A, A_new, rtol=1e-3, atol=1e-2)
+
+
+@pytest.mark.parametrize("Estimator", [NMF, MiniBatchNMF])
+def test_n_components_greater_n_features(Estimator):
+    # Smoke test for the case of more components than features.
+    rng = np.random.mtrand.RandomState(42)
+    A = np.abs(rng.randn(30, 10))
+    Estimator(n_components=15, random_state=0, tol=1e-2).fit(A)
+
+
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+@pytest.mark.parametrize("sparse_container", CSC_CONTAINERS + CSR_CONTAINERS)
+@pytest.mark.parametrize("alpha_W", (0.0, 1.0))
+@pytest.mark.parametrize("alpha_H", (0.0, 1.0, "same"))
+def test_nmf_sparse_input(Estimator, solver, sparse_container, alpha_W, alpha_H):
+    # Test that sparse matrices are accepted as input
+    rng = np.random.mtrand.RandomState(42)
+    A = np.abs(rng.randn(10, 10))
+    A[:, 2 * np.arange(5)] = 0
+    A_sparse = sparse_container(A)
+
+    est1 = Estimator(
+        n_components=5,
+        init="random",
+        alpha_W=alpha_W,
+        alpha_H=alpha_H,
+        random_state=0,
+        tol=0,
+        max_iter=100,
+        **solver,
+    )
+    est2 = clone(est1)
+
+    W1 = est1.fit_transform(A)
+    W2 = est2.fit_transform(A_sparse)
+    H1 = est1.components_
+    H2 = est2.components_
+
+    assert_allclose(W1, W2)
+    assert_allclose(H1, H2)
+
+
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+@pytest.mark.parametrize("csc_container", CSC_CONTAINERS)
+def test_nmf_sparse_transform(Estimator, solver, csc_container):
+    # 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_container(A)
+
+    model = Estimator(random_state=0, n_components=2, max_iter=400, **solver)
+    A_fit_tr = model.fit_transform(A)
+    A_tr = model.transform(A)
+    assert_allclose(A_fit_tr, A_tr, atol=1e-1)
+
+
+# TODO(1.6): remove the warning filter
+@pytest.mark.filterwarnings("ignore:The default value of `n_components` will change")
+@pytest.mark.parametrize("init", ["random", "nndsvd"])
+@pytest.mark.parametrize("solver", ("cd", "mu"))
+@pytest.mark.parametrize("alpha_W", (0.0, 1.0))
+@pytest.mark.parametrize("alpha_H", (0.0, 1.0, "same"))
+def test_non_negative_factorization_consistency(init, solver, alpha_W, alpha_H):
+    # Test that the function is called in the same way, either directly
+    # or through the NMF class
+    max_iter = 500
+    rng = np.random.mtrand.RandomState(42)
+    A = np.abs(rng.randn(10, 10))
+    A[:, 2 * np.arange(5)] = 0
+
+    W_nmf, H, _ = non_negative_factorization(
+        A,
+        init=init,
+        solver=solver,
+        max_iter=max_iter,
+        alpha_W=alpha_W,
+        alpha_H=alpha_H,
+        random_state=1,
+        tol=1e-2,
+    )
+    W_nmf_2, H, _ = non_negative_factorization(
+        A,
+        H=H,
+        update_H=False,
+        init=init,
+        solver=solver,
+        max_iter=max_iter,
+        alpha_W=alpha_W,
+        alpha_H=alpha_H,
+        random_state=1,
+        tol=1e-2,
+    )
+
+    model_class = NMF(
+        init=init,
+        solver=solver,
+        max_iter=max_iter,
+        alpha_W=alpha_W,
+        alpha_H=alpha_H,
+        random_state=1,
+        tol=1e-2,
+    )
+    W_cls = model_class.fit_transform(A)
+    W_cls_2 = model_class.transform(A)
+
+    assert_allclose(W_nmf, W_cls)
+    assert_allclose(W_nmf_2, W_cls_2)
+
+
+def test_non_negative_factorization_checking():
+    # Note that the validity of parameter types and range of possible values
+    # for scalar numerical or str parameters is already checked in the common
+    # tests. Here we only check for problems that cannot be captured by simple
+    # declarative constraints on the valid parameter values.
+
+    A = np.ones((2, 2))
+    # Test parameters checking in public function
+    nnmf = non_negative_factorization
+    msg = re.escape("Negative values in data passed to NMF (input H)")
+    with pytest.raises(ValueError, match=msg):
+        nnmf(A, A, -A, 2, init="custom")
+    msg = re.escape("Negative values in data passed to NMF (input W)")
+    with pytest.raises(ValueError, match=msg):
+        nnmf(A, -A, A, 2, init="custom")
+    msg = re.escape("Array passed to NMF (input H) is full of zeros")
+    with pytest.raises(ValueError, match=msg):
+        nnmf(A, A, 0 * A, 2, init="custom")
+
+
+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
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_beta_divergence(csr_container):
+    # Compare _beta_divergence with the reference _beta_divergence_dense
+    n_samples = 20
+    n_features = 10
+    n_components = 5
+    beta_losses = [0.0, 0.5, 1.0, 1.5, 2.0, 3.0]
+
+    # initialization
+    rng = np.random.mtrand.RandomState(42)
+    X = rng.randn(n_samples, n_features)
+    np.clip(X, 0, None, out=X)
+    X_csr = csr_container(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)
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_special_sparse_dot(csr_container):
+    # 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 = csr_container(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)
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_nmf_multiplicative_update_sparse(csr_container):
+    # 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 = csr_container(X)
+    W0, H0 = nmf._initialize_nmf(X, n_components, init="random", random_state=42)
+
+    for beta_loss in (-1.2, 0, 0.2, 1.0, 2.0, 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_W=alpha,
+            l1_ratio=l1_ratio,
+            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_W=alpha,
+            l1_ratio=l1_ratio,
+            random_state=42,
+        )
+
+        assert_allclose(W1, W2, atol=1e-7)
+        assert_allclose(H1, H2, atol=1e-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 -= 1.0e-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_W=alpha,
+            l1_ratio=l1_ratio,
+            random_state=42,
+        )
+
+        assert_allclose(W1, W3, atol=1e-4)
+        assert_allclose(H1, H3, atol=1e-4)
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_nmf_negative_beta_loss(csr_container):
+    # 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 = csr_container(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, 0.0):
+        with pytest.raises(ValueError, match=msg):
+            _assert_nmf_no_nan(X, beta_loss)
+        _assert_nmf_no_nan(X + 1e-9, beta_loss)
+
+    for beta_loss in (0.2, 1.0, 1.2, 2.0, 2.5):
+        _assert_nmf_no_nan(X, beta_loss)
+        _assert_nmf_no_nan(X_csr, beta_loss)
+
+
+# TODO(1.6): remove the warning filter
+@pytest.mark.filterwarnings("ignore:The default value of `n_components` will change")
+@pytest.mark.parametrize("beta_loss", [-0.5, 0.0])
+def test_minibatch_nmf_negative_beta_loss(beta_loss):
+    """Check that an error is raised if beta_loss < 0 and X contains zeros."""
