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@@ -711,3 +711,4 @@ mplug_owl2/lib/python3.10/site-packages/torch/sparse/__pycache__/_triton_ops_met
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+mplug_owl2/lib/python3.10/site-packages/accelerate/__pycache__/accelerator.cpython-310.pyc filter=lfs diff=lfs merge=lfs -text

mplug_owl2/lib/python3.10/site-packages/accelerate/__pycache__/accelerator.cpython-310.pyc

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mplug_owl2/lib/python3.10/site-packages/sklearn/covariance/__init__.py

@@ -0,0 +1,45 @@
+"""
+The :mod:`sklearn.covariance` module includes methods and algorithms to
+robustly estimate the covariance of features given a set of points. The
+precision matrix defined as the inverse of the covariance is also estimated.
+Covariance estimation is closely related to the theory of Gaussian Graphical
+Models.
+"""
+
+from ._empirical_covariance import (
+    empirical_covariance,
+    EmpiricalCovariance,
+    log_likelihood,
+)
+from ._shrunk_covariance import (
+    shrunk_covariance,
+    ShrunkCovariance,
+    ledoit_wolf,
+    ledoit_wolf_shrinkage,
+    LedoitWolf,
+    oas,
+    OAS,
+)
+from ._robust_covariance import fast_mcd, MinCovDet
+from ._graph_lasso import graphical_lasso, GraphicalLasso, GraphicalLassoCV
+from ._elliptic_envelope import EllipticEnvelope
+
+
+__all__ = [
+    "EllipticEnvelope",
+    "EmpiricalCovariance",
+    "GraphicalLasso",
+    "GraphicalLassoCV",
+    "LedoitWolf",
+    "MinCovDet",
+    "OAS",
+    "ShrunkCovariance",
+    "empirical_covariance",
+    "fast_mcd",
+    "graphical_lasso",
+    "ledoit_wolf",
+    "ledoit_wolf_shrinkage",
+    "log_likelihood",
+    "oas",
+    "shrunk_covariance",
+]

mplug_owl2/lib/python3.10/site-packages/sklearn/covariance/_elliptic_envelope.py

@@ -0,0 +1,265 @@
+# Author: Virgile Fritsch <virgile.fritsch@inria.fr>
+#
+# License: BSD 3 clause
+
+import numpy as np
+from numbers import Real
+from . import MinCovDet
+from ..utils._param_validation import Interval
+from ..utils.validation import check_is_fitted
+from ..metrics import accuracy_score
+from ..base import OutlierMixin
+
+
+class EllipticEnvelope(OutlierMixin, MinCovDet):
+    """An object for detecting outliers in a Gaussian distributed dataset.
+
+    Read more in the :ref:`User Guide <outlier_detection>`.
+
+    Parameters
+    ----------
+    store_precision : bool, default=True
+        Specify if the estimated precision is stored.
+
+    assume_centered : bool, default=False
+        If True, the support of robust location and covariance estimates
+        is computed, and a covariance estimate is recomputed from it,
+        without centering the data.
+        Useful to work with data whose mean is significantly equal to
+        zero but is not exactly zero.
+        If False, the robust location and covariance are directly computed
+        with the FastMCD algorithm without additional treatment.
+
+    support_fraction : float, default=None
+        The proportion of points to be included in the support of the raw
+        MCD estimate. If None, the minimum value of support_fraction will
+        be used within the algorithm: `[n_sample + n_features + 1] / 2`.
+        Range is (0, 1).
+
+    contamination : float, default=0.1
+        The amount of contamination of the data set, i.e. the proportion
+        of outliers in the data set. Range is (0, 0.5].
+
+    random_state : int, RandomState instance or None, default=None
+        Determines the pseudo random number generator for shuffling
+        the data. Pass an int for reproducible results across multiple function
+        calls. See :term:`Glossary <random_state>`.
+
+    Attributes
+    ----------
+    location_ : ndarray of shape (n_features,)
+        Estimated robust location.
+
+    covariance_ : ndarray of shape (n_features, n_features)
+        Estimated robust covariance matrix.
+
+    precision_ : ndarray of shape (n_features, n_features)
+        Estimated pseudo inverse matrix.
+        (stored only if store_precision is True)
+
+    support_ : ndarray of shape (n_samples,)
+        A mask of the observations that have been used to compute the
+        robust estimates of location and shape.
+
+    offset_ : float
+        Offset used to define the decision function from the raw scores.
+        We have the relation: ``decision_function = score_samples - offset_``.
+        The offset depends on the contamination parameter and is defined in
+        such a way we obtain the expected number of outliers (samples with
+        decision function < 0) in training.
+
+        .. versionadded:: 0.20
+
+    raw_location_ : ndarray of shape (n_features,)
+        The raw robust estimated location before correction and re-weighting.
+
+    raw_covariance_ : ndarray of shape (n_features, n_features)
+        The raw robust estimated covariance before correction and re-weighting.
+
+    raw_support_ : ndarray of shape (n_samples,)
+        A mask of the observations that have been used to compute
+        the raw robust estimates of location and shape, before correction
+        and re-weighting.
+
+    dist_ : ndarray of shape (n_samples,)
+        Mahalanobis distances of the training set (on which :meth:`fit` is
+        called) observations.
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+        .. versionadded:: 0.24
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
+    See Also
+    --------
+    EmpiricalCovariance : Maximum likelihood covariance estimator.
+    GraphicalLasso : Sparse inverse covariance estimation
+        with an l1-penalized estimator.
+    LedoitWolf : LedoitWolf Estimator.
+    MinCovDet : Minimum Covariance Determinant
+        (robust estimator of covariance).
+    OAS : Oracle Approximating Shrinkage Estimator.
+    ShrunkCovariance : Covariance estimator with shrinkage.
+
+    Notes
+    -----
+    Outlier detection from covariance estimation may break or not
+    perform well in high-dimensional settings. In particular, one will
+    always take care to work with ``n_samples > n_features ** 2``.
+
+    References
+    ----------
+    .. [1] Rousseeuw, P.J., Van Driessen, K. "A fast algorithm for the
+       minimum covariance determinant estimator" Technometrics 41(3), 212
+       (1999)
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from sklearn.covariance import EllipticEnvelope
+    >>> true_cov = np.array([[.8, .3],
+    ...                      [.3, .4]])
+    >>> X = np.random.RandomState(0).multivariate_normal(mean=[0, 0],
+    ...                                                  cov=true_cov,
+    ...                                                  size=500)
+    >>> cov = EllipticEnvelope(random_state=0).fit(X)
+    >>> # predict returns 1 for an inlier and -1 for an outlier
+    >>> cov.predict([[0, 0],
+    ...              [3, 3]])
+    array([ 1, -1])
+    >>> cov.covariance_
+    array([[0.7411..., 0.2535...],
+           [0.2535..., 0.3053...]])
+    >>> cov.location_
+    array([0.0813... , 0.0427...])
+    """
+
+    _parameter_constraints: dict = {
+        **MinCovDet._parameter_constraints,
+        "contamination": [Interval(Real, 0, 0.5, closed="right")],
+    }
+
+    def __init__(
+        self,
+        *,
+        store_precision=True,
+        assume_centered=False,
+        support_fraction=None,
+        contamination=0.1,
+        random_state=None,
+    ):
+        super().__init__(
+            store_precision=store_precision,
+            assume_centered=assume_centered,
+            support_fraction=support_fraction,
+            random_state=random_state,
+        )
+        self.contamination = contamination
+
+    def fit(self, X, y=None):
+        """Fit the EllipticEnvelope model.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            Training data.
+
+        y : Ignored
+            Not used, present for API consistency by convention.
+
+        Returns
+        -------
+        self : object
+            Returns the instance itself.
+        """
+        # `_validate_params` is called in `MinCovDet`
+        super().fit(X)
+        self.offset_ = np.percentile(-self.dist_, 100.0 * self.contamination)
+        return self
+
+    def decision_function(self, X):
+        """Compute the decision function of the given observations.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            The data matrix.
+
+        Returns
+        -------
+        decision : ndarray of shape (n_samples,)
+            Decision function of the samples.
+            It is equal to the shifted Mahalanobis distances.
+            The threshold for being an outlier is 0, which ensures a
+            compatibility with other outlier detection algorithms.
+        """
+        check_is_fitted(self)
+        negative_mahal_dist = self.score_samples(X)
+        return negative_mahal_dist - self.offset_
+
+    def score_samples(self, X):
+        """Compute the negative Mahalanobis distances.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            The data matrix.
+
+        Returns
+        -------
+        negative_mahal_distances : array-like of shape (n_samples,)
+            Opposite of the Mahalanobis distances.
+        """
+        check_is_fitted(self)
+        return -self.mahalanobis(X)
+
+    def predict(self, X):
+        """
+        Predict labels (1 inlier, -1 outlier) of X according to fitted model.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            The data matrix.
+
+        Returns
+        -------
+        is_inlier : ndarray of shape (n_samples,)
+            Returns -1 for anomalies/outliers and +1 for inliers.
+        """
+        values = self.decision_function(X)
+        is_inlier = np.full(values.shape[0], -1, dtype=int)
+        is_inlier[values >= 0] = 1
+
+        return is_inlier
+
+    def score(self, X, y, sample_weight=None):
+        """Return the mean accuracy on the given test data and labels.
+
+        In multi-label classification, this is the subset accuracy
+        which is a harsh metric since you require for each sample that
+        each label set be correctly predicted.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            Test samples.
+
+        y : array-like of shape (n_samples,) or (n_samples, n_outputs)
+            True labels for X.
+
+        sample_weight : array-like of shape (n_samples,), default=None
+            Sample weights.
+
+        Returns
+        -------
+        score : float
+            Mean accuracy of self.predict(X) w.r.t. y.
+        """
+        return accuracy_score(y, self.predict(X), sample_weight=sample_weight)

mplug_owl2/lib/python3.10/site-packages/sklearn/covariance/_empirical_covariance.py

@@ -0,0 +1,348 @@
+"""
+Maximum likelihood covariance estimator.
+
+"""
+
+# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
+#         Gael Varoquaux <gael.varoquaux@normalesup.org>
+#         Virgile Fritsch <virgile.fritsch@inria.fr>
+#
+# License: BSD 3 clause
+
+# avoid division truncation
+import warnings
+import numpy as np
+from scipy import linalg
+
+from .. import config_context
+from ..base import BaseEstimator
+from ..utils import check_array
+from ..utils.extmath import fast_logdet
+from ..metrics.pairwise import pairwise_distances
+
+
+def log_likelihood(emp_cov, precision):
+    """Compute the sample mean of the log_likelihood under a covariance model.
+
+    Computes the empirical expected log-likelihood, allowing for universal
+    comparison (beyond this software package), and accounts for normalization
+    terms and scaling.
+
+    Parameters
+    ----------
+    emp_cov : ndarray of shape (n_features, n_features)
+        Maximum Likelihood Estimator of covariance.
+
+    precision : ndarray of shape (n_features, n_features)
+        The precision matrix of the covariance model to be tested.
+
+    Returns
+    -------
+    log_likelihood_ : float
+        Sample mean of the log-likelihood.
+    """
+    p = precision.shape[0]
+    log_likelihood_ = -np.sum(emp_cov * precision) + fast_logdet(precision)
+    log_likelihood_ -= p * np.log(2 * np.pi)
+    log_likelihood_ /= 2.0
+    return log_likelihood_
+
+
+def empirical_covariance(X, *, assume_centered=False):
+    """Compute the Maximum likelihood covariance estimator.
+
+    Parameters
+    ----------
+    X : ndarray of shape (n_samples, n_features)
+        Data from which to compute the covariance estimate.
+
+    assume_centered : bool, default=False
+        If `True`, data will not be centered before computation.
+        Useful when working with data whose mean is almost, but not exactly
+        zero.
+        If `False`, data will be centered before computation.
+
+    Returns
+    -------
+    covariance : ndarray of shape (n_features, n_features)
+        Empirical covariance (Maximum Likelihood Estimator).
+
+    Examples
+    --------
+    >>> from sklearn.covariance import empirical_covariance
+    >>> X = [[1,1,1],[1,1,1],[1,1,1],
+    ...      [0,0,0],[0,0,0],[0,0,0]]
+    >>> empirical_covariance(X)
+    array([[0.25, 0.25, 0.25],
+           [0.25, 0.25, 0.25],
+           [0.25, 0.25, 0.25]])
+    """
+    X = np.asarray(X)
+
+    if X.ndim == 1:
+        X = np.reshape(X, (1, -1))
+
+    if X.shape[0] == 1:
+        warnings.warn(
+            "Only one sample available. You may want to reshape your data array"
+        )
+
+    if assume_centered:
+        covariance = np.dot(X.T, X) / X.shape[0]
+    else:
+        covariance = np.cov(X.T, bias=1)
+
+    if covariance.ndim == 0:
+        covariance = np.array([[covariance]])
+    return covariance
+
+
+class EmpiricalCovariance(BaseEstimator):
+    """Maximum likelihood covariance estimator.
+
+    Read more in the :ref:`User Guide <covariance>`.
+
+    Parameters
+    ----------
+    store_precision : bool, default=True
+        Specifies if the estimated precision is stored.
+
+    assume_centered : bool, default=False
+        If True, data are not centered before computation.
+        Useful when working with data whose mean is almost, but not exactly
+        zero.
+        If False (default), data are centered before computation.
+
+    Attributes
+    ----------
+    location_ : ndarray of shape (n_features,)
+        Estimated location, i.e. the estimated mean.
+
+    covariance_ : ndarray of shape (n_features, n_features)
+        Estimated covariance matrix
+
+    precision_ : ndarray of shape (n_features, n_features)
+        Estimated pseudo-inverse matrix.
+        (stored only if store_precision is True)
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+        .. versionadded:: 0.24
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
+    See Also
+    --------
+    EllipticEnvelope : An object for detecting outliers in
+        a Gaussian distributed dataset.
+    GraphicalLasso : Sparse inverse covariance estimation
+        with an l1-penalized estimator.
+    LedoitWolf : LedoitWolf Estimator.
+    MinCovDet : Minimum Covariance Determinant
+        (robust estimator of covariance).
+    OAS : Oracle Approximating Shrinkage Estimator.
+    ShrunkCovariance : Covariance estimator with shrinkage.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from sklearn.covariance import EmpiricalCovariance
+    >>> from sklearn.datasets import make_gaussian_quantiles
+    >>> real_cov = np.array([[.8, .3],
+    ...                      [.3, .4]])
+    >>> rng = np.random.RandomState(0)
+    >>> X = rng.multivariate_normal(mean=[0, 0],
+    ...                             cov=real_cov,
+    ...                             size=500)
+    >>> cov = EmpiricalCovariance().fit(X)
+    >>> cov.covariance_
+    array([[0.7569..., 0.2818...],
+           [0.2818..., 0.3928...]])
+    >>> cov.location_
+    array([0.0622..., 0.0193...])
+    """
+
+    _parameter_constraints: dict = {
+        "store_precision": ["boolean"],
+        "assume_centered": ["boolean"],
+    }
+
+    def __init__(self, *, store_precision=True, assume_centered=False):
+        self.store_precision = store_precision
+        self.assume_centered = assume_centered
+
+    def _set_covariance(self, covariance):
+        """Saves the covariance and precision estimates
+
+        Storage is done accordingly to `self.store_precision`.
+        Precision stored only if invertible.
+
+        Parameters
+        ----------
+        covariance : array-like of shape (n_features, n_features)
+            Estimated covariance matrix to be stored, and from which precision
+            is computed.
+        """
+        covariance = check_array(covariance)
+        # set covariance
+        self.covariance_ = covariance
+        # set precision
+        if self.store_precision:
+            self.precision_ = linalg.pinvh(covariance, check_finite=False)
+        else:
+            self.precision_ = None
+
+    def get_precision(self):
+        """Getter for the precision matrix.
+
+        Returns
+        -------
+        precision_ : array-like of shape (n_features, n_features)
+            The precision matrix associated to the current covariance object.
+        """
+        if self.store_precision:
+            precision = self.precision_
+        else:
+            precision = linalg.pinvh(self.covariance_, check_finite=False)
+        return precision
+
+    def fit(self, X, y=None):
+        """Fit the maximum likelihood covariance estimator to X.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+          Training data, where `n_samples` is the number of samples and
+          `n_features` is the number of features.
+
+        y : Ignored
+            Not used, present for API consistency by convention.
+
+        Returns
+        -------
+        self : object
+            Returns the instance itself.
+        """
+        self._validate_params()
+        X = self._validate_data(X)
+        if self.assume_centered:
+            self.location_ = np.zeros(X.shape[1])
+        else:
+            self.location_ = X.mean(0)
+        covariance = empirical_covariance(X, assume_centered=self.assume_centered)
+        self._set_covariance(covariance)
+
+        return self
+
+    def score(self, X_test, y=None):
+        """Compute the log-likelihood of `X_test` under the estimated Gaussian model.
+
+        The Gaussian model is defined by its mean and covariance matrix which are
+        represented respectively by `self.location_` and `self.covariance_`.
+
+        Parameters
+        ----------
+        X_test : array-like of shape (n_samples, n_features)
+            Test data of which we compute the likelihood, where `n_samples` is
+            the number of samples and `n_features` is the number of features.
+            `X_test` is assumed to be drawn from the same distribution than
+            the data used in fit (including centering).
+
+        y : Ignored
+            Not used, present for API consistency by convention.
+
+        Returns
+        -------
+        res : float
+            The log-likelihood of `X_test` with `self.location_` and `self.covariance_`
+            as estimators of the Gaussian model mean and covariance matrix respectively.
+        """
+        X_test = self._validate_data(X_test, reset=False)
+        # compute empirical covariance of the test set
+        test_cov = empirical_covariance(X_test - self.location_, assume_centered=True)
+        # compute log likelihood
+        res = log_likelihood(test_cov, self.get_precision())
+
+        return res
+
+    def error_norm(self, comp_cov, norm="frobenius", scaling=True, squared=True):
+        """Compute the Mean Squared Error between two covariance estimators.
+
+        Parameters
+        ----------
+        comp_cov : array-like of shape (n_features, n_features)
+            The covariance to compare with.
+
+        norm : {"frobenius", "spectral"}, default="frobenius"
+            The type of norm used to compute the error. Available error types:
+            - 'frobenius' (default): sqrt(tr(A^t.A))
+            - 'spectral': sqrt(max(eigenvalues(A^t.A))
+            where A is the error ``(comp_cov - self.covariance_)``.
+
+        scaling : bool, default=True
+            If True (default), the squared error norm is divided by n_features.
+            If False, the squared error norm is not rescaled.
+
+        squared : bool, default=True
+            Whether to compute the squared error norm or the error norm.
+            If True (default), the squared error norm is returned.
+            If False, the error norm is returned.
+
+        Returns
+        -------
+        result : float
+            The Mean Squared Error (in the sense of the Frobenius norm) between
+            `self` and `comp_cov` covariance estimators.
+        """
+        # compute the error
+        error = comp_cov - self.covariance_
+        # compute the error norm
+        if norm == "frobenius":
+            squared_norm = np.sum(error**2)
+        elif norm == "spectral":
+            squared_norm = np.amax(linalg.svdvals(np.dot(error.T, error)))
+        else:
+            raise NotImplementedError(
+                "Only spectral and frobenius norms are implemented"
+            )
+        # optionally scale the error norm
+        if scaling:
+            squared_norm = squared_norm / error.shape[0]
+        # finally get either the squared norm or the norm
+        if squared:
+            result = squared_norm
+        else:
+            result = np.sqrt(squared_norm)
+
+        return result
+
+    def mahalanobis(self, X):
+        """Compute the squared Mahalanobis distances of given observations.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            The observations, the Mahalanobis distances of the which we
+            compute. Observations are assumed to be drawn from the same
+            distribution than the data used in fit.
+
+        Returns
+        -------
+        dist : ndarray of shape (n_samples,)
+            Squared Mahalanobis distances of the observations.
+        """
+        X = self._validate_data(X, reset=False)
+
+        precision = self.get_precision()
+        with config_context(assume_finite=True):
+            # compute mahalanobis distances
+            dist = pairwise_distances(
+                X, self.location_[np.newaxis, :], metric="mahalanobis", VI=precision
+            )
+
+        return np.reshape(dist, (len(X),)) ** 2

