Videre

linedance-app/venv/lib/python3.12/site-packages/sklearn/metrics/tests/test_dist_metrics.py

@@ -0,0 +1,431 @@
+import copy
+import itertools
+import pickle
+
+import numpy as np
+import pytest
+from scipy.spatial.distance import cdist
+
+from sklearn.metrics import DistanceMetric
+from sklearn.metrics._dist_metrics import (
+    BOOL_METRICS,
+    DEPRECATED_METRICS,
+    DistanceMetric32,
+    DistanceMetric64,
+)
+from sklearn.utils import check_random_state
+from sklearn.utils._testing import (
+    assert_allclose,
+    create_memmap_backed_data,
+    ignore_warnings,
+)
+from sklearn.utils.fixes import CSR_CONTAINERS
+
+
+def dist_func(x1, x2, p):
+    return np.sum((x1 - x2) ** p) ** (1.0 / p)
+
+
+rng = check_random_state(0)
+d = 4
+n1 = 20
+n2 = 25
+X64 = rng.random_sample((n1, d))
+Y64 = rng.random_sample((n2, d))
+X32 = X64.astype("float32")
+Y32 = Y64.astype("float32")
+
+[X_mmap, Y_mmap] = create_memmap_backed_data([X64, Y64])
+
+# make boolean arrays: ones and zeros
+X_bool = (X64 < 0.3).astype(np.float64)  # quite sparse
+Y_bool = (Y64 < 0.7).astype(np.float64)  # not too sparse
+
+[X_bool_mmap, Y_bool_mmap] = create_memmap_backed_data([X_bool, Y_bool])
+
+
+V = rng.random_sample((d, d))
+VI = np.dot(V, V.T)
+
+METRICS_DEFAULT_PARAMS = [
+    ("euclidean", {}),
+    ("cityblock", {}),
+    ("minkowski", dict(p=(0.5, 1, 1.5, 2, 3))),
+    ("chebyshev", {}),
+    ("seuclidean", dict(V=(rng.random_sample(d),))),
+    ("mahalanobis", dict(VI=(VI,))),
+    ("hamming", {}),
+    ("canberra", {}),
+    ("braycurtis", {}),
+    ("minkowski", dict(p=(0.5, 1, 1.5, 3), w=(rng.random_sample(d),))),
+]
+
+
+@pytest.mark.parametrize(
+    "metric_param_grid", METRICS_DEFAULT_PARAMS, ids=lambda params: params[0]
+)
+@pytest.mark.parametrize("X, Y", [(X64, Y64), (X32, Y32), (X_mmap, Y_mmap)])
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_cdist(metric_param_grid, X, Y, csr_container):
+    metric, param_grid = metric_param_grid
+    keys = param_grid.keys()
+    X_csr, Y_csr = csr_container(X), csr_container(Y)
+    for vals in itertools.product(*param_grid.values()):
+        kwargs = dict(zip(keys, vals))
+        rtol_dict = {}
+        if metric == "mahalanobis" and X.dtype == np.float32:
+            # Computation of mahalanobis differs between
+            # the scipy and scikit-learn implementation.
+            # Hence, we increase the relative tolerance.
+            # TODO: Inspect slight numerical discrepancy
+            # with scipy
+            rtol_dict = {"rtol": 1e-6}
+
+        D_scipy_cdist = cdist(X, Y, metric, **kwargs)
+
+        dm = DistanceMetric.get_metric(metric, X.dtype, **kwargs)
+
+        # DistanceMetric.pairwise must be consistent for all
+        # combinations of formats in {sparse, dense}.
+        D_sklearn = dm.pairwise(X, Y)
+        assert D_sklearn.flags.c_contiguous
+        assert_allclose(D_sklearn, D_scipy_cdist, **rtol_dict)
+
+        D_sklearn = dm.pairwise(X_csr, Y_csr)
+        assert D_sklearn.flags.c_contiguous
+        assert_allclose(D_sklearn, D_scipy_cdist, **rtol_dict)
+
+        D_sklearn = dm.pairwise(X_csr, Y)
+        assert D_sklearn.flags.c_contiguous
+        assert_allclose(D_sklearn, D_scipy_cdist, **rtol_dict)
+
+        D_sklearn = dm.pairwise(X, Y_csr)
+        assert D_sklearn.flags.c_contiguous
+        assert_allclose(D_sklearn, D_scipy_cdist, **rtol_dict)
+
+
+@pytest.mark.parametrize("metric", BOOL_METRICS)
+@pytest.mark.parametrize(
+    "X_bool, Y_bool", [(X_bool, Y_bool), (X_bool_mmap, Y_bool_mmap)]
+)
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_cdist_bool_metric(metric, X_bool, Y_bool, csr_container):
+    if metric in DEPRECATED_METRICS:
+        with ignore_warnings(category=DeprecationWarning):
+            # Some metrics can be deprecated depending on the scipy version.
+            # But if they are present, we still want to test whether
+            # scikit-learn gives the same result, whether or not they are
+            # deprecated.
+            D_scipy_cdist = cdist(X_bool, Y_bool, metric)
+    else:
+        D_scipy_cdist = cdist(X_bool, Y_bool, metric)
+
+    dm = DistanceMetric.get_metric(metric)
+    D_sklearn = dm.pairwise(X_bool, Y_bool)
+    assert_allclose(D_sklearn, D_scipy_cdist)
+
+    # DistanceMetric.pairwise must be consistent
+    # on all combinations of format in {sparse, dense}².
+    X_bool_csr, Y_bool_csr = csr_container(X_bool), csr_container(Y_bool)
+
+    D_sklearn = dm.pairwise(X_bool, Y_bool)
+    assert D_sklearn.flags.c_contiguous
+    assert_allclose(D_sklearn, D_scipy_cdist)
+
+    D_sklearn = dm.pairwise(X_bool_csr, Y_bool_csr)
+    assert D_sklearn.flags.c_contiguous
+    assert_allclose(D_sklearn, D_scipy_cdist)
+
+    D_sklearn = dm.pairwise(X_bool, Y_bool_csr)
+    assert D_sklearn.flags.c_contiguous
+    assert_allclose(D_sklearn, D_scipy_cdist)
+
+    D_sklearn = dm.pairwise(X_bool_csr, Y_bool)
+    assert D_sklearn.flags.c_contiguous
+    assert_allclose(D_sklearn, D_scipy_cdist)
+
+
+@pytest.mark.parametrize(
+    "metric_param_grid", METRICS_DEFAULT_PARAMS, ids=lambda params: params[0]
+)
+@pytest.mark.parametrize("X", [X64, X32, X_mmap])
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_pdist(metric_param_grid, X, csr_container):
+    metric, param_grid = metric_param_grid
+    keys = param_grid.keys()
+    X_csr = csr_container(X)
+    for vals in itertools.product(*param_grid.values()):
+        kwargs = dict(zip(keys, vals))
+        rtol_dict = {}
+        if metric == "mahalanobis" and X.dtype == np.float32:
+            # Computation of mahalanobis differs between
+            # the scipy and scikit-learn implementation.