+    rng = np.random.RandomState(0)
+    X = rng.normal(size=(6, 5))
+    X[X < 0] = 0
+
+    nmf = MiniBatchNMF(beta_loss=beta_loss, random_state=0)
+
+    msg = "When beta_loss <= 0 and X contains zeros, the solver may diverge."
+    with pytest.raises(ValueError, match=msg):
+        nmf.fit(X)
+
+
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+def test_nmf_regularization(Estimator, solver):
+    # 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 = 1.0
+    regul = Estimator(
+        n_components=n_components,
+        alpha_W=0.5,
+        l1_ratio=l1_ratio,
+        random_state=42,
+        **solver,
+    )
+    model = Estimator(
+        n_components=n_components,
+        alpha_W=0.0,
+        l1_ratio=l1_ratio,
+        random_state=42,
+        **solver,
+    )
+
+    W_regul = regul.fit_transform(X)
+    W_model = model.fit_transform(X)
+
+    H_regul = regul.components_
+    H_model = model.components_
+
+    eps = np.finfo(np.float64).eps
+    W_regul_n_zeros = W_regul[W_regul <= eps].size
+    W_model_n_zeros = W_model[W_model <= eps].size
+    H_regul_n_zeros = H_regul[H_regul <= eps].size
+    H_model_n_zeros = H_model[H_model <= eps].size
+
+    assert W_regul_n_zeros > W_model_n_zeros
+    assert H_regul_n_zeros > H_model_n_zeros
+
+    # L2 regularization should decrease the sum of the squared norm
+    # of the matrices W and H
+    l1_ratio = 0.0
+    regul = Estimator(
+        n_components=n_components,
+        alpha_W=0.5,
+        l1_ratio=l1_ratio,
+        random_state=42,
+        **solver,
+    )
+    model = Estimator(
+        n_components=n_components,
+        alpha_W=0.0,
+        l1_ratio=l1_ratio,
+        random_state=42,
+        **solver,
+    )
+
+    W_regul = regul.fit_transform(X)
+    W_model = model.fit_transform(X)
+
+    H_regul = regul.components_
+    H_model = model.components_
+
+    assert (linalg.norm(W_model)) ** 2.0 + (linalg.norm(H_model)) ** 2.0 > (
+        linalg.norm(W_regul)
+    ) ** 2.0 + (linalg.norm(H_regul)) ** 2.0
+
+
+@ignore_warnings(category=ConvergenceWarning)
+@pytest.mark.parametrize("solver", ("cd", "mu"))
+def test_nmf_decreasing(solver):
+    # 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 = 0.0
+
+    # 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, 1.0, 2.0, 2.5):
+        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_W=alpha,
+                solver=solver,
+                tol=tol,
+                l1_ratio=l1_ratio,
+                verbose=0,
+                random_state=0,
+                update_H=True,
+            )
+
+            loss = (
+                nmf._beta_divergence(X, W, H, beta_loss)
+                + alpha * l1_ratio * n_features * W.sum()
+                + alpha * l1_ratio * n_samples * H.sum()
+                + alpha * (1 - l1_ratio) * n_features * (W**2).sum()
+                + alpha * (1 - l1_ratio) * n_samples * (H**2).sum()
+            )
+            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)
+
+
+# TODO(1.6): remove the warning filter
+@pytest.mark.filterwarnings("ignore:The default value of `n_components` will change")
+@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(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+def test_nmf_dtype_match(Estimator, solver, dtype_in, dtype_out):
+    # 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 = Estimator(
+        alpha_W=1.0,
+        alpha_H=1.0,
+        tol=1e-2,
+        random_state=0,
+        **solver,
+    )
+
+    assert nmf.fit(X).transform(X).dtype == dtype_out
+    assert nmf.fit_transform(X).dtype == dtype_out
+    assert nmf.components_.dtype == dtype_out
+
+
+# TODO(1.6): remove the warning filter
+@pytest.mark.filterwarnings("ignore:The default value of `n_components` will change")
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+def test_nmf_float32_float64_consistency(Estimator, 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 = Estimator(random_state=0, tol=1e-3, **solver)
+    W32 = nmf32.fit_transform(X.astype(np.float32))
+    nmf64 = Estimator(random_state=0, tol=1e-3, **solver)
+    W64 = nmf64.fit_transform(X)
+
+    assert_allclose(W32, W64, atol=1e-5)
+
+
+# TODO(1.6): remove the warning filter
+@pytest.mark.filterwarnings("ignore:The default value of `n_components` will change")
+@pytest.mark.parametrize("Estimator", [NMF, MiniBatchNMF])
+def test_nmf_custom_init_dtype_error(Estimator):
+    # 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"):
+        Estimator(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)
+
+
+@pytest.mark.parametrize("beta_loss", [-0.5, 0, 0.5, 1, 1.5, 2, 2.5])
+def test_nmf_minibatchnmf_equivalence(beta_loss):
+    # Test that MiniBatchNMF is equivalent to NMF when batch_size = n_samples and
+    # forget_factor 0.0 (stopping criterion put aside)
+    rng = np.random.mtrand.RandomState(42)
+    X = np.abs(rng.randn(48, 5))
+
+    nmf = NMF(
+        n_components=5,
+        beta_loss=beta_loss,
+        solver="mu",
+        random_state=0,
+        tol=0,
+    )
+    mbnmf = MiniBatchNMF(
+        n_components=5,
+        beta_loss=beta_loss,
+        random_state=0,
+        tol=0,
+        max_no_improvement=None,
+        batch_size=X.shape[0],
+        forget_factor=0.0,
+    )
+    W = nmf.fit_transform(X)
+    mbW = mbnmf.fit_transform(X)
+    assert_allclose(W, mbW)
+
+
+def test_minibatch_nmf_partial_fit():
+    # Check fit / partial_fit equivalence. Applicable only with fresh restarts.
+    rng = np.random.mtrand.RandomState(42)
+    X = np.abs(rng.randn(100, 5))
+
+    n_components = 5
+    batch_size = 10
+    max_iter = 2
+
+    mbnmf1 = MiniBatchNMF(
+        n_components=n_components,
+        init="custom",
+        random_state=0,
+        max_iter=max_iter,
+        batch_size=batch_size,
+        tol=0,
+        max_no_improvement=None,
+        fresh_restarts=False,
+    )
+    mbnmf2 = MiniBatchNMF(n_components=n_components, init="custom", random_state=0)
+
+    # Force the same init of H (W is recomputed anyway) to be able to compare results.
