import warnings
from itertools import product

import numpy as np
import pytest
from scipy import linalg

from sklearn import config_context, datasets
from sklearn.base import clone
from sklearn.datasets import (
    make_classification,
    make_low_rank_matrix,
    make_multilabel_classification,
    make_regression,
)
from sklearn.exceptions import ConvergenceWarning
from sklearn.linear_model import (
    LinearRegression,
    Ridge,
    RidgeClassifier,
    RidgeClassifierCV,
    RidgeCV,
    ridge_regression,
)
from sklearn.linear_model._ridge import (
    _check_gcv_mode,
    _RidgeGCV,
    _solve_cholesky,
    _solve_cholesky_kernel,
    _solve_lbfgs,
    _solve_svd,
    _X_CenterStackOp,
)
from sklearn.metrics import get_scorer, make_scorer, mean_squared_error
from sklearn.model_selection import (
    GridSearchCV,
    GroupKFold,
    KFold,
    LeaveOneOut,
    cross_val_predict,
)
from sklearn.preprocessing import minmax_scale
from sklearn.utils import check_random_state
from sklearn.utils._array_api import (
    _NUMPY_NAMESPACE_NAMES,
    _atol_for_type,
    _convert_to_numpy,
    _get_namespace_device_dtype_ids,
    yield_namespace_device_dtype_combinations,
    yield_namespaces,
)
from sklearn.utils._test_common.instance_generator import _get_check_estimator_ids
from sklearn.utils._testing import (
    assert_allclose,
    assert_almost_equal,
    assert_array_almost_equal,
    assert_array_equal,
    ignore_warnings,
)
from sklearn.utils.estimator_checks import (
    _array_api_for_tests,
    check_array_api_input_and_values,
)
from sklearn.utils.fixes import (
    _IS_32BIT,
    COO_CONTAINERS,
    CSC_CONTAINERS,
    CSR_CONTAINERS,
    DOK_CONTAINERS,
    LIL_CONTAINERS,
)

SOLVERS = ["svd", "sparse_cg", "cholesky", "lsqr", "sag", "saga"]
SPARSE_SOLVERS_WITH_INTERCEPT = ("sparse_cg", "sag")
SPARSE_SOLVERS_WITHOUT_INTERCEPT = ("sparse_cg", "cholesky", "lsqr", "sag", "saga")

diabetes = datasets.load_diabetes()
X_diabetes, y_diabetes = diabetes.data, diabetes.target
ind = np.arange(X_diabetes.shape[0])
rng = np.random.RandomState(0)
rng.shuffle(ind)
ind = ind[:200]
X_diabetes, y_diabetes = X_diabetes[ind], y_diabetes[ind]

iris = datasets.load_iris()
X_iris, y_iris = iris.data, iris.target


def _accuracy_callable(y_test, y_pred, **kwargs):
    return np.mean(y_test == y_pred)


def _mean_squared_error_callable(y_test, y_pred):
    return ((y_test - y_pred) ** 2).mean()


@pytest.fixture(params=["long", "wide"])
def ols_ridge_dataset(global_random_seed, request):
    """Dataset with OLS and Ridge solutions, well conditioned X.

    The construction is based on the SVD decomposition of X = U S V'.

    Parameters
    ----------
    type : {"long", "wide"}
        If "long", then n_samples > n_features.
        If "wide", then n_features > n_samples.

    For "wide", we return the minimum norm solution w = X' (XX')^-1 y:

        min ||w||_2 subject to X w = y

    Returns
    -------
    X : ndarray
        Last column of 1, i.e. intercept.
    y : ndarray
    coef_ols : ndarray of shape
        Minimum norm OLS solutions, i.e. min ||X w - y||_2_2 (with minimum ||w||_2 in
        case of ambiguity)
        Last coefficient is intercept.
    coef_ridge : ndarray of shape (5,)
        Ridge solution with alpha=1, i.e. min ||X w - y||_2_2 + ||w||_2^2.
        Last coefficient is intercept.
    """
    # Make larger dim more than double as big as the smaller one.
    # This helps when constructing singular matrices like (X, X).
    if request.param == "long":
        n_samples, n_features = 12, 4
    else:
        n_samples, n_features = 4, 12
    k = min(n_samples, n_features)
    rng = np.random.RandomState(global_random_seed)
    X = make_low_rank_matrix(
        n_samples=n_samples, n_features=n_features, effective_rank=k, random_state=rng
    )
    X[:, -1] = 1  # last columns acts as intercept
    U, s, Vt = linalg.svd(X)
    assert np.all(s > 1e-3)  # to be sure
    U1, U2 = U[:, :k], U[:, k:]
    Vt1, _ = Vt[:k, :], Vt[k:, :]

    if request.param == "long":
        # Add a term that vanishes in the product X'y
        coef_ols = rng.uniform(low=-10, high=10, size=n_features)
        y = X @ coef_ols
        y += U2 @ rng.normal(size=n_samples - n_features) ** 2
    else:
        y = rng.uniform(low=-10, high=10, size=n_samples)
        # w = X'(XX')^-1 y = V s^-1 U' y
        coef_ols = Vt1.T @ np.diag(1 / s) @ U1.T @ y

    # Add penalty alpha * ||coef||_2^2 for alpha=1 and solve via normal equations.
    # Note that the problem is well conditioned such that we get accurate results.
    alpha = 1
    d = alpha * np.identity(n_features)
    d[-1, -1] = 0  # intercept gets no penalty
    coef_ridge = linalg.solve(X.T @ X + d, X.T @ y)

    # To be sure
    R_OLS = y - X @ coef_ols
    R_Ridge = y - X @ coef_ridge
    assert np.linalg.norm(R_OLS) < np.linalg.norm(R_Ridge)

    return X, y, coef_ols, coef_ridge


@pytest.mark.parametrize("solver", SOLVERS)
@pytest.mark.parametrize("fit_intercept", [True, False])
def test_ridge_regression(solver, fit_intercept, ols_ridge_dataset, global_random_seed):
    """Test that Ridge converges for all solvers to correct solution.

    We work with a simple constructed data set with known solution.
    """
    X, y, _, coef = ols_ridge_dataset
    alpha = 1.0  # because ols_ridge_dataset uses this.
    params = dict(
        alpha=alpha,
        fit_intercept=True,
        solver=solver,
        tol=1e-15 if solver in ("sag", "saga") else 1e-10,
        random_state=global_random_seed,
    )

    # Calculate residuals and R2.
    res_null = y - np.mean(y)
    res_Ridge = y - X @ coef
    R2_Ridge = 1 - np.sum(res_Ridge**2) / np.sum(res_null**2)

    model = Ridge(**params)
    X = X[:, :-1]  # remove intercept
    if fit_intercept:
        intercept = coef[-1]
    else:
        X = X - X.mean(axis=0)
        y = y - y.mean()
        intercept = 0
    model.fit(X, y)
    coef = coef[:-1]

    assert model.intercept_ == pytest.approx(intercept)
    assert_allclose(model.coef_, coef)
    assert model.score(X, y) == pytest.approx(R2_Ridge)

    # Same with sample_weight.
    model = Ridge(**params).fit(X, y, sample_weight=np.ones(X.shape[0]))
    assert model.intercept_ == pytest.approx(intercept)
    assert_allclose(model.coef_, coef)
    assert model.score(X, y) == pytest.approx(R2_Ridge)

    assert model.solver_ == solver


@pytest.mark.parametrize("solver", SOLVERS)
@pytest.mark.parametrize("fit_intercept", [True, False])
def test_ridge_regression_hstacked_X(
    solver, fit_intercept, ols_ridge_dataset, global_random_seed
):
    """Test that Ridge converges for all solvers to correct solution on hstacked data.

    We work with a simple constructed data set with known solution.
    Fit on [X] with alpha is the same as fit on [X, X]/2 with alpha/2.
    For long X, [X, X] is a singular matrix.
    """
    X, y, _, coef = ols_ridge_dataset
    n_samples, n_features = X.shape
    alpha = 1.0  # because ols_ridge_dataset uses this.

    model = Ridge(
        alpha=alpha / 2,
        fit_intercept=fit_intercept,
        solver=solver,
        tol=1e-15 if solver in ("sag", "saga") else 1e-10,
        random_state=global_random_seed,
    )
    X = X[:, :-1]  # remove intercept
    X = 0.5 * np.concatenate((X, X), axis=1)
    assert np.linalg.matrix_rank(X) <= min(n_samples, n_features - 1)
    if fit_intercept:
        intercept = coef[-1]
    else:
        X = X - X.mean(axis=0)
        y = y - y.mean()
        intercept = 0
    model.fit(X, y)
    coef = coef[:-1]

    assert model.intercept_ == pytest.approx(intercept)
    # coefficients are not all on the same magnitude, adding a small atol to
    # make this test less brittle
    assert_allclose(model.coef_, np.r_[coef, coef], atol=1e-8)


@pytest.mark.parametrize("solver", SOLVERS)
@pytest.mark.parametrize("fit_intercept", [True, False])
def test_ridge_regression_vstacked_X(
    solver, fit_intercept, ols_ridge_dataset, global_random_seed
):
    """Test that Ridge converges for all solvers to correct solution on vstacked data.

    We work with a simple constructed data set with known solution.
    Fit on [X] with alpha is the same as fit on [X], [y]
                                                [X], [y] with 2 * alpha.
    For wide X, [X', X'] is a singular matrix.
    """
    X, y, _, coef = ols_ridge_dataset
    n_samples, n_features = X.shape
    alpha = 1.0  # because ols_ridge_dataset uses this.

    model = Ridge(
        alpha=2 * alpha,
        fit_intercept=fit_intercept,
        solver=solver,
        tol=1e-15 if solver in ("sag", "saga") else 1e-10,
        random_state=global_random_seed,
    )
    X = X[:, :-1]  # remove intercept
    X = np.concatenate((X, X), axis=0)
    assert np.linalg.matrix_rank(X) <= min(n_samples, n_features)
    y = np.r_[y, y]
    if fit_intercept:
        intercept = coef[-1]
    else:
        X = X - X.mean(axis=0)
        y = y - y.mean()
        intercept = 0
    model.fit(X, y)
    coef = coef[:-1]

    assert model.intercept_ == pytest.approx(intercept)
    # coefficients are not all on the same magnitude, adding a small atol to
    # make this test less brittle
    assert_allclose(model.coef_, coef, atol=1e-8)


@pytest.mark.parametrize("solver", SOLVERS)
@pytest.mark.parametrize("fit_intercept", [True, False])
def test_ridge_regression_unpenalized(
    solver, fit_intercept, ols_ridge_dataset, global_random_seed
):
    """Test that unpenalized Ridge = OLS converges for all solvers to correct solution.