mplug_owl2/lib/python3.10/site-packages/sklearn/covariance/_robust_covariance.py

@@ -0,0 +1,866 @@
+"""
+Robust location and covariance estimators.
+
+Here are implemented estimators that are resistant to outliers.
+
+"""
+# Author: Virgile Fritsch <virgile.fritsch@inria.fr>
+#
+# License: BSD 3 clause
+
+import warnings
+from numbers import Integral, Real
+import numpy as np
+from scipy import linalg
+from scipy.stats import chi2
+
+from . import empirical_covariance, EmpiricalCovariance
+from ..utils.extmath import fast_logdet
+from ..utils import check_random_state, check_array
+from ..utils._param_validation import Interval
+
+
+# Minimum Covariance Determinant
+#   Implementing of an algorithm by Rousseeuw & Van Driessen described in
+#   (A Fast Algorithm for the Minimum Covariance Determinant Estimator,
+#   1999, American Statistical Association and the American Society
+#   for Quality, TECHNOMETRICS)
+# XXX Is this really a public function? It's not listed in the docs or
+# exported by sklearn.covariance. Deprecate?
+def c_step(
+    X,
+    n_support,
+    remaining_iterations=30,
+    initial_estimates=None,
+    verbose=False,
+    cov_computation_method=empirical_covariance,
+    random_state=None,
+):
+    """C_step procedure described in [Rouseeuw1984]_ aiming at computing MCD.
+
+    Parameters
+    ----------
+    X : array-like of shape (n_samples, n_features)
+        Data set in which we look for the n_support observations whose
+        scatter matrix has minimum determinant.
+
+    n_support : int
+        Number of observations to compute the robust estimates of location
+        and covariance from. This parameter must be greater than
+        `n_samples / 2`.
+
+    remaining_iterations : int, default=30
+        Number of iterations to perform.
+        According to [Rouseeuw1999]_, two iterations are sufficient to get
+        close to the minimum, and we never need more than 30 to reach
+        convergence.
+
+    initial_estimates : tuple of shape (2,), default=None
+        Initial estimates of location and shape from which to run the c_step
+        procedure:
+        - initial_estimates[0]: an initial location estimate
+        - initial_estimates[1]: an initial covariance estimate
+
+    verbose : bool, default=False
+        Verbose mode.
+
+    cov_computation_method : callable, \
+            default=:func:`sklearn.covariance.empirical_covariance`
+        The function which will be used to compute the covariance.
+        Must return array of shape (n_features, n_features).
+
+    random_state : int, RandomState instance or None, default=None
+        Determines the pseudo random number generator for shuffling the data.
+        Pass an int for reproducible results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+    Returns
+    -------
+    location : ndarray of shape (n_features,)
+        Robust location estimates.
+
+    covariance : ndarray of shape (n_features, n_features)
+        Robust covariance estimates.
+
+    support : ndarray of shape (n_samples,)
+        A mask for the `n_support` observations whose scatter matrix has
+        minimum determinant.
+
+    References
+    ----------
+    .. [Rouseeuw1999] A Fast Algorithm for the Minimum Covariance Determinant
+        Estimator, 1999, American Statistical Association and the American
+        Society for Quality, TECHNOMETRICS
+    """
+    X = np.asarray(X)
+    random_state = check_random_state(random_state)
+    return _c_step(
+        X,
+        n_support,
+        remaining_iterations=remaining_iterations,
+        initial_estimates=initial_estimates,
+        verbose=verbose,
+        cov_computation_method=cov_computation_method,
+        random_state=random_state,
+    )
+
+
+def _c_step(
+    X,
+    n_support,
+    random_state,
+    remaining_iterations=30,
+    initial_estimates=None,
+    verbose=False,
+    cov_computation_method=empirical_covariance,
+):
+    n_samples, n_features = X.shape
+    dist = np.inf
+
+    # Initialisation
+    support = np.zeros(n_samples, dtype=bool)
+    if initial_estimates is None:
+        # compute initial robust estimates from a random subset
+        support[random_state.permutation(n_samples)[:n_support]] = True
+    else:
+        # get initial robust estimates from the function parameters
+        location = initial_estimates[0]
+        covariance = initial_estimates[1]
+        # run a special iteration for that case (to get an initial support)
+        precision = linalg.pinvh(covariance)
+        X_centered = X - location
+        dist = (np.dot(X_centered, precision) * X_centered).sum(1)
+        # compute new estimates
+        support[np.argsort(dist)[:n_support]] = True
+
+    X_support = X[support]
+    location = X_support.mean(0)
+    covariance = cov_computation_method(X_support)
+
+    # Iterative procedure for Minimum Covariance Determinant computation
+    det = fast_logdet(covariance)
+    # If the data already has singular covariance, calculate the precision,
+    # as the loop below will not be entered.
+    if np.isinf(det):
+        precision = linalg.pinvh(covariance)
+
+    previous_det = np.inf
+    while det < previous_det and remaining_iterations > 0 and not np.isinf(det):
+        # save old estimates values
+        previous_location = location
+        previous_covariance = covariance
+        previous_det = det
+        previous_support = support
+        # compute a new support from the full data set mahalanobis distances
+        precision = linalg.pinvh(covariance)
+        X_centered = X - location
+        dist = (np.dot(X_centered, precision) * X_centered).sum(axis=1)
+        # compute new estimates
+        support = np.zeros(n_samples, dtype=bool)
+        support[np.argsort(dist)[:n_support]] = True
+        X_support = X[support]
+        location = X_support.mean(axis=0)
+        covariance = cov_computation_method(X_support)
+        det = fast_logdet(covariance)
+        # update remaining iterations for early stopping
+        remaining_iterations -= 1
+
+    previous_dist = dist
+    dist = (np.dot(X - location, precision) * (X - location)).sum(axis=1)
+    # Check if best fit already found (det => 0, logdet => -inf)
+    if np.isinf(det):
+        results = location, covariance, det, support, dist
+    # Check convergence
+    if np.allclose(det, previous_det):
+        # c_step procedure converged
+        if verbose:
+            print(
+                "Optimal couple (location, covariance) found before"
+                " ending iterations (%d left)" % (remaining_iterations)
+            )
+        results = location, covariance, det, support, dist
+    elif det > previous_det:
+        # determinant has increased (should not happen)
+        warnings.warn(
+            "Determinant has increased; this should not happen: "
+            "log(det) > log(previous_det) (%.15f > %.15f). "
+            "You may want to try with a higher value of "
+            "support_fraction (current value: %.3f)."
+            % (det, previous_det, n_support / n_samples),
+            RuntimeWarning,
+        )
+        results = (
+            previous_location,
+            previous_covariance,
+            previous_det,
+            previous_support,
+            previous_dist,
+        )
+
+    # Check early stopping
+    if remaining_iterations == 0:
+        if verbose:
+            print("Maximum number of iterations reached")
+        results = location, covariance, det, support, dist
+
+    return results
+
+
+def select_candidates(
+    X,
+    n_support,
+    n_trials,
+    select=1,
+    n_iter=30,
+    verbose=False,
+    cov_computation_method=empirical_covariance,
+    random_state=None,
+):
+    """Finds the best pure subset of observations to compute MCD from it.
+
+    The purpose of this function is to find the best sets of n_support
+    observations with respect to a minimization of their covariance
+    matrix determinant. Equivalently, it removes n_samples-n_support
+    observations to construct what we call a pure data set (i.e. not
+    containing outliers). The list of the observations of the pure
+    data set is referred to as the `support`.
+
+    Starting from a random support, the pure data set is found by the
+    c_step procedure introduced by Rousseeuw and Van Driessen in
+    [RV]_.
+
+    Parameters
+    ----------
+    X : array-like of shape (n_samples, n_features)
+        Data (sub)set in which we look for the n_support purest observations.
+
+    n_support : int
+        The number of samples the pure data set must contain.
+        This parameter must be in the range `[(n + p + 1)/2] < n_support < n`.
+
+    n_trials : int or tuple of shape (2,)
+        Number of different initial sets of observations from which to
+        run the algorithm. This parameter should be a strictly positive
+        integer.
+        Instead of giving a number of trials to perform, one can provide a
+        list of initial estimates that will be used to iteratively run
+        c_step procedures. In this case:
+        - n_trials[0]: array-like, shape (n_trials, n_features)
+          is the list of `n_trials` initial location estimates
+        - n_trials[1]: array-like, shape (n_trials, n_features, n_features)
+          is the list of `n_trials` initial covariances estimates
+
+    select : int, default=1
+        Number of best candidates results to return. This parameter must be
+        a strictly positive integer.
+
+    n_iter : int, default=30
+        Maximum number of iterations for the c_step procedure.
+        (2 is enough to be close to the final solution. "Never" exceeds 20).
+        This parameter must be a strictly positive integer.
+
+    verbose : bool, default=False
+        Control the output verbosity.
+
+    cov_computation_method : callable, \
+            default=:func:`sklearn.covariance.empirical_covariance`
+        The function which will be used to compute the covariance.
+        Must return an array of shape (n_features, n_features).
+
+    random_state : int, RandomState instance or None, default=None
+        Determines the pseudo random number generator for shuffling the data.
+        Pass an int for reproducible results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+    See Also
+    ---------
+    c_step
+
+    Returns
+    -------
+    best_locations : ndarray of shape (select, n_features)
+        The `select` location estimates computed from the `select` best
+        supports found in the data set (`X`).
+
+    best_covariances : ndarray of shape (select, n_features, n_features)
+        The `select` covariance estimates computed from the `select`
+        best supports found in the data set (`X`).
+
+    best_supports : ndarray of shape (select, n_samples)
+        The `select` best supports found in the data set (`X`).
+
+    References
+    ----------
+    .. [RV] A Fast Algorithm for the Minimum Covariance Determinant
+        Estimator, 1999, American Statistical Association and the American
+        Society for Quality, TECHNOMETRICS
+    """
+    random_state = check_random_state(random_state)
+
+    if isinstance(n_trials, Integral):
+        run_from_estimates = False
+    elif isinstance(n_trials, tuple):
+        run_from_estimates = True
+        estimates_list = n_trials
+        n_trials = estimates_list[0].shape[0]
+    else:
+        raise TypeError(
+            "Invalid 'n_trials' parameter, expected tuple or  integer, got %s (%s)"
+            % (n_trials, type(n_trials))
+        )
+
+    # compute `n_trials` location and shape estimates candidates in the subset
+    all_estimates = []
+    if not run_from_estimates:
+        # perform `n_trials` computations from random initial supports
+        for j in range(n_trials):
+            all_estimates.append(
+                _c_step(
+                    X,
+                    n_support,
+                    remaining_iterations=n_iter,
+                    verbose=verbose,
+                    cov_computation_method=cov_computation_method,
+                    random_state=random_state,
+                )
+            )
+    else:
+        # perform computations from every given initial estimates
+        for j in range(n_trials):
+            initial_estimates = (estimates_list[0][j], estimates_list[1][j])
+            all_estimates.append(
+                _c_step(
+                    X,
+                    n_support,
+                    remaining_iterations=n_iter,
+                    initial_estimates=initial_estimates,
+                    verbose=verbose,
+                    cov_computation_method=cov_computation_method,
+                    random_state=random_state,
+                )
+            )
+    all_locs_sub, all_covs_sub, all_dets_sub, all_supports_sub, all_ds_sub = zip(
+        *all_estimates
+    )
+    # find the `n_best` best results among the `n_trials` ones
+    index_best = np.argsort(all_dets_sub)[:select]
+    best_locations = np.asarray(all_locs_sub)[index_best]
+    best_covariances = np.asarray(all_covs_sub)[index_best]
+    best_supports = np.asarray(all_supports_sub)[index_best]
+    best_ds = np.asarray(all_ds_sub)[index_best]
+
+    return best_locations, best_covariances, best_supports, best_ds
+
+
+def fast_mcd(
+    X,
+    support_fraction=None,
+    cov_computation_method=empirical_covariance,
+    random_state=None,
+):
+    """Estimate the Minimum Covariance Determinant matrix.
+
+    Read more in the :ref:`User Guide <robust_covariance>`.
+
+    Parameters
+    ----------
+    X : array-like of shape (n_samples, n_features)
+        The data matrix, with p features and n samples.
+
+    support_fraction : float, default=None
+        The proportion of points to be included in the support of the raw
+        MCD estimate. Default is `None`, which implies that the minimum
+        value of `support_fraction` will be used within the algorithm:
+        `(n_sample + n_features + 1) / 2`. This parameter must be in the
+        range (0, 1).
+
+    cov_computation_method : callable, \
+            default=:func:`sklearn.covariance.empirical_covariance`
+        The function which will be used to compute the covariance.
+        Must return an array of shape (n_features, n_features).
+
+    random_state : int, RandomState instance or None, default=None
+        Determines the pseudo random number generator for shuffling the data.
+        Pass an int for reproducible results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+    Returns
+    -------
+    location : ndarray of shape (n_features,)
+        Robust location of the data.
+
+    covariance : ndarray of shape (n_features, n_features)
+        Robust covariance of the features.
+
+    support : ndarray of shape (n_samples,), dtype=bool
+        A mask of the observations that have been used to compute
+        the robust location and covariance estimates of the data set.
+
+    Notes
+    -----
+    The FastMCD algorithm has been introduced by Rousseuw and Van Driessen
+    in "A Fast Algorithm for the Minimum Covariance Determinant Estimator,
+    1999, American Statistical Association and the American Society
+    for Quality, TECHNOMETRICS".
+    The principle is to compute robust estimates and random subsets before
+    pooling them into a larger subsets, and finally into the full data set.
+    Depending on the size of the initial sample, we have one, two or three
+    such computation levels.
+
+    Note that only raw estimates are returned. If one is interested in
+    the correction and reweighting steps described in [RouseeuwVan]_,
+    see the MinCovDet object.
+
+    References
+    ----------
+
+    .. [RouseeuwVan] A Fast Algorithm for the Minimum Covariance
+        Determinant Estimator, 1999, American Statistical Association
+        and the American Society for Quality, TECHNOMETRICS
+
+    .. [Butler1993] R. W. Butler, P. L. Davies and M. Jhun,
+        Asymptotics For The Minimum Covariance Determinant Estimator,
+        The Annals of Statistics, 1993, Vol. 21, No. 3, 1385-1400
+    """
+    random_state = check_random_state(random_state)
+
+    X = check_array(X, ensure_min_samples=2, estimator="fast_mcd")
+    n_samples, n_features = X.shape
+
+    # minimum breakdown value
+    if support_fraction is None:
+        n_support = int(np.ceil(0.5 * (n_samples + n_features + 1)))
+    else:
+        n_support = int(support_fraction * n_samples)
+
+    # 1-dimensional case quick computation
+    # (Rousseeuw, P. J. and Leroy, A. M. (2005) References, in Robust
+    #  Regression and Outlier Detection, John Wiley & Sons, chapter 4)
+    if n_features == 1:
+        if n_support < n_samples:
+            # find the sample shortest halves
+            X_sorted = np.sort(np.ravel(X))
+            diff = X_sorted[n_support:] - X_sorted[: (n_samples - n_support)]
+            halves_start = np.where(diff == np.min(diff))[0]
+            # take the middle points' mean to get the robust location estimate
+            location = (
+                0.5
+                * (X_sorted[n_support + halves_start] + X_sorted[halves_start]).mean()