+            # Hence, we increase the relative tolerance.
+            # TODO: Inspect slight numerical discrepancy
+            # with scipy
+            rtol_dict = {"rtol": 1e-6}
+
+        D_scipy_pdist = cdist(X, X, metric, **kwargs)
+
+        dm = DistanceMetric.get_metric(metric, X.dtype, **kwargs)
+        D_sklearn = dm.pairwise(X)
+        assert D_sklearn.flags.c_contiguous
+        assert_allclose(D_sklearn, D_scipy_pdist, **rtol_dict)
+
+        D_sklearn_csr = dm.pairwise(X_csr)
+        assert D_sklearn.flags.c_contiguous
+        assert_allclose(D_sklearn_csr, D_scipy_pdist, **rtol_dict)
+
+        D_sklearn_csr = dm.pairwise(X_csr, X_csr)
+        assert D_sklearn.flags.c_contiguous
+        assert_allclose(D_sklearn_csr, D_scipy_pdist, **rtol_dict)
+
+
+@pytest.mark.parametrize(
+    "metric_param_grid", METRICS_DEFAULT_PARAMS, ids=lambda params: params[0]
+)
+def test_distance_metrics_dtype_consistency(metric_param_grid):
+    # DistanceMetric must return similar distances for both float32 and float64
+    # input data.
+    metric, param_grid = metric_param_grid
+    keys = param_grid.keys()
+
+    # Choose rtol to make sure that this test is robust to changes in the random
+    # seed in the module-level test data generation code.
+    rtol = 1e-5
+
+    for vals in itertools.product(*param_grid.values()):
+        kwargs = dict(zip(keys, vals))
+        dm64 = DistanceMetric.get_metric(metric, np.float64, **kwargs)
+        dm32 = DistanceMetric.get_metric(metric, np.float32, **kwargs)
+
+        D64 = dm64.pairwise(X64)
+        D32 = dm32.pairwise(X32)
+
+        assert D64.dtype == np.float64
+        assert D32.dtype == np.float32
+
+        # assert_allclose introspects the dtype of the input arrays to decide
+        # which rtol value to use by default but in this case we know that D32
+        # is not computed with the same precision so we set rtol manually.
+        assert_allclose(D64, D32, rtol=rtol)
+
+        D64 = dm64.pairwise(X64, Y64)
+        D32 = dm32.pairwise(X32, Y32)
+        assert_allclose(D64, D32, rtol=rtol)
+
+
+@pytest.mark.parametrize("metric", BOOL_METRICS)
+@pytest.mark.parametrize("X_bool", [X_bool, X_bool_mmap])
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_pdist_bool_metrics(metric, X_bool, csr_container):
+    if metric in DEPRECATED_METRICS:
+        with ignore_warnings(category=DeprecationWarning):
+            # Some metrics can be deprecated depending on the scipy version.
+            # But if they are present, we still want to test whether
+            # scikit-learn gives the same result, whether or not they are
+            # deprecated.
+            D_scipy_pdist = cdist(X_bool, X_bool, metric)
+    else:
+        D_scipy_pdist = cdist(X_bool, X_bool, metric)
+
+    dm = DistanceMetric.get_metric(metric)
+    D_sklearn = dm.pairwise(X_bool)
+    assert_allclose(D_sklearn, D_scipy_pdist)
+
+    X_bool_csr = csr_container(X_bool)
+    D_sklearn = dm.pairwise(X_bool_csr)
+    assert_allclose(D_sklearn, D_scipy_pdist)
+
+
+@pytest.mark.parametrize("writable_kwargs", [True, False])
+@pytest.mark.parametrize(
+    "metric_param_grid", METRICS_DEFAULT_PARAMS, ids=lambda params: params[0]
+)
+@pytest.mark.parametrize("X", [X64, X32])
+def test_pickle(writable_kwargs, metric_param_grid, X):
+    metric, param_grid = metric_param_grid
+    keys = param_grid.keys()
+    for vals in itertools.product(*param_grid.values()):
+        if any(isinstance(val, np.ndarray) for val in vals):
+            vals = copy.deepcopy(vals)
+            for val in vals:
+                if isinstance(val, np.ndarray):
+                    val.setflags(write=writable_kwargs)
+        kwargs = dict(zip(keys, vals))
+        dm = DistanceMetric.get_metric(metric, X.dtype, **kwargs)
+        D1 = dm.pairwise(X)
+        dm2 = pickle.loads(pickle.dumps(dm))
+        D2 = dm2.pairwise(X)
+        assert_allclose(D1, D2)
+
+
+@pytest.mark.parametrize("metric", BOOL_METRICS)
+@pytest.mark.parametrize("X_bool", [X_bool, X_bool_mmap])
+def test_pickle_bool_metrics(metric, X_bool):
+    dm = DistanceMetric.get_metric(metric)
+    D1 = dm.pairwise(X_bool)
+    dm2 = pickle.loads(pickle.dumps(dm))
+    D2 = dm2.pairwise(X_bool)
+    assert_allclose(D1, D2)
+
+
+@pytest.mark.parametrize("X, Y", [(X64, Y64), (X32, Y32), (X_mmap, Y_mmap)])
+@pytest.mark.parametrize("csr_container", CSR_CONTAINERS)
+def test_haversine_metric(X, Y, csr_container):
+    # The Haversine DistanceMetric only works on 2 features.
+    X = np.asarray(X[:, :2])
+    Y = np.asarray(Y[:, :2])
+
+    X_csr, Y_csr = csr_container(X), csr_container(Y)
+
+    # Haversine is not supported by scipy.special.distance.{cdist,pdist}
+    # So we reimplement it to have a reference.