+    W, H = nmf._initialize_nmf(
+        X, n_components=n_components, init="random", random_state=0
+    )
+
+    mbnmf1.fit(X, W=W, H=H)
+    for i in range(max_iter):
+        for j in range(batch_size):
+            mbnmf2.partial_fit(X[j : j + batch_size], W=W[:batch_size], H=H)
+
+    assert mbnmf1.n_steps_ == mbnmf2.n_steps_
+    assert_allclose(mbnmf1.components_, mbnmf2.components_)
+
+
+def test_feature_names_out():
+    """Check feature names out for NMF."""
+    random_state = np.random.RandomState(0)
+    X = np.abs(random_state.randn(10, 4))
+    nmf = NMF(n_components=3).fit(X)
+
+    names = nmf.get_feature_names_out()
+    assert_array_equal([f"nmf{i}" for i in range(3)], names)
+
+
+# TODO(1.6): remove the warning filter
+@pytest.mark.filterwarnings("ignore:The default value of `n_components` will change")
+def test_minibatch_nmf_verbose():
+    # Check verbose mode of MiniBatchNMF for better coverage.
+    A = np.random.RandomState(0).random_sample((100, 10))
+    nmf = MiniBatchNMF(tol=1e-2, random_state=0, verbose=1)
+    old_stdout = sys.stdout
+    sys.stdout = StringIO()
+    try:
+        nmf.fit(A)
+    finally:
+        sys.stdout = old_stdout
+
+
+# TODO(1.5): remove this test
+def test_NMF_inverse_transform_W_deprecation():
+    rng = np.random.mtrand.RandomState(42)
+    A = np.abs(rng.randn(6, 5))
+    est = NMF(
+        n_components=3,
+        init="random",
+        random_state=0,
+        tol=1e-6,
+    )
+    Xt = est.fit_transform(A)
+
+    with pytest.raises(TypeError, match="Missing required positional argument"):
+        est.inverse_transform()
+
+    with pytest.raises(ValueError, match="Please provide only"):
+        est.inverse_transform(Xt=Xt, W=Xt)
+
+    with warnings.catch_warnings(record=True):
+        warnings.simplefilter("error")
+        est.inverse_transform(Xt)
+
+    with pytest.warns(FutureWarning, match="Input argument `W` was renamed to `Xt`"):
+        est.inverse_transform(W=Xt)
+
+
+@pytest.mark.parametrize("Estimator", [NMF, MiniBatchNMF])
+def test_nmf_n_components_auto(Estimator):
+    # Check that n_components is correctly inferred
+    # from the provided custom initialization.
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((6, 5))
+    W = rng.random_sample((6, 2))
+    H = rng.random_sample((2, 5))
+    est = Estimator(
+        n_components="auto",
+        init="custom",
+        random_state=0,
+        tol=1e-6,
+    )
+    est.fit_transform(X, W=W, H=H)
+    assert est._n_components == H.shape[0]
+
+
+def test_nmf_non_negative_factorization_n_components_auto():
+    # Check that n_components is correctly inferred from the provided
+    # custom initialization.
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((6, 5))
+    W_init = rng.random_sample((6, 2))
+    H_init = rng.random_sample((2, 5))
+    W, H, _ = non_negative_factorization(
+        X, W=W_init, H=H_init, init="custom", n_components="auto"
+    )
+    assert H.shape == H_init.shape
+    assert W.shape == W_init.shape
+
+
+# TODO(1.6): remove
+def test_nmf_n_components_default_value_warning():
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((6, 5))
+    H = rng.random_sample((2, 5))
+    with pytest.warns(
+        FutureWarning, match="The default value of `n_components` will change from"
+    ):
+        non_negative_factorization(X, H=H)
+
+
+def test_nmf_n_components_auto_no_h_update():
+    # Tests that non_negative_factorization does not fail when setting
+    # n_components="auto" also tests that the inferred n_component
+    # value is the right one.
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((6, 5))
+    H_true = rng.random_sample((2, 5))
+    W, H, _ = non_negative_factorization(
+        X, H=H_true, n_components="auto", update_H=False
+    )  # should not fail
+    assert_allclose(H, H_true)
+    assert W.shape == (X.shape[0], H_true.shape[0])
+
+
+def test_nmf_w_h_not_used_warning():
+    # Check that warnings are raised if user provided W and H are not used
+    # and initialization overrides value of W or H
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((6, 5))
+    W_init = rng.random_sample((6, 2))
+    H_init = rng.random_sample((2, 5))
+    with pytest.warns(
+        RuntimeWarning,
+        match="When init!='custom', provided W or H are ignored",
+    ):
+        non_negative_factorization(X, H=H_init, update_H=True, n_components="auto")
+
+    with pytest.warns(
+        RuntimeWarning,
+        match="When init!='custom', provided W or H are ignored",
+    ):
+        non_negative_factorization(
+            X, W=W_init, H=H_init, update_H=True, n_components="auto"
+        )
+
+    with pytest.warns(
+        RuntimeWarning, match="When update_H=False, the provided initial W is not used."
+    ):
+        # When update_H is False, W is ignored regardless of init
+        # TODO: use the provided W when init="custom".
+        non_negative_factorization(
+            X, W=W_init, H=H_init, update_H=False, n_components="auto"
+        )
+
+
+def test_nmf_custom_init_shape_error():
+    # Check that an informative error is raised when custom initialization does not
+    # have the right shape
+    rng = np.random.RandomState(0)
+    X = rng.random_sample((6, 5))
+    H = rng.random_sample((2, 5))
+    nmf = NMF(n_components=2, init="custom", random_state=0)
+
+    with pytest.raises(ValueError, match="Array with wrong first dimension passed"):
+        nmf.fit(X, H=H, W=rng.random_sample((5, 2)))
+
+    with pytest.raises(ValueError, match="Array with wrong second dimension passed"):
+        nmf.fit(X, H=H, W=rng.random_sample((6, 3)))

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/tests/test_online_lda.py

@@ -0,0 +1,477 @@
+import sys
+from io import StringIO
+
+import numpy as np
+import pytest
+from numpy.testing import assert_array_equal
+from scipy.linalg import block_diag
+from scipy.special import psi
+
+from sklearn.decomposition import LatentDirichletAllocation
+from sklearn.decomposition._online_lda_fast import (
+    _dirichlet_expectation_1d,
+    _dirichlet_expectation_2d,
+)
+from sklearn.exceptions import NotFittedError
+from sklearn.utils._testing import (
+    assert_allclose,
+    assert_almost_equal,
+    assert_array_almost_equal,
+    if_safe_multiprocessing_with_blas,
+)
+from sklearn.utils.fixes import CSR_CONTAINERS
+
+
+def _build_sparse_array(csr_container):
+    # 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=int)
+    blocks = [block] * n_components
+    X = block_diag(*blocks)
+    X = csr_container(X)
+    return (n_components, X)
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_lda_default_prior_params(csr_container):
+    # default prior parameter should be `1 / topics`
+    # and verbose params should not affect result
+    n_components, X = _build_sparse_array(csr_container)
+    prior = 1.0 / 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)
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_lda_fit_batch(csr_container):
+    # Test LDA batch learning_offset (`fit` method with 'batch' learning)
+    rng = np.random.RandomState(0)
+    n_components, X = _build_sparse_array(csr_container)
+    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
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_lda_fit_online(csr_container):
+    # Test LDA online learning (`fit` method with 'online' learning)
+    rng = np.random.RandomState(0)
+    n_components, X = _build_sparse_array(csr_container)
+    lda = LatentDirichletAllocation(
+        n_components=n_components,
+        learning_offset=10.0,
+        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
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_lda_partial_fit(csr_container):
+    # Test LDA online learning (`partial_fit` method)
+    # (same as test_lda_batch)
+    rng = np.random.RandomState(0)
+    n_components, X = _build_sparse_array(csr_container)
+    lda = LatentDirichletAllocation(
+        n_components=n_components,
+        learning_offset=10.0,
+        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
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_lda_dense_input(csr_container):
+    # Test LDA with dense input.