+            )
+            support = np.zeros(n_samples, dtype=bool)
+            X_centered = X - location
+            support[np.argsort(np.abs(X_centered), 0)[:n_support]] = True
+            covariance = np.asarray([[np.var(X[support])]])
+            location = np.array([location])
+            # get precision matrix in an optimized way
+            precision = linalg.pinvh(covariance)
+            dist = (np.dot(X_centered, precision) * (X_centered)).sum(axis=1)
+        else:
+            support = np.ones(n_samples, dtype=bool)
+            covariance = np.asarray([[np.var(X)]])
+            location = np.asarray([np.mean(X)])
+            X_centered = X - location
+            # get precision matrix in an optimized way
+            precision = linalg.pinvh(covariance)
+            dist = (np.dot(X_centered, precision) * (X_centered)).sum(axis=1)
+    # Starting FastMCD algorithm for p-dimensional case
+    if (n_samples > 500) and (n_features > 1):
+        # 1. Find candidate supports on subsets
+        # a. split the set in subsets of size ~ 300
+        n_subsets = n_samples // 300
+        n_samples_subsets = n_samples // n_subsets
+        samples_shuffle = random_state.permutation(n_samples)
+        h_subset = int(np.ceil(n_samples_subsets * (n_support / float(n_samples))))
+        # b. perform a total of 500 trials
+        n_trials_tot = 500
+        # c. select 10 best (location, covariance) for each subset
+        n_best_sub = 10
+        n_trials = max(10, n_trials_tot // n_subsets)
+        n_best_tot = n_subsets * n_best_sub
+        all_best_locations = np.zeros((n_best_tot, n_features))
+        try:
+            all_best_covariances = np.zeros((n_best_tot, n_features, n_features))
+        except MemoryError:
+            # The above is too big. Let's try with something much small
+            # (and less optimal)
+            n_best_tot = 10
+            all_best_covariances = np.zeros((n_best_tot, n_features, n_features))
+            n_best_sub = 2
+        for i in range(n_subsets):
+            low_bound = i * n_samples_subsets
+            high_bound = low_bound + n_samples_subsets
+            current_subset = X[samples_shuffle[low_bound:high_bound]]
+            best_locations_sub, best_covariances_sub, _, _ = select_candidates(
+                current_subset,
+                h_subset,
+                n_trials,
+                select=n_best_sub,
+                n_iter=2,
+                cov_computation_method=cov_computation_method,
+                random_state=random_state,
+            )
+            subset_slice = np.arange(i * n_best_sub, (i + 1) * n_best_sub)
+            all_best_locations[subset_slice] = best_locations_sub
+            all_best_covariances[subset_slice] = best_covariances_sub
+        # 2. Pool the candidate supports into a merged set
+        # (possibly the full dataset)
+        n_samples_merged = min(1500, n_samples)
+        h_merged = int(np.ceil(n_samples_merged * (n_support / float(n_samples))))
+        if n_samples > 1500:
+            n_best_merged = 10
+        else:
+            n_best_merged = 1
+        # find the best couples (location, covariance) on the merged set
+        selection = random_state.permutation(n_samples)[:n_samples_merged]
+        locations_merged, covariances_merged, supports_merged, d = select_candidates(
+            X[selection],
+            h_merged,
+            n_trials=(all_best_locations, all_best_covariances),
+            select=n_best_merged,
+            cov_computation_method=cov_computation_method,
+            random_state=random_state,
+        )
+        # 3. Finally get the overall best (locations, covariance) couple
+        if n_samples < 1500:
+            # directly get the best couple (location, covariance)
+            location = locations_merged[0]
+            covariance = covariances_merged[0]
+            support = np.zeros(n_samples, dtype=bool)
+            dist = np.zeros(n_samples)
+            support[selection] = supports_merged[0]
+            dist[selection] = d[0]
+        else:
+            # select the best couple on the full dataset
+            locations_full, covariances_full, supports_full, d = select_candidates(
+                X,
+                n_support,
+                n_trials=(locations_merged, covariances_merged),
+                select=1,
+                cov_computation_method=cov_computation_method,
+                random_state=random_state,
+            )
+            location = locations_full[0]
+            covariance = covariances_full[0]
+            support = supports_full[0]
+            dist = d[0]
+    elif n_features > 1:
+        # 1. Find the 10 best couples (location, covariance)
+        # considering two iterations
+        n_trials = 30
+        n_best = 10
+        locations_best, covariances_best, _, _ = select_candidates(
+            X,
+            n_support,
+            n_trials=n_trials,
+            select=n_best,
+            n_iter=2,
+            cov_computation_method=cov_computation_method,
+            random_state=random_state,
+        )
+        # 2. Select the best couple on the full dataset amongst the 10
+        locations_full, covariances_full, supports_full, d = select_candidates(
+            X,
+            n_support,
+            n_trials=(locations_best, covariances_best),
+            select=1,
+            cov_computation_method=cov_computation_method,
+            random_state=random_state,
+        )
+        location = locations_full[0]
+        covariance = covariances_full[0]
+        support = supports_full[0]
+        dist = d[0]
+
+    return location, covariance, support, dist
+
+
+class MinCovDet(EmpiricalCovariance):
+    """Minimum Covariance Determinant (MCD): robust estimator of covariance.
+
+    The Minimum Covariance Determinant covariance estimator is to be applied
+    on Gaussian-distributed data, but could still be relevant on data
+    drawn from a unimodal, symmetric distribution. It is not meant to be used
+    with multi-modal data (the algorithm used to fit a MinCovDet object is
+    likely to fail in such a case).
+    One should consider projection pursuit methods to deal with multi-modal
+    datasets.
+
+    Read more in the :ref:`User Guide <robust_covariance>`.
+
+    Parameters
+    ----------
+    store_precision : bool, default=True
+        Specify if the estimated precision is stored.
+
+    assume_centered : bool, default=False
+        If True, the support of the robust location and the covariance
+        estimates is computed, and a covariance estimate is recomputed from
+        it, without centering the data.
+        Useful to work with data whose mean is significantly equal to
+        zero but is not exactly zero.
+        If False, the robust location and covariance are directly computed
+        with the FastMCD algorithm without additional treatment.
+
+    support_fraction : float, default=None
+        The proportion of points to be included in the support of the raw
+        MCD estimate. Default is None, which implies that the minimum
+        value of support_fraction will be used within the algorithm:
+        `(n_sample + n_features + 1) / 2`. The parameter must be in the range
+        (0, 1].
+
+    random_state : int, RandomState instance or None, default=None
+        Determines the pseudo random number generator for shuffling the data.
+        Pass an int for reproducible results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+    Attributes
+    ----------
+    raw_location_ : ndarray of shape (n_features,)
+        The raw robust estimated location before correction and re-weighting.
+
+    raw_covariance_ : ndarray of shape (n_features, n_features)
+        The raw robust estimated covariance before correction and re-weighting.
+
+    raw_support_ : ndarray of shape (n_samples,)
+        A mask of the observations that have been used to compute
+        the raw robust estimates of location and shape, before correction
+        and re-weighting.
+
+    location_ : ndarray of shape (n_features,)
+        Estimated robust location.
+
+    covariance_ : ndarray of shape (n_features, n_features)
+        Estimated robust covariance matrix.
+
+    precision_ : ndarray of shape (n_features, n_features)
+        Estimated pseudo inverse matrix.
+        (stored only if store_precision is True)
+
+    support_ : ndarray of shape (n_samples,)
+        A mask of the observations that have been used to compute
+        the robust estimates of location and shape.
+
+    dist_ : ndarray of shape (n_samples,)
+        Mahalanobis distances of the training set (on which :meth:`fit` is
+        called) observations.
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+        .. versionadded:: 0.24
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
+    See Also
+    --------
+    EllipticEnvelope : An object for detecting outliers in
+        a Gaussian distributed dataset.
+    EmpiricalCovariance : Maximum likelihood covariance estimator.
+    GraphicalLasso : Sparse inverse covariance estimation
+        with an l1-penalized estimator.
+    GraphicalLassoCV : Sparse inverse covariance with cross-validated
+        choice of the l1 penalty.
+    LedoitWolf : LedoitWolf Estimator.
+    OAS : Oracle Approximating Shrinkage Estimator.
+    ShrunkCovariance : Covariance estimator with shrinkage.
+
+    References
+    ----------
+
+    .. [Rouseeuw1984] P. J. Rousseeuw. Least median of squares regression.
+        J. Am Stat Ass, 79:871, 1984.
+    .. [Rousseeuw] A Fast Algorithm for the Minimum Covariance Determinant
+        Estimator, 1999, American Statistical Association and the American
+        Society for Quality, TECHNOMETRICS
+    .. [ButlerDavies] R. W. Butler, P. L. Davies and M. Jhun,
+        Asymptotics For The Minimum Covariance Determinant Estimator,
+        The Annals of Statistics, 1993, Vol. 21, No. 3, 1385-1400
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from sklearn.covariance import MinCovDet
+    >>> from sklearn.datasets import make_gaussian_quantiles
+    >>> real_cov = np.array([[.8, .3],
+    ...                      [.3, .4]])
+    >>> rng = np.random.RandomState(0)
+    >>> X = rng.multivariate_normal(mean=[0, 0],
+    ...                                   cov=real_cov,
+    ...                                   size=500)
+    >>> cov = MinCovDet(random_state=0).fit(X)
+    >>> cov.covariance_
+    array([[0.7411..., 0.2535...],
+           [0.2535..., 0.3053...]])
+    >>> cov.location_
+    array([0.0813... , 0.0427...])
+    """
+
+    _parameter_constraints: dict = {
+        **EmpiricalCovariance._parameter_constraints,
+        "support_fraction": [Interval(Real, 0, 1, closed="right"), None],
+        "random_state": ["random_state"],
+    }
+    _nonrobust_covariance = staticmethod(empirical_covariance)
+
+    def __init__(
+        self,
+        *,
+        store_precision=True,
+        assume_centered=False,
+        support_fraction=None,
+        random_state=None,
+    ):
+        self.store_precision = store_precision
+        self.assume_centered = assume_centered
+        self.support_fraction = support_fraction
+        self.random_state = random_state
+
+    def fit(self, X, y=None):
+        """Fit a Minimum Covariance Determinant with the FastMCD algorithm.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            Training data, where `n_samples` is the number of samples
+            and `n_features` is the number of features.
+
+        y : Ignored
+            Not used, present for API consistency by convention.
+
+        Returns
+        -------
+        self : object
+            Returns the instance itself.
+        """
+        self._validate_params()
+        X = self._validate_data(X, ensure_min_samples=2, estimator="MinCovDet")
+        random_state = check_random_state(self.random_state)
+        n_samples, n_features = X.shape
+        # check that the empirical covariance is full rank
+        if (linalg.svdvals(np.dot(X.T, X)) > 1e-8).sum() != n_features:
+            warnings.warn(
+                "The covariance matrix associated to your dataset is not full rank"
+            )
+        # compute and store raw estimates
+        raw_location, raw_covariance, raw_support, raw_dist = fast_mcd(
+            X,
+            support_fraction=self.support_fraction,
+            cov_computation_method=self._nonrobust_covariance,
+            random_state=random_state,
+        )
+        if self.assume_centered:
+            raw_location = np.zeros(n_features)
+            raw_covariance = self._nonrobust_covariance(
+                X[raw_support], assume_centered=True
+            )
+            # get precision matrix in an optimized way
+            precision = linalg.pinvh(raw_covariance)
+            raw_dist = np.sum(np.dot(X, precision) * X, 1)
+        self.raw_location_ = raw_location
+        self.raw_covariance_ = raw_covariance
+        self.raw_support_ = raw_support
+        self.location_ = raw_location
+        self.support_ = raw_support
+        self.dist_ = raw_dist
+        # obtain consistency at normal models
+        self.correct_covariance(X)
+        # re-weight estimator
+        self.reweight_covariance(X)
+
+        return self
+
+    def correct_covariance(self, data):
+        """Apply a correction to raw Minimum Covariance Determinant estimates.
+
+        Correction using the empirical correction factor suggested
+        by Rousseeuw and Van Driessen in [RVD]_.
+
+        Parameters
+        ----------
+        data : array-like of shape (n_samples, n_features)
+            The data matrix, with p features and n samples.
+            The data set must be the one which was used to compute
+            the raw estimates.
+
+        Returns
+        -------
+        covariance_corrected : ndarray of shape (n_features, n_features)
+            Corrected robust covariance estimate.
+
+        References
+        ----------
+
+        .. [RVD] A Fast Algorithm for the Minimum Covariance
+            Determinant Estimator, 1999, American Statistical Association
+            and the American Society for Quality, TECHNOMETRICS
+        """
+
+        # Check that the covariance of the support data is not equal to 0.
+        # Otherwise self.dist_ = 0 and thus correction = 0.
+        n_samples = len(self.dist_)
+        n_support = np.sum(self.support_)
+        if n_support < n_samples and np.allclose(self.raw_covariance_, 0):
+            raise ValueError(
+                "The covariance matrix of the support data "
+                "is equal to 0, try to increase support_fraction"
+            )
+        correction = np.median(self.dist_) / chi2(data.shape[1]).isf(0.5)
+        covariance_corrected = self.raw_covariance_ * correction
+        self.dist_ /= correction
+        return covariance_corrected
+
+    def reweight_covariance(self, data):
+        """Re-weight raw Minimum Covariance Determinant estimates.
+
+        Re-weight observations using Rousseeuw's method (equivalent to
+        deleting outlying observations from the data set before
+        computing location and covariance estimates) described
+        in [RVDriessen]_.
+
+        Parameters
+        ----------
+        data : array-like of shape (n_samples, n_features)
+            The data matrix, with p features and n samples.
+            The data set must be the one which was used to compute
+            the raw estimates.
+
+        Returns
+        -------
+        location_reweighted : ndarray of shape (n_features,)
+            Re-weighted robust location estimate.
+
+        covariance_reweighted : ndarray of shape (n_features, n_features)
+            Re-weighted robust covariance estimate.
+
+        support_reweighted : ndarray of shape (n_samples,), dtype=bool
+            A mask of the observations that have been used to compute
+            the re-weighted robust location and covariance estimates.
+
+        References
+        ----------
+
+        .. [RVDriessen] A Fast Algorithm for the Minimum Covariance
+            Determinant Estimator, 1999, American Statistical Association
+            and the American Society for Quality, TECHNOMETRICS
+        """
+        n_samples, n_features = data.shape
+        mask = self.dist_ < chi2(n_features).isf(0.025)
+        if self.assume_centered:
+            location_reweighted = np.zeros(n_features)
+        else:
+            location_reweighted = data[mask].mean(0)
+        covariance_reweighted = self._nonrobust_covariance(
+            data[mask], assume_centered=self.assume_centered
+        )
+        support_reweighted = np.zeros(n_samples, dtype=bool)
+        support_reweighted[mask] = True
+        self._set_covariance(covariance_reweighted)
+        self.location_ = location_reweighted
+        self.support_ = support_reweighted
+        X_centered = data - self.location_
+        self.dist_ = np.sum(np.dot(X_centered, self.get_precision()) * X_centered, 1)
+        return location_reweighted, covariance_reweighted, support_reweighted

