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+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)
+
+
+# TODO: remove mark once loky bug is fixed:
+# https://github.com/joblib/loky/issues/458
+@pytest.mark.thread_unsafe
+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 = 256
+    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)
+        )
+    ]
+
+    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=500
+        )
+        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)
+    assert_array_almost_equal(dico.inverse_transform(code), X)
+
+    dico.set_params(transform_algorithm="lasso_lars")
+    code = dico.transform(X)
+    assert_array_almost_equal(np.dot(code, dico.components_), X, decimal=2)
+    assert_array_almost_equal(dico.inverse_transform(code), X, decimal=2)
+
+    # test error raised for wrong code size
+    with pytest.raises(ValueError, match="Expected 12, got 11."):
+        dico.inverse_transform(code[:, :-1])
+
+    # used to test lars here too, but there's no guarantee the number of
+    # nonzero atoms is right.
+
+
+# TODO: remove mark once loky bug is fixed:
+# https://github.com/joblib/loky/issues/458
+@pytest.mark.thread_unsafe
+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)
+
+
+# TODO: remove mark once loky bug is fixed:
+# https://github.com/joblib/loky/issues/458
+@pytest.mark.thread_unsafe
+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)
+    Xr = dico.inverse_transform(code)
+
+    dico.split_sign = True
+    split_code = dico.transform(X)
+
+    assert_array_almost_equal(
+        split_code[:, :n_components] - split_code[:, n_components:], code
+    )
+
+    Xr2 = dico.inverse_transform(split_code)
+    assert_array_almost_equal(Xr, Xr2)
+
+
+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
+    )
+    code = coder.fit_transform(X)
+    Xr = coder.inverse_transform(code)
+    assert not np.all(code == 0)
+    assert np.sqrt(np.sum((np.dot(code, V) - X) ** 2)) < 0.1
+    np.testing.assert_allclose(Xr, np.dot(code, V))
+
+
+def test_sparse_coder_estimator_clone():
+    n_components = 12
+    rng = np.random.RandomState(0)
+    V = rng.normal(size=(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)
+    data = np.random.rand(n_samples, n_features).astype(np.float32)
+    np.testing.assert_allclose(cloned.transform(data), coder.transform(data))
+
+
+# TODO: remove mark once loky bug is fixed:
+# https://github.com/joblib/loky/issues/458
+@pytest.mark.thread_unsafe
+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]])
+    X = np.array([[1, 2, 3]])
+    sc = SparseCoder(d)
+    sc.fit(X)
+    assert sc.n_features_in_ == d.shape[1]
+
+
+def test_sparse_encoder_feature_number_error():
+    n_components = 10
+    rng = np.random.RandomState(0)
+    D = rng.uniform(size=(n_components, n_features))
+    X = rng.uniform(size=(n_samples, n_features + 1))
+    coder = SparseCoder(D)
+    with pytest.raises(
+        ValueError, match="Dictionary and X have different numbers of features"
+    ):
+        coder.fit(X)
+
+
+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-4
+    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(rng_global.uniform(size=(n_features, n_features))),
+        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)],
+    )
+
+
+# TODO: remove mark once loky bug is fixed:
+# https://github.com/joblib/loky/issues/458
+@pytest.mark.thread_unsafe
+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)