+    rng = np.random.RandomState(0)
+    n_components, X = _build_sparse_array(csr_container)
+    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_negative_input():
+    # test pass dense matrix with sparse negative input.
+    X = np.full((5, 10), -1.0)
+    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)
+
+
+@if_safe_multiprocessing_with_blas
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+@pytest.mark.parametrize("method", ("online", "batch"))
+def test_lda_multi_jobs(method, csr_container):
+    n_components, X = _build_sparse_array(csr_container)
+    # 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
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_lda_partial_fit_multi_jobs(csr_container):
+    # Test LDA online training with multi CPU
+    rng = np.random.RandomState(0)
+    n_components, X = _build_sparse_array(csr_container)
+    lda = LatentDirichletAllocation(
+        n_components=n_components,
+        n_jobs=2,
+        learning_offset=5.0,
+        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=5.0,
+        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"))
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_lda_perplexity(method, csr_container):
+    # Test LDA perplexity for batch training
+    # perplexity should be lower after each iteration
+    n_components, X = _build_sparse_array(csr_container)
+    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"))
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_lda_score(method, csr_container):
+    # Test LDA score for batch training
+    # score should be higher after each iteration
+    n_components, X = _build_sparse_array(csr_container)
+    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
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_perplexity_input_format(csr_container):
+    # Test LDA perplexity for sparse and dense input
+    # score should be the same for both dense and sparse input
+    n_components, X = _build_sparse_array(csr_container)
+    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)
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_lda_score_perplexity(csr_container):
+    # Test the relationship between LDA score and perplexity
+    n_components, X = _build_sparse_array(csr_container)
+    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(-1.0 * (score / np.sum(X.data)))
+    assert_almost_equal(perplexity_1, perplexity_2)
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_lda_fit_perplexity(csr_container):
+    # Test that the perplexity computed during fit is consistent with what is
+    # returned by the perplexity method
+    n_components, X = _build_sparse_array(csr_container)
+    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)
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_lda_empty_docs(csr_container):
+    """Test LDA on empty document (all-zero rows)."""
+    Z = np.zeros((5, 4))
+    for X in [Z, csr_container(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, csr_container
+):
+    n_components, X = _build_sparse_array(csr_container)
+    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),
+    ],
+)
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_verbosity(
+    verbose, evaluate_every, expected_lines, expected_perplexities, csr_container
+):
+    check_verbosity(
+        verbose, evaluate_every, expected_lines, expected_perplexities, csr_container
+    )
+
+
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_lda_feature_names_out(csr_container):
+    """Check feature names out for LatentDirichletAllocation."""
+    n_components, X = _build_sparse_array(csr_container)
+    lda = LatentDirichletAllocation(n_components=n_components).fit(X)
+
+    names = lda.get_feature_names_out()
+    assert_array_equal(
+        [f"latentdirichletallocation{i}" for i in range(n_components)], names
+    )
+
+
+@pytest.mark.parametrize("learning_method", ("batch", "online"))
+def test_lda_dtype_match(learning_method, global_dtype):
+    """Check data type preservation of fitted attributes."""
+    rng = np.random.RandomState(0)
+    X = rng.uniform(size=(20, 10)).astype(global_dtype, copy=False)
+
+    lda = LatentDirichletAllocation(
+        n_components=5, random_state=0, learning_method=learning_method
+    )
+    lda.fit(X)
+    assert lda.components_.dtype == global_dtype
+    assert lda.exp_dirichlet_component_.dtype == global_dtype
+
+
+@pytest.mark.parametrize("learning_method", ("batch", "online"))
+def test_lda_numerical_consistency(learning_method, global_random_seed):
+    """Check numerical consistency between np.float32 and np.float64."""