mplug_owl2/lib/python3.10/site-packages/sklearn/covariance/_shrunk_covariance.py

@@ -0,0 +1,764 @@
+"""
+Covariance estimators using shrinkage.
+
+Shrinkage corresponds to regularising `cov` using a convex combination:
+shrunk_cov = (1-shrinkage)*cov + shrinkage*structured_estimate.
+
+"""
+
+# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
+#         Gael Varoquaux <gael.varoquaux@normalesup.org>
+#         Virgile Fritsch <virgile.fritsch@inria.fr>
+#
+# License: BSD 3 clause
+
+# avoid division truncation
+import warnings
+from numbers import Real, Integral
+import numpy as np
+
+from . import empirical_covariance, EmpiricalCovariance
+from .._config import config_context
+from ..utils import check_array
+from ..utils._param_validation import Interval
+
+
+def _oas(X, *, assume_centered=False):
+    """Estimate covariance with the Oracle Approximating Shrinkage algorithm.
+
+    The formulation is based on [1]_.
+    [1] "Shrinkage algorithms for MMSE covariance estimation.",
+        Chen, Y., Wiesel, A., Eldar, Y. C., & Hero, A. O.
+        IEEE Transactions on Signal Processing, 58(10), 5016-5029, 2010.
+        https://arxiv.org/pdf/0907.4698.pdf
+    """
+    if len(X.shape) == 2 and X.shape[1] == 1:
+        # for only one feature, the result is the same whatever the shrinkage
+        if not assume_centered:
+            X = X - X.mean()
+        return np.atleast_2d((X**2).mean()), 0.0
+
+    n_samples, n_features = X.shape
+
+    emp_cov = empirical_covariance(X, assume_centered=assume_centered)
+
+    # The shrinkage is defined as:
+    # shrinkage = min(
+    # trace(S @ S.T) + trace(S)**2) / ((n + 1) (trace(S @ S.T) - trace(S)**2 / p), 1
+    # )
+    # where n and p are n_samples and n_features, respectively (cf. Eq. 23 in [1]).
+    # The factor 2 / p is omitted since it does not impact the value of the estimator
+    # for large p.
+
+    # Instead of computing trace(S)**2, we can compute the average of the squared
+    # elements of S that is equal to trace(S)**2 / p**2.
+    # See the definition of the Frobenius norm:
+    # https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm
+    alpha = np.mean(emp_cov**2)
+    mu = np.trace(emp_cov) / n_features
+    mu_squared = mu**2
+
+    # The factor 1 / p**2 will cancel out since it is in both the numerator and
+    # denominator
+    num = alpha + mu_squared
+    den = (n_samples + 1) * (alpha - mu_squared / n_features)
+    shrinkage = 1.0 if den == 0 else min(num / den, 1.0)
+
+    # The shrunk covariance is defined as:
+    # (1 - shrinkage) * S + shrinkage * F (cf. Eq. 4 in [1])
+    # where S is the empirical covariance and F is the shrinkage target defined as
+    # F = trace(S) / n_features * np.identity(n_features) (cf. Eq. 3 in [1])
+    shrunk_cov = (1.0 - shrinkage) * emp_cov
+    shrunk_cov.flat[:: n_features + 1] += shrinkage * mu
+
+    return shrunk_cov, shrinkage
+
+
+###############################################################################
+# Public API
+# ShrunkCovariance estimator
+
+
+def shrunk_covariance(emp_cov, shrinkage=0.1):
+    """Calculate a covariance matrix shrunk on the diagonal.
+
+    Read more in the :ref:`User Guide <shrunk_covariance>`.
+
+    Parameters
+    ----------
+    emp_cov : array-like of shape (n_features, n_features)
+        Covariance matrix to be shrunk.
+
+    shrinkage : float, default=0.1
+        Coefficient in the convex combination used for the computation
+        of the shrunk estimate. Range is [0, 1].
+
+    Returns
+    -------
+    shrunk_cov : ndarray of shape (n_features, n_features)
+        Shrunk covariance.
+
+    Notes
+    -----
+    The regularized (shrunk) covariance is given by::
+
+        (1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features)
+
+    where `mu = trace(cov) / n_features`.
+    """
+    emp_cov = check_array(emp_cov)
+    n_features = emp_cov.shape[0]
+
+    mu = np.trace(emp_cov) / n_features
+    shrunk_cov = (1.0 - shrinkage) * emp_cov
+    shrunk_cov.flat[:: n_features + 1] += shrinkage * mu
+
+    return shrunk_cov
+
+
+class ShrunkCovariance(EmpiricalCovariance):
+    """Covariance estimator with shrinkage.
+
+    Read more in the :ref:`User Guide <shrunk_covariance>`.
+
+    Parameters
+    ----------
+    store_precision : bool, default=True
+        Specify if the estimated precision is stored.
+
+    assume_centered : bool, default=False
+        If True, data will not be centered before computation.
+        Useful when working with data whose mean is almost, but not exactly
+        zero.
+        If False, data will be centered before computation.
+
+    shrinkage : float, default=0.1
+        Coefficient in the convex combination used for the computation
+        of the shrunk estimate. Range is [0, 1].
+
+    Attributes
+    ----------
+    covariance_ : ndarray of shape (n_features, n_features)
+        Estimated covariance matrix
+
+    location_ : ndarray of shape (n_features,)
+        Estimated location, i.e. the estimated mean.
+
+    precision_ : ndarray of shape (n_features, n_features)
+        Estimated pseudo inverse matrix.
+        (stored only if store_precision is True)
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+        .. versionadded:: 0.24
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
+    See Also
+    --------
+    EllipticEnvelope : An object for detecting outliers in
+        a Gaussian distributed dataset.
+    EmpiricalCovariance : Maximum likelihood covariance estimator.
+    GraphicalLasso : Sparse inverse covariance estimation
+        with an l1-penalized estimator.
+    GraphicalLassoCV : Sparse inverse covariance with cross-validated
+        choice of the l1 penalty.
+    LedoitWolf : LedoitWolf Estimator.
+    MinCovDet : Minimum Covariance Determinant
+        (robust estimator of covariance).
+    OAS : Oracle Approximating Shrinkage Estimator.
+
+    Notes
+    -----
+    The regularized covariance is given by:
+
+    (1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features)
+
+    where mu = trace(cov) / n_features
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from sklearn.covariance import ShrunkCovariance
+    >>> from sklearn.datasets import make_gaussian_quantiles
+    >>> real_cov = np.array([[.8, .3],
+    ...                      [.3, .4]])
+    >>> rng = np.random.RandomState(0)
+    >>> X = rng.multivariate_normal(mean=[0, 0],
+    ...                                   cov=real_cov,
+    ...                                   size=500)
+    >>> cov = ShrunkCovariance().fit(X)
+    >>> cov.covariance_
+    array([[0.7387..., 0.2536...],
+           [0.2536..., 0.4110...]])
+    >>> cov.location_
+    array([0.0622..., 0.0193...])
+    """
+
+    _parameter_constraints: dict = {
+        **EmpiricalCovariance._parameter_constraints,
+        "shrinkage": [Interval(Real, 0, 1, closed="both")],
+    }
+
+    def __init__(self, *, store_precision=True, assume_centered=False, shrinkage=0.1):
+        super().__init__(
+            store_precision=store_precision, assume_centered=assume_centered
+        )
+        self.shrinkage = shrinkage
+
+    def fit(self, X, y=None):
+        """Fit the shrunk covariance model to X.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            Training data, where `n_samples` is the number of samples
+            and `n_features` is the number of features.
+
+        y : Ignored
+            Not used, present for API consistency by convention.
+
+        Returns
+        -------
+        self : object
+            Returns the instance itself.
+        """
+        self._validate_params()
+        X = self._validate_data(X)
+        # Not calling the parent object to fit, to avoid a potential
+        # matrix inversion when setting the precision
+        if self.assume_centered:
+            self.location_ = np.zeros(X.shape[1])
+        else:
+            self.location_ = X.mean(0)
+        covariance = empirical_covariance(X, assume_centered=self.assume_centered)
+        covariance = shrunk_covariance(covariance, self.shrinkage)
+        self._set_covariance(covariance)
+
+        return self
+
+
+# Ledoit-Wolf estimator
+
+
+def ledoit_wolf_shrinkage(X, assume_centered=False, block_size=1000):
+    """Estimate the shrunk Ledoit-Wolf covariance matrix.
+
+    Read more in the :ref:`User Guide <shrunk_covariance>`.
+
+    Parameters
+    ----------
+    X : array-like of shape (n_samples, n_features)
+        Data from which to compute the Ledoit-Wolf shrunk covariance shrinkage.
+
+    assume_centered : bool, default=False
+        If True, data will not be centered before computation.
+        Useful to work with data whose mean is significantly equal to
+        zero but is not exactly zero.
+        If False, data will be centered before computation.
+
+    block_size : int, default=1000
+        Size of blocks into which the covariance matrix will be split.
+
+    Returns
+    -------
+    shrinkage : float
+        Coefficient in the convex combination used for the computation
+        of the shrunk estimate.
+
+    Notes
+    -----
+    The regularized (shrunk) covariance is:
+
+    (1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features)
+
+    where mu = trace(cov) / n_features
+    """
+    X = check_array(X)
+    # for only one feature, the result is the same whatever the shrinkage
+    if len(X.shape) == 2 and X.shape[1] == 1:
+        return 0.0
+    if X.ndim == 1:
+        X = np.reshape(X, (1, -1))
+
+    if X.shape[0] == 1:
+        warnings.warn(
+            "Only one sample available. You may want to reshape your data array"
+        )
+    n_samples, n_features = X.shape
+
+    # optionally center data
+    if not assume_centered:
+        X = X - X.mean(0)
+
+    # A non-blocked version of the computation is present in the tests
+    # in tests/test_covariance.py
+
+    # number of blocks to split the covariance matrix into
+    n_splits = int(n_features / block_size)
+    X2 = X**2
+    emp_cov_trace = np.sum(X2, axis=0) / n_samples
+    mu = np.sum(emp_cov_trace) / n_features
+    beta_ = 0.0  # sum of the coefficients of <X2.T, X2>
+    delta_ = 0.0  # sum of the *squared* coefficients of <X.T, X>
+    # starting block computation
+    for i in range(n_splits):
+        for j in range(n_splits):
+            rows = slice(block_size * i, block_size * (i + 1))
+            cols = slice(block_size * j, block_size * (j + 1))
+            beta_ += np.sum(np.dot(X2.T[rows], X2[:, cols]))
+            delta_ += np.sum(np.dot(X.T[rows], X[:, cols]) ** 2)
+        rows = slice(block_size * i, block_size * (i + 1))
+        beta_ += np.sum(np.dot(X2.T[rows], X2[:, block_size * n_splits :]))
+        delta_ += np.sum(np.dot(X.T[rows], X[:, block_size * n_splits :]) ** 2)
+    for j in range(n_splits):
+        cols = slice(block_size * j, block_size * (j + 1))
+        beta_ += np.sum(np.dot(X2.T[block_size * n_splits :], X2[:, cols]))
+        delta_ += np.sum(np.dot(X.T[block_size * n_splits :], X[:, cols]) ** 2)
+    delta_ += np.sum(
+        np.dot(X.T[block_size * n_splits :], X[:, block_size * n_splits :]) ** 2
+    )
+    delta_ /= n_samples**2
+    beta_ += np.sum(
+        np.dot(X2.T[block_size * n_splits :], X2[:, block_size * n_splits :])
+    )
+    # use delta_ to compute beta
+    beta = 1.0 / (n_features * n_samples) * (beta_ / n_samples - delta_)
+    # delta is the sum of the squared coefficients of (<X.T,X> - mu*Id) / p
+    delta = delta_ - 2.0 * mu * emp_cov_trace.sum() + n_features * mu**2
+    delta /= n_features
+    # get final beta as the min between beta and delta
+    # We do this to prevent shrinking more than "1", which would invert
+    # the value of covariances
+    beta = min(beta, delta)
+    # finally get shrinkage
+    shrinkage = 0 if beta == 0 else beta / delta
+    return shrinkage
+
+
+def ledoit_wolf(X, *, assume_centered=False, block_size=1000):
+    """Estimate the shrunk Ledoit-Wolf covariance matrix.
+
+    Read more in the :ref:`User Guide <shrunk_covariance>`.
+
+    Parameters
+    ----------
+    X : array-like of shape (n_samples, n_features)
+        Data from which to compute the covariance estimate.
+
+    assume_centered : bool, default=False
+        If True, data will not be centered before computation.
+        Useful to work with data whose mean is significantly equal to
+        zero but is not exactly zero.
+        If False, data will be centered before computation.
+
+    block_size : int, default=1000
+        Size of blocks into which the covariance matrix will be split.
+        This is purely a memory optimization and does not affect results.
+
+    Returns
+    -------
+    shrunk_cov : ndarray of shape (n_features, n_features)
+        Shrunk covariance.
+
+    shrinkage : float
+        Coefficient in the convex combination used for the computation
+        of the shrunk estimate.
+
+    Notes
+    -----
+    The regularized (shrunk) covariance is:
+
+    (1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features)
+
+    where mu = trace(cov) / n_features
+    """
+    X = check_array(X)