+    def haversine_slow(x1, x2):
+        return 2 * np.arcsin(
+            np.sqrt(
+                np.sin(0.5 * (x1[0] - x2[0])) ** 2
+                + np.cos(x1[0]) * np.cos(x2[0]) * np.sin(0.5 * (x1[1] - x2[1])) ** 2
+            )
+        )
+
+    D_reference = np.zeros((X_csr.shape[0], Y_csr.shape[0]))
+    for i, xi in enumerate(X):
+        for j, yj in enumerate(Y):
+            D_reference[i, j] = haversine_slow(xi, yj)
+
+    haversine = DistanceMetric.get_metric("haversine", X.dtype)
+
+    D_sklearn = haversine.pairwise(X, Y)
+    assert_allclose(
+        haversine.dist_to_rdist(D_sklearn), np.sin(0.5 * D_reference) ** 2, rtol=1e-6
+    )
+
+    assert_allclose(D_sklearn, D_reference)
+
+    D_sklearn = haversine.pairwise(X_csr, Y_csr)
+    assert D_sklearn.flags.c_contiguous
+    assert_allclose(D_sklearn, D_reference)
+
+    D_sklearn = haversine.pairwise(X_csr, Y)
+    assert D_sklearn.flags.c_contiguous
+    assert_allclose(D_sklearn, D_reference)
+
+    D_sklearn = haversine.pairwise(X, Y_csr)
+    assert D_sklearn.flags.c_contiguous
+    assert_allclose(D_sklearn, D_reference)
+
+
+def test_pyfunc_metric():
+    X = np.random.random((10, 3))
+
+    euclidean = DistanceMetric.get_metric("euclidean")
+    pyfunc = DistanceMetric.get_metric("pyfunc", func=dist_func, p=2)
+
+    # Check if both callable metric and predefined metric initialized
+    # DistanceMetric object is picklable
+    euclidean_pkl = pickle.loads(pickle.dumps(euclidean))
+    pyfunc_pkl = pickle.loads(pickle.dumps(pyfunc))
+
+    D1 = euclidean.pairwise(X)
+    D2 = pyfunc.pairwise(X)
+
+    D1_pkl = euclidean_pkl.pairwise(X)
+    D2_pkl = pyfunc_pkl.pairwise(X)
+
+    assert_allclose(D1, D2)
+    assert_allclose(D1_pkl, D2_pkl)
+
+
+def test_input_data_size():
+    # Regression test for #6288
+    # Previously, a metric requiring a particular input dimension would fail
+    def custom_metric(x, y):
+        assert x.shape[0] == 3
+        return np.sum((x - y) ** 2)
+
+    rng = check_random_state(0)
+    X = rng.rand(10, 3)
+
+    pyfunc = DistanceMetric.get_metric("pyfunc", func=custom_metric)
+    eucl = DistanceMetric.get_metric("euclidean")
+    assert_allclose(pyfunc.pairwise(X), eucl.pairwise(X) ** 2)
+
+
+def test_readonly_kwargs():
+    # Non-regression test for:
+    # https://github.com/scikit-learn/scikit-learn/issues/21685
+
+    rng = check_random_state(0)
+
+    weights = rng.rand(100)
+    VI = rng.rand(10, 10)
+    weights.setflags(write=False)
+    VI.setflags(write=False)
+
+    # Those distances metrics have to support readonly buffers.
+    DistanceMetric.get_metric("seuclidean", V=weights)
+    DistanceMetric.get_metric("mahalanobis", VI=VI)
+
+
+@pytest.mark.parametrize(
+    "w, err_type, err_msg",
+    [
+        (np.array([1, 1.5, -13]), ValueError, "w cannot contain negative weights"),
+        (np.array([1, 1.5, np.nan]), ValueError, "w contains NaN"),
+        *[
+            (
+                csr_container([[1, 1.5, 1]]),
+                TypeError,
+                "Sparse data was passed for w, but dense data is required",
+            )
+            for csr_container in CSR_CONTAINERS
+        ],
+        (np.array(["a", "b", "c"]), ValueError, "could not convert string to float"),
+        (np.array([]), ValueError, "a minimum of 1 is required"),
+    ],
+)
+def test_minkowski_metric_validate_weights_values(w, err_type, err_msg):
+    with pytest.raises(err_type, match=err_msg):
+        DistanceMetric.get_metric("minkowski", p=3, w=w)
+
+
+def test_minkowski_metric_validate_weights_size():
+    w2 = rng.random_sample(d + 1)
+    dm = DistanceMetric.get_metric("minkowski", p=3, w=w2)
+    msg = (
+        "MinkowskiDistance: the size of w must match "
+        f"the number of features \\({X64.shape[1]}\\). "
+        f"Currently len\\(w\\)={w2.shape[0]}."