    We work with a simple constructed data set with known solution.
    Note: This checks the minimum norm solution for wide X, i.e.
    n_samples < n_features:
        min ||w||_2 subject to X w = y
    """
    X, y, coef, _ = ols_ridge_dataset
    n_samples, n_features = X.shape
    alpha = 0  # OLS
    params = dict(
        alpha=alpha,
        fit_intercept=fit_intercept,
        solver=solver,
        tol=1e-15 if solver in ("sag", "saga") else 1e-10,
        random_state=global_random_seed,
    )

    model = Ridge(**params)
    # Note that cholesky might give a warning: "Singular matrix in solving dual
    # problem. Using least-squares solution instead."
    if fit_intercept:
        X = X[:, :-1]  # remove intercept
        intercept = coef[-1]
        coef = coef[:-1]
    else:
        intercept = 0
    model.fit(X, y)

    # FIXME: `assert_allclose(model.coef_, coef)` should work for all cases but fails
    # for the wide/fat case with n_features > n_samples. The current Ridge solvers do
    # NOT return the minimum norm solution with fit_intercept=True.
    if n_samples > n_features or not fit_intercept:
        assert model.intercept_ == pytest.approx(intercept)
        assert_allclose(model.coef_, coef)
    else:
        # As it is an underdetermined problem, residuals = 0. This shows that we get
        # a solution to X w = y ....
        assert_allclose(model.predict(X), y)
        assert_allclose(X @ coef + intercept, y)
        # But it is not the minimum norm solution. (This should be equal.)
        assert np.linalg.norm(np.r_[model.intercept_, model.coef_]) > np.linalg.norm(
            np.r_[intercept, coef]
        )

        pytest.xfail(reason="Ridge does not provide the minimum norm solution.")
        assert model.intercept_ == pytest.approx(intercept)
        assert_allclose(model.coef_, coef)


@pytest.mark.parametrize("solver", SOLVERS)
@pytest.mark.parametrize("fit_intercept", [True, False])
def test_ridge_regression_unpenalized_hstacked_X(
    solver, fit_intercept, ols_ridge_dataset, global_random_seed
):
    """Test that unpenalized Ridge = OLS converges for all solvers to correct solution.

    We work with a simple constructed data set with known solution.
    OLS fit on [X] is the same as fit on [X, X]/2.
    For long X, [X, X] is a singular matrix and we check against the minimum norm
    solution:
        min ||w||_2 subject to min ||X w - y||_2
    """
    X, y, coef, _ = ols_ridge_dataset
    n_samples, n_features = X.shape
    alpha = 0  # OLS

    model = Ridge(
        alpha=alpha,
        fit_intercept=fit_intercept,
        solver=solver,
        tol=1e-15 if solver in ("sag", "saga") else 1e-10,
        random_state=global_random_seed,
    )
    if fit_intercept:
        X = X[:, :-1]  # remove intercept
        intercept = coef[-1]
        coef = coef[:-1]
    else:
        intercept = 0
    X = 0.5 * np.concatenate((X, X), axis=1)
    assert np.linalg.matrix_rank(X) <= min(n_samples, n_features)
    model.fit(X, y)

    if n_samples > n_features or not fit_intercept:
        assert model.intercept_ == pytest.approx(intercept)
        if solver == "cholesky":
            # Cholesky is a bad choice for singular X.
            pytest.skip()
        assert_allclose(model.coef_, np.r_[coef, coef])
    else:
        # FIXME: Same as in test_ridge_regression_unpenalized.
        # As it is an underdetermined problem, residuals = 0. This shows that we get
        # a solution to X w = y ....
        assert_allclose(model.predict(X), y)
        # But it is not the minimum norm solution. (This should be equal.)
        assert np.linalg.norm(np.r_[model.intercept_, model.coef_]) > np.linalg.norm(
            np.r_[intercept, coef, coef]
        )

        pytest.xfail(reason="Ridge does not provide the minimum norm solution.")
        assert model.intercept_ == pytest.approx(intercept)
        assert_allclose(model.coef_, np.r_[coef, coef])


@pytest.mark.parametrize("solver", SOLVERS)
@pytest.mark.parametrize("fit_intercept", [True, False])
def test_ridge_regression_unpenalized_vstacked_X(
    solver, fit_intercept, ols_ridge_dataset, global_random_seed
):
    """Test that unpenalized Ridge = OLS converges for all solvers to correct solution.

    We work with a simple constructed data set with known solution.
    OLS fit on [X] is the same as fit on [X], [y]
                                         [X], [y].
    For wide X, [X', X'] is a singular matrix and we check against the minimum norm
    solution:
        min ||w||_2 subject to X w = y
    """
    X, y, coef, _ = ols_ridge_dataset
    n_samples, n_features = X.shape
    alpha = 0  # OLS

    model = Ridge(
        alpha=alpha,
        fit_intercept=fit_intercept,
        solver=solver,
        tol=1e-15 if solver in ("sag", "saga") else 1e-10,
        random_state=global_random_seed,
    )

    if fit_intercept:
        X = X[:, :-1]  # remove intercept
        intercept = coef[-1]
        coef = coef[:-1]
    else:
        intercept = 0
    X = np.concatenate((X, X), axis=0)
    assert np.linalg.matrix_rank(X) <= min(n_samples, n_features)
    y = np.r_[y, y]
    model.fit(X, y)

    if n_samples > n_features or not fit_intercept:
        assert model.intercept_ == pytest.approx(intercept)
        assert_allclose(model.coef_, coef)
    else:
        # FIXME: Same as in test_ridge_regression_unpenalized.
        # As it is an underdetermined problem, residuals = 0. This shows that we get
        # a solution to X w = y ....
        assert_allclose(model.predict(X), y)
        # But it is not the minimum norm solution. (This should be equal.)
        assert np.linalg.norm(np.r_[model.intercept_, model.coef_]) > np.linalg.norm(
            np.r_[intercept, coef]
        )

        pytest.xfail(reason="Ridge does not provide the minimum norm solution.")
        assert model.intercept_ == pytest.approx(intercept)
        assert_allclose(model.coef_, coef)


@pytest.mark.parametrize("solver", SOLVERS)
@pytest.mark.parametrize("fit_intercept", [True, False])
@pytest.mark.parametrize("sparse_container", [None] + CSR_CONTAINERS)
@pytest.mark.parametrize("alpha", [1.0, 1e-2])
def test_ridge_regression_sample_weights(
    solver,
    fit_intercept,
    sparse_container,
    alpha,
    ols_ridge_dataset,
    global_random_seed,
):
    """Test that Ridge with sample weights gives correct results.

    We use the following trick:
        ||y - Xw||_2 = (z - Aw)' W (z - Aw)
    for z=[y, y], A' = [X', X'] (vstacked), and W[:n/2] + W[n/2:] = 1, W=diag(W)
    """
    if sparse_container is not None:
        if fit_intercept and solver not in SPARSE_SOLVERS_WITH_INTERCEPT:
            pytest.skip()
        elif not fit_intercept and solver not in SPARSE_SOLVERS_WITHOUT_INTERCEPT:
            pytest.skip()
    X, y, _, coef = ols_ridge_dataset
    n_samples, n_features = X.shape
    sw = rng.uniform(low=0, high=1, size=n_samples)

    model = Ridge(
        alpha=alpha,
        fit_intercept=fit_intercept,
        solver=solver,
        tol=1e-15 if solver in ["sag", "saga"] else 1e-10,
        max_iter=100_000,
        random_state=global_random_seed,
    )
    X = X[:, :-1]  # remove intercept
    X = np.concatenate((X, X), axis=0)
    y = np.r_[y, y]
    sw = np.r_[sw, 1 - sw] * alpha
    if fit_intercept:
        intercept = coef[-1]
    else:
        X = X - X.mean(axis=0)
        y = y - y.mean()
        intercept = 0
    if sparse_container is not None:
        X = sparse_container(X)
    model.fit(X, y, sample_weight=sw)
    coef = coef[:-1]

    assert model.intercept_ == pytest.approx(intercept)
    assert_allclose(model.coef_, coef)


def test_primal_dual_relationship():
    y = y_diabetes.reshape(-1, 1)
    coef = _solve_cholesky(X_diabetes, y, alpha=[1e-2])
    K = np.dot(X_diabetes, X_diabetes.T)
    dual_coef = _solve_cholesky_kernel(K, y, alpha=[1e-2])
    coef2 = np.dot(X_diabetes.T, dual_coef).T
    assert_array_almost_equal(coef, coef2)


def test_ridge_regression_convergence_fail():
    rng = np.random.RandomState(0)
    y = rng.randn(5)
    X = rng.randn(5, 10)
    warning_message = r"sparse_cg did not converge after [0-9]+ iterations."
    with pytest.warns(ConvergenceWarning, match=warning_message):
        ridge_regression(
            X, y, alpha=1.0, solver="sparse_cg", tol=0.0, max_iter=None, verbose=1
        )


def test_ridge_shapes_type():
    # Test shape of coef_ and intercept_
    rng = np.random.RandomState(0)
    n_samples, n_features = 5, 10
    X = rng.randn(n_samples, n_features)
    y = rng.randn(n_samples)
    Y1 = y[:, np.newaxis]
    Y = np.c_[y, 1 + y]

    ridge = Ridge()

    ridge.fit(X, y)
    assert ridge.coef_.shape == (n_features,)
    assert ridge.intercept_.shape == ()
    assert isinstance(ridge.coef_, np.ndarray)
    assert isinstance(ridge.intercept_, float)

    ridge.fit(X, Y1)
    assert ridge.coef_.shape == (n_features,)
    assert ridge.intercept_.shape == (1,)
    assert isinstance(ridge.coef_, np.ndarray)
    assert isinstance(ridge.intercept_, np.ndarray)

    ridge.fit(X, Y)
    assert ridge.coef_.shape == (2, n_features)
    assert ridge.intercept_.shape == (2,)
    assert isinstance(ridge.coef_, np.ndarray)
    assert isinstance(ridge.intercept_, np.ndarray)


def test_ridge_intercept():
    # Test intercept with multiple targets GH issue #708
    rng = np.random.RandomState(0)
    n_samples, n_features = 5, 10
    X = rng.randn(n_samples, n_features)
    y = rng.randn(n_samples)
    Y = np.c_[y, 1.0 + y]

    ridge = Ridge()

    ridge.fit(X, y)
    intercept = ridge.intercept_

    ridge.fit(X, Y)
    assert_almost_equal(ridge.intercept_[0], intercept)
    assert_almost_equal(ridge.intercept_[1], intercept + 1.0)


def test_ridge_vs_lstsq():
    # On alpha=0., Ridge and OLS yield the same solution.

    rng = np.random.RandomState(0)
    # we need more samples than features
    n_samples, n_features = 5, 4
    y = rng.randn(n_samples)
    X = rng.randn(n_samples, n_features)

    ridge = Ridge(alpha=0.0, fit_intercept=False)
    ols = LinearRegression(fit_intercept=False)

    ridge.fit(X, y)
    ols.fit(X, y)
    assert_almost_equal(ridge.coef_, ols.coef_)

    ridge.fit(X, y)
    ols.fit(X, y)
    assert_almost_equal(ridge.coef_, ols.coef_)


def test_ridge_individual_penalties():
    # Tests the ridge object using individual penalties

    rng = np.random.RandomState(42)

    n_samples, n_features, n_targets = 20, 10, 5
    X = rng.randn(n_samples, n_features)
    y = rng.randn(n_samples, n_targets)

    penalties = np.arange(n_targets)

    coef_cholesky = np.array(
        [
            Ridge(alpha=alpha, solver="cholesky").fit(X, target).coef_
            for alpha, target in zip(penalties, y.T)
        ]
    )

    coefs_indiv_pen = [
        Ridge(alpha=penalties, solver=solver, tol=1e-12).fit(X, y).coef_
        for solver in ["svd", "sparse_cg", "lsqr", "cholesky", "sag", "saga"]
    ]
    for coef_indiv_pen in coefs_indiv_pen:
        assert_array_almost_equal(coef_cholesky, coef_indiv_pen)