+    # for only one feature, the result is the same whatever the shrinkage
+    if len(X.shape) == 2 and X.shape[1] == 1:
+        if not assume_centered:
+            X = X - X.mean()
+        return np.atleast_2d((X**2).mean()), 0.0
+    if X.ndim == 1:
+        X = np.reshape(X, (1, -1))
+        warnings.warn(
+            "Only one sample available. You may want to reshape your data array"
+        )
+        n_features = X.size
+    else:
+        _, n_features = X.shape
+
+    # get Ledoit-Wolf shrinkage
+    shrinkage = ledoit_wolf_shrinkage(
+        X, assume_centered=assume_centered, block_size=block_size
+    )
+    emp_cov = empirical_covariance(X, assume_centered=assume_centered)
+    mu = np.sum(np.trace(emp_cov)) / n_features
+    shrunk_cov = (1.0 - shrinkage) * emp_cov
+    shrunk_cov.flat[:: n_features + 1] += shrinkage * mu
+
+    return shrunk_cov, shrinkage
+
+
+class LedoitWolf(EmpiricalCovariance):
+    """LedoitWolf Estimator.
+
+    Ledoit-Wolf is a particular form of shrinkage, where the shrinkage
+    coefficient is computed using O. Ledoit and M. Wolf's formula as
+    described in "A Well-Conditioned Estimator for Large-Dimensional
+    Covariance Matrices", Ledoit and Wolf, Journal of Multivariate
+    Analysis, Volume 88, Issue 2, February 2004, pages 365-411.
+
+    Read more in the :ref:`User Guide <shrunk_covariance>`.
+
+    Parameters
+    ----------
+    store_precision : bool, default=True
+        Specify if the estimated precision is stored.
+
+    assume_centered : bool, default=False
+        If True, data will not be centered before computation.
+        Useful when working with data whose mean is almost, but not exactly
+        zero.
+        If False (default), data will be centered before computation.
+
+    block_size : int, default=1000
+        Size of blocks into which the covariance matrix will be split
+        during its Ledoit-Wolf estimation. This is purely a memory
+        optimization and does not affect results.
+
+    Attributes
+    ----------
+    covariance_ : ndarray of shape (n_features, n_features)
+        Estimated covariance matrix.
+
+    location_ : ndarray of shape (n_features,)
+        Estimated location, i.e. the estimated mean.
+
+    precision_ : ndarray of shape (n_features, n_features)
+        Estimated pseudo inverse matrix.
+        (stored only if store_precision is True)
+
+    shrinkage_ : float
+        Coefficient in the convex combination used for the computation
+        of the shrunk estimate. Range is [0, 1].
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+        .. versionadded:: 0.24
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
+    See Also
+    --------
+    EllipticEnvelope : An object for detecting outliers in
+        a Gaussian distributed dataset.
+    EmpiricalCovariance : Maximum likelihood covariance estimator.
+    GraphicalLasso : Sparse inverse covariance estimation
+        with an l1-penalized estimator.
+    GraphicalLassoCV : Sparse inverse covariance with cross-validated
+        choice of the l1 penalty.
+    MinCovDet : Minimum Covariance Determinant
+        (robust estimator of covariance).
+    OAS : Oracle Approximating Shrinkage Estimator.
+    ShrunkCovariance : Covariance estimator with shrinkage.
+
+    Notes
+    -----
+    The regularised covariance is:
+
+    (1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features)
+
+    where mu = trace(cov) / n_features
+    and shrinkage is given by the Ledoit and Wolf formula (see References)
+
+    References
+    ----------
+    "A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices",
+    Ledoit and Wolf, Journal of Multivariate Analysis, Volume 88, Issue 2,
+    February 2004, pages 365-411.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from sklearn.covariance import LedoitWolf
+    >>> real_cov = np.array([[.4, .2],
+    ...                      [.2, .8]])
+    >>> np.random.seed(0)
+    >>> X = np.random.multivariate_normal(mean=[0, 0],
+    ...                                   cov=real_cov,
+    ...                                   size=50)
+    >>> cov = LedoitWolf().fit(X)
+    >>> cov.covariance_
+    array([[0.4406..., 0.1616...],
+           [0.1616..., 0.8022...]])
+    >>> cov.location_
+    array([ 0.0595... , -0.0075...])
+    """
+
+    _parameter_constraints: dict = {
+        **EmpiricalCovariance._parameter_constraints,
+        "block_size": [Interval(Integral, 1, None, closed="left")],
+    }
+
+    def __init__(self, *, store_precision=True, assume_centered=False, block_size=1000):
+        super().__init__(
+            store_precision=store_precision, assume_centered=assume_centered
+        )
+        self.block_size = block_size
+
+    def fit(self, X, y=None):
+        """Fit the Ledoit-Wolf shrunk covariance model to X.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            Training data, where `n_samples` is the number of samples
+            and `n_features` is the number of features.
+        y : Ignored
+            Not used, present for API consistency by convention.
+
+        Returns
+        -------
+        self : object
+            Returns the instance itself.
+        """
+        self._validate_params()
+        # Not calling the parent object to fit, to avoid computing the
+        # covariance matrix (and potentially the precision)
+        X = self._validate_data(X)
+        if self.assume_centered:
+            self.location_ = np.zeros(X.shape[1])
+        else:
+            self.location_ = X.mean(0)
+        with config_context(assume_finite=True):
+            covariance, shrinkage = ledoit_wolf(
+                X - self.location_, assume_centered=True, block_size=self.block_size
+            )
+        self.shrinkage_ = shrinkage
+        self._set_covariance(covariance)
+
+        return self
+
+
+# OAS estimator
+def oas(X, *, assume_centered=False):
+    """Estimate covariance with the Oracle Approximating Shrinkage as proposed in [1]_.
+
+    Read more in the :ref:`User Guide <shrunk_covariance>`.
+
+    Parameters
+    ----------
+    X : array-like of shape (n_samples, n_features)
+        Data from which to compute the covariance estimate.
+
+    assume_centered : bool, default=False
+      If True, data will not be centered before computation.
+      Useful to work with data whose mean is significantly equal to
+      zero but is not exactly zero.
+      If False, data will be centered before computation.
+
+    Returns
+    -------
+    shrunk_cov : array-like of shape (n_features, n_features)
+        Shrunk covariance.
+
+    shrinkage : float
+        Coefficient in the convex combination used for the computation
+        of the shrunk estimate.
+
+    Notes
+    -----
+    The regularised covariance is:
+
+    (1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features),
+
+    where mu = trace(cov) / n_features and shrinkage is given by the OAS formula
+    (see [1]_).
+
+    The shrinkage formulation implemented here differs from Eq. 23 in [1]_. In
+    the original article, formula (23) states that 2/p (p being the number of
+    features) is multiplied by Trace(cov*cov) in both the numerator and
+    denominator, but this operation is omitted because for a large p, the value
+    of 2/p is so small that it doesn't affect the value of the estimator.
+
+    References
+    ----------
+    .. [1] :arxiv:`"Shrinkage algorithms for MMSE covariance estimation.",
+           Chen, Y., Wiesel, A., Eldar, Y. C., & Hero, A. O.
+           IEEE Transactions on Signal Processing, 58(10), 5016-5029, 2010.
+           <0907.4698>`
+    """
+    X = np.asarray(X)
+    # for only one feature, the result is the same whatever the shrinkage
+    if len(X.shape) == 2 and X.shape[1] == 1:
+        if not assume_centered:
+            X = X - X.mean()
+        return np.atleast_2d((X**2).mean()), 0.0
+    if X.ndim == 1:
+        X = np.reshape(X, (1, -1))
+        warnings.warn(
+            "Only one sample available. You may want to reshape your data array"
+        )
+        n_samples = 1
+        n_features = X.size
+    else:
+        n_samples, n_features = X.shape
+
+    emp_cov = empirical_covariance(X, assume_centered=assume_centered)
+    mu = np.trace(emp_cov) / n_features
+
+    # formula from Chen et al.'s **implementation**
+    alpha = np.mean(emp_cov**2)
+    num = alpha + mu**2
+    den = (n_samples + 1.0) * (alpha - (mu**2) / n_features)
+
+    shrinkage = 1.0 if den == 0 else min(num / den, 1.0)
+    shrunk_cov = (1.0 - shrinkage) * emp_cov
+    shrunk_cov.flat[:: n_features + 1] += shrinkage * mu
+
+    return shrunk_cov, shrinkage
+
+
+class OAS(EmpiricalCovariance):
+    """Oracle Approximating Shrinkage Estimator as proposed in [1]_.
+
+    Read more in the :ref:`User Guide <shrunk_covariance>`.
+
+    Parameters
+    ----------
+    store_precision : bool, default=True
+        Specify if the estimated precision is stored.
+
+    assume_centered : bool, default=False
+        If True, data will not be centered before computation.
+        Useful when working with data whose mean is almost, but not exactly
+        zero.
+        If False (default), data will be centered before computation.
+
+    Attributes
+    ----------
+    covariance_ : ndarray of shape (n_features, n_features)
+        Estimated covariance matrix.
+
+    location_ : ndarray of shape (n_features,)
+        Estimated location, i.e. the estimated mean.
+
+    precision_ : ndarray of shape (n_features, n_features)
+        Estimated pseudo inverse matrix.
+        (stored only if store_precision is True)
+
+    shrinkage_ : float
+      coefficient in the convex combination used for the computation
+      of the shrunk estimate. Range is [0, 1].
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+        .. versionadded:: 0.24
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
+    See Also
+    --------
+    EllipticEnvelope : An object for detecting outliers in
+        a Gaussian distributed dataset.
+    EmpiricalCovariance : Maximum likelihood covariance estimator.
+    GraphicalLasso : Sparse inverse covariance estimation
+        with an l1-penalized estimator.
+    GraphicalLassoCV : Sparse inverse covariance with cross-validated
+        choice of the l1 penalty.
+    LedoitWolf : LedoitWolf Estimator.
+    MinCovDet : Minimum Covariance Determinant
+        (robust estimator of covariance).
+    ShrunkCovariance : Covariance estimator with shrinkage.
+
+    Notes
+    -----
+    The regularised covariance is:
+
+    (1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features),
+
+    where mu = trace(cov) / n_features and shrinkage is given by the OAS formula
+    (see [1]_).
+
+    The shrinkage formulation implemented here differs from Eq. 23 in [1]_. In
+    the original article, formula (23) states that 2/p (p being the number of
+    features) is multiplied by Trace(cov*cov) in both the numerator and
+    denominator, but this operation is omitted because for a large p, the value
+    of 2/p is so small that it doesn't affect the value of the estimator.
+
+    References
+    ----------
+    .. [1] :arxiv:`"Shrinkage algorithms for MMSE covariance estimation.",
+           Chen, Y., Wiesel, A., Eldar, Y. C., & Hero, A. O.
+           IEEE Transactions on Signal Processing, 58(10), 5016-5029, 2010.
+           <0907.4698>`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from sklearn.covariance import OAS
+    >>> from sklearn.datasets import make_gaussian_quantiles
+    >>> real_cov = np.array([[.8, .3],
+    ...                      [.3, .4]])
+    >>> rng = np.random.RandomState(0)
+    >>> X = rng.multivariate_normal(mean=[0, 0],
+    ...                             cov=real_cov,
+    ...                             size=500)
+    >>> oas = OAS().fit(X)
+    >>> oas.covariance_
+    array([[0.7533..., 0.2763...],
+           [0.2763..., 0.3964...]])
+    >>> oas.precision_
+    array([[ 1.7833..., -1.2431... ],
+           [-1.2431...,  3.3889...]])
+    >>> oas.shrinkage_
+    0.0195...
+    """
+
+    def fit(self, X, y=None):
+        """Fit the Oracle Approximating Shrinkage covariance model to X.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            Training data, where `n_samples` is the number of samples
+            and `n_features` is the number of features.
+        y : Ignored
+            Not used, present for API consistency by convention.
+
+        Returns
+        -------
+        self : object
+            Returns the instance itself.
+        """
+        self._validate_params()
+
+        X = self._validate_data(X)
+        # Not calling the parent object to fit, to avoid computing the
+        # covariance matrix (and potentially the precision)
+        if self.assume_centered:
+            self.location_ = np.zeros(X.shape[1])
+        else:
+            self.location_ = X.mean(0)
+
+        covariance, shrinkage = oas(X - self.location_, assume_centered=True)
+        self.shrinkage_ = shrinkage
+        self._set_covariance(covariance)
+
+        return self

mplug_owl2/lib/python3.10/site-packages/sklearn/covariance/tests/test_elliptic_envelope.py