+    )
+    with pytest.raises(ValueError, match=msg):
+        dm.pairwise(X64, Y64)
+
+
+@pytest.mark.parametrize("metric, metric_kwargs", METRICS_DEFAULT_PARAMS)
+@pytest.mark.parametrize("dtype", (np.float32, np.float64))
+def test_get_metric_dtype(metric, metric_kwargs, dtype):
+    specialized_cls = {
+        np.float32: DistanceMetric32,
+        np.float64: DistanceMetric64,
+    }[dtype]
+
+    # We don't need the entire grid, just one for a sanity check
+    metric_kwargs = {k: v[0] for k, v in metric_kwargs.items()}
+    generic_type = type(DistanceMetric.get_metric(metric, dtype, **metric_kwargs))
+    specialized_type = type(specialized_cls.get_metric(metric, **metric_kwargs))
+
+    assert generic_type is specialized_type
+
+
+def test_get_metric_bad_dtype():
+    dtype = np.int32
+    msg = r"Unexpected dtype .* provided. Please select a dtype from"
+    with pytest.raises(ValueError, match=msg):
+        DistanceMetric.get_metric("manhattan", dtype)
+
+
+def test_minkowski_metric_validate_bad_p_parameter():
+    msg = "p must be greater than 0"
+    with pytest.raises(ValueError, match=msg):
+        DistanceMetric.get_metric("minkowski", p=0)

linedance-app/venv/lib/python3.12/site-packages/sklearn/metrics/tests/test_regression.py

@@ -0,0 +1,636 @@
+from itertools import product
+
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+from scipy import optimize
+from scipy.special import factorial, xlogy
+
+from sklearn.dummy import DummyRegressor
+from sklearn.exceptions import UndefinedMetricWarning
+from sklearn.metrics import (
+    d2_absolute_error_score,
+    d2_pinball_score,
+    d2_tweedie_score,
+    explained_variance_score,
+    make_scorer,
+    max_error,
+    mean_absolute_error,
+    mean_absolute_percentage_error,
+    mean_pinball_loss,
+    mean_squared_error,
+    mean_squared_log_error,
+    mean_tweedie_deviance,
+    median_absolute_error,
+    r2_score,
+    root_mean_squared_error,
+    root_mean_squared_log_error,
+)
+from sklearn.metrics._regression import _check_reg_targets
+from sklearn.model_selection import GridSearchCV
+from sklearn.utils._testing import (
+    assert_almost_equal,
+    assert_array_almost_equal,
+    assert_array_equal,
+)
+
+
+def test_regression_metrics(n_samples=50):
+    y_true = np.arange(n_samples)
+    y_pred = y_true + 1
+    y_pred_2 = y_true - 1
+
+    assert_almost_equal(mean_squared_error(y_true, y_pred), 1.0)
+    assert_almost_equal(
+        mean_squared_log_error(y_true, y_pred),
+        mean_squared_error(np.log(1 + y_true), np.log(1 + y_pred)),
+    )
+    assert_almost_equal(mean_absolute_error(y_true, y_pred), 1.0)
+    assert_almost_equal(mean_pinball_loss(y_true, y_pred), 0.5)
+    assert_almost_equal(mean_pinball_loss(y_true, y_pred_2), 0.5)
+    assert_almost_equal(mean_pinball_loss(y_true, y_pred, alpha=0.4), 0.6)
+    assert_almost_equal(mean_pinball_loss(y_true, y_pred_2, alpha=0.4), 0.4)
+    assert_almost_equal(median_absolute_error(y_true, y_pred), 1.0)
+    mape = mean_absolute_percentage_error(y_true, y_pred)
+    assert np.isfinite(mape)
+    assert mape > 1e6
+    assert_almost_equal(max_error(y_true, y_pred), 1.0)
+    assert_almost_equal(r2_score(y_true, y_pred), 0.995, 2)
+    assert_almost_equal(r2_score(y_true, y_pred, force_finite=False), 0.995, 2)
+    assert_almost_equal(explained_variance_score(y_true, y_pred), 1.0)
+    assert_almost_equal(
+        explained_variance_score(y_true, y_pred, force_finite=False), 1.0
+    )
+    assert_almost_equal(
+        mean_tweedie_deviance(y_true, y_pred, power=0),
+        mean_squared_error(y_true, y_pred),
+    )
+    assert_almost_equal(
+        d2_tweedie_score(y_true, y_pred, power=0), r2_score(y_true, y_pred)
+    )
+    dev_median = np.abs(y_true - np.median(y_true)).sum()
+    assert_array_almost_equal(
+        d2_absolute_error_score(y_true, y_pred),
+        1 - np.abs(y_true - y_pred).sum() / dev_median,
+    )
+    alpha = 0.2
+    pinball_loss = lambda y_true, y_pred, alpha: alpha * np.maximum(
+        y_true - y_pred, 0
+    ) + (1 - alpha) * np.maximum(y_pred - y_true, 0)
+    y_quantile = np.percentile(y_true, q=alpha * 100)
+    assert_almost_equal(
+        d2_pinball_score(y_true, y_pred, alpha=alpha),
+        1
+        - pinball_loss(y_true, y_pred, alpha).sum()
+        / pinball_loss(y_true, y_quantile, alpha).sum(),
+    )
+    assert_almost_equal(
+        d2_absolute_error_score(y_true, y_pred),
+        d2_pinball_score(y_true, y_pred, alpha=0.5),
+    )
+
+    # Tweedie deviance needs positive y_pred, except for p=0,
+    # p>=2 needs positive y_true
+    # results evaluated by sympy
+    y_true = np.arange(1, 1 + n_samples)
+    y_pred = 2 * y_true
+    n = n_samples
+    assert_almost_equal(
+        mean_tweedie_deviance(y_true, y_pred, power=-1),
+        5 / 12 * n * (n**2 + 2 * n + 1),
+    )
+    assert_almost_equal(
+        mean_tweedie_deviance(y_true, y_pred, power=1), (n + 1) * (1 - np.log(2))
+    )
+    assert_almost_equal(
+        mean_tweedie_deviance(y_true, y_pred, power=2), 2 * np.log(2) - 1
+    )
+    assert_almost_equal(
+        mean_tweedie_deviance(y_true, y_pred, power=3 / 2),
+        ((6 * np.sqrt(2) - 8) / n) * np.sqrt(y_true).sum(),
+    )
+    assert_almost_equal(
+        mean_tweedie_deviance(y_true, y_pred, power=3), np.sum(1 / y_true) / (4 * n)
+    )
+
+    dev_mean = 2 * np.mean(xlogy(y_true, 2 * y_true / (n + 1)))
+    assert_almost_equal(
+        d2_tweedie_score(y_true, y_pred, power=1),
+        1 - (n + 1) * (1 - np.log(2)) / dev_mean,
+    )
+
+    dev_mean = 2 * np.log((n + 1) / 2) - 2 / n * np.log(factorial(n))
+    assert_almost_equal(
+        d2_tweedie_score(y_true, y_pred, power=2), 1 - (2 * np.log(2) - 1) / dev_mean
+    )
+
+
+def test_root_mean_squared_error_multioutput_raw_value():
+    # non-regression test for
+    # https://github.com/scikit-learn/scikit-learn/pull/16323
+    mse = mean_squared_error([[1]], [[10]], multioutput="raw_values")
+    rmse = root_mean_squared_error([[1]], [[10]], multioutput="raw_values")
+    assert np.sqrt(mse) == pytest.approx(rmse)
+
+
+def test_multioutput_regression():
+    y_true = np.array([[1, 0, 0, 1], [0, 1, 1, 1], [1, 1, 0, 1]])
+    y_pred = np.array([[0, 0, 0, 1], [1, 0, 1, 1], [0, 0, 0, 1]])
+
+    error = mean_squared_error(y_true, y_pred)
+    assert_almost_equal(error, (1.0 / 3 + 2.0 / 3 + 2.0 / 3) / 4.0)
+
+    error = root_mean_squared_error(y_true, y_pred)
+    assert_almost_equal(error, 0.454, decimal=2)
+
+    error = mean_squared_log_error(y_true, y_pred)
+    assert_almost_equal(error, 0.200, decimal=2)
+
+    error = root_mean_squared_log_error(y_true, y_pred)
+    assert_almost_equal(error, 0.315, decimal=2)
+
+    # mean_absolute_error and mean_squared_error are equal because
+    # it is a binary problem.