    # Test error is raised when number of targets and penalties do not match.
    ridge = Ridge(alpha=penalties[:-1])
    err_msg = "Number of targets and number of penalties do not correspond: 4 != 5"
    with pytest.raises(ValueError, match=err_msg):
        ridge.fit(X, y)


@pytest.mark.parametrize("n_col", [(), (1,), (3,)])
@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
def test_X_CenterStackOp(n_col, csr_container):
    rng = np.random.RandomState(0)
    X = rng.randn(11, 8)
    X_m = rng.randn(8)
    sqrt_sw = rng.randn(len(X))
    Y = rng.randn(11, *n_col)
    A = rng.randn(9, *n_col)
    operator = _X_CenterStackOp(csr_container(X), X_m, sqrt_sw)
    reference_operator = np.hstack([X - sqrt_sw[:, None] * X_m, sqrt_sw[:, None]])
    assert_allclose(reference_operator.dot(A), operator.dot(A))
    assert_allclose(reference_operator.T.dot(Y), operator.T.dot(Y))


@pytest.mark.parametrize("shape", [(10, 1), (13, 9), (3, 7), (2, 2), (20, 20)])
@pytest.mark.parametrize("uniform_weights", [True, False])
@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
def test_compute_gram(shape, uniform_weights, csr_container):
    rng = np.random.RandomState(0)
    X = rng.randn(*shape)
    if uniform_weights:
        sw = np.ones(X.shape[0])
    else:
        sw = rng.chisquare(1, shape[0])
    sqrt_sw = np.sqrt(sw)
    X_mean = np.average(X, axis=0, weights=sw)
    X_centered = (X - X_mean) * sqrt_sw[:, None]
    true_gram = X_centered.dot(X_centered.T)
    X_sparse = csr_container(X * sqrt_sw[:, None])
    gcv = _RidgeGCV(fit_intercept=True)
    computed_gram, computed_mean = gcv._compute_gram(X_sparse, sqrt_sw)
    assert_allclose(X_mean, computed_mean)
    assert_allclose(true_gram, computed_gram)


@pytest.mark.parametrize("shape", [(10, 1), (13, 9), (3, 7), (2, 2), (20, 20)])
@pytest.mark.parametrize("uniform_weights", [True, False])
@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
def test_compute_covariance(shape, uniform_weights, csr_container):
    rng = np.random.RandomState(0)
    X = rng.randn(*shape)
    if uniform_weights:
        sw = np.ones(X.shape[0])
    else:
        sw = rng.chisquare(1, shape[0])
    sqrt_sw = np.sqrt(sw)
    X_mean = np.average(X, axis=0, weights=sw)
    X_centered = (X - X_mean) * sqrt_sw[:, None]
    true_covariance = X_centered.T.dot(X_centered)
    X_sparse = csr_container(X * sqrt_sw[:, None])
    gcv = _RidgeGCV(fit_intercept=True)
    computed_cov, computed_mean = gcv._compute_covariance(X_sparse, sqrt_sw)
    assert_allclose(X_mean, computed_mean)
    assert_allclose(true_covariance, computed_cov)


def _make_sparse_offset_regression(
    n_samples=100,
    n_features=100,
    proportion_nonzero=0.5,
    n_informative=10,
    n_targets=1,
    bias=13.0,
    X_offset=30.0,
    noise=30.0,
    shuffle=True,
    coef=False,
    positive=False,
    random_state=None,
):
    X, y, c = make_regression(
        n_samples=n_samples,
        n_features=n_features,
        n_informative=n_informative,
        n_targets=n_targets,
        bias=bias,
        noise=noise,
        shuffle=shuffle,
        coef=True,
        random_state=random_state,
    )
    if n_features == 1:
        c = np.asarray([c])
    X += X_offset
    mask = (
        np.random.RandomState(random_state).binomial(1, proportion_nonzero, X.shape) > 0
    )
    removed_X = X.copy()
    X[~mask] = 0.0
    removed_X[mask] = 0.0
    y -= removed_X.dot(c)
    if positive:
        y += X.dot(np.abs(c) + 1 - c)
        c = np.abs(c) + 1
    if n_features == 1:
        c = c[0]
    if coef:
        return X, y, c
    return X, y


@pytest.mark.parametrize(
    "solver, sparse_container",
    (
        (solver, sparse_container)
        for (solver, sparse_container) in product(
            ["cholesky", "sag", "sparse_cg", "lsqr", "saga", "ridgecv"],
            [None] + CSR_CONTAINERS,
        )
        if sparse_container is None or solver in ["sparse_cg", "ridgecv"]
    ),
)
@pytest.mark.parametrize(
    "n_samples,dtype,proportion_nonzero",
    [(20, "float32", 0.1), (40, "float32", 1.0), (20, "float64", 0.2)],
)
def test_solver_consistency(
    solver, proportion_nonzero, n_samples, dtype, sparse_container, global_random_seed
):
    alpha = 1.0
    noise = 50.0 if proportion_nonzero > 0.9 else 500.0
    X, y = _make_sparse_offset_regression(
        bias=10,
        n_features=30,
        proportion_nonzero=proportion_nonzero,
        noise=noise,
        random_state=global_random_seed,
        n_samples=n_samples,
    )
    # Manually scale the data to avoid pathological cases. We use
    # minmax_scale to deal with the sparse case without breaking
    # the sparsity pattern.
    X = minmax_scale(X)

    svd_ridge = Ridge(solver="svd", alpha=alpha).fit(X, y)
    X = X.astype(dtype, copy=False)
    y = y.astype(dtype, copy=False)
    if sparse_container is not None:
        X = sparse_container(X)
    if solver == "ridgecv":
        ridge = RidgeCV(alphas=[alpha])
    else:
        if solver.startswith("sag"):
            # Avoid ConvergenceWarning for sag and saga solvers.
            tol = 1e-7
            max_iter = 100_000
        else:
            tol = 1e-10
            max_iter = None

        ridge = Ridge(
            alpha=alpha,
            solver=solver,
            max_iter=max_iter,
            tol=tol,
            random_state=global_random_seed,
        )
    ridge.fit(X, y)
    assert_allclose(ridge.coef_, svd_ridge.coef_, atol=1e-3, rtol=1e-3)
    assert_allclose(ridge.intercept_, svd_ridge.intercept_, atol=1e-3, rtol=1e-3)


@pytest.mark.parametrize("gcv_mode", ["svd", "eigen"])
@pytest.mark.parametrize("X_container", [np.asarray] + CSR_CONTAINERS)
@pytest.mark.parametrize("X_shape", [(11, 8), (11, 20)])
@pytest.mark.parametrize("fit_intercept", [True, False])
@pytest.mark.parametrize(
    "y_shape, noise",
    [
        ((11,), 1.0),
        ((11, 1), 30.0),
        ((11, 3), 150.0),
    ],
)
def test_ridge_gcv_vs_ridge_loo_cv(
    gcv_mode, X_container, X_shape, y_shape, fit_intercept, noise
):
    n_samples, n_features = X_shape
    n_targets = y_shape[-1] if len(y_shape) == 2 else 1
    X, y = _make_sparse_offset_regression(
        n_samples=n_samples,
        n_features=n_features,
        n_targets=n_targets,
        random_state=0,
        shuffle=False,
        noise=noise,
        n_informative=5,
    )
    y = y.reshape(y_shape)

    alphas = [1e-3, 0.1, 1.0, 10.0, 1e3]
    loo_ridge = RidgeCV(
        cv=n_samples,
        fit_intercept=fit_intercept,
        alphas=alphas,
        scoring="neg_mean_squared_error",
    )
    gcv_ridge = RidgeCV(
        gcv_mode=gcv_mode,
        fit_intercept=fit_intercept,
        alphas=alphas,
    )

    loo_ridge.fit(X, y)

    X_gcv = X_container(X)
    gcv_ridge.fit(X_gcv, y)

    assert gcv_ridge.alpha_ == pytest.approx(loo_ridge.alpha_)
    assert_allclose(gcv_ridge.coef_, loo_ridge.coef_, rtol=1e-3)
    assert_allclose(gcv_ridge.intercept_, loo_ridge.intercept_, rtol=1e-3)


def test_ridge_loo_cv_asym_scoring():
    # checking on asymmetric scoring
    scoring = "explained_variance"
    n_samples, n_features = 10, 5
    n_targets = 1
    X, y = _make_sparse_offset_regression(
        n_samples=n_samples,
        n_features=n_features,
        n_targets=n_targets,
        random_state=0,
        shuffle=False,
        noise=1,
        n_informative=5,
    )

    alphas = [1e-3, 0.1, 1.0, 10.0, 1e3]
    loo_ridge = RidgeCV(
        cv=n_samples, fit_intercept=True, alphas=alphas, scoring=scoring
    )

    gcv_ridge = RidgeCV(fit_intercept=True, alphas=alphas, scoring=scoring)

    loo_ridge.fit(X, y)
    gcv_ridge.fit(X, y)

    assert gcv_ridge.alpha_ == pytest.approx(loo_ridge.alpha_), (
        f"{gcv_ridge.alpha_=}, {loo_ridge.alpha_=}"
    )
    assert_allclose(gcv_ridge.coef_, loo_ridge.coef_, rtol=1e-3)
    assert_allclose(gcv_ridge.intercept_, loo_ridge.intercept_, rtol=1e-3)


@pytest.mark.parametrize("gcv_mode", ["svd", "eigen"])
@pytest.mark.parametrize("X_container", [np.asarray] + CSR_CONTAINERS)
@pytest.mark.parametrize("n_features", [8, 20])
@pytest.mark.parametrize(
    "y_shape, fit_intercept, noise",
    [
        ((11,), True, 1.0),
        ((11, 1), True, 20.0),
        ((11, 3), True, 150.0),
        ((11, 3), False, 30.0),
    ],
)
def test_ridge_gcv_sample_weights(
    gcv_mode, X_container, fit_intercept, n_features, y_shape, noise
):
    alphas = [1e-3, 0.1, 1.0, 10.0, 1e3]
    rng = np.random.RandomState(0)
    n_targets = y_shape[-1] if len(y_shape) == 2 else 1
    X, y = _make_sparse_offset_regression(
        n_samples=11,
        n_features=n_features,
        n_targets=n_targets,
        random_state=0,
        shuffle=False,
        noise=noise,
    )
    y = y.reshape(y_shape)

    sample_weight = 3 * rng.randn(len(X))
    sample_weight = (sample_weight - sample_weight.min() + 1).astype(int)
    indices = np.repeat(np.arange(X.shape[0]), sample_weight)
    sample_weight = sample_weight.astype(float)
    X_tiled, y_tiled = X[indices], y[indices]

    cv = GroupKFold(n_splits=X.shape[0])
    splits = cv.split(X_tiled, y_tiled, groups=indices)
    kfold = RidgeCV(
        alphas=alphas,
        cv=splits,
        scoring="neg_mean_squared_error",
        fit_intercept=fit_intercept,
    )
    kfold.fit(X_tiled, y_tiled)

    ridge_reg = Ridge(alpha=kfold.alpha_, fit_intercept=fit_intercept)
    splits = cv.split(X_tiled, y_tiled, groups=indices)
    predictions = cross_val_predict(ridge_reg, X_tiled, y_tiled, cv=splits)
    if predictions.shape != y_tiled.shape:
        predictions = predictions.reshape(y_tiled.shape)
    kfold_errors = (y_tiled - predictions) ** 2
    kfold_errors = [
        np.sum(kfold_errors[indices == i], axis=0) for i in np.arange(X.shape[0])
    ]
    kfold_errors = np.asarray(kfold_errors)