@@ -0,0 +1,50 @@
+"""
+Testing for Elliptic Envelope algorithm (sklearn.covariance.elliptic_envelope).
+"""
+
+import numpy as np
+import pytest
+
+from sklearn.covariance import EllipticEnvelope
+from sklearn.utils._testing import assert_almost_equal
+from sklearn.utils._testing import assert_array_almost_equal
+from sklearn.utils._testing import assert_array_equal
+from sklearn.exceptions import NotFittedError
+
+
+def test_elliptic_envelope(global_random_seed):
+    rnd = np.random.RandomState(global_random_seed)
+    X = rnd.randn(100, 10)
+    clf = EllipticEnvelope(contamination=0.1)
+    with pytest.raises(NotFittedError):
+        clf.predict(X)
+    with pytest.raises(NotFittedError):
+        clf.decision_function(X)
+    clf.fit(X)
+    y_pred = clf.predict(X)
+    scores = clf.score_samples(X)
+    decisions = clf.decision_function(X)
+
+    assert_array_almost_equal(scores, -clf.mahalanobis(X))
+    assert_array_almost_equal(clf.mahalanobis(X), clf.dist_)
+    assert_almost_equal(
+        clf.score(X, np.ones(100)), (100 - y_pred[y_pred == -1].size) / 100.0
+    )
+    assert sum(y_pred == -1) == sum(decisions < 0)
+
+
+def test_score_samples():
+    X_train = [[1, 1], [1, 2], [2, 1]]
+    clf1 = EllipticEnvelope(contamination=0.2).fit(X_train)
+    clf2 = EllipticEnvelope().fit(X_train)
+    assert_array_equal(
+        clf1.score_samples([[2.0, 2.0]]),
+        clf1.decision_function([[2.0, 2.0]]) + clf1.offset_,
+    )
+    assert_array_equal(
+        clf2.score_samples([[2.0, 2.0]]),
+        clf2.decision_function([[2.0, 2.0]]) + clf2.offset_,
+    )
+    assert_array_equal(
+        clf1.score_samples([[2.0, 2.0]]), clf2.score_samples([[2.0, 2.0]])
+    )

mplug_owl2/lib/python3.10/site-packages/sklearn/covariance/tests/test_graphical_lasso.py

@@ -0,0 +1,242 @@
+""" Test the graphical_lasso module.
+"""
+import sys
+import pytest
+
+import numpy as np
+from scipy import linalg
+
+from numpy.testing import assert_allclose
+from sklearn.utils._testing import assert_array_almost_equal
+from sklearn.utils._testing import assert_array_less
+from sklearn.utils._testing import _convert_container
+
+from sklearn.covariance import (
+    graphical_lasso,
+    GraphicalLasso,
+    GraphicalLassoCV,
+    empirical_covariance,
+)
+from sklearn.datasets import make_sparse_spd_matrix
+from io import StringIO
+from sklearn.utils import check_random_state
+from sklearn import datasets
+
+
+def test_graphical_lasso(random_state=0):
+    # Sample data from a sparse multivariate normal
+    dim = 20
+    n_samples = 100
+    random_state = check_random_state(random_state)
+    prec = make_sparse_spd_matrix(dim, alpha=0.95, random_state=random_state)
+    cov = linalg.inv(prec)
+    X = random_state.multivariate_normal(np.zeros(dim), cov, size=n_samples)
+    emp_cov = empirical_covariance(X)
+
+    for alpha in (0.0, 0.1, 0.25):
+        covs = dict()
+        icovs = dict()
+        for method in ("cd", "lars"):
+            cov_, icov_, costs = graphical_lasso(
+                emp_cov, return_costs=True, alpha=alpha, mode=method
+            )
+            covs[method] = cov_
+            icovs[method] = icov_
+            costs, dual_gap = np.array(costs).T
+            # Check that the costs always decrease (doesn't hold if alpha == 0)
+            if not alpha == 0:
+                assert_array_less(np.diff(costs), 0)
+        # Check that the 2 approaches give similar results
+        assert_array_almost_equal(covs["cd"], covs["lars"], decimal=4)
+        assert_array_almost_equal(icovs["cd"], icovs["lars"], decimal=4)
+
+    # Smoke test the estimator
+    model = GraphicalLasso(alpha=0.25).fit(X)
+    model.score(X)
+    assert_array_almost_equal(model.covariance_, covs["cd"], decimal=4)
+    assert_array_almost_equal(model.covariance_, covs["lars"], decimal=4)
+
+    # For a centered matrix, assume_centered could be chosen True or False
+    # Check that this returns indeed the same result for centered data
+    Z = X - X.mean(0)
+    precs = list()
+    for assume_centered in (False, True):
+        prec_ = GraphicalLasso(assume_centered=assume_centered).fit(Z).precision_
+        precs.append(prec_)
+    assert_array_almost_equal(precs[0], precs[1])
+
+
+def test_graphical_lasso_iris():
+    # Hard-coded solution from R glasso package for alpha=1.0
+    # (need to set penalize.diagonal to FALSE)
+    cov_R = np.array(
+        [
+            [0.68112222, 0.0000000, 0.265820, 0.02464314],
+            [0.00000000, 0.1887129, 0.000000, 0.00000000],
+            [0.26582000, 0.0000000, 3.095503, 0.28697200],
+            [0.02464314, 0.0000000, 0.286972, 0.57713289],
+        ]
+    )
+    icov_R = np.array(
+        [
+            [1.5190747, 0.000000, -0.1304475, 0.0000000],
+            [0.0000000, 5.299055, 0.0000000, 0.0000000],
+            [-0.1304475, 0.000000, 0.3498624, -0.1683946],
+            [0.0000000, 0.000000, -0.1683946, 1.8164353],
+        ]
+    )
+    X = datasets.load_iris().data
+    emp_cov = empirical_covariance(X)
+    for method in ("cd", "lars"):
+        cov, icov = graphical_lasso(emp_cov, alpha=1.0, return_costs=False, mode=method)
+        assert_array_almost_equal(cov, cov_R)
+        assert_array_almost_equal(icov, icov_R)
+
+
+def test_graph_lasso_2D():
+    # Hard-coded solution from Python skggm package
+    # obtained by calling `quic(emp_cov, lam=.1, tol=1e-8)`
+    cov_skggm = np.array([[3.09550269, 1.186972], [1.186972, 0.57713289]])
+
+    icov_skggm = np.array([[1.52836773, -3.14334831], [-3.14334831, 8.19753385]])
+    X = datasets.load_iris().data[:, 2:]
+    emp_cov = empirical_covariance(X)
+    for method in ("cd", "lars"):
+        cov, icov = graphical_lasso(emp_cov, alpha=0.1, return_costs=False, mode=method)
+        assert_array_almost_equal(cov, cov_skggm)
+        assert_array_almost_equal(icov, icov_skggm)
+
+
+def test_graphical_lasso_iris_singular():
+    # Small subset of rows to test the rank-deficient case
+    # Need to choose samples such that none of the variances are zero
+    indices = np.arange(10, 13)
+
+    # Hard-coded solution from R glasso package for alpha=0.01
+    cov_R = np.array(
+        [
+            [0.08, 0.056666662595, 0.00229729713223, 0.00153153142149],
+            [0.056666662595, 0.082222222222, 0.00333333333333, 0.00222222222222],
+            [0.002297297132, 0.003333333333, 0.00666666666667, 0.00009009009009],
+            [0.001531531421, 0.002222222222, 0.00009009009009, 0.00222222222222],
+        ]
+    )
+    icov_R = np.array(
+        [
+            [24.42244057, -16.831679593, 0.0, 0.0],
+            [-16.83168201, 24.351841681, -6.206896552, -12.5],
+            [0.0, -6.206896171, 153.103448276, 0.0],
+            [0.0, -12.499999143, 0.0, 462.5],
+        ]
+    )
+    X = datasets.load_iris().data[indices, :]
+    emp_cov = empirical_covariance(X)
+    for method in ("cd", "lars"):
+        cov, icov = graphical_lasso(
+            emp_cov, alpha=0.01, return_costs=False, mode=method
+        )
+        assert_array_almost_equal(cov, cov_R, decimal=5)
+        assert_array_almost_equal(icov, icov_R, decimal=5)
+
+
+def test_graphical_lasso_cv(random_state=1):
+    # Sample data from a sparse multivariate normal
+    dim = 5
+    n_samples = 6
+    random_state = check_random_state(random_state)
+    prec = make_sparse_spd_matrix(dim, alpha=0.96, random_state=random_state)
+    cov = linalg.inv(prec)
+    X = random_state.multivariate_normal(np.zeros(dim), cov, size=n_samples)
+    # Capture stdout, to smoke test the verbose mode
+    orig_stdout = sys.stdout
+    try:
+        sys.stdout = StringIO()
+        # We need verbose very high so that Parallel prints on stdout
+        GraphicalLassoCV(verbose=100, alphas=5, tol=1e-1).fit(X)
+    finally:
+        sys.stdout = orig_stdout
+
+
+@pytest.mark.parametrize("alphas_container_type", ["list", "tuple", "array"])
+def test_graphical_lasso_cv_alphas_iterable(alphas_container_type):
+    """Check that we can pass an array-like to `alphas`.
+
+    Non-regression test for:
+    https://github.com/scikit-learn/scikit-learn/issues/22489
+    """
+    true_cov = np.array(
+        [
+            [0.8, 0.0, 0.2, 0.0],
+            [0.0, 0.4, 0.0, 0.0],
+            [0.2, 0.0, 0.3, 0.1],
+            [0.0, 0.0, 0.1, 0.7],
+        ]
+    )
+    rng = np.random.RandomState(0)
+    X = rng.multivariate_normal(mean=[0, 0, 0, 0], cov=true_cov, size=200)
+    alphas = _convert_container([0.02, 0.03], alphas_container_type)
+    GraphicalLassoCV(alphas=alphas, tol=1e-1, n_jobs=1).fit(X)
+
+
+@pytest.mark.parametrize(
+    "alphas,err_type,err_msg",
+    [
+        ([-0.02, 0.03], ValueError, "must be > 0"),
+        ([0, 0.03], ValueError, "must be > 0"),
+        (["not_number", 0.03], TypeError, "must be an instance of float"),
+    ],
+)
+def test_graphical_lasso_cv_alphas_invalid_array(alphas, err_type, err_msg):
+    """Check that if an array-like containing a value
+    outside of (0, inf] is passed to `alphas`, a ValueError is raised.
+    Check if a string is passed, a TypeError is raised.
+    """
+    true_cov = np.array(
+        [
+            [0.8, 0.0, 0.2, 0.0],
+            [0.0, 0.4, 0.0, 0.0],
+            [0.2, 0.0, 0.3, 0.1],
+            [0.0, 0.0, 0.1, 0.7],
+        ]
+    )
+    rng = np.random.RandomState(0)
+    X = rng.multivariate_normal(mean=[0, 0, 0, 0], cov=true_cov, size=200)
+
+    with pytest.raises(err_type, match=err_msg):
+        GraphicalLassoCV(alphas=alphas, tol=1e-1, n_jobs=1).fit(X)
+
+
+def test_graphical_lasso_cv_scores():
+    splits = 4
+    n_alphas = 5
+    n_refinements = 3
+    true_cov = np.array(
+        [
+            [0.8, 0.0, 0.2, 0.0],
+            [0.0, 0.4, 0.0, 0.0],
+            [0.2, 0.0, 0.3, 0.1],
+            [0.0, 0.0, 0.1, 0.7],
+        ]
+    )
+    rng = np.random.RandomState(0)
+    X = rng.multivariate_normal(mean=[0, 0, 0, 0], cov=true_cov, size=200)
+    cov = GraphicalLassoCV(cv=splits, alphas=n_alphas, n_refinements=n_refinements).fit(
+        X
+    )
+
+    cv_results = cov.cv_results_
+    # alpha and one for each split
+
+    total_alphas = n_refinements * n_alphas + 1
+    keys = ["alphas"]
+    split_keys = [f"split{i}_test_score" for i in range(splits)]
+    for key in keys + split_keys:
+        assert key in cv_results
+        assert len(cv_results[key]) == total_alphas
+
+    cv_scores = np.asarray([cov.cv_results_[key] for key in split_keys])
+    expected_mean = cv_scores.mean(axis=0)
+    expected_std = cv_scores.std(axis=0)
+
+    assert_allclose(cov.cv_results_["mean_test_score"], expected_mean)
+    assert_allclose(cov.cv_results_["std_test_score"], expected_std)

mplug_owl2/lib/python3.10/site-packages/sklearn/covariance/tests/test_robust_covariance.py

