File size: 33,070 Bytes

7885a28

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,
)
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())


@pytest.mark.filterwarnings(
    r"ignore:The multiplicative update \('mu'\) solver cannot update zeros present in"
    r" the initialization",
)
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'
@pytest.mark.filterwarnings(
    r"ignore:The multiplicative update \('mu'\) solver cannot update zeros present in"
    r" the initialization"
)
@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)


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)


@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)


@pytest.mark.filterwarnings("ignore::sklearn.exceptions.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)


@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


@pytest.mark.filterwarnings("ignore::sklearn.exceptions.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)


@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


@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)


@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)


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(1.7): remove this test
@pytest.mark.parametrize("Estimator", [NMF, MiniBatchNMF])
def test_NMF_inverse_transform_Xt_deprecation(Estimator):
    rng = np.random.RandomState(42)
    A = np.abs(rng.randn(6, 5))
    est = Estimator(
        n_components=3,
        init="random",
        random_state=0,
        tol=1e-6,
    )
    X = est.fit_transform(A)

    with pytest.raises(TypeError, match="Missing required positional argument"):
        est.inverse_transform()

    with pytest.raises(TypeError, match="Cannot use both X and Xt. Use X only"):
        est.inverse_transform(X=X, Xt=X)

    with warnings.catch_warnings(record=True):
        warnings.simplefilter("error")
        est.inverse_transform(X)

    with pytest.warns(FutureWarning, match="Xt was renamed X in version 1.5"):
        est.inverse_transform(Xt=X)


@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


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)))