    X_gcv = X_container(X)
    gcv_ridge = RidgeCV(
        alphas=alphas,
        store_cv_results=True,
        gcv_mode=gcv_mode,
        fit_intercept=fit_intercept,
    )
    gcv_ridge.fit(X_gcv, y, sample_weight=sample_weight)
    if len(y_shape) == 2:
        gcv_errors = gcv_ridge.cv_results_[:, :, alphas.index(kfold.alpha_)]
    else:
        gcv_errors = gcv_ridge.cv_results_[:, alphas.index(kfold.alpha_)]

    assert kfold.alpha_ == pytest.approx(gcv_ridge.alpha_)
    assert_allclose(gcv_errors, kfold_errors, rtol=1e-3)
    assert_allclose(gcv_ridge.coef_, kfold.coef_, rtol=1e-3)
    assert_allclose(gcv_ridge.intercept_, kfold.intercept_, rtol=1e-3)


@pytest.mark.parametrize("sparse_container", [None] + CSR_CONTAINERS)
@pytest.mark.parametrize(
    "mode, mode_n_greater_than_p, mode_p_greater_than_n",
    [
        (None, "svd", "eigen"),
        ("auto", "svd", "eigen"),
        ("eigen", "eigen", "eigen"),
        ("svd", "svd", "svd"),
    ],
)
def test_check_gcv_mode_choice(
    sparse_container, mode, mode_n_greater_than_p, mode_p_greater_than_n
):
    X, _ = make_regression(n_samples=5, n_features=2)
    if sparse_container is not None:
        X = sparse_container(X)
    assert _check_gcv_mode(X, mode) == mode_n_greater_than_p
    assert _check_gcv_mode(X.T, mode) == mode_p_greater_than_n


def _test_ridge_loo(sparse_container):
    # test that can work with both dense or sparse matrices
    n_samples = X_diabetes.shape[0]

    ret = []

    if sparse_container is None:
        X, fit_intercept = X_diabetes, True
    else:
        X, fit_intercept = sparse_container(X_diabetes), False
    ridge_gcv = _RidgeGCV(fit_intercept=fit_intercept)

    # check best alpha
    ridge_gcv.fit(X, y_diabetes)
    alpha_ = ridge_gcv.alpha_
    ret.append(alpha_)

    # check that we get same best alpha with custom loss_func
    f = ignore_warnings
    scoring = make_scorer(mean_squared_error, greater_is_better=False)
    ridge_gcv2 = RidgeCV(fit_intercept=False, scoring=scoring)
    f(ridge_gcv2.fit)(X, y_diabetes)
    assert ridge_gcv2.alpha_ == pytest.approx(alpha_)

    # check that we get same best alpha with custom score_func
    def func(x, y):
        return -mean_squared_error(x, y)

    scoring = make_scorer(func)
    ridge_gcv3 = RidgeCV(fit_intercept=False, scoring=scoring)
    f(ridge_gcv3.fit)(X, y_diabetes)
    assert ridge_gcv3.alpha_ == pytest.approx(alpha_)

    # check that we get same best alpha with a scorer
    scorer = get_scorer("neg_mean_squared_error")
    ridge_gcv4 = RidgeCV(fit_intercept=False, scoring=scorer)
    ridge_gcv4.fit(X, y_diabetes)
    assert ridge_gcv4.alpha_ == pytest.approx(alpha_)

    # check that we get same best alpha with sample weights
    if sparse_container is None:
        ridge_gcv.fit(X, y_diabetes, sample_weight=np.ones(n_samples))
        assert ridge_gcv.alpha_ == pytest.approx(alpha_)

    # simulate several responses
    Y = np.vstack((y_diabetes, y_diabetes)).T

    ridge_gcv.fit(X, Y)
    Y_pred = ridge_gcv.predict(X)
    ridge_gcv.fit(X, y_diabetes)
    y_pred = ridge_gcv.predict(X)

    assert_allclose(np.vstack((y_pred, y_pred)).T, Y_pred, rtol=1e-5)

    return ret


def _test_ridge_cv(sparse_container):
    X = X_diabetes if sparse_container is None else sparse_container(X_diabetes)
    ridge_cv = RidgeCV()
    ridge_cv.fit(X, y_diabetes)
    ridge_cv.predict(X)

    assert len(ridge_cv.coef_.shape) == 1
    assert type(ridge_cv.intercept_) is np.float64

    cv = KFold(5)
    ridge_cv.set_params(cv=cv)
    ridge_cv.fit(X, y_diabetes)
    ridge_cv.predict(X)

    assert len(ridge_cv.coef_.shape) == 1
    assert type(ridge_cv.intercept_) is np.float64


@pytest.mark.parametrize(
    "ridge, make_dataset",
    [
        (RidgeCV(store_cv_results=False), make_regression),
        (RidgeClassifierCV(store_cv_results=False), make_classification),
    ],
)
def test_ridge_gcv_cv_results_not_stored(ridge, make_dataset):
    # Check that `cv_results_` is not stored when store_cv_results is False
    X, y = make_dataset(n_samples=6, random_state=42)
    ridge.fit(X, y)
    assert not hasattr(ridge, "cv_results_")


@pytest.mark.parametrize(
    "ridge, make_dataset",
    [(RidgeCV(), make_regression), (RidgeClassifierCV(), make_classification)],
)
@pytest.mark.parametrize("cv", [None, 3])
def test_ridge_best_score(ridge, make_dataset, cv):
    # check that the best_score_ is store
    X, y = make_dataset(n_samples=6, random_state=42)
    ridge.set_params(store_cv_results=False, cv=cv)
    ridge.fit(X, y)
    assert hasattr(ridge, "best_score_")
    assert isinstance(ridge.best_score_, float)


def test_ridge_cv_individual_penalties():
    # Tests the ridge_cv object optimizing individual penalties for each target

    rng = np.random.RandomState(42)

    # Create random dataset with multiple targets. Each target should have
    # a different optimal alpha.
    n_samples, n_features, n_targets = 20, 5, 3
    y = rng.randn(n_samples, n_targets)
    X = (
        np.dot(y[:, [0]], np.ones((1, n_features)))
        + np.dot(y[:, [1]], 0.05 * np.ones((1, n_features)))
        + np.dot(y[:, [2]], 0.001 * np.ones((1, n_features)))
        + rng.randn(n_samples, n_features)
    )

    alphas = (1, 100, 1000)

    # Find optimal alpha for each target
    optimal_alphas = [RidgeCV(alphas=alphas).fit(X, target).alpha_ for target in y.T]

    # Find optimal alphas for all targets simultaneously
    ridge_cv = RidgeCV(alphas=alphas, alpha_per_target=True).fit(X, y)
    assert_array_equal(optimal_alphas, ridge_cv.alpha_)

    # The resulting regression weights should incorporate the different
    # alpha values.
    assert_array_almost_equal(
        Ridge(alpha=ridge_cv.alpha_).fit(X, y).coef_, ridge_cv.coef_
    )

    # Test shape of alpha_ and cv_results_
    ridge_cv = RidgeCV(alphas=alphas, alpha_per_target=True, store_cv_results=True).fit(
        X, y
    )
    assert ridge_cv.alpha_.shape == (n_targets,)
    assert ridge_cv.best_score_.shape == (n_targets,)
    assert ridge_cv.cv_results_.shape == (n_samples, len(alphas), n_targets)

    # Test edge case of there being only one alpha value
    ridge_cv = RidgeCV(alphas=1, alpha_per_target=True, store_cv_results=True).fit(X, y)
    assert ridge_cv.alpha_.shape == (n_targets,)
    assert ridge_cv.best_score_.shape == (n_targets,)
    assert ridge_cv.cv_results_.shape == (n_samples, n_targets, 1)

    # Test edge case of there being only one target
    ridge_cv = RidgeCV(alphas=alphas, alpha_per_target=True, store_cv_results=True).fit(
        X, y[:, 0]
    )
    assert np.isscalar(ridge_cv.alpha_)
    assert np.isscalar(ridge_cv.best_score_)
    assert ridge_cv.cv_results_.shape == (n_samples, len(alphas))

    # Try with a custom scoring function
    ridge_cv = RidgeCV(alphas=alphas, alpha_per_target=True, scoring="r2").fit(X, y)
    assert_array_equal(optimal_alphas, ridge_cv.alpha_)
    assert_array_almost_equal(
        Ridge(alpha=ridge_cv.alpha_).fit(X, y).coef_, ridge_cv.coef_
    )

    # Using a custom CV object should throw an error in combination with
    # alpha_per_target=True
    ridge_cv = RidgeCV(alphas=alphas, cv=LeaveOneOut(), alpha_per_target=True)
    msg = "cv!=None and alpha_per_target=True are incompatible"
    with pytest.raises(ValueError, match=msg):
        ridge_cv.fit(X, y)
    ridge_cv = RidgeCV(alphas=alphas, cv=6, alpha_per_target=True)
    with pytest.raises(ValueError, match=msg):
        ridge_cv.fit(X, y)


def _test_ridge_diabetes(sparse_container):
    X = X_diabetes if sparse_container is None else sparse_container(X_diabetes)
    ridge = Ridge(fit_intercept=False)
    ridge.fit(X, y_diabetes)
    return np.round(ridge.score(X, y_diabetes), 5)


def _test_multi_ridge_diabetes(sparse_container):
    # simulate several responses
    X = X_diabetes if sparse_container is None else sparse_container(X_diabetes)
    Y = np.vstack((y_diabetes, y_diabetes)).T
    n_features = X_diabetes.shape[1]

    ridge = Ridge(fit_intercept=False)
    ridge.fit(X, Y)
    assert ridge.coef_.shape == (2, n_features)
    Y_pred = ridge.predict(X)
    ridge.fit(X, y_diabetes)
    y_pred = ridge.predict(X)
    assert_array_almost_equal(np.vstack((y_pred, y_pred)).T, Y_pred, decimal=3)


def _test_ridge_classifiers(sparse_container):
    n_classes = np.unique(y_iris).shape[0]
    n_features = X_iris.shape[1]
    X = X_iris if sparse_container is None else sparse_container(X_iris)

    for reg in (RidgeClassifier(), RidgeClassifierCV()):
        reg.fit(X, y_iris)
        assert reg.coef_.shape == (n_classes, n_features)
        y_pred = reg.predict(X)
        assert np.mean(y_iris == y_pred) > 0.79

    cv = KFold(5)
    reg = RidgeClassifierCV(cv=cv)
    reg.fit(X, y_iris)
    y_pred = reg.predict(X)
    assert np.mean(y_iris == y_pred) >= 0.8


@pytest.mark.parametrize("scoring", [None, "accuracy", _accuracy_callable])
@pytest.mark.parametrize("cv", [None, KFold(5)])
@pytest.mark.parametrize("sparse_container", [None] + CSR_CONTAINERS)
def test_ridge_classifier_with_scoring(sparse_container, scoring, cv):
    # non-regression test for #14672
    # check that RidgeClassifierCV works with all sort of scoring and
    # cross-validation
    X = X_iris if sparse_container is None else sparse_container(X_iris)
    scoring_ = make_scorer(scoring) if callable(scoring) else scoring
    clf = RidgeClassifierCV(scoring=scoring_, cv=cv)
    # Smoke test to check that fit/predict does not raise error
    clf.fit(X, y_iris).predict(X)