+    error = mean_absolute_error(y_true, y_pred)
+    assert_almost_equal(error, (1.0 + 2.0 / 3) / 4.0)
+
+    error = mean_pinball_loss(y_true, y_pred)
+    assert_almost_equal(error, (1.0 + 2.0 / 3) / 8.0)
+
+    error = np.around(mean_absolute_percentage_error(y_true, y_pred), decimals=2)
+    assert np.isfinite(error)
+    assert error > 1e6
+    error = median_absolute_error(y_true, y_pred)
+    assert_almost_equal(error, (1.0 + 1.0) / 4.0)
+
+    error = r2_score(y_true, y_pred, multioutput="variance_weighted")
+    assert_almost_equal(error, 1.0 - 5.0 / 2)
+    error = r2_score(y_true, y_pred, multioutput="uniform_average")
+    assert_almost_equal(error, -0.875)
+
+    score = d2_pinball_score(y_true, y_pred, alpha=0.5, multioutput="raw_values")
+    raw_expected_score = [
+        1
+        - np.abs(y_true[:, i] - y_pred[:, i]).sum()
+        / np.abs(y_true[:, i] - np.median(y_true[:, i])).sum()
+        for i in range(y_true.shape[1])
+    ]
+    # in the last case, the denominator vanishes and hence we get nan,
+    # but since the numerator vanishes as well the expected score is 1.0
+    raw_expected_score = np.where(np.isnan(raw_expected_score), 1, raw_expected_score)
+    assert_array_almost_equal(score, raw_expected_score)
+
+    score = d2_pinball_score(y_true, y_pred, alpha=0.5, multioutput="uniform_average")
+    assert_almost_equal(score, raw_expected_score.mean())
+    # constant `y_true` with force_finite=True leads to 1. or 0.
+    yc = [5.0, 5.0]
+    error = r2_score(yc, [5.0, 5.0], multioutput="variance_weighted")
+    assert_almost_equal(error, 1.0)
+    error = r2_score(yc, [5.0, 5.1], multioutput="variance_weighted")
+    assert_almost_equal(error, 0.0)
+
+    # Setting force_finite=False results in the nan for 4th output propagating
+    error = r2_score(
+        y_true, y_pred, multioutput="variance_weighted", force_finite=False
+    )
+    assert_almost_equal(error, np.nan)
+    error = r2_score(y_true, y_pred, multioutput="uniform_average", force_finite=False)
+    assert_almost_equal(error, np.nan)
+
+    # Dropping the 4th output to check `force_finite=False` for nominal
+    y_true = y_true[:, :-1]
+    y_pred = y_pred[:, :-1]
+    error = r2_score(y_true, y_pred, multioutput="variance_weighted")
+    error2 = r2_score(
+        y_true, y_pred, multioutput="variance_weighted", force_finite=False
+    )
+    assert_almost_equal(error, error2)
+    error = r2_score(y_true, y_pred, multioutput="uniform_average")
+    error2 = r2_score(y_true, y_pred, multioutput="uniform_average", force_finite=False)
+    assert_almost_equal(error, error2)
+
+    # constant `y_true` with force_finite=False leads to NaN or -Inf.
+    error = r2_score(
+        yc, [5.0, 5.0], multioutput="variance_weighted", force_finite=False
+    )
+    assert_almost_equal(error, np.nan)
+    error = r2_score(
+        yc, [5.0, 6.0], multioutput="variance_weighted", force_finite=False
+    )
+    assert_almost_equal(error, -np.inf)
+
+
+def test_regression_metrics_at_limits():
+    # Single-sample case
+    # Note: for r2 and d2_tweedie see also test_regression_single_sample
+    assert_almost_equal(mean_squared_error([0.0], [0.0]), 0.0)
+    assert_almost_equal(root_mean_squared_error([0.0], [0.0]), 0.0)
+    assert_almost_equal(mean_squared_log_error([0.0], [0.0]), 0.0)
+    assert_almost_equal(mean_absolute_error([0.0], [0.0]), 0.0)
+    assert_almost_equal(mean_pinball_loss([0.0], [0.0]), 0.0)
+    assert_almost_equal(mean_absolute_percentage_error([0.0], [0.0]), 0.0)
+    assert_almost_equal(median_absolute_error([0.0], [0.0]), 0.0)
+    assert_almost_equal(max_error([0.0], [0.0]), 0.0)
+    assert_almost_equal(explained_variance_score([0.0], [0.0]), 1.0)
+
+    # Perfect cases
+    assert_almost_equal(r2_score([0.0, 1], [0.0, 1]), 1.0)
+    assert_almost_equal(d2_pinball_score([0.0, 1], [0.0, 1]), 1.0)
+
+    # Non-finite cases
+    # R² and explained variance have a fix by default for non-finite cases
+    for s in (r2_score, explained_variance_score):
+        assert_almost_equal(s([0, 0], [1, -1]), 0.0)
+        assert_almost_equal(s([0, 0], [1, -1], force_finite=False), -np.inf)
+        assert_almost_equal(s([1, 1], [1, 1]), 1.0)
+        assert_almost_equal(s([1, 1], [1, 1], force_finite=False), np.nan)
+    msg = (
+        "Mean Squared Logarithmic Error cannot be used when "
+        "targets contain values less than or equal to -1."
+    )
+    with pytest.raises(ValueError, match=msg):
+        mean_squared_log_error([-1.0], [-1.0])
+    msg = (
+        "Mean Squared Logarithmic Error cannot be used when "
+        "targets contain values less than or equal to -1."
+    )
+    with pytest.raises(ValueError, match=msg):
+        mean_squared_log_error([1.0, 2.0, 3.0], [1.0, -2.0, 3.0])
+    msg = (
+        "Mean Squared Logarithmic Error cannot be used when "
+        "targets contain values less than or equal to -1."