@@ -0,0 +1,174 @@
+# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
+#         Gael Varoquaux <gael.varoquaux@normalesup.org>
+#         Virgile Fritsch <virgile.fritsch@inria.fr>
+#
+# License: BSD 3 clause
+
+import itertools
+
+import numpy as np
+import pytest
+
+from sklearn.utils._testing import assert_array_almost_equal
+
+from sklearn import datasets
+from sklearn.covariance import empirical_covariance, MinCovDet
+from sklearn.covariance import fast_mcd
+
+X = datasets.load_iris().data
+X_1d = X[:, 0]
+n_samples, n_features = X.shape
+
+
+def test_mcd():
+    # Tests the FastMCD algorithm implementation
+    # Small data set
+    # test without outliers (random independent normal data)
+    launch_mcd_on_dataset(100, 5, 0, 0.01, 0.1, 80)
+    # test with a contaminated data set (medium contamination)
+    launch_mcd_on_dataset(100, 5, 20, 0.01, 0.01, 70)
+    # test with a contaminated data set (strong contamination)
+    launch_mcd_on_dataset(100, 5, 40, 0.1, 0.1, 50)
+
+    # Medium data set
+    launch_mcd_on_dataset(1000, 5, 450, 0.1, 0.1, 540)
+
+    # Large data set
+    launch_mcd_on_dataset(1700, 5, 800, 0.1, 0.1, 870)
+
+    # 1D data set
+    launch_mcd_on_dataset(500, 1, 100, 0.001, 0.001, 350)
+
+
+def test_fast_mcd_on_invalid_input():
+    X = np.arange(100)
+    msg = "Expected 2D array, got 1D array instead"
+    with pytest.raises(ValueError, match=msg):
+        fast_mcd(X)
+
+
+def test_mcd_class_on_invalid_input():
+    X = np.arange(100)
+    mcd = MinCovDet()
+    msg = "Expected 2D array, got 1D array instead"
+    with pytest.raises(ValueError, match=msg):
+        mcd.fit(X)
+
+
+def launch_mcd_on_dataset(
+    n_samples, n_features, n_outliers, tol_loc, tol_cov, tol_support
+):
+
+    rand_gen = np.random.RandomState(0)
+    data = rand_gen.randn(n_samples, n_features)
+    # add some outliers
+    outliers_index = rand_gen.permutation(n_samples)[:n_outliers]
+    outliers_offset = 10.0 * (rand_gen.randint(2, size=(n_outliers, n_features)) - 0.5)
+    data[outliers_index] += outliers_offset
+    inliers_mask = np.ones(n_samples).astype(bool)
+    inliers_mask[outliers_index] = False
+
+    pure_data = data[inliers_mask]
+    # compute MCD by fitting an object
+    mcd_fit = MinCovDet(random_state=rand_gen).fit(data)
+    T = mcd_fit.location_
+    S = mcd_fit.covariance_
+    H = mcd_fit.support_
+    # compare with the estimates learnt from the inliers
+    error_location = np.mean((pure_data.mean(0) - T) ** 2)
+    assert error_location < tol_loc
+    error_cov = np.mean((empirical_covariance(pure_data) - S) ** 2)
+    assert error_cov < tol_cov
+    assert np.sum(H) >= tol_support
+    assert_array_almost_equal(mcd_fit.mahalanobis(data), mcd_fit.dist_)
+
+
+def test_mcd_issue1127():
+    # Check that the code does not break with X.shape = (3, 1)
+    # (i.e. n_support = n_samples)
+    rnd = np.random.RandomState(0)
+    X = rnd.normal(size=(3, 1))
+    mcd = MinCovDet()
+    mcd.fit(X)
+
+
+def test_mcd_issue3367():
+    # Check that MCD completes when the covariance matrix is singular
+    # i.e. one of the rows and columns are all zeros
+    rand_gen = np.random.RandomState(0)
+
+    # Think of these as the values for X and Y -> 10 values between -5 and 5
+    data_values = np.linspace(-5, 5, 10).tolist()
+    # Get the cartesian product of all possible coordinate pairs from above set
+    data = np.array(list(itertools.product(data_values, data_values)))
+
+    # Add a third column that's all zeros to make our data a set of point
+    # within a plane, which means that the covariance matrix will be singular
+    data = np.hstack((data, np.zeros((data.shape[0], 1))))
+
+    # The below line of code should raise an exception if the covariance matrix
+    # is singular. As a further test, since we have points in XYZ, the
+    # principle components (Eigenvectors) of these directly relate to the
+    # geometry of the points. Since it's a plane, we should be able to test
+    # that the Eigenvector that corresponds to the smallest Eigenvalue is the
+    # plane normal, specifically [0, 0, 1], since everything is in the XY plane
+    # (as I've set it up above). To do this one would start by:
+    #
+    #     evals, evecs = np.linalg.eigh(mcd_fit.covariance_)
+    #     normal = evecs[:, np.argmin(evals)]
+    #
+    # After which we need to assert that our `normal` is equal to [0, 0, 1].
+    # Do note that there is floating point error associated with this, so it's
+    # best to subtract the two and then compare some small tolerance (e.g.
+    # 1e-12).
+    MinCovDet(random_state=rand_gen).fit(data)
+
+
+def test_mcd_support_covariance_is_zero():
+    # Check that MCD returns a ValueError with informative message when the
+    # covariance of the support data is equal to 0.
+    X_1 = np.array([0.5, 0.1, 0.1, 0.1, 0.957, 0.1, 0.1, 0.1, 0.4285, 0.1])
+    X_1 = X_1.reshape(-1, 1)
+    X_2 = np.array([0.5, 0.3, 0.3, 0.3, 0.957, 0.3, 0.3, 0.3, 0.4285, 0.3])
+    X_2 = X_2.reshape(-1, 1)
+    msg = (
+        "The covariance matrix of the support data is equal to 0, try to "
+        "increase support_fraction"
+    )
+    for X in [X_1, X_2]:
+        with pytest.raises(ValueError, match=msg):
+            MinCovDet().fit(X)
+
+
+def test_mcd_increasing_det_warning():
+    # Check that a warning is raised if we observe increasing determinants
+    # during the c_step. In theory the sequence of determinants should be
+    # decreasing. Increasing determinants are likely due to ill-conditioned
+    # covariance matrices that result in poor precision matrices.
+
+    X = [
+        [5.1, 3.5, 1.4, 0.2],
+        [4.9, 3.0, 1.4, 0.2],
+        [4.7, 3.2, 1.3, 0.2],
+        [4.6, 3.1, 1.5, 0.2],
+        [5.0, 3.6, 1.4, 0.2],
+        [4.6, 3.4, 1.4, 0.3],
+        [5.0, 3.4, 1.5, 0.2],
+        [4.4, 2.9, 1.4, 0.2],
+        [4.9, 3.1, 1.5, 0.1],
+        [5.4, 3.7, 1.5, 0.2],
+        [4.8, 3.4, 1.6, 0.2],
+        [4.8, 3.0, 1.4, 0.1],
+        [4.3, 3.0, 1.1, 0.1],
+        [5.1, 3.5, 1.4, 0.3],
+        [5.7, 3.8, 1.7, 0.3],
+        [5.4, 3.4, 1.7, 0.2],
+        [4.6, 3.6, 1.0, 0.2],
+        [5.0, 3.0, 1.6, 0.2],
+        [5.2, 3.5, 1.5, 0.2],
+    ]
+
+    mcd = MinCovDet(random_state=1)
+    warn_msg = "Determinant has increased"
+    with pytest.warns(RuntimeWarning, match=warn_msg):
+        mcd.fit(X)

mplug_owl2/lib/python3.10/site-packages/sklearn/experimental/enable_iterative_imputer.py

@@ -0,0 +1,20 @@
+"""Enables IterativeImputer
+
+The API and results of this estimator might change without any deprecation
+cycle.
+
+Importing this file dynamically sets :class:`~sklearn.impute.IterativeImputer`
+as an attribute of the impute module::
+
+    >>> # explicitly require this experimental feature
+    >>> from sklearn.experimental import enable_iterative_imputer  # noqa
+    >>> # now you can import normally from impute
+    >>> from sklearn.impute import IterativeImputer
+"""
+
+from ..impute._iterative import IterativeImputer
+from .. import impute
+
+# use settattr to avoid mypy errors when monkeypatching
+setattr(impute, "IterativeImputer", IterativeImputer)
+impute.__all__ += ["IterativeImputer"]

mplug_owl2/lib/python3.10/site-packages/sklearn/experimental/tests/test_enable_hist_gradient_boosting.py

@@ -0,0 +1,14 @@
+"""Tests for making sure experimental imports work as expected."""
+
+import textwrap
+
+from sklearn.utils._testing import assert_run_python_script
+
+
+def test_import_raises_warning():
+    code = """
+    import pytest
+    with pytest.warns(UserWarning, match="it is not needed to import"):
+        from sklearn.experimental import enable_hist_gradient_boosting  # noqa
+    """
+    assert_run_python_script(textwrap.dedent(code))

mplug_owl2/lib/python3.10/site-packages/sklearn/gaussian_process/__init__.py

@@ -0,0 +1,16 @@
+# Author: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
+#         Vincent Dubourg <vincent.dubourg@gmail.com>
+#         (mostly translation, see implementation details)
+# License: BSD 3 clause
+
+"""
+The :mod:`sklearn.gaussian_process` module implements Gaussian Process
+based regression and classification.
+"""
+
+from ._gpr import GaussianProcessRegressor
+from ._gpc import GaussianProcessClassifier
+from . import kernels
+
+
+__all__ = ["GaussianProcessRegressor", "GaussianProcessClassifier", "kernels"]