@pytest.mark.parametrize("cv", [None, KFold(5)])
@pytest.mark.parametrize("sparse_container", [None] + CSR_CONTAINERS)
def test_ridge_regression_custom_scoring(sparse_container, cv):
    # check that custom scoring is working as expected
    # check the tie breaking strategy (keep the first alpha tried)

    def _dummy_score(y_test, y_pred, **kwargs):
        return 0.42

    X = X_iris if sparse_container is None else sparse_container(X_iris)
    alphas = np.logspace(-2, 2, num=5)
    clf = RidgeClassifierCV(alphas=alphas, scoring=make_scorer(_dummy_score), cv=cv)
    clf.fit(X, y_iris)
    assert clf.best_score_ == pytest.approx(0.42)
    # In case of tie score, the first alphas will be kept
    assert clf.alpha_ == pytest.approx(alphas[0])


def _test_tolerance(sparse_container):
    X = X_diabetes if sparse_container is None else sparse_container(X_diabetes)

    ridge = Ridge(tol=1e-5, fit_intercept=False)
    ridge.fit(X, y_diabetes)
    score = ridge.score(X, y_diabetes)

    ridge2 = Ridge(tol=1e-3, fit_intercept=False)
    ridge2.fit(X, y_diabetes)
    score2 = ridge2.score(X, y_diabetes)

    assert score >= score2


def check_array_api_attributes(name, estimator, array_namespace, device, dtype_name):
    xp = _array_api_for_tests(array_namespace, device)

    X_iris_np = X_iris.astype(dtype_name)
    y_iris_np = y_iris.astype(dtype_name)

    X_iris_xp = xp.asarray(X_iris_np, device=device)
    y_iris_xp = xp.asarray(y_iris_np, device=device)

    estimator.fit(X_iris_np, y_iris_np)
    coef_np = estimator.coef_
    intercept_np = estimator.intercept_

    with config_context(array_api_dispatch=True):
        estimator_xp = clone(estimator).fit(X_iris_xp, y_iris_xp)
        coef_xp = estimator_xp.coef_
        assert coef_xp.shape == (4,)
        assert coef_xp.dtype == X_iris_xp.dtype

        assert_allclose(
            _convert_to_numpy(coef_xp, xp=xp),
            coef_np,
            atol=_atol_for_type(dtype_name),
        )
        intercept_xp = estimator_xp.intercept_
        assert intercept_xp.shape == ()
        assert intercept_xp.dtype == X_iris_xp.dtype

        assert_allclose(
            _convert_to_numpy(intercept_xp, xp=xp),
            intercept_np,
            atol=_atol_for_type(dtype_name),
        )


@pytest.mark.parametrize(
    "array_namespace, device, dtype_name",
    yield_namespace_device_dtype_combinations(),
    ids=_get_namespace_device_dtype_ids,
)
@pytest.mark.parametrize(
    "check",
    [check_array_api_input_and_values, check_array_api_attributes],
    ids=_get_check_estimator_ids,
)
@pytest.mark.parametrize(
    "estimator",
    [Ridge(solver="svd")],
    ids=_get_check_estimator_ids,
)
def test_ridge_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", yield_namespaces(include_numpy_namespaces=False)
)
def test_array_api_error_and_warnings_for_solver_parameter(array_namespace):
    xp = _array_api_for_tests(array_namespace, device=None)

    X_iris_xp = xp.asarray(X_iris[:5])
    y_iris_xp = xp.asarray(y_iris[:5])

    available_solvers = Ridge._parameter_constraints["solver"][0].options
    for solver in available_solvers - {"auto", "svd"}:
        ridge = Ridge(solver=solver, positive=solver == "lbfgs")
        expected_msg = (
            f"Array API dispatch to namespace {xp.__name__} only supports "
            f"solver 'svd'. Got '{solver}'."
        )

        with pytest.raises(ValueError, match=expected_msg):
            with config_context(array_api_dispatch=True):
                ridge.fit(X_iris_xp, y_iris_xp)

    ridge = Ridge(solver="auto", positive=True)
    expected_msg = (
        "The solvers that support positive fitting do not support "
        f"Array API dispatch to namespace {xp.__name__}. Please "
        "either disable Array API dispatch, or use a numpy-like "
        "namespace, or set `positive=False`."
    )

    with pytest.raises(ValueError, match=expected_msg):
        with config_context(array_api_dispatch=True):
            ridge.fit(X_iris_xp, y_iris_xp)

    ridge = Ridge()
    expected_msg = (
        f"Using Array API dispatch to namespace {xp.__name__} with `solver='auto'` "
        "will result in using the solver 'svd'. The results may differ from those "
        "when using a Numpy array, because in that case the preferred solver would "
        "be cholesky. Set `solver='svd'` to suppress this warning."
    )
    with pytest.warns(UserWarning, match=expected_msg):
        with config_context(array_api_dispatch=True):
            ridge.fit(X_iris_xp, y_iris_xp)


@pytest.mark.parametrize("array_namespace", sorted(_NUMPY_NAMESPACE_NAMES))
def test_array_api_numpy_namespace_no_warning(array_namespace):
    xp = _array_api_for_tests(array_namespace, device=None)

    X_iris_xp = xp.asarray(X_iris[:5])
    y_iris_xp = xp.asarray(y_iris[:5])

    ridge = Ridge()
    expected_msg = (
        "Results might be different than when Array API dispatch is "
        "disabled, or when a numpy-like namespace is used"
    )

    with warnings.catch_warnings():
        warnings.filterwarnings("error", message=expected_msg, category=UserWarning)
        with config_context(array_api_dispatch=True):
            ridge.fit(X_iris_xp, y_iris_xp)

    # All numpy namespaces are compatible with all solver, in particular
    # solvers that support `positive=True` (like 'lbfgs') should work.
    with config_context(array_api_dispatch=True):
        Ridge(solver="auto", positive=True).fit(X_iris_xp, y_iris_xp)


@pytest.mark.parametrize(
    "test_func",
    (
        _test_ridge_loo,
        _test_ridge_cv,
        _test_ridge_diabetes,
        _test_multi_ridge_diabetes,
        _test_ridge_classifiers,
        _test_tolerance,
    ),
)
@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
def test_dense_sparse(test_func, csr_container):
    # test dense matrix
    ret_dense = test_func(None)
    # test sparse matrix
    ret_sparse = test_func(csr_container)
    # test that the outputs are the same
    if ret_dense is not None and ret_sparse is not None:
        assert_array_almost_equal(ret_dense, ret_sparse, decimal=3)


def test_class_weights():
    # Test class weights.
    X = np.array([[-1.0, -1.0], [-1.0, 0], [-0.8, -1.0], [1.0, 1.0], [1.0, 0.0]])
    y = [1, 1, 1, -1, -1]

    reg = RidgeClassifier(class_weight=None)
    reg.fit(X, y)
    assert_array_equal(reg.predict([[0.2, -1.0]]), np.array([1]))

    # we give a small weights to class 1
    reg = RidgeClassifier(class_weight={1: 0.001})
    reg.fit(X, y)

    # now the hyperplane should rotate clock-wise and
    # the prediction on this point should shift
    assert_array_equal(reg.predict([[0.2, -1.0]]), np.array([-1]))

    # check if class_weight = 'balanced' can handle negative labels.
    reg = RidgeClassifier(class_weight="balanced")
    reg.fit(X, y)
    assert_array_equal(reg.predict([[0.2, -1.0]]), np.array([1]))

    # class_weight = 'balanced', and class_weight = None should return
    # same values when y has equal number of all labels
    X = np.array([[-1.0, -1.0], [-1.0, 0], [-0.8, -1.0], [1.0, 1.0]])
    y = [1, 1, -1, -1]
    reg = RidgeClassifier(class_weight=None)
    reg.fit(X, y)
    rega = RidgeClassifier(class_weight="balanced")
    rega.fit(X, y)
    assert len(rega.classes_) == 2
    assert_array_almost_equal(reg.coef_, rega.coef_)
    assert_array_almost_equal(reg.intercept_, rega.intercept_)


@pytest.mark.parametrize("reg", (RidgeClassifier, RidgeClassifierCV))
def test_class_weight_vs_sample_weight(reg):
    """Check class_weights resemble sample_weights behavior."""

    # Iris is balanced, so no effect expected for using 'balanced' weights
    reg1 = reg()
    reg1.fit(iris.data, iris.target)
    reg2 = reg(class_weight="balanced")
    reg2.fit(iris.data, iris.target)
    assert_almost_equal(reg1.coef_, reg2.coef_)

    # Inflate importance of class 1, check against user-defined weights
    sample_weight = np.ones(iris.target.shape)
    sample_weight[iris.target == 1] *= 100
    class_weight = {0: 1.0, 1: 100.0, 2: 1.0}
    reg1 = reg()
    reg1.fit(iris.data, iris.target, sample_weight)
    reg2 = reg(class_weight=class_weight)
    reg2.fit(iris.data, iris.target)
    assert_almost_equal(reg1.coef_, reg2.coef_)

    # Check that sample_weight and class_weight are multiplicative
    reg1 = reg()
    reg1.fit(iris.data, iris.target, sample_weight**2)
    reg2 = reg(class_weight=class_weight)
    reg2.fit(iris.data, iris.target, sample_weight)
    assert_almost_equal(reg1.coef_, reg2.coef_)


def test_class_weights_cv():
    # Test class weights for cross validated ridge classifier.
    X = np.array([[-1.0, -1.0], [-1.0, 0], [-0.8, -1.0], [1.0, 1.0], [1.0, 0.0]])
    y = [1, 1, 1, -1, -1]

    reg = RidgeClassifierCV(class_weight=None, alphas=[0.01, 0.1, 1])
    reg.fit(X, y)

    # we give a small weights to class 1
    reg = RidgeClassifierCV(class_weight={1: 0.001}, alphas=[0.01, 0.1, 1, 10])
    reg.fit(X, y)

    assert_array_equal(reg.predict([[-0.2, 2]]), np.array([-1]))


@pytest.mark.parametrize(
    "scoring", [None, "neg_mean_squared_error", _mean_squared_error_callable]
)
def test_ridgecv_store_cv_results(scoring):
    rng = np.random.RandomState(42)

    n_samples = 8
    n_features = 5
    x = rng.randn(n_samples, n_features)
    alphas = [1e-1, 1e0, 1e1]
    n_alphas = len(alphas)

    scoring_ = make_scorer(scoring) if callable(scoring) else scoring

    r = RidgeCV(alphas=alphas, cv=None, store_cv_results=True, scoring=scoring_)

    # with len(y.shape) == 1
    y = rng.randn(n_samples)
    r.fit(x, y)
    assert r.cv_results_.shape == (n_samples, n_alphas)

    # with len(y.shape) == 2
    n_targets = 3
    y = rng.randn(n_samples, n_targets)
    r.fit(x, y)
    assert r.cv_results_.shape == (n_samples, n_targets, n_alphas)

    r = RidgeCV(cv=3, store_cv_results=True, scoring=scoring)
    with pytest.raises(ValueError, match="cv!=None and store_cv_results"):
        r.fit(x, y)


@pytest.mark.parametrize("scoring", [None, "accuracy", _accuracy_callable])
def test_ridge_classifier_cv_store_cv_results(scoring):
    x = np.array([[-1.0, -1.0], [-1.0, 0], [-0.8, -1.0], [1.0, 1.0], [1.0, 0.0]])
    y = np.array([1, 1, 1, -1, -1])

    n_samples = x.shape[0]
    alphas = [1e-1, 1e0, 1e1]
    n_alphas = len(alphas)

    scoring_ = make_scorer(scoring) if callable(scoring) else scoring

    r = RidgeClassifierCV(
        alphas=alphas, cv=None, store_cv_results=True, scoring=scoring_
    )