+    rng = np.random.RandomState(global_random_seed)
+    X64 = rng.uniform(size=(20, 10))
+    X32 = X64.astype(np.float32)
+
+    lda_64 = LatentDirichletAllocation(
+        n_components=5, random_state=global_random_seed, learning_method=learning_method
+    ).fit(X64)
+    lda_32 = LatentDirichletAllocation(
+        n_components=5, random_state=global_random_seed, learning_method=learning_method
+    ).fit(X32)
+
+    assert_allclose(lda_32.components_, lda_64.components_)
+    assert_allclose(lda_32.transform(X32), lda_64.transform(X64))

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/tests/test_pca.py

@@ -0,0 +1,987 @@
+import re
+import warnings
+
+import numpy as np
+import pytest
+import scipy as sp
+from numpy.testing import assert_array_equal
+
+from sklearn import config_context, datasets
+from sklearn.base import clone
+from sklearn.datasets import load_iris, make_classification
+from sklearn.decomposition import PCA
+from sklearn.decomposition._pca import _assess_dimension, _infer_dimension
+from sklearn.utils._array_api import (
+    _atol_for_type,
+    _convert_to_numpy,
+    yield_namespace_device_dtype_combinations,
+)
+from sklearn.utils._array_api import device as array_device
+from sklearn.utils._testing import _array_api_for_tests, assert_allclose
+from sklearn.utils.estimator_checks import (
+    _get_check_estimator_ids,
+    check_array_api_input_and_values,
+)
+from sklearn.utils.fixes import CSC_CONTAINERS, CSR_CONTAINERS
+
+iris = datasets.load_iris()
+PCA_SOLVERS = ["full", "arpack", "randomized", "auto"]
+
+# `SPARSE_M` and `SPARSE_N` could be larger, but be aware:
+# * SciPy's generation of random sparse matrix can be costly
+# * A (SPARSE_M, SPARSE_N) dense array is allocated to compare against
+SPARSE_M, SPARSE_N = 1000, 300  # arbitrary
+SPARSE_MAX_COMPONENTS = min(SPARSE_M, SPARSE_N)
+
+
+def _check_fitted_pca_close(pca1, pca2, rtol):
+    assert_allclose(pca1.components_, pca2.components_, rtol=rtol)
+    assert_allclose(pca1.explained_variance_, pca2.explained_variance_, rtol=rtol)
+    assert_allclose(pca1.singular_values_, pca2.singular_values_, rtol=rtol)
+    assert_allclose(pca1.mean_, pca2.mean_, rtol=rtol)
+    assert_allclose(pca1.n_components_, pca2.n_components_, rtol=rtol)
+    assert_allclose(pca1.n_samples_, pca2.n_samples_, rtol=rtol)
+    assert_allclose(pca1.noise_variance_, pca2.noise_variance_, rtol=rtol)
+    assert_allclose(pca1.n_features_in_, pca2.n_features_in_, rtol=rtol)
+
+
+@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)
+
+
+@pytest.mark.parametrize("density", [0.01, 0.1, 0.30])
+@pytest.mark.parametrize("n_components", [1, 2, 10])
+@pytest.mark.parametrize("sparse_container", CSR_CONTAINERS + CSC_CONTAINERS)
+@pytest.mark.parametrize("svd_solver", ["arpack"])
+@pytest.mark.parametrize("scale", [1, 10, 100])
+def test_pca_sparse(
+    global_random_seed, svd_solver, sparse_container, n_components, density, scale
+):
+    # Make sure any tolerance changes pass with SKLEARN_TESTS_GLOBAL_RANDOM_SEED="all"
+    rtol = 5e-07
+    transform_rtol = 3e-05
+
+    random_state = np.random.default_rng(global_random_seed)
+    X = sparse_container(
+        sp.sparse.random(
+            SPARSE_M,
+            SPARSE_N,
+            random_state=random_state,
+            density=density,
+        )
+    )
+    # Scale the data + vary the column means
+    scale_vector = random_state.random(X.shape[1]) * scale
+    X = X.multiply(scale_vector)
+
+    pca = PCA(
+        n_components=n_components,
+        svd_solver=svd_solver,
+        random_state=global_random_seed,
+    )
+    pca.fit(X)
+
+    Xd = X.toarray()
+    pcad = PCA(
+        n_components=n_components,
+        svd_solver=svd_solver,
+        random_state=global_random_seed,
+    )
+    pcad.fit(Xd)
+
+    # Fitted attributes equality
+    _check_fitted_pca_close(pca, pcad, rtol=rtol)
+
+    # Test transform
+    X2 = sparse_container(
+        sp.sparse.random(
+            SPARSE_M,
+            SPARSE_N,
+            random_state=random_state,
+            density=density,
+        )
+    )
+    X2d = X2.toarray()
+
+    assert_allclose(pca.transform(X2), pca.transform(X2d), rtol=transform_rtol)
+    assert_allclose(pca.transform(X2), pcad.transform(X2d), rtol=transform_rtol)
+
+
+@pytest.mark.parametrize("sparse_container", CSR_CONTAINERS + CSC_CONTAINERS)
+def test_pca_sparse_fit_transform(global_random_seed, sparse_container):
+    random_state = np.random.default_rng(global_random_seed)
+    X = sparse_container(
+        sp.sparse.random(
+            SPARSE_M,
+            SPARSE_N,
+            random_state=random_state,
+            density=0.01,
+        )
+    )
+    X2 = sparse_container(
+        sp.sparse.random(
+            SPARSE_M,
+            SPARSE_N,
+            random_state=random_state,
+            density=0.01,
+        )
+    )
+
+    pca_fit = PCA(n_components=10, svd_solver="arpack", random_state=global_random_seed)
+    pca_fit_transform = PCA(
+        n_components=10, svd_solver="arpack", random_state=global_random_seed
+    )
+
+    pca_fit.fit(X)
+    transformed_X = pca_fit_transform.fit_transform(X)
+
+    _check_fitted_pca_close(pca_fit, pca_fit_transform, rtol=1e-10)
+    assert_allclose(transformed_X, pca_fit_transform.transform(X), rtol=2e-9)
+    assert_allclose(transformed_X, pca_fit.transform(X), rtol=2e-9)
+    assert_allclose(pca_fit.transform(X2), pca_fit_transform.transform(X2), rtol=2e-9)
+
+
+@pytest.mark.parametrize("svd_solver", ["randomized", "full", "auto"])
+@pytest.mark.parametrize("sparse_container", CSR_CONTAINERS + CSC_CONTAINERS)
+def test_sparse_pca_solver_error(global_random_seed, svd_solver, sparse_container):
+    random_state = np.random.RandomState(global_random_seed)
+    X = sparse_container(
+        sp.sparse.random(
+            SPARSE_M,
+            SPARSE_N,
+            random_state=random_state,
+        )
+    )
+    pca = PCA(n_components=30, svd_solver=svd_solver)
+    error_msg_pattern = (
+        f'PCA only support sparse inputs with the "arpack" solver, while "{svd_solver}"'
+        " was passed"
+    )
+    with pytest.raises(TypeError, match=error_msg_pattern):
+        pca.fit(X)
+
+
+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 warnings.catch_warnings():
+        warnings.simplefilter("error", RuntimeWarning)
+        pca.fit(X)
+
+
+@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_.copy())
+    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) * 0.1
+    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]), 1.0, 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] *= 0.00001  # 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",
+            3,
+            (
+                r"n_components=3 must be between 0 and min\(n_samples, "
+                r"n_features\)=2 with svd_solver='full'"
+            ),
+        ),
+    ],
+)
+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
+    pca_fitted = PCA(n_components, svd_solver=svd_solver)
+
+    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) * 0.1
+    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) * 0.1
+        + 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() - 0.01 * 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) * 0.1
+    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) * 0.1
+    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) * 0.1 + 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) * 0.2 + 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) * 0.1 + np.array([3, 4, 5])
+
+    pca = PCA(n_components=p, svd_solver=svd_solver)
+    pca.fit(X)
+    assert pca.noise_variance_ == 0
+    # Non-regression test for gh-12489
+    # ensure no divide-by-zero error for n_components == n_features < n_samples
+    pca.score(X)
+
+    pca.fit(X.T)
+    assert pca.noise_variance_ == 0
+    # Non-regression test for gh-12489
+    # ensure no divide-by-zero error for n_components == n_samples < n_features
+    pca.score(X.T)
+
+
+@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_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)
+    # except for rank 1, all eigenvalues are 0 resp. close to 0 (FP)
+    assert_allclose(s[1:], np.zeros(n_features - 1), atol=1e-12)
+
+    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
+
+
+def test_pca_randomized_svd_n_oversamples():
+    """Check that exposing and setting `n_oversamples` will provide accurate results
+    even when `X` as a large number of features.