+    )
+    with pytest.raises(ValueError, match=msg):
+        mean_squared_log_error([1.0, -2.0, 3.0], [1.0, 2.0, 3.0])
+    msg = (
+        "Mean Squared Logarithmic Error cannot be used when "
+        "targets contain values less than or equal to -1."
+    )
+    with pytest.raises(ValueError, match=msg):
+        root_mean_squared_log_error([1.0, -2.0, 3.0], [1.0, 2.0, 3.0])
+    msg = (
+        "Root Mean Squared Logarithmic Error cannot be used when "
+        "targets contain values less than or equal to -1."
+    )
+
+    # Tweedie deviance error
+    power = -1.2
+    assert_allclose(
+        mean_tweedie_deviance([0], [1.0], power=power), 2 / (2 - power), rtol=1e-3
+    )
+    msg = "can only be used on strictly positive y_pred."
+    with pytest.raises(ValueError, match=msg):
+        mean_tweedie_deviance([0.0], [0.0], power=power)
+    with pytest.raises(ValueError, match=msg):
+        d2_tweedie_score([0.0] * 2, [0.0] * 2, power=power)
+
+    assert_almost_equal(mean_tweedie_deviance([0.0], [0.0], power=0), 0.0, 2)
+
+    power = 1.0
+    msg = "only be used on non-negative y and strictly positive y_pred."
+    with pytest.raises(ValueError, match=msg):
+        mean_tweedie_deviance([0.0], [0.0], power=power)
+    with pytest.raises(ValueError, match=msg):
+        d2_tweedie_score([0.0] * 2, [0.0] * 2, power=power)
+
+    power = 1.5
+    assert_allclose(mean_tweedie_deviance([0.0], [1.0], power=power), 2 / (2 - power))
+    msg = "only be used on non-negative y and strictly positive y_pred."
+    with pytest.raises(ValueError, match=msg):
+        mean_tweedie_deviance([0.0], [0.0], power=power)
+    with pytest.raises(ValueError, match=msg):
+        d2_tweedie_score([0.0] * 2, [0.0] * 2, power=power)
+
+    power = 2.0
+    assert_allclose(mean_tweedie_deviance([1.0], [1.0], power=power), 0.00, atol=1e-8)
+    msg = "can only be used on strictly positive y and y_pred."
+    with pytest.raises(ValueError, match=msg):
+        mean_tweedie_deviance([0.0], [0.0], power=power)
+    with pytest.raises(ValueError, match=msg):
+        d2_tweedie_score([0.0] * 2, [0.0] * 2, power=power)
+
+    power = 3.0
+    assert_allclose(mean_tweedie_deviance([1.0], [1.0], power=power), 0.00, atol=1e-8)
+    msg = "can only be used on strictly positive y and y_pred."
+    with pytest.raises(ValueError, match=msg):
+        mean_tweedie_deviance([0.0], [0.0], power=power)
+    with pytest.raises(ValueError, match=msg):
+        d2_tweedie_score([0.0] * 2, [0.0] * 2, power=power)
+
+
+def test__check_reg_targets():
+    # All of length 3
+    EXAMPLES = [
+        ("continuous", [1, 2, 3], 1),
+        ("continuous", [[1], [2], [3]], 1),
+        ("continuous-multioutput", [[1, 1], [2, 2], [3, 1]], 2),
+        ("continuous-multioutput", [[5, 1], [4, 2], [3, 1]], 2),
+        ("continuous-multioutput", [[1, 3, 4], [2, 2, 2], [3, 1, 1]], 3),
+    ]
+
+    for (type1, y1, n_out1), (type2, y2, n_out2) in product(EXAMPLES, repeat=2):
+        if type1 == type2 and n_out1 == n_out2:
+            y_type, y_check1, y_check2, _, _ = _check_reg_targets(
+                y1, y2, sample_weight=None, multioutput=None
+            )
+            assert type1 == y_type
+            if type1 == "continuous":
+                assert_array_equal(y_check1, np.reshape(y1, (-1, 1)))
+                assert_array_equal(y_check2, np.reshape(y2, (-1, 1)))
+            else:
+                assert_array_equal(y_check1, y1)
+                assert_array_equal(y_check2, y2)
+        else:
+            with pytest.raises(ValueError):
+                _check_reg_targets(y1, y2, sample_weight=None, multioutput=None)
+
+
+def test__check_reg_targets_exception():
+    invalid_multioutput = "this_value_is_not_valid"
+    expected_message = (
+        "Allowed 'multioutput' string values are.+You provided multioutput={!r}".format(
+            invalid_multioutput
+        )
+    )
+    with pytest.raises(ValueError, match=expected_message):
+        _check_reg_targets([1, 2, 3], [[1], [2], [3]], None, invalid_multioutput)
+
+
+def test_regression_multioutput_array():
+    y_true = [[1, 2], [2.5, -1], [4.5, 3], [5, 7]]
+    y_pred = [[1, 1], [2, -1], [5, 4], [5, 6.5]]
+
+    mse = mean_squared_error(y_true, y_pred, multioutput="raw_values")
+    mae = mean_absolute_error(y_true, y_pred, multioutput="raw_values")
+
+    pbl = mean_pinball_loss(y_true, y_pred, multioutput="raw_values")
+    mape = mean_absolute_percentage_error(y_true, y_pred, multioutput="raw_values")
+    r = r2_score(y_true, y_pred, multioutput="raw_values")
+    evs = explained_variance_score(y_true, y_pred, multioutput="raw_values")
+    d2ps = d2_pinball_score(y_true, y_pred, alpha=0.5, multioutput="raw_values")
+    evs2 = explained_variance_score(
+        y_true, y_pred, multioutput="raw_values", force_finite=False
+    )
+
+    assert_array_almost_equal(mse, [0.125, 0.5625], decimal=2)
+    assert_array_almost_equal(mae, [0.25, 0.625], decimal=2)
+    assert_array_almost_equal(pbl, [0.25 / 2, 0.625 / 2], decimal=2)
+    assert_array_almost_equal(mape, [0.0778, 0.2262], decimal=2)
+    assert_array_almost_equal(r, [0.95, 0.93], decimal=2)
+    assert_array_almost_equal(evs, [0.95, 0.93], decimal=2)
+    assert_array_almost_equal(d2ps, [0.833, 0.722], decimal=2)
+    assert_array_almost_equal(evs2, [0.95, 0.93], decimal=2)
+
+    # mean_absolute_error and mean_squared_error are equal because
+    # it is a binary problem.