    # with len(y.shape) == 1
    n_targets = 1
    r.fit(x, y)
    assert r.cv_results_.shape == (n_samples, n_targets, n_alphas)

    # with len(y.shape) == 2
    y = np.array(
        [[1, 1, 1, -1, -1], [1, -1, 1, -1, 1], [-1, -1, 1, -1, -1]]
    ).transpose()
    n_targets = y.shape[1]
    r.fit(x, y)
    assert r.cv_results_.shape == (n_samples, n_targets, n_alphas)


@pytest.mark.parametrize("Estimator", [RidgeCV, RidgeClassifierCV])
def test_ridgecv_alphas_conversion(Estimator):
    rng = np.random.RandomState(0)
    alphas = (0.1, 1.0, 10.0)

    n_samples, n_features = 5, 5
    if Estimator is RidgeCV:
        y = rng.randn(n_samples)
    else:
        y = rng.randint(0, 2, n_samples)
    X = rng.randn(n_samples, n_features)

    ridge_est = Estimator(alphas=alphas)
    assert ridge_est.alphas is alphas, (
        f"`alphas` was mutated in `{Estimator.__name__}.__init__`"
    )

    ridge_est.fit(X, y)
    assert_array_equal(ridge_est.alphas, np.asarray(alphas))


@pytest.mark.parametrize("cv", [None, 3])
@pytest.mark.parametrize("Estimator", [RidgeCV, RidgeClassifierCV])
def test_ridgecv_alphas_zero(cv, Estimator):
    """Check alpha=0.0 raises error only when `cv=None`."""
    rng = np.random.RandomState(0)
    alphas = (0.0, 1.0, 10.0)

    n_samples, n_features = 5, 5
    if Estimator is RidgeCV:
        y = rng.randn(n_samples)
    else:
        y = rng.randint(0, 2, n_samples)
    X = rng.randn(n_samples, n_features)

    ridge_est = Estimator(alphas=alphas, cv=cv)
    if cv is None:
        with pytest.raises(ValueError, match=r"alphas\[0\] == 0.0, must be > 0.0."):
            ridge_est.fit(X, y)
    else:
        ridge_est.fit(X, y)


def test_ridgecv_sample_weight():
    rng = np.random.RandomState(0)
    alphas = (0.1, 1.0, 10.0)

    # There are different algorithms for n_samples > n_features
    # and the opposite, so test them both.
    for n_samples, n_features in ((6, 5), (5, 10)):
        y = rng.randn(n_samples)
        X = rng.randn(n_samples, n_features)
        sample_weight = 1.0 + rng.rand(n_samples)

        cv = KFold(5)
        ridgecv = RidgeCV(alphas=alphas, cv=cv)
        ridgecv.fit(X, y, sample_weight=sample_weight)

        # Check using GridSearchCV directly
        parameters = {"alpha": alphas}
        gs = GridSearchCV(Ridge(), parameters, cv=cv)
        gs.fit(X, y, sample_weight=sample_weight)

        assert ridgecv.alpha_ == gs.best_estimator_.alpha
        assert_array_almost_equal(ridgecv.coef_, gs.best_estimator_.coef_)


def test_raises_value_error_if_sample_weights_greater_than_1d():
    # Sample weights must be either scalar or 1D

    n_sampless = [2, 3]
    n_featuress = [3, 2]

    rng = np.random.RandomState(42)

    for n_samples, n_features in zip(n_sampless, n_featuress):
        X = rng.randn(n_samples, n_features)
        y = rng.randn(n_samples)
        sample_weights_OK = rng.randn(n_samples) ** 2 + 1
        sample_weights_OK_1 = 1.0
        sample_weights_OK_2 = 2.0
        sample_weights_not_OK = sample_weights_OK[:, np.newaxis]
        sample_weights_not_OK_2 = sample_weights_OK[np.newaxis, :]

        ridge = Ridge(alpha=1)

        # make sure the "OK" sample weights actually work
        ridge.fit(X, y, sample_weights_OK)
        ridge.fit(X, y, sample_weights_OK_1)
        ridge.fit(X, y, sample_weights_OK_2)

        def fit_ridge_not_ok():
            ridge.fit(X, y, sample_weights_not_OK)

        def fit_ridge_not_ok_2():
            ridge.fit(X, y, sample_weights_not_OK_2)

        err_msg = "Sample weights must be 1D array or scalar"
        with pytest.raises(ValueError, match=err_msg):
            fit_ridge_not_ok()

        err_msg = "Sample weights must be 1D array or scalar"
        with pytest.raises(ValueError, match=err_msg):
            fit_ridge_not_ok_2()


@pytest.mark.parametrize("n_samples,n_features", [[2, 3], [3, 2]])
@pytest.mark.parametrize(
    "sparse_container",
    COO_CONTAINERS + CSC_CONTAINERS + CSR_CONTAINERS + DOK_CONTAINERS + LIL_CONTAINERS,
)
def test_sparse_design_with_sample_weights(n_samples, n_features, sparse_container):
    # Sample weights must work with sparse matrices
    rng = np.random.RandomState(42)

    sparse_ridge = Ridge(alpha=1.0, fit_intercept=False)
    dense_ridge = Ridge(alpha=1.0, fit_intercept=False)

    X = rng.randn(n_samples, n_features)
    y = rng.randn(n_samples)
    sample_weights = rng.randn(n_samples) ** 2 + 1
    X_sparse = sparse_container(X)
    sparse_ridge.fit(X_sparse, y, sample_weight=sample_weights)
    dense_ridge.fit(X, y, sample_weight=sample_weights)

    assert_array_almost_equal(sparse_ridge.coef_, dense_ridge.coef_, decimal=6)


def test_ridgecv_int_alphas():
    X = np.array([[-1.0, -1.0], [-1.0, 0], [-0.8, -1.0], [1.0, 1.0], [1.0, 0.0]])
    y = [1, 1, 1, -1, -1]

    # Integers
    ridge = RidgeCV(alphas=(1, 10, 100))
    ridge.fit(X, y)


@pytest.mark.parametrize("Estimator", [RidgeCV, RidgeClassifierCV])
@pytest.mark.parametrize(
    "params, err_type, err_msg",
    [
        ({"alphas": (1, -1, -100)}, ValueError, r"alphas\[1\] == -1, must be > 0.0"),
        (
            {"alphas": (-0.1, -1.0, -10.0)},
            ValueError,
            r"alphas\[0\] == -0.1, must be > 0.0",
        ),
        (
            {"alphas": (1, 1.0, "1")},
            TypeError,
            r"alphas\[2\] must be an instance of float, not str",
        ),
    ],
)
def test_ridgecv_alphas_validation(Estimator, params, err_type, err_msg):
    """Check the `alphas` validation in RidgeCV and RidgeClassifierCV."""

    n_samples, n_features = 5, 5
    X = rng.randn(n_samples, n_features)
    y = rng.randint(0, 2, n_samples)

    with pytest.raises(err_type, match=err_msg):
        Estimator(**params).fit(X, y)


@pytest.mark.parametrize("Estimator", [RidgeCV, RidgeClassifierCV])
def test_ridgecv_alphas_scalar(Estimator):
    """Check the case when `alphas` is a scalar.
    This case was supported in the past when `alphas` where converted
    into array in `__init__`.
    We add this test to ensure backward compatibility.
    """

    n_samples, n_features = 5, 5
    X = rng.randn(n_samples, n_features)
    if Estimator is RidgeCV:
        y = rng.randn(n_samples)
    else:
        y = rng.randint(0, 2, n_samples)

    Estimator(alphas=1).fit(X, y)


def test_sparse_cg_max_iter():
    reg = Ridge(solver="sparse_cg", max_iter=1)
    reg.fit(X_diabetes, y_diabetes)
    assert reg.coef_.shape[0] == X_diabetes.shape[1]


@pytest.mark.filterwarnings("ignore::sklearn.exceptions.ConvergenceWarning")
def test_n_iter():
    # Test that self.n_iter_ is correct.
    n_targets = 2
    X, y = X_diabetes, y_diabetes
    y_n = np.tile(y, (n_targets, 1)).T

    for max_iter in range(1, 4):
        for solver in ("sag", "saga", "lsqr"):
            reg = Ridge(solver=solver, max_iter=max_iter, tol=1e-12)
            reg.fit(X, y_n)
            assert_array_equal(reg.n_iter_, np.tile(max_iter, n_targets))

    for solver in ("sparse_cg", "svd", "cholesky"):
        reg = Ridge(solver=solver, max_iter=1, tol=1e-1)
        reg.fit(X, y_n)
        assert reg.n_iter_ is None


@pytest.mark.parametrize("solver", ["lsqr", "sparse_cg", "lbfgs", "auto"])
@pytest.mark.parametrize("with_sample_weight", [True, False])
@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
def test_ridge_fit_intercept_sparse(
    solver, with_sample_weight, global_random_seed, csr_container
):
    """Check that ridge finds the same coefs and intercept on dense and sparse input
    in the presence of sample weights.

    For now only sparse_cg and lbfgs can correctly fit an intercept
    with sparse X with default tol and max_iter.
    'sag' is tested separately in test_ridge_fit_intercept_sparse_sag because it
    requires more iterations and should raise a warning if default max_iter is used.
    Other solvers raise an exception, as checked in
    test_ridge_fit_intercept_sparse_error
    """
    positive = solver == "lbfgs"
    X, y = _make_sparse_offset_regression(
        n_features=20, random_state=global_random_seed, positive=positive
    )

    sample_weight = None
    if with_sample_weight:
        rng = np.random.RandomState(global_random_seed)
        sample_weight = 1.0 + rng.uniform(size=X.shape[0])

    # "auto" should switch to "sparse_cg" when X is sparse
    # so the reference we use for both ("auto" and "sparse_cg") is
    # Ridge(solver="sparse_cg"), fitted using the dense representation (note
    # that "sparse_cg" can fit sparse or dense data)
    dense_solver = "sparse_cg" if solver == "auto" else solver
    dense_ridge = Ridge(solver=dense_solver, tol=1e-12, positive=positive)
    sparse_ridge = Ridge(solver=solver, tol=1e-12, positive=positive)

    dense_ridge.fit(X, y, sample_weight=sample_weight)
    sparse_ridge.fit(csr_container(X), y, sample_weight=sample_weight)

    assert_allclose(dense_ridge.intercept_, sparse_ridge.intercept_)
    assert_allclose(dense_ridge.coef_, sparse_ridge.coef_, rtol=5e-7)


@pytest.mark.parametrize("solver", ["saga", "svd", "cholesky"])
@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
def test_ridge_fit_intercept_sparse_error(solver, csr_container):
    X, y = _make_sparse_offset_regression(n_features=20, random_state=0)
    X_csr = csr_container(X)
    sparse_ridge = Ridge(solver=solver)
    err_msg = "solver='{}' does not support".format(solver)
    with pytest.raises(ValueError, match=err_msg):
        sparse_ridge.fit(X_csr, y)