+
+    Non-regression test for:
+    https://github.com/scikit-learn/scikit-learn/issues/20589
+    """
+    rng = np.random.RandomState(0)
+    n_features = 100
+    X = rng.randn(1_000, n_features)
+
+    # The default value of `n_oversamples` will lead to inaccurate results
+    # We force it to the number of features.
+    pca_randomized = PCA(
+        n_components=1,
+        svd_solver="randomized",
+        n_oversamples=n_features,
+        random_state=0,
+    ).fit(X)
+    pca_full = PCA(n_components=1, svd_solver="full").fit(X)
+    pca_arpack = PCA(n_components=1, svd_solver="arpack", random_state=0).fit(X)
+
+    assert_allclose(np.abs(pca_full.components_), np.abs(pca_arpack.components_))
+    assert_allclose(np.abs(pca_randomized.components_), np.abs(pca_arpack.components_))
+
+
+def test_feature_names_out():
+    """Check feature names out for PCA."""
+    pca = PCA(n_components=2).fit(iris.data)
+
+    names = pca.get_feature_names_out()
+    assert_array_equal([f"pca{i}" for i in range(2)], names)
+
+
+@pytest.mark.parametrize("copy", [True, False])
+def test_variance_correctness(copy):
+    """Check the accuracy of PCA's internal variance calculation"""
+    rng = np.random.RandomState(0)
+    X = rng.randn(1000, 200)
+    pca = PCA().fit(X)
+    pca_var = pca.explained_variance_ / pca.explained_variance_ratio_
+    true_var = np.var(X, ddof=1, axis=0).sum()
+    np.testing.assert_allclose(pca_var, true_var)
+
+
+def check_array_api_get_precision(name, estimator, array_namespace, device, dtype_name):
+    xp = _array_api_for_tests(array_namespace, device)
+    iris_np = iris.data.astype(dtype_name)
+    iris_xp = xp.asarray(iris_np, device=device)
+
+    estimator.fit(iris_np)
+    precision_np = estimator.get_precision()
+    covariance_np = estimator.get_covariance()
+
+    with config_context(array_api_dispatch=True):
+        estimator_xp = clone(estimator).fit(iris_xp)
+        precision_xp = estimator_xp.get_precision()
+        assert precision_xp.shape == (4, 4)
+        assert precision_xp.dtype == iris_xp.dtype
+
+        assert_allclose(
+            _convert_to_numpy(precision_xp, xp=xp),
+            precision_np,
+            atol=_atol_for_type(dtype_name),
+        )
+        covariance_xp = estimator_xp.get_covariance()
+        assert covariance_xp.shape == (4, 4)
+        assert covariance_xp.dtype == iris_xp.dtype
+
+        assert_allclose(
+            _convert_to_numpy(covariance_xp, xp=xp),
+            covariance_np,
+            atol=_atol_for_type(dtype_name),
+        )
+
+
+@pytest.mark.parametrize(
+    "array_namespace, device, dtype_name", yield_namespace_device_dtype_combinations()
+)
+@pytest.mark.parametrize(
+    "check",
+    [check_array_api_input_and_values, check_array_api_get_precision],
+    ids=_get_check_estimator_ids,
+)
+@pytest.mark.parametrize(
+    "estimator",
+    [
+        PCA(n_components=2, svd_solver="full"),
+        PCA(n_components=0.1, svd_solver="full", whiten=True),
+        PCA(
+            n_components=2,
+            svd_solver="randomized",
+            power_iteration_normalizer="QR",
+            random_state=0,  # how to use global_random_seed here?
+        ),
+    ],
+    ids=_get_check_estimator_ids,
+)
+def test_pca_array_api_compliance(
+    estimator, check, array_namespace, device, dtype_name
+):
+    name = estimator.__class__.__name__
+    check(name, estimator, array_namespace, device=device, dtype_name=dtype_name)
+
+
+@pytest.mark.parametrize(
+    "array_namespace, device, dtype_name", yield_namespace_device_dtype_combinations()
+)
+@pytest.mark.parametrize(
+    "check",
+    [check_array_api_get_precision],
+    ids=_get_check_estimator_ids,
+)
+@pytest.mark.parametrize(
+    "estimator",
+    [
+        # PCA with mle cannot use check_array_api_input_and_values because of
+        # rounding errors in the noisy (low variance) components. Even checking
+        # the shape of the `components_` is problematic because the number of
+        # components depends on trimming threshold of the mle algorithm which
+        # can depend on device-specific rounding errors.
+        PCA(n_components="mle", svd_solver="full"),
+    ],
+    ids=_get_check_estimator_ids,
+)
+def test_pca_mle_array_api_compliance(
+    estimator, check, array_namespace, device, dtype_name
+):
+    name = estimator.__class__.__name__
+    check(name, estimator, array_namespace, device=device, dtype_name=dtype_name)
+
+    # Simpler variant of the generic check_array_api_input checker tailored for
+    # the specific case of PCA with mle-trimmed components.
+    xp = _array_api_for_tests(array_namespace, device)
+
+    X, y = make_classification(random_state=42)
+    X = X.astype(dtype_name, copy=False)
+    atol = _atol_for_type(X.dtype)
+
+    est = clone(estimator)
+
+    X_xp = xp.asarray(X, device=device)
+    y_xp = xp.asarray(y, device=device)
+
+    est.fit(X, y)
+
+    components_np = est.components_
+    explained_variance_np = est.explained_variance_
+
+    est_xp = clone(est)
+    with config_context(array_api_dispatch=True):
+        est_xp.fit(X_xp, y_xp)
+        components_xp = est_xp.components_
+        assert array_device(components_xp) == array_device(X_xp)
+        components_xp_np = _convert_to_numpy(components_xp, xp=xp)
+
+        explained_variance_xp = est_xp.explained_variance_
+        assert array_device(explained_variance_xp) == array_device(X_xp)
+        explained_variance_xp_np = _convert_to_numpy(explained_variance_xp, xp=xp)
+
+    assert components_xp_np.dtype == components_np.dtype
+    assert components_xp_np.shape[1] == components_np.shape[1]
+    assert explained_variance_xp_np.dtype == explained_variance_np.dtype
+
+    # Check that the explained variance values match for the
+    # common components:
+    min_components = min(components_xp_np.shape[0], components_np.shape[0])
+    assert_allclose(
+        explained_variance_xp_np[:min_components],
+        explained_variance_np[:min_components],
+        atol=atol,
+    )
+
+    # If the number of components differ, check that the explained variance of
+    # the trimmed components is very small.