+    y_true = [[0, 0]] * 4
+    y_pred = [[1, 1]] * 4
+    mse = mean_squared_error(y_true, y_pred, multioutput="raw_values")
+    mae = mean_absolute_error(y_true, y_pred, multioutput="raw_values")
+    pbl = mean_pinball_loss(y_true, y_pred, multioutput="raw_values")
+    r = r2_score(y_true, y_pred, multioutput="raw_values")
+    d2ps = d2_pinball_score(y_true, y_pred, multioutput="raw_values")
+    assert_array_almost_equal(mse, [1.0, 1.0], decimal=2)
+    assert_array_almost_equal(mae, [1.0, 1.0], decimal=2)
+    assert_array_almost_equal(pbl, [0.5, 0.5], decimal=2)
+    assert_array_almost_equal(r, [0.0, 0.0], decimal=2)
+    assert_array_almost_equal(d2ps, [0.0, 0.0], decimal=2)
+
+    r = r2_score([[0, -1], [0, 1]], [[2, 2], [1, 1]], multioutput="raw_values")
+    assert_array_almost_equal(r, [0, -3.5], decimal=2)
+    assert np.mean(r) == r2_score(
+        [[0, -1], [0, 1]], [[2, 2], [1, 1]], multioutput="uniform_average"
+    )
+    evs = explained_variance_score(
+        [[0, -1], [0, 1]], [[2, 2], [1, 1]], multioutput="raw_values"
+    )
+    assert_array_almost_equal(evs, [0, -1.25], decimal=2)
+    evs2 = explained_variance_score(
+        [[0, -1], [0, 1]],
+        [[2, 2], [1, 1]],
+        multioutput="raw_values",
+        force_finite=False,
+    )
+    assert_array_almost_equal(evs2, [-np.inf, -1.25], decimal=2)
+
+    # Checking for the condition in which both numerator and denominator is
+    # zero.
+    y_true = [[1, 3], [1, 2]]
+    y_pred = [[1, 4], [1, 1]]
+    r2 = r2_score(y_true, y_pred, multioutput="raw_values")
+    assert_array_almost_equal(r2, [1.0, -3.0], decimal=2)
+    assert np.mean(r2) == r2_score(y_true, y_pred, multioutput="uniform_average")
+    r22 = r2_score(y_true, y_pred, multioutput="raw_values", force_finite=False)
+    assert_array_almost_equal(r22, [np.nan, -3.0], decimal=2)
+    assert_almost_equal(
+        np.mean(r22),
+        r2_score(y_true, y_pred, multioutput="uniform_average", force_finite=False),
+    )
+
+    evs = explained_variance_score(y_true, y_pred, multioutput="raw_values")
+    assert_array_almost_equal(evs, [1.0, -3.0], decimal=2)
+    assert np.mean(evs) == explained_variance_score(y_true, y_pred)
+    d2ps = d2_pinball_score(y_true, y_pred, alpha=0.5, multioutput="raw_values")
+    assert_array_almost_equal(d2ps, [1.0, -1.0], decimal=2)
+    evs2 = explained_variance_score(
+        y_true, y_pred, multioutput="raw_values", force_finite=False
+    )
+    assert_array_almost_equal(evs2, [np.nan, -3.0], decimal=2)
+    assert_almost_equal(
+        np.mean(evs2), explained_variance_score(y_true, y_pred, force_finite=False)
+    )
+
+    # Handling msle separately as it does not accept negative inputs.
+    y_true = np.array([[0.5, 1], [1, 2], [7, 6]])
+    y_pred = np.array([[0.5, 2], [1, 2.5], [8, 8]])
+    msle = mean_squared_log_error(y_true, y_pred, multioutput="raw_values")
+    msle2 = mean_squared_error(
+        np.log(1 + y_true), np.log(1 + y_pred), multioutput="raw_values"
+    )
+    assert_array_almost_equal(msle, msle2, decimal=2)
+
+
+def test_regression_custom_weights():
+    y_true = [[1, 2], [2.5, -1], [4.5, 3], [5, 7]]
+    y_pred = [[1, 1], [2, -1], [5, 4], [5, 6.5]]
+
+    msew = mean_squared_error(y_true, y_pred, multioutput=[0.4, 0.6])
+    rmsew = root_mean_squared_error(y_true, y_pred, multioutput=[0.4, 0.6])
+    maew = mean_absolute_error(y_true, y_pred, multioutput=[0.4, 0.6])
+    mapew = mean_absolute_percentage_error(y_true, y_pred, multioutput=[0.4, 0.6])
+    rw = r2_score(y_true, y_pred, multioutput=[0.4, 0.6])
+    evsw = explained_variance_score(y_true, y_pred, multioutput=[0.4, 0.6])
+    d2psw = d2_pinball_score(y_true, y_pred, alpha=0.5, multioutput=[0.4, 0.6])
+    evsw2 = explained_variance_score(
+        y_true, y_pred, multioutput=[0.4, 0.6], force_finite=False
+    )
+
+    assert_almost_equal(msew, 0.39, decimal=2)
+    assert_almost_equal(rmsew, 0.59, decimal=2)
+    assert_almost_equal(maew, 0.475, decimal=3)
+    assert_almost_equal(mapew, 0.1668, decimal=2)
+    assert_almost_equal(rw, 0.94, decimal=2)
+    assert_almost_equal(evsw, 0.94, decimal=2)
+    assert_almost_equal(d2psw, 0.766, decimal=2)
+    assert_almost_equal(evsw2, 0.94, decimal=2)
+
+    # Handling msle separately as it does not accept negative inputs.
+    y_true = np.array([[0.5, 1], [1, 2], [7, 6]])
+    y_pred = np.array([[0.5, 2], [1, 2.5], [8, 8]])
+    msle = mean_squared_log_error(y_true, y_pred, multioutput=[0.3, 0.7])
+    msle2 = mean_squared_error(
+        np.log(1 + y_true), np.log(1 + y_pred), multioutput=[0.3, 0.7]
+    )
+    assert_almost_equal(msle, msle2, decimal=2)
+
+
+@pytest.mark.parametrize("metric", [r2_score, d2_tweedie_score, d2_pinball_score])
+def test_regression_single_sample(metric):
+    y_true = [0]
+    y_pred = [1]
+    warning_msg = "not well-defined with less than two samples."