@pytest.mark.parametrize("with_sample_weight", [True, False])
@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
def test_ridge_fit_intercept_sparse_sag(
    with_sample_weight, global_random_seed, csr_container
):
    X, y = _make_sparse_offset_regression(
        n_features=5, n_samples=20, random_state=global_random_seed, X_offset=5.0
    )
    if with_sample_weight:
        rng = np.random.RandomState(global_random_seed)
        sample_weight = 1.0 + rng.uniform(size=X.shape[0])
    else:
        sample_weight = None
    X_csr = csr_container(X)

    params = dict(
        alpha=1.0, solver="sag", fit_intercept=True, tol=1e-10, max_iter=100000
    )
    dense_ridge = Ridge(**params)
    sparse_ridge = Ridge(**params)
    dense_ridge.fit(X, y, sample_weight=sample_weight)
    with warnings.catch_warnings():
        warnings.simplefilter("error", UserWarning)
        sparse_ridge.fit(X_csr, y, sample_weight=sample_weight)
    assert_allclose(dense_ridge.intercept_, sparse_ridge.intercept_, rtol=1e-4)
    assert_allclose(dense_ridge.coef_, sparse_ridge.coef_, rtol=1e-4)
    with pytest.warns(UserWarning, match='"sag" solver requires.*'):
        Ridge(solver="sag", fit_intercept=True, tol=1e-3, max_iter=None).fit(X_csr, y)


@pytest.mark.parametrize("return_intercept", [False, True])
@pytest.mark.parametrize("sample_weight", [None, np.ones(1000)])
@pytest.mark.parametrize("container", [np.array] + CSR_CONTAINERS)
@pytest.mark.parametrize(
    "solver", ["auto", "sparse_cg", "cholesky", "lsqr", "sag", "saga", "lbfgs"]
)
def test_ridge_regression_check_arguments_validity(
    return_intercept, sample_weight, container, solver
):
    """check if all combinations of arguments give valid estimations"""

    # test excludes 'svd' solver because it raises exception for sparse inputs

    rng = check_random_state(42)
    X = rng.rand(1000, 3)
    true_coefs = [1, 2, 0.1]
    y = np.dot(X, true_coefs)
    true_intercept = 0.0
    if return_intercept:
        true_intercept = 10000.0
    y += true_intercept
    X_testing = container(X)

    alpha, tol = 1e-3, 1e-6
    atol = 1e-3 if _IS_32BIT else 1e-4

    positive = solver == "lbfgs"

    if solver not in ["sag", "auto"] and return_intercept:
        with pytest.raises(ValueError, match="In Ridge, only 'sag' solver"):
            ridge_regression(
                X_testing,
                y,
                alpha=alpha,
                solver=solver,
                sample_weight=sample_weight,
                return_intercept=return_intercept,
                positive=positive,
                tol=tol,
            )
        return

    out = ridge_regression(
        X_testing,
        y,
        alpha=alpha,
        solver=solver,
        sample_weight=sample_weight,
        positive=positive,
        return_intercept=return_intercept,
        tol=tol,
    )

    if return_intercept:
        coef, intercept = out
        assert_allclose(coef, true_coefs, rtol=0, atol=atol)
        assert_allclose(intercept, true_intercept, rtol=0, atol=atol)
    else:
        assert_allclose(out, true_coefs, rtol=0, atol=atol)


@pytest.mark.parametrize(
    "solver", ["svd", "sparse_cg", "cholesky", "lsqr", "sag", "saga", "lbfgs"]
)
def test_dtype_match(solver):
    rng = np.random.RandomState(0)
    alpha = 1.0
    positive = solver == "lbfgs"

    n_samples, n_features = 6, 5
    X_64 = rng.randn(n_samples, n_features)
    y_64 = rng.randn(n_samples)
    X_32 = X_64.astype(np.float32)
    y_32 = y_64.astype(np.float32)

    tol = 2 * np.finfo(np.float32).resolution
    # Check type consistency 32bits
    ridge_32 = Ridge(
        alpha=alpha, solver=solver, max_iter=500, tol=tol, positive=positive
    )
    ridge_32.fit(X_32, y_32)
    coef_32 = ridge_32.coef_

    # Check type consistency 64 bits
    ridge_64 = Ridge(
        alpha=alpha, solver=solver, max_iter=500, tol=tol, positive=positive
    )
    ridge_64.fit(X_64, y_64)
    coef_64 = ridge_64.coef_

    # Do the actual checks at once for easier debug
    assert coef_32.dtype == X_32.dtype
    assert coef_64.dtype == X_64.dtype
    assert ridge_32.predict(X_32).dtype == X_32.dtype
    assert ridge_64.predict(X_64).dtype == X_64.dtype
    assert_allclose(ridge_32.coef_, ridge_64.coef_, rtol=1e-4, atol=5e-4)


def test_dtype_match_cholesky():
    # Test different alphas in cholesky solver to ensure full coverage.
    # This test is separated from test_dtype_match for clarity.
    rng = np.random.RandomState(0)
    alpha = np.array([1.0, 0.5])

    n_samples, n_features, n_target = 6, 7, 2
    X_64 = rng.randn(n_samples, n_features)
    y_64 = rng.randn(n_samples, n_target)
    X_32 = X_64.astype(np.float32)
    y_32 = y_64.astype(np.float32)

    # Check type consistency 32bits
    ridge_32 = Ridge(alpha=alpha, solver="cholesky")
    ridge_32.fit(X_32, y_32)
    coef_32 = ridge_32.coef_

    # Check type consistency 64 bits
    ridge_64 = Ridge(alpha=alpha, solver="cholesky")
    ridge_64.fit(X_64, y_64)
    coef_64 = ridge_64.coef_

    # Do all the checks at once, like this is easier to debug
    assert coef_32.dtype == X_32.dtype
    assert coef_64.dtype == X_64.dtype
    assert ridge_32.predict(X_32).dtype == X_32.dtype
    assert ridge_64.predict(X_64).dtype == X_64.dtype
    assert_almost_equal(ridge_32.coef_, ridge_64.coef_, decimal=5)


@pytest.mark.parametrize(
    "solver", ["svd", "cholesky", "lsqr", "sparse_cg", "sag", "saga", "lbfgs"]
)
@pytest.mark.parametrize("seed", range(1))
def test_ridge_regression_dtype_stability(solver, seed):
    random_state = np.random.RandomState(seed)
    n_samples, n_features = 6, 5
    X = random_state.randn(n_samples, n_features)
    coef = random_state.randn(n_features)
    y = np.dot(X, coef) + 0.01 * random_state.randn(n_samples)
    alpha = 1.0
    positive = solver == "lbfgs"
    results = dict()
    # XXX: Sparse CG seems to be far less numerically stable than the
    # others, maybe we should not enable float32 for this one.
    atol = 1e-3 if solver == "sparse_cg" else 1e-5
    for current_dtype in (np.float32, np.float64):
        results[current_dtype] = ridge_regression(
            X.astype(current_dtype),
            y.astype(current_dtype),
            alpha=alpha,
            solver=solver,
            random_state=random_state,
            sample_weight=None,
            positive=positive,
            max_iter=500,
            tol=1e-10,
            return_n_iter=False,
            return_intercept=False,
        )

    assert results[np.float32].dtype == np.float32
    assert results[np.float64].dtype == np.float64
    assert_allclose(results[np.float32], results[np.float64], atol=atol)


def test_ridge_sag_with_X_fortran():
    # check that Fortran array are converted when using SAG solver
    X, y = make_regression(random_state=42)
    # for the order of X and y to not be C-ordered arrays
    X = np.asfortranarray(X)
    X = X[::2, :]
    y = y[::2]
    Ridge(solver="sag").fit(X, y)


@pytest.mark.parametrize(
    "Classifier, params",
    [
        (RidgeClassifier, {}),
        (RidgeClassifierCV, {"cv": None}),
        (RidgeClassifierCV, {"cv": 3}),
    ],
)
def test_ridgeclassifier_multilabel(Classifier, params):
    """Check that multilabel classification is supported and give meaningful
    results."""
    X, y = make_multilabel_classification(n_classes=1, random_state=0)
    y = y.reshape(-1, 1)
    Y = np.concatenate([y, y], axis=1)
    clf = Classifier(**params).fit(X, Y)
    Y_pred = clf.predict(X)

    assert Y_pred.shape == Y.shape
    assert_array_equal(Y_pred[:, 0], Y_pred[:, 1])
    Ridge(solver="sag").fit(X, y)


@pytest.mark.parametrize("solver", ["auto", "lbfgs"])
@pytest.mark.parametrize("fit_intercept", [True, False])
@pytest.mark.parametrize("alpha", [1e-3, 1e-2, 0.1, 1.0])
def test_ridge_positive_regression_test(solver, fit_intercept, alpha):
    """Test that positive Ridge finds true positive coefficients."""
    X = np.array([[1, 2], [3, 4], [5, 6], [7, 8]])
    coef = np.array([1, -10])
    if fit_intercept:
        intercept = 20
        y = X.dot(coef) + intercept
    else:
        y = X.dot(coef)

    model = Ridge(
        alpha=alpha, positive=True, solver=solver, fit_intercept=fit_intercept
    )
    model.fit(X, y)
    assert np.all(model.coef_ >= 0)


@pytest.mark.parametrize("fit_intercept", [True, False])
@pytest.mark.parametrize("alpha", [1e-3, 1e-2, 0.1, 1.0])
def test_ridge_ground_truth_positive_test(fit_intercept, alpha):
    """Test that Ridge w/wo positive converges to the same solution.

    Ridge with positive=True and positive=False must give the same
    when the ground truth coefs are all positive.
    """
    rng = np.random.RandomState(42)
    X = rng.randn(300, 100)
    coef = rng.uniform(0.1, 1.0, size=X.shape[1])
    if fit_intercept:
        intercept = 1
        y = X @ coef + intercept
    else:
        y = X @ coef
    y += rng.normal(size=X.shape[0]) * 0.01

    results = []
    for positive in [True, False]:
        model = Ridge(
            alpha=alpha, positive=positive, fit_intercept=fit_intercept, tol=1e-10
        )
        results.append(model.fit(X, y).coef_)
    assert_allclose(*results, atol=1e-6, rtol=0)


@pytest.mark.parametrize(
    "solver", ["svd", "cholesky", "lsqr", "sparse_cg", "sag", "saga"]
)
def test_ridge_positive_error_test(solver):
    """Test input validation for positive argument in Ridge."""
    alpha = 0.1
    X = np.array([[1, 2], [3, 4]])
    coef = np.array([1, -1])
    y = X @ coef

    model = Ridge(alpha=alpha, positive=True, solver=solver, fit_intercept=False)
    with pytest.raises(ValueError, match="does not support positive"):
        model.fit(X, y)

    with pytest.raises(ValueError, match="only 'lbfgs' solver can be used"):
        _, _ = ridge_regression(
            X, y, alpha, positive=True, solver=solver, return_intercept=False
        )


@pytest.mark.parametrize("alpha", [1e-3, 1e-2, 0.1, 1.0])
def test_positive_ridge_loss(alpha):
    """Check ridge loss consistency when positive argument is enabled."""
    X, y = make_regression(n_samples=300, n_features=300, random_state=42)
    alpha = 0.10
    n_checks = 100

    def ridge_loss(model, random_state=None, noise_scale=1e-8):
        intercept = model.intercept_
        if random_state is not None:
            rng = np.random.RandomState(random_state)
            coef = model.coef_ + rng.uniform(0, noise_scale, size=model.coef_.shape)
        else:
            coef = model.coef_

        return 0.5 * np.sum((y - X @ coef - intercept) ** 2) + 0.5 * alpha * np.sum(
            coef**2
        )

    model = Ridge(alpha=alpha).fit(X, y)
    model_positive = Ridge(alpha=alpha, positive=True).fit(X, y)