+    if components_xp_np.shape[0] != components_np.shape[0]:
+        reference_variance = explained_variance_np[-1]
+        extra_variance_np = explained_variance_np[min_components:]
+        extra_variance_xp_np = explained_variance_xp_np[min_components:]
+        assert all(np.abs(extra_variance_np - reference_variance) < atol)
+        assert all(np.abs(extra_variance_xp_np - reference_variance) < atol)
+
+
+def test_array_api_error_and_warnings_on_unsupported_params():
+    pytest.importorskip("array_api_compat")
+    xp = pytest.importorskip("numpy.array_api")
+    iris_xp = xp.asarray(iris.data)
+
+    pca = PCA(n_components=2, svd_solver="arpack", random_state=0)
+    expected_msg = re.escape(
+        "PCA with svd_solver='arpack' is not supported for Array API inputs."
+    )
+    with pytest.raises(ValueError, match=expected_msg):
+        with config_context(array_api_dispatch=True):
+            pca.fit(iris_xp)
+
+    pca.set_params(svd_solver="randomized", power_iteration_normalizer="LU")
+    expected_msg = re.escape(
+        "Array API does not support LU factorization. Set"
+        " `power_iteration_normalizer='QR'` instead."
+    )
+    with pytest.raises(ValueError, match=expected_msg):
+        with config_context(array_api_dispatch=True):
+            pca.fit(iris_xp)
+
+    pca.set_params(svd_solver="randomized", power_iteration_normalizer="auto")
+    expected_msg = re.escape(
+        "Array API does not support LU factorization, falling back to QR instead. Set"
+        " `power_iteration_normalizer='QR'` explicitly to silence this warning."
+    )
+    with pytest.warns(UserWarning, match=expected_msg):
+        with config_context(array_api_dispatch=True):
+            pca.fit(iris_xp)

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/tests/test_sparse_pca.py

@@ -0,0 +1,367 @@
+# Author: Vlad Niculae
+# License: BSD 3 clause
+
+import sys
+
+import numpy as np
+import pytest
+from numpy.testing import assert_array_equal
+
+from sklearn.decomposition import PCA, MiniBatchSparsePCA, SparsePCA
+from sklearn.utils import check_random_state
+from sklearn.utils._testing import (
+    assert_allclose,
+    assert_array_almost_equal,
+    if_safe_multiprocessing_with_blas,
+)
+
+
+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, max_iter=1, 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, max_iter=1, 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])
+@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
+
+
+@pytest.mark.parametrize("SPCA", (SparsePCA, MiniBatchSparsePCA))
+@pytest.mark.parametrize("method", ("lars", "cd"))
+@pytest.mark.parametrize(
+    "data_type, expected_type",
+    (
+        (np.float32, np.float32),
+        (np.float64, np.float64),
+        (np.int32, np.float64),
+        (np.int64, np.float64),
+    ),
+)
+def test_sparse_pca_dtype_match(SPCA, method, data_type, expected_type):
+    # Verify output matrix dtype
+    n_samples, n_features, n_components = 12, 10, 3
+    rng = np.random.RandomState(0)
+    input_array = rng.randn(n_samples, n_features).astype(data_type)
+    model = SPCA(n_components=n_components, method=method)
+    transformed = model.fit_transform(input_array)
+
+    assert transformed.dtype == expected_type
+    assert model.components_.dtype == expected_type
+
+
+@pytest.mark.parametrize("SPCA", (SparsePCA, MiniBatchSparsePCA))
+@pytest.mark.parametrize("method", ("lars", "cd"))
+def test_sparse_pca_numerical_consistency(SPCA, method):
+    # Verify numericall consistentency among np.float32 and np.float64
+    rtol = 1e-3
+    alpha = 2
+    n_samples, n_features, n_components = 12, 10, 3
+    rng = np.random.RandomState(0)
+    input_array = rng.randn(n_samples, n_features)
+
+    model_32 = SPCA(
+        n_components=n_components, alpha=alpha, method=method, random_state=0
+    )
+    transformed_32 = model_32.fit_transform(input_array.astype(np.float32))
+
+    model_64 = SPCA(
+        n_components=n_components, alpha=alpha, method=method, random_state=0
+    )
+    transformed_64 = model_64.fit_transform(input_array.astype(np.float64))
+
+    assert_allclose(transformed_64, transformed_32, rtol=rtol)
+    assert_allclose(model_64.components_, model_32.components_, rtol=rtol)
+
+
+@pytest.mark.parametrize("SPCA", [SparsePCA, MiniBatchSparsePCA])
+def test_spca_feature_names_out(SPCA):
+    """Check feature names out for *SparsePCA."""
+    rng = np.random.RandomState(0)
+    n_samples, n_features = 12, 10
+    X = rng.randn(n_samples, n_features)
+
+    model = SPCA(n_components=4).fit(X)
+    names = model.get_feature_names_out()
+
+    estimator_name = SPCA.__name__.lower()
+    assert_array_equal([f"{estimator_name}{i}" for i in range(4)], names)
+
+
+# TODO(1.6): remove in 1.6
+def test_spca_max_iter_None_deprecation():
+    """Check that we raise a warning for the deprecation of `max_iter=None`."""
+    rng = np.random.RandomState(0)
+    n_samples, n_features = 12, 10
+    X = rng.randn(n_samples, n_features)
+
+    warn_msg = "`max_iter=None` is deprecated in version 1.4 and will be removed"
+    with pytest.warns(FutureWarning, match=warn_msg):
+        MiniBatchSparsePCA(max_iter=None).fit(X)
+
+
+def test_spca_early_stopping(global_random_seed):
+    """Check that `tol` and `max_no_improvement` act as early stopping."""
+    rng = np.random.RandomState(global_random_seed)
+    n_samples, n_features = 50, 10
+    X = rng.randn(n_samples, n_features)
+
+    # vary the tolerance to force the early stopping of one of the model
+    model_early_stopped = MiniBatchSparsePCA(
+        max_iter=100, tol=0.5, random_state=global_random_seed
+    ).fit(X)
+    model_not_early_stopped = MiniBatchSparsePCA(
+        max_iter=100, tol=1e-3, random_state=global_random_seed
+    ).fit(X)
+    assert model_early_stopped.n_iter_ < model_not_early_stopped.n_iter_
+
+    # force the max number of no improvement to a large value to check that
+    # it does help to early stop
+    model_early_stopped = MiniBatchSparsePCA(
+        max_iter=100, tol=1e-6, max_no_improvement=2, random_state=global_random_seed
+    ).fit(X)
+    model_not_early_stopped = MiniBatchSparsePCA(
+        max_iter=100, tol=1e-6, max_no_improvement=100, random_state=global_random_seed
+    ).fit(X)
+    assert model_early_stopped.n_iter_ < model_not_early_stopped.n_iter_
+
+
+def test_equivalence_components_pca_spca(global_random_seed):
+    """Check the equivalence of the components found by PCA and SparsePCA.