+
+    # Trigger the warning
+    with pytest.warns(UndefinedMetricWarning, match=warning_msg):
+        score = metric(y_true, y_pred)
+        assert np.isnan(score)
+
+
+def test_tweedie_deviance_continuity(global_random_seed):
+    n_samples = 100
+
+    rng = np.random.RandomState(global_random_seed)
+
+    y_true = rng.rand(n_samples) + 0.1
+    y_pred = rng.rand(n_samples) + 0.1
+
+    assert_allclose(
+        mean_tweedie_deviance(y_true, y_pred, power=0 - 1e-10),
+        mean_tweedie_deviance(y_true, y_pred, power=0),
+    )
+
+    # Ws we get closer to the limit, with 1e-12 difference the
+    # tolerance to pass the below check increases. There are likely
+    # numerical precision issues on the edges of different definition
+    # regions.
+    assert_allclose(
+        mean_tweedie_deviance(y_true, y_pred, power=1 + 1e-10),
+        mean_tweedie_deviance(y_true, y_pred, power=1),
+        rtol=1e-5,
+    )
+
+    assert_allclose(
+        mean_tweedie_deviance(y_true, y_pred, power=2 - 1e-10),
+        mean_tweedie_deviance(y_true, y_pred, power=2),
+        rtol=1e-5,
+    )
+
+    assert_allclose(
+        mean_tweedie_deviance(y_true, y_pred, power=2 + 1e-10),
+        mean_tweedie_deviance(y_true, y_pred, power=2),
+        rtol=1e-5,
+    )
+
+
+def test_mean_absolute_percentage_error(global_random_seed):
+    random_number_generator = np.random.RandomState(global_random_seed)
+    y_true = random_number_generator.exponential(size=100)
+    y_pred = 1.2 * y_true
+    assert mean_absolute_percentage_error(y_true, y_pred) == pytest.approx(0.2)
+
+
+@pytest.mark.parametrize(
+    "distribution", ["normal", "lognormal", "exponential", "uniform"]
+)
+@pytest.mark.parametrize("target_quantile", [0.05, 0.5, 0.75])
+def test_mean_pinball_loss_on_constant_predictions(
+    distribution, target_quantile, global_random_seed
+):
+    if not hasattr(np, "quantile"):
+        pytest.skip(
+            "This test requires a more recent version of numpy "
+            "with support for np.quantile."
+        )
+
+    # Check that the pinball loss is minimized by the empirical quantile.
+    n_samples = 3000
+    rng = np.random.RandomState(global_random_seed)
+    data = getattr(rng, distribution)(size=n_samples)
+
+    # Compute the best possible pinball loss for any constant predictor:
+    best_pred = np.quantile(data, target_quantile)
+    best_constant_pred = np.full(n_samples, fill_value=best_pred)
+    best_pbl = mean_pinball_loss(data, best_constant_pred, alpha=target_quantile)
+
+    # Evaluate the loss on a grid of quantiles
+    candidate_predictions = np.quantile(data, np.linspace(0, 1, 100))
+    for pred in candidate_predictions:
+        # Compute the pinball loss of a constant predictor:
+        constant_pred = np.full(n_samples, fill_value=pred)
+        pbl = mean_pinball_loss(data, constant_pred, alpha=target_quantile)
+
+        # Check that the loss of this constant predictor is greater or equal
+        # than the loss of using the optimal quantile (up to machine
+        # precision):
+        assert pbl >= best_pbl - np.finfo(np.float64).eps
+
+        # Check that the value of the pinball loss matches the analytical
+        # formula.
+        expected_pbl = (pred - data[data < pred]).sum() * (1 - target_quantile) + (
+            data[data >= pred] - pred
+        ).sum() * target_quantile
+        expected_pbl /= n_samples
+        assert_almost_equal(expected_pbl, pbl)
+
+    # Check that we can actually recover the target_quantile by minimizing the
+    # pinball loss w.r.t. the constant prediction quantile.
+    def objective_func(x):
+        constant_pred = np.full(n_samples, fill_value=x)
+        return mean_pinball_loss(data, constant_pred, alpha=target_quantile)
+
+    result = optimize.minimize(objective_func, data.mean())
+    assert result.success
+    # The minimum is not unique with limited data, hence the large tolerance.
+    # For the normal distribution and the 0.5 quantile, the expected result is close to
+    # 0, hence the additional use of absolute tolerance.
+    assert_allclose(result.x, best_pred, rtol=1e-1, atol=1e-3)
+    assert result.fun == pytest.approx(best_pbl)
+
+
+def test_dummy_quantile_parameter_tuning(global_random_seed):
+    # Integration test to check that it is possible to use the pinball loss to
+    # tune the hyperparameter of a quantile regressor. This is conceptually
+    # similar to the previous test but using the scikit-learn estimator and
+    # scoring API instead.
+    n_samples = 1000
+    rng = np.random.RandomState(global_random_seed)
+    X = rng.normal(size=(n_samples, 5))  # Ignored
+    y = rng.exponential(size=n_samples)
+
+    all_quantiles = [0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 0.95]
+    for alpha in all_quantiles:
+        neg_mean_pinball_loss = make_scorer(
+            mean_pinball_loss,
+            alpha=alpha,
+            greater_is_better=False,
+        )
+        regressor = DummyRegressor(strategy="quantile", quantile=0.25)
+        grid_search = GridSearchCV(
+            regressor,
+            param_grid=dict(quantile=all_quantiles),
+            scoring=neg_mean_pinball_loss,
+        ).fit(X, y)
+
+        assert grid_search.best_params_["quantile"] == pytest.approx(alpha)
+
+
+def test_pinball_loss_relation_with_mae(global_random_seed):
+    # Test that mean_pinball loss with alpha=0.5 if half of mean absolute error
+    rng = np.random.RandomState(global_random_seed)
+    n = 100
+    y_true = rng.normal(size=n)
+    y_pred = y_true.copy() + rng.uniform(n)
+    assert (
+        mean_absolute_error(y_true, y_pred)
+        == mean_pinball_loss(y_true, y_pred, alpha=0.5) * 2
+    )