    # Check 1:
    #   Loss for solution found by Ridge(positive=False)
    #   is lower than that for solution found by Ridge(positive=True)
    loss = ridge_loss(model)
    loss_positive = ridge_loss(model_positive)
    assert loss <= loss_positive

    # Check 2:
    #   Loss for solution found by Ridge(positive=True)
    #   is lower than that for small random positive perturbation
    #   of the positive solution.
    for random_state in range(n_checks):
        loss_perturbed = ridge_loss(model_positive, random_state=random_state)
        assert loss_positive <= loss_perturbed


@pytest.mark.parametrize("alpha", [1e-3, 1e-2, 0.1, 1.0])
def test_lbfgs_solver_consistency(alpha):
    """Test that LBGFS gets almost the same coef of svd when positive=False."""
    X, y = make_regression(n_samples=300, n_features=300, random_state=42)
    y = np.expand_dims(y, 1)
    alpha = np.asarray([alpha])
    config = {
        "positive": False,
        "tol": 1e-16,
        "max_iter": 500000,
    }

    coef_lbfgs = _solve_lbfgs(X, y, alpha, **config)
    coef_cholesky = _solve_svd(X, y, alpha)
    assert_allclose(coef_lbfgs, coef_cholesky, atol=1e-4, rtol=0)


def test_lbfgs_solver_error():
    """Test that LBFGS solver raises ConvergenceWarning."""
    X = np.array([[1, -1], [1, 1]])
    y = np.array([-1e10, 1e10])

    model = Ridge(
        alpha=0.01,
        solver="lbfgs",
        fit_intercept=False,
        tol=1e-12,
        positive=True,
        max_iter=1,
    )
    with pytest.warns(ConvergenceWarning, match="lbfgs solver did not converge"):
        model.fit(X, y)


@pytest.mark.parametrize("fit_intercept", [False, True])
@pytest.mark.parametrize("sparse_container", [None] + CSR_CONTAINERS)
@pytest.mark.parametrize("data", ["tall", "wide"])
@pytest.mark.parametrize("solver", SOLVERS + ["lbfgs"])
def test_ridge_sample_weight_consistency(
    fit_intercept, sparse_container, data, solver, global_random_seed
):
    """Test that the impact of sample_weight is consistent.

    Note that this test is stricter than the common test
    check_sample_weight_equivalence alone.
    """
    # filter out solver that do not support sparse input
    if sparse_container is not None:
        if solver == "svd" or (solver in ("cholesky", "saga") and fit_intercept):
            pytest.skip("unsupported configuration")

    # XXX: this test is quite sensitive to the seed used to generate the data:
    # ideally we would like the test to pass for any global_random_seed but this is not
    # the case at the moment.
    rng = np.random.RandomState(42)
    n_samples = 12
    if data == "tall":
        n_features = n_samples // 2
    else:
        n_features = n_samples * 2

    X = rng.rand(n_samples, n_features)
    y = rng.rand(n_samples)
    if sparse_container is not None:
        X = sparse_container(X)
    params = dict(
        fit_intercept=fit_intercept,
        alpha=1.0,
        solver=solver,
        positive=(solver == "lbfgs"),
        random_state=global_random_seed,  # for sag/saga
        tol=1e-12,
    )

    # 1) sample_weight=np.ones(..) should be equivalent to sample_weight=None,
    # a special case of check_sample_weight_equivalence(name, reg), but we also
    # test with sparse input.
    reg = Ridge(**params).fit(X, y, sample_weight=None)
    coef = reg.coef_.copy()
    if fit_intercept:
        intercept = reg.intercept_
    sample_weight = np.ones_like(y)
    reg.fit(X, y, sample_weight=sample_weight)
    assert_allclose(reg.coef_, coef, rtol=1e-6)
    if fit_intercept:
        assert_allclose(reg.intercept_, intercept)

    # 2) setting elements of sample_weight to 0 is equivalent to removing these samples,
    # another special case of check_sample_weight_equivalence(name, reg), but we
    # also test with sparse input
    sample_weight = rng.uniform(low=0.01, high=2, size=X.shape[0])
    sample_weight[-5:] = 0
    y[-5:] *= 1000  # to make excluding those samples important
    reg.fit(X, y, sample_weight=sample_weight)
    coef = reg.coef_.copy()
    if fit_intercept:
        intercept = reg.intercept_
    reg.fit(X[:-5, :], y[:-5], sample_weight=sample_weight[:-5])
    assert_allclose(reg.coef_, coef, rtol=1e-6)
    if fit_intercept:
        assert_allclose(reg.intercept_, intercept)

    # 3) scaling of sample_weight should have no effect
    # Note: For models with penalty, scaling the penalty term might work.
    reg2 = Ridge(**params).set_params(alpha=np.pi * params["alpha"])
    reg2.fit(X, y, sample_weight=np.pi * sample_weight)
    if solver in ("sag", "saga") and not fit_intercept:
        pytest.xfail(f"Solver {solver} does fail test for scaling of sample_weight.")
    assert_allclose(reg2.coef_, coef, rtol=1e-6)
    if fit_intercept:
        assert_allclose(reg2.intercept_, intercept)

    # 4) check that multiplying sample_weight by 2 is equivalent
    # to repeating corresponding samples twice
    if sparse_container is not None:
        X = X.toarray()
    X2 = np.concatenate([X, X[: n_samples // 2]], axis=0)
    y2 = np.concatenate([y, y[: n_samples // 2]])
    sample_weight_1 = sample_weight.copy()
    sample_weight_1[: n_samples // 2] *= 2
    sample_weight_2 = np.concatenate(
        [sample_weight, sample_weight[: n_samples // 2]], axis=0
    )
    if sparse_container is not None:
        X = sparse_container(X)
        X2 = sparse_container(X2)
    reg1 = Ridge(**params).fit(X, y, sample_weight=sample_weight_1)
    reg2 = Ridge(**params).fit(X2, y2, sample_weight=sample_weight_2)
    assert_allclose(reg1.coef_, reg2.coef_)
    if fit_intercept:
        assert_allclose(reg1.intercept_, reg2.intercept_)


@pytest.mark.parametrize("with_sample_weight", [False, True])
@pytest.mark.parametrize("fit_intercept", [False, True])
@pytest.mark.parametrize("n_targets", [1, 2])
def test_ridge_cv_results_predictions(with_sample_weight, fit_intercept, n_targets):
    """Check that the predictions stored in `cv_results_` are on the original scale.

    The GCV approach works on scaled data: centered by an offset and scaled by the
    square root of the sample weights. Thus, prior to computing scores, the
    predictions need to be scaled back to the original scale. These predictions are
    the ones stored in `cv_results_` in `RidgeCV`.

    In this test, we check that the internal predictions stored in `cv_results_` are
    equivalent to a naive LOO-CV grid search with a `Ridge` estimator.

    Non-regression test for:
    https://github.com/scikit-learn/scikit-learn/issues/13998
    """
    X, y = make_regression(
        n_samples=100, n_features=10, n_targets=n_targets, random_state=0
    )
    sample_weight = np.ones(shape=(X.shape[0],))
    if with_sample_weight:
        sample_weight[::2] = 0.5

    alphas = (0.1, 1.0, 10.0)

    # scoring should be set to store predictions and not the squared error
    ridge_cv = RidgeCV(
        alphas=alphas,
        scoring="neg_mean_squared_error",
        fit_intercept=fit_intercept,
        store_cv_results=True,
    )
    ridge_cv.fit(X, y, sample_weight=sample_weight)

    # manual grid-search with a `Ridge` estimator
    predictions = np.empty(shape=(*y.shape, len(alphas)))
    cv = LeaveOneOut()
    for alpha_idx, alpha in enumerate(alphas):
        for idx, (train_idx, test_idx) in enumerate(cv.split(X, y)):
            ridge = Ridge(alpha=alpha, fit_intercept=fit_intercept)
            ridge.fit(X[train_idx], y[train_idx], sample_weight[train_idx])
            predictions[idx, ..., alpha_idx] = ridge.predict(X[test_idx])
    assert_allclose(ridge_cv.cv_results_, predictions)


def test_ridge_cv_multioutput_sample_weight(global_random_seed):
    """Check that `RidgeCV` works properly with multioutput and sample_weight
    when `scoring != None`.

    We check the error reported by the RidgeCV is close to a naive LOO-CV using a
    Ridge estimator.
    """
    X, y = make_regression(n_targets=2, random_state=global_random_seed)
    sample_weight = np.ones(shape=(X.shape[0],))

    ridge_cv = RidgeCV(scoring="neg_mean_squared_error", store_cv_results=True)
    ridge_cv.fit(X, y, sample_weight=sample_weight)

    cv = LeaveOneOut()
    ridge = Ridge(alpha=ridge_cv.alpha_)
    y_pred_loo = np.squeeze(
        [
            ridge.fit(X[train], y[train], sample_weight=sample_weight[train]).predict(
                X[test]
            )
            for train, test in cv.split(X)
        ]
    )
    assert_allclose(ridge_cv.best_score_, -mean_squared_error(y, y_pred_loo))


def test_ridge_cv_custom_multioutput_scorer():
    """Check that `RidgeCV` works properly with a custom multioutput scorer."""
    X, y = make_regression(n_targets=2, random_state=0)

    def custom_error(y_true, y_pred):
        errors = (y_true - y_pred) ** 2
        mean_errors = np.mean(errors, axis=0)
        if mean_errors.ndim == 1:
            # case of multioutput
            return -np.average(mean_errors, weights=[2, 1])
        # single output - this part of the code should not be reached in the case of
        # multioutput scoring
        return -mean_errors  # pragma: no cover

    def custom_multioutput_scorer(estimator, X, y):
        """Multioutput score that give twice more importance to the second target."""
        return -custom_error(y, estimator.predict(X))

    ridge_cv = RidgeCV(scoring=custom_multioutput_scorer)
    ridge_cv.fit(X, y)

    cv = LeaveOneOut()
    ridge = Ridge(alpha=ridge_cv.alpha_)
    y_pred_loo = np.squeeze(
        [ridge.fit(X[train], y[train]).predict(X[test]) for train, test in cv.split(X)]
    )

    assert_allclose(ridge_cv.best_score_, -custom_error(y, y_pred_loo))


# Metadata Routing Tests
# ======================


@pytest.mark.parametrize("metaestimator", [RidgeCV, RidgeClassifierCV])
@config_context(enable_metadata_routing=True)
def test_metadata_routing_with_default_scoring(metaestimator):
    """Test that `RidgeCV` or `RidgeClassifierCV` with default `scoring`
    argument (`None`), don't enter into `RecursionError` when metadata is routed.
    """
    metaestimator().get_metadata_routing()


@pytest.mark.parametrize(
    "metaestimator, make_dataset",
    [
        (RidgeCV(), make_regression),
        (RidgeClassifierCV(), make_classification),
    ],
)
@config_context(enable_metadata_routing=True)
def test_set_score_request_with_default_scoring(metaestimator, make_dataset):
    """Test that `set_score_request` is set within `RidgeCV.fit()` and
    `RidgeClassifierCV.fit()` when using the default scoring and no
    UnsetMetadataPassedError is raised. Regression test for the fix in PR #29634."""
    X, y = make_dataset(n_samples=100, n_features=5, random_state=42)
    metaestimator.fit(X, y, sample_weight=np.ones(X.shape[0]))


# End of Metadata Routing Tests
# =============================