+
+    Non-regression test for:
+    https://github.com/scikit-learn/scikit-learn/issues/23932
+    """
+    rng = np.random.RandomState(global_random_seed)
+    X = rng.randn(50, 4)
+
+    n_components = 2
+    pca = PCA(
+        n_components=n_components,
+        svd_solver="randomized",
+        random_state=0,
+    ).fit(X)
+    spca = SparsePCA(
+        n_components=n_components,
+        method="lars",
+        ridge_alpha=0,
+        alpha=0,
+        random_state=0,
+    ).fit(X)
+
+    assert_allclose(pca.components_, spca.components_)
+
+
+def test_sparse_pca_inverse_transform():
+    """Check that `inverse_transform` in `SparsePCA` and `PCA` are similar."""
+    rng = np.random.RandomState(0)
+    n_samples, n_features = 10, 5
+    X = rng.randn(n_samples, n_features)
+
+    n_components = 2
+    spca = SparsePCA(
+        n_components=n_components, alpha=1e-12, ridge_alpha=1e-12, random_state=0
+    )
+    pca = PCA(n_components=n_components, random_state=0)
+    X_trans_spca = spca.fit_transform(X)
+    X_trans_pca = pca.fit_transform(X)
+    assert_allclose(
+        spca.inverse_transform(X_trans_spca), pca.inverse_transform(X_trans_pca)
+    )
+
+
+@pytest.mark.parametrize("SPCA", [SparsePCA, MiniBatchSparsePCA])
+def test_transform_inverse_transform_round_trip(SPCA):
+    """Check the `transform` and `inverse_transform` round trip with no loss of
+    information.
+    """
+    rng = np.random.RandomState(0)
+    n_samples, n_features = 10, 5
+    X = rng.randn(n_samples, n_features)
+
+    n_components = n_features
+    spca = SPCA(
+        n_components=n_components, alpha=1e-12, ridge_alpha=1e-12, random_state=0
+    )
+    X_trans_spca = spca.fit_transform(X)
+    assert_allclose(spca.inverse_transform(X_trans_spca), X)

llmeval-env/lib/python3.10/site-packages/sklearn/decomposition/tests/test_truncated_svd.py

@@ -0,0 +1,212 @@
+"""Test truncated SVD transformer."""
+
+import numpy as np
+import pytest
+import scipy.sparse as sp
+
+from sklearn.decomposition import PCA, TruncatedSVD
+from sklearn.utils import check_random_state
+from sklearn.utils._testing import assert_allclose, assert_array_less
+
+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, n_oversamples=100)
+
+    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, 55))
+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, n_components",
+    [
+        ("arpack", 55),
+        ("arpack", 56),
+        ("randomized", 56),
+    ],
+)
+def test_too_many_components(X_sparse, algorithm, n_components):
+    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_)
+
+
+@pytest.mark.parametrize(
+    "algorithm, tol", [("randomized", 0.0), ("arpack", 1e-6), ("arpack", 0.0)]
+)
+@pytest.mark.parametrize("kind", ("dense", "sparse"))
+def test_fit_transform(X_sparse, algorithm, tol, kind):
+    # fit_transform(X) should equal fit(X).transform(X)
+    X = X_sparse if kind == "sparse" else X_sparse.toarray()
+    svd = TruncatedSVD(
+        n_components=5, n_iter=7, random_state=42, algorithm=algorithm, tol=tol
+    )
+    X_transformed_1 = svd.fit_transform(X)
+    X_transformed_2 = svd.fit(X).transform(X)
+    assert_allclose(X_transformed_1, X_transformed_2)

llmeval-env/lib/python3.10/site-packages/sklearn/model_selection/__init__.py

@@ -0,0 +1,88 @@
+import typing
+
+from ._plot import LearningCurveDisplay, ValidationCurveDisplay
+from ._search import GridSearchCV, ParameterGrid, ParameterSampler, RandomizedSearchCV
+from ._split import (
+    BaseCrossValidator,
+    BaseShuffleSplit,
+    GroupKFold,
+    GroupShuffleSplit,
+    KFold,
+    LeaveOneGroupOut,
+    LeaveOneOut,
+    LeavePGroupsOut,
+    LeavePOut,
+    PredefinedSplit,
+    RepeatedKFold,
+    RepeatedStratifiedKFold,
+    ShuffleSplit,
+    StratifiedGroupKFold,
+    StratifiedKFold,
+    StratifiedShuffleSplit,
+    TimeSeriesSplit,
+    check_cv,
+    train_test_split,
+)
+from ._validation import (
+    cross_val_predict,
+    cross_val_score,
+    cross_validate,
+    learning_curve,
+    permutation_test_score,
+    validation_curve,
+)
+
+if typing.TYPE_CHECKING:
+    # Avoid errors in type checkers (e.g. mypy) for experimental estimators.
+    # TODO: remove this check once the estimator is no longer experimental.
+    from ._search_successive_halving import (  # noqa
+        HalvingGridSearchCV,
+        HalvingRandomSearchCV,
+    )
+
+
+__all__ = [
+    "BaseCrossValidator",
+    "BaseShuffleSplit",
+    "GridSearchCV",
+    "TimeSeriesSplit",
+    "KFold",
+    "GroupKFold",
+    "GroupShuffleSplit",
+    "LeaveOneGroupOut",
+    "LeaveOneOut",
+    "LeavePGroupsOut",
+    "LeavePOut",
+    "RepeatedKFold",
+    "RepeatedStratifiedKFold",
+    "ParameterGrid",
+    "ParameterSampler",
+    "PredefinedSplit",
+    "RandomizedSearchCV",
+    "ShuffleSplit",
+    "StratifiedKFold",
+    "StratifiedGroupKFold",
+    "StratifiedShuffleSplit",
+    "check_cv",
+    "cross_val_predict",
+    "cross_val_score",
+    "cross_validate",
+    "learning_curve",
+    "LearningCurveDisplay",
+    "permutation_test_score",
+    "train_test_split",
+    "validation_curve",
+    "ValidationCurveDisplay",
+]
+
+
+# TODO: remove this check once the estimator is no longer experimental.
+def __getattr__(name):
+    if name in {"HalvingGridSearchCV", "HalvingRandomSearchCV"}:
+        raise ImportError(
+            f"{name} is experimental and the API might change without any "
+            "deprecation cycle. To use it, you need to explicitly import "
+            "enable_halving_search_cv:\n"
+            "from sklearn.experimental import enable_halving_search_cv"
+        )
+    raise AttributeError(f"module {__name__} has no attribute {name}")