mplug_owl2/lib/python3.10/site-packages/sklearn/gaussian_process/_gpc.py

@@ -0,0 +1,903 @@
+"""Gaussian processes classification."""
+
+# Authors: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
+#
+# License: BSD 3 clause
+
+from numbers import Integral
+from operator import itemgetter
+
+import numpy as np
+from scipy.linalg import cholesky, cho_solve, solve
+import scipy.optimize
+from scipy.special import erf, expit
+
+from ..base import BaseEstimator, ClassifierMixin, clone
+from .kernels import Kernel, RBF, CompoundKernel, ConstantKernel as C
+from ..utils.validation import check_is_fitted
+from ..utils import check_random_state
+from ..utils.optimize import _check_optimize_result
+from ..utils._param_validation import Interval, StrOptions
+from ..preprocessing import LabelEncoder
+from ..multiclass import OneVsRestClassifier, OneVsOneClassifier
+
+
+# Values required for approximating the logistic sigmoid by
+# error functions. coefs are obtained via:
+# x = np.array([0, 0.6, 2, 3.5, 4.5, np.inf])
+# b = logistic(x)
+# A = (erf(np.dot(x, self.lambdas)) + 1) / 2
+# coefs = lstsq(A, b)[0]
+LAMBDAS = np.array([0.41, 0.4, 0.37, 0.44, 0.39])[:, np.newaxis]
+COEFS = np.array(
+    [-1854.8214151, 3516.89893646, 221.29346712, 128.12323805, -2010.49422654]
+)[:, np.newaxis]
+
+
+class _BinaryGaussianProcessClassifierLaplace(BaseEstimator):
+    """Binary Gaussian process classification based on Laplace approximation.
+
+    The implementation is based on Algorithm 3.1, 3.2, and 5.1 from [RW2006]_.
+
+    Internally, the Laplace approximation is used for approximating the
+    non-Gaussian posterior by a Gaussian.
+
+    Currently, the implementation is restricted to using the logistic link
+    function.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    kernel : kernel instance, default=None
+        The kernel specifying the covariance function of the GP. If None is
+        passed, the kernel "1.0 * RBF(1.0)" is used as default. Note that
+        the kernel's hyperparameters are optimized during fitting.
+
+    optimizer : 'fmin_l_bfgs_b' or callable, default='fmin_l_bfgs_b'
+        Can either be one of the internally supported optimizers for optimizing
+        the kernel's parameters, specified by a string, or an externally
+        defined optimizer passed as a callable. If a callable is passed, it
+        must have the  signature::
+
+            def optimizer(obj_func, initial_theta, bounds):
+                # * 'obj_func' is the objective function to be maximized, which
+                #   takes the hyperparameters theta as parameter and an
+                #   optional flag eval_gradient, which determines if the
+                #   gradient is returned additionally to the function value
+                # * 'initial_theta': the initial value for theta, which can be
+                #   used by local optimizers
+                # * 'bounds': the bounds on the values of theta
+                ....
+                # Returned are the best found hyperparameters theta and
+                # the corresponding value of the target function.
+                return theta_opt, func_min
+
+        Per default, the 'L-BFGS-B' algorithm from scipy.optimize.minimize
+        is used. If None is passed, the kernel's parameters are kept fixed.
+        Available internal optimizers are::
+
+            'fmin_l_bfgs_b'
+
+    n_restarts_optimizer : int, default=0
+        The number of restarts of the optimizer for finding the kernel's
+        parameters which maximize the log-marginal likelihood. The first run
+        of the optimizer is performed from the kernel's initial parameters,
+        the remaining ones (if any) from thetas sampled log-uniform randomly
+        from the space of allowed theta-values. If greater than 0, all bounds
+        must be finite. Note that n_restarts_optimizer=0 implies that one
+        run is performed.
+
+    max_iter_predict : int, default=100
+        The maximum number of iterations in Newton's method for approximating
+        the posterior during predict. Smaller values will reduce computation
+        time at the cost of worse results.
+
+    warm_start : bool, default=False
+        If warm-starts are enabled, the solution of the last Newton iteration
+        on the Laplace approximation of the posterior mode is used as
+        initialization for the next call of _posterior_mode(). This can speed
+        up convergence when _posterior_mode is called several times on similar
+        problems as in hyperparameter optimization. See :term:`the Glossary
+        <warm_start>`.
+
+    copy_X_train : bool, default=True
+        If True, a persistent copy of the training data is stored in the
+        object. Otherwise, just a reference to the training data is stored,
+        which might cause predictions to change if the data is modified
+        externally.
+
+    random_state : int, RandomState instance or None, default=None
+        Determines random number generation used to initialize the centers.
+        Pass an int for reproducible results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+    Attributes
+    ----------
+    X_train_ : array-like of shape (n_samples, n_features) or list of object
+        Feature vectors or other representations of training data (also
+        required for prediction).
+
+    y_train_ : array-like of shape (n_samples,)
+        Target values in training data (also required for prediction)
+
+    classes_ : array-like of shape (n_classes,)
+        Unique class labels.
+
+    kernel_ : kernl instance
+        The kernel used for prediction. The structure of the kernel is the
+        same as the one passed as parameter but with optimized hyperparameters
+
+    L_ : array-like of shape (n_samples, n_samples)
+        Lower-triangular Cholesky decomposition of the kernel in X_train_
+
+    pi_ : array-like of shape (n_samples,)
+        The probabilities of the positive class for the training points
+        X_train_
+
+    W_sr_ : array-like of shape (n_samples,)
+        Square root of W, the Hessian of log-likelihood of the latent function
+        values for the observed labels. Since W is diagonal, only the diagonal
+        of sqrt(W) is stored.
+
+    log_marginal_likelihood_value_ : float
+        The log-marginal-likelihood of ``self.kernel_.theta``
+
+    References
+    ----------
+    .. [RW2006] `Carl E. Rasmussen and Christopher K.I. Williams,
+       "Gaussian Processes for Machine Learning",
+       MIT Press 2006 <https://www.gaussianprocess.org/gpml/chapters/RW.pdf>`_
+    """
+
+    def __init__(
+        self,
+        kernel=None,
+        *,
+        optimizer="fmin_l_bfgs_b",
+        n_restarts_optimizer=0,
+        max_iter_predict=100,
+        warm_start=False,
+        copy_X_train=True,
+        random_state=None,
+    ):
+        self.kernel = kernel
+        self.optimizer = optimizer
+        self.n_restarts_optimizer = n_restarts_optimizer
+        self.max_iter_predict = max_iter_predict
+        self.warm_start = warm_start
+        self.copy_X_train = copy_X_train
+        self.random_state = random_state
+
+    def fit(self, X, y):
+        """Fit Gaussian process classification model.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features) or list of object
+            Feature vectors or other representations of training data.
+
+        y : array-like of shape (n_samples,)
+            Target values, must be binary.
+
+        Returns
+        -------
+        self : returns an instance of self.
+        """
+        if self.kernel is None:  # Use an RBF kernel as default
+            self.kernel_ = C(1.0, constant_value_bounds="fixed") * RBF(
+                1.0, length_scale_bounds="fixed"
+            )
+        else:
+            self.kernel_ = clone(self.kernel)
+
+        self.rng = check_random_state(self.random_state)
+
+        self.X_train_ = np.copy(X) if self.copy_X_train else X
+
+        # Encode class labels and check that it is a binary classification
+        # problem
+        label_encoder = LabelEncoder()
+        self.y_train_ = label_encoder.fit_transform(y)
+        self.classes_ = label_encoder.classes_
+        if self.classes_.size > 2:
+            raise ValueError(
+                "%s supports only binary classification. y contains classes %s"
+                % (self.__class__.__name__, self.classes_)
+            )
+        elif self.classes_.size == 1:
+            raise ValueError(
+                "{0:s} requires 2 classes; got {1:d} class".format(
+                    self.__class__.__name__, self.classes_.size
+                )
+            )
+
+        if self.optimizer is not None and self.kernel_.n_dims > 0:
+            # Choose hyperparameters based on maximizing the log-marginal
+            # likelihood (potentially starting from several initial values)
+            def obj_func(theta, eval_gradient=True):
+                if eval_gradient:
+                    lml, grad = self.log_marginal_likelihood(
+                        theta, eval_gradient=True, clone_kernel=False
+                    )
+                    return -lml, -grad
+                else:
+                    return -self.log_marginal_likelihood(theta, clone_kernel=False)
+
+            # First optimize starting from theta specified in kernel
+            optima = [
+                self._constrained_optimization(
+                    obj_func, self.kernel_.theta, self.kernel_.bounds
+                )
+            ]
+
+            # Additional runs are performed from log-uniform chosen initial
+            # theta
+            if self.n_restarts_optimizer > 0:
+                if not np.isfinite(self.kernel_.bounds).all():
+                    raise ValueError(
+                        "Multiple optimizer restarts (n_restarts_optimizer>0) "
+                        "requires that all bounds are finite."
+                    )
+                bounds = self.kernel_.bounds
+                for iteration in range(self.n_restarts_optimizer):
+                    theta_initial = np.exp(self.rng.uniform(bounds[:, 0], bounds[:, 1]))
+                    optima.append(
+                        self._constrained_optimization(obj_func, theta_initial, bounds)
+                    )
+            # Select result from run with minimal (negative) log-marginal
+            # likelihood
+            lml_values = list(map(itemgetter(1), optima))
+            self.kernel_.theta = optima[np.argmin(lml_values)][0]
+            self.kernel_._check_bounds_params()
+
+            self.log_marginal_likelihood_value_ = -np.min(lml_values)
+        else:
+            self.log_marginal_likelihood_value_ = self.log_marginal_likelihood(
+                self.kernel_.theta
+            )
+
+        # Precompute quantities required for predictions which are independent
+        # of actual query points
+        K = self.kernel_(self.X_train_)
+
+        _, (self.pi_, self.W_sr_, self.L_, _, _) = self._posterior_mode(
+            K, return_temporaries=True
+        )
+
+        return self
+
+    def predict(self, X):
+        """Perform classification on an array of test vectors X.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features) or list of object
+            Query points where the GP is evaluated for classification.
+
+        Returns
+        -------
+        C : ndarray of shape (n_samples,)
+            Predicted target values for X, values are from ``classes_``
+        """
+        check_is_fitted(self)
+
+        # As discussed on Section 3.4.2 of GPML, for making hard binary
+        # decisions, it is enough to compute the MAP of the posterior and
+        # pass it through the link function
+        K_star = self.kernel_(self.X_train_, X)  # K_star =k(x_star)
+        f_star = K_star.T.dot(self.y_train_ - self.pi_)  # Algorithm 3.2,Line 4
+
+        return np.where(f_star > 0, self.classes_[1], self.classes_[0])
+
+    def predict_proba(self, X):
+        """Return probability estimates for the test vector X.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features) or list of object
+            Query points where the GP is evaluated for classification.
+
+        Returns
+        -------
+        C : array-like of shape (n_samples, n_classes)
+            Returns the probability of the samples for each class in
+            the model. The columns correspond to the classes in sorted
+            order, as they appear in the attribute ``classes_``.
+        """
+        check_is_fitted(self)
+
+        # Based on Algorithm 3.2 of GPML
+        K_star = self.kernel_(self.X_train_, X)  # K_star =k(x_star)
+        f_star = K_star.T.dot(self.y_train_ - self.pi_)  # Line 4
+        v = solve(self.L_, self.W_sr_[:, np.newaxis] * K_star)  # Line 5
+        # Line 6 (compute np.diag(v.T.dot(v)) via einsum)
+        var_f_star = self.kernel_.diag(X) - np.einsum("ij,ij->j", v, v)
+
+        # Line 7:
+        # Approximate \int log(z) * N(z | f_star, var_f_star)
+        # Approximation is due to Williams & Barber, "Bayesian Classification
+        # with Gaussian Processes", Appendix A: Approximate the logistic
+        # sigmoid by a linear combination of 5 error functions.
+        # For information on how this integral can be computed see
+        # blitiri.blogspot.de/2012/11/gaussian-integral-of-error-function.html
+        alpha = 1 / (2 * var_f_star)
+        gamma = LAMBDAS * f_star
+        integrals = (
+            np.sqrt(np.pi / alpha)
+            * erf(gamma * np.sqrt(alpha / (alpha + LAMBDAS**2)))
+            / (2 * np.sqrt(var_f_star * 2 * np.pi))
+        )
+        pi_star = (COEFS * integrals).sum(axis=0) + 0.5 * COEFS.sum()
+
+        return np.vstack((1 - pi_star, pi_star)).T
+
+    def log_marginal_likelihood(
+        self, theta=None, eval_gradient=False, clone_kernel=True
+    ):
+        """Returns log-marginal likelihood of theta for training data.
+
+        Parameters
+        ----------
+        theta : array-like of shape (n_kernel_params,), default=None
+            Kernel hyperparameters for which the log-marginal likelihood is
+            evaluated. If None, the precomputed log_marginal_likelihood
+            of ``self.kernel_.theta`` is returned.
+
+        eval_gradient : bool, default=False
+            If True, the gradient of the log-marginal likelihood with respect
+            to the kernel hyperparameters at position theta is returned
+            additionally. If True, theta must not be None.
+
+        clone_kernel : bool, default=True
+            If True, the kernel attribute is copied. If False, the kernel
+            attribute is modified, but may result in a performance improvement.
+
+        Returns
+        -------
+        log_likelihood : float
+            Log-marginal likelihood of theta for training data.
+
+        log_likelihood_gradient : ndarray of shape (n_kernel_params,), \
+                optional
+            Gradient of the log-marginal likelihood with respect to the kernel
+            hyperparameters at position theta.
+            Only returned when `eval_gradient` is True.
+        """
+        if theta is None:
+            if eval_gradient:
+                raise ValueError("Gradient can only be evaluated for theta!=None")
+            return self.log_marginal_likelihood_value_
+
+        if clone_kernel:
+            kernel = self.kernel_.clone_with_theta(theta)
+        else:
+            kernel = self.kernel_
+            kernel.theta = theta
+
+        if eval_gradient:
+            K, K_gradient = kernel(self.X_train_, eval_gradient=True)
+        else:
+            K = kernel(self.X_train_)
+
+        # Compute log-marginal-likelihood Z and also store some temporaries
+        # which can be reused for computing Z's gradient
+        Z, (pi, W_sr, L, b, a) = self._posterior_mode(K, return_temporaries=True)
+
+        if not eval_gradient:
+            return Z
+
+        # Compute gradient based on Algorithm 5.1 of GPML
+        d_Z = np.empty(theta.shape[0])
+        # XXX: Get rid of the np.diag() in the next line
+        R = W_sr[:, np.newaxis] * cho_solve((L, True), np.diag(W_sr))  # Line 7
+        C = solve(L, W_sr[:, np.newaxis] * K)  # Line 8
+        # Line 9: (use einsum to compute np.diag(C.T.dot(C))))
+        s_2 = (
+            -0.5
+            * (np.diag(K) - np.einsum("ij, ij -> j", C, C))
+            * (pi * (1 - pi) * (1 - 2 * pi))
+        )  # third derivative
+
+        for j in range(d_Z.shape[0]):
+            C = K_gradient[:, :, j]  # Line 11
+            # Line 12: (R.T.ravel().dot(C.ravel()) = np.trace(R.dot(C)))
+            s_1 = 0.5 * a.T.dot(C).dot(a) - 0.5 * R.T.ravel().dot(C.ravel())
+
+            b = C.dot(self.y_train_ - pi)  # Line 13
+            s_3 = b - K.dot(R.dot(b))  # Line 14
+
+            d_Z[j] = s_1 + s_2.T.dot(s_3)  # Line 15
+
+        return Z, d_Z
+
+    def _posterior_mode(self, K, return_temporaries=False):
+        """Mode-finding for binary Laplace GPC and fixed kernel.
+
+        This approximates the posterior of the latent function values for given
+        inputs and target observations with a Gaussian approximation and uses
+        Newton's iteration to find the mode of this approximation.
+        """
+        # Based on Algorithm 3.1 of GPML
+
+        # If warm_start are enabled, we reuse the last solution for the
+        # posterior mode as initialization; otherwise, we initialize with 0
+        if (
+            self.warm_start
+            and hasattr(self, "f_cached")
+            and self.f_cached.shape == self.y_train_.shape
+        ):
+            f = self.f_cached
+        else:
+            f = np.zeros_like(self.y_train_, dtype=np.float64)
+
+        # Use Newton's iteration method to find mode of Laplace approximation
+        log_marginal_likelihood = -np.inf
+        for _ in range(self.max_iter_predict):
+            # Line 4
+            pi = expit(f)
+            W = pi * (1 - pi)
+            # Line 5
+            W_sr = np.sqrt(W)
+            W_sr_K = W_sr[:, np.newaxis] * K
+            B = np.eye(W.shape[0]) + W_sr_K * W_sr
+            L = cholesky(B, lower=True)
+            # Line 6
+            b = W * f + (self.y_train_ - pi)
+            # Line 7
+            a = b - W_sr * cho_solve((L, True), W_sr_K.dot(b))
+            # Line 8
+            f = K.dot(a)
+
+            # Line 10: Compute log marginal likelihood in loop and use as
+            #          convergence criterion
+            lml = (
+                -0.5 * a.T.dot(f)
+                - np.log1p(np.exp(-(self.y_train_ * 2 - 1) * f)).sum()
+                - np.log(np.diag(L)).sum()
+            )
+            # Check if we have converged (log marginal likelihood does
+            # not decrease)
+            # XXX: more complex convergence criterion
+            if lml - log_marginal_likelihood < 1e-10:
+                break
+            log_marginal_likelihood = lml
+
+        self.f_cached = f  # Remember solution for later warm-starts
+        if return_temporaries:
+            return log_marginal_likelihood, (pi, W_sr, L, b, a)
+        else:
+            return log_marginal_likelihood
+
+    def _constrained_optimization(self, obj_func, initial_theta, bounds):
+        if self.optimizer == "fmin_l_bfgs_b":
+            opt_res = scipy.optimize.minimize(
+                obj_func, initial_theta, method="L-BFGS-B", jac=True, bounds=bounds
+            )
+            _check_optimize_result("lbfgs", opt_res)
+            theta_opt, func_min = opt_res.x, opt_res.fun
+        elif callable(self.optimizer):
+            theta_opt, func_min = self.optimizer(obj_func, initial_theta, bounds=bounds)
+        else:
+            raise ValueError("Unknown optimizer %s." % self.optimizer)
+
+        return theta_opt, func_min
+
+
+class GaussianProcessClassifier(ClassifierMixin, BaseEstimator):
+    """Gaussian process classification (GPC) based on Laplace approximation.
+
+    The implementation is based on Algorithm 3.1, 3.2, and 5.1 from [RW2006]_.
+
+    Internally, the Laplace approximation is used for approximating the
+    non-Gaussian posterior by a Gaussian.
+
+    Currently, the implementation is restricted to using the logistic link
+    function. For multi-class classification, several binary one-versus rest
+    classifiers are fitted. Note that this class thus does not implement
+    a true multi-class Laplace approximation.
+
+    Read more in the :ref:`User Guide <gaussian_process>`.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    kernel : kernel instance, default=None
+        The kernel specifying the covariance function of the GP. If None is
+        passed, the kernel "1.0 * RBF(1.0)" is used as default. Note that
+        the kernel's hyperparameters are optimized during fitting. Also kernel
+        cannot be a `CompoundKernel`.
+
+    optimizer : 'fmin_l_bfgs_b', callable or None, default='fmin_l_bfgs_b'
+        Can either be one of the internally supported optimizers for optimizing
+        the kernel's parameters, specified by a string, or an externally
+        defined optimizer passed as a callable. If a callable is passed, it
+        must have the  signature::
+
+            def optimizer(obj_func, initial_theta, bounds):
+                # * 'obj_func' is the objective function to be maximized, which
+                #   takes the hyperparameters theta as parameter and an
+                #   optional flag eval_gradient, which determines if the
+                #   gradient is returned additionally to the function value
+                # * 'initial_theta': the initial value for theta, which can be
+                #   used by local optimizers
+                # * 'bounds': the bounds on the values of theta
+                ....
+                # Returned are the best found hyperparameters theta and
+                # the corresponding value of the target function.
+                return theta_opt, func_min
+
+        Per default, the 'L-BFGS-B' algorithm from scipy.optimize.minimize
+        is used. If None is passed, the kernel's parameters are kept fixed.
+        Available internal optimizers are::
+
+            'fmin_l_bfgs_b'
+
+    n_restarts_optimizer : int, default=0
+        The number of restarts of the optimizer for finding the kernel's
+        parameters which maximize the log-marginal likelihood. The first run
+        of the optimizer is performed from the kernel's initial parameters,
+        the remaining ones (if any) from thetas sampled log-uniform randomly
+        from the space of allowed theta-values. If greater than 0, all bounds
+        must be finite. Note that n_restarts_optimizer=0 implies that one
+        run is performed.
+
+    max_iter_predict : int, default=100
+        The maximum number of iterations in Newton's method for approximating
+        the posterior during predict. Smaller values will reduce computation
+        time at the cost of worse results.
+
+    warm_start : bool, default=False
+        If warm-starts are enabled, the solution of the last Newton iteration
+        on the Laplace approximation of the posterior mode is used as
+        initialization for the next call of _posterior_mode(). This can speed
+        up convergence when _posterior_mode is called several times on similar
+        problems as in hyperparameter optimization. See :term:`the Glossary
+        <warm_start>`.
+
+    copy_X_train : bool, default=True
+        If True, a persistent copy of the training data is stored in the
+        object. Otherwise, just a reference to the training data is stored,
+        which might cause predictions to change if the data is modified
+        externally.
+
+    random_state : int, RandomState instance or None, default=None
+        Determines random number generation used to initialize the centers.
+        Pass an int for reproducible results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+    multi_class : {'one_vs_rest', 'one_vs_one'}, default='one_vs_rest'
+        Specifies how multi-class classification problems are handled.
+        Supported are 'one_vs_rest' and 'one_vs_one'. In 'one_vs_rest',
+        one binary Gaussian process classifier is fitted for each class, which
+        is trained to separate this class from the rest. In 'one_vs_one', one
+        binary Gaussian process classifier is fitted for each pair of classes,
+        which is trained to separate these two classes. The predictions of
+        these binary predictors are combined into multi-class predictions.
+        Note that 'one_vs_one' does not support predicting probability
+        estimates.
+
+    n_jobs : int, default=None
+        The number of jobs to use for the computation: the specified
+        multiclass problems are computed in parallel.
+        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
+        ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
+        for more details.
+
+    Attributes
+    ----------
+    base_estimator_ : ``Estimator`` instance
+        The estimator instance that defines the likelihood function
+        using the observed data.
+
+    kernel_ : kernel instance
+        The kernel used for prediction. In case of binary classification,
+        the structure of the kernel is the same as the one passed as parameter
+        but with optimized hyperparameters. In case of multi-class
+        classification, a CompoundKernel is returned which consists of the
+        different kernels used in the one-versus-rest classifiers.
+
+    log_marginal_likelihood_value_ : float
+        The log-marginal-likelihood of ``self.kernel_.theta``
+
+    classes_ : array-like of shape (n_classes,)
+        Unique class labels.
+
+    n_classes_ : int
+        The number of classes in the training data
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+        .. versionadded:: 0.24
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
+    See Also
+    --------
+    GaussianProcessRegressor : Gaussian process regression (GPR).
+
+    References
+    ----------
+    .. [RW2006] `Carl E. Rasmussen and Christopher K.I. Williams,
+       "Gaussian Processes for Machine Learning",
+       MIT Press 2006 <https://www.gaussianprocess.org/gpml/chapters/RW.pdf>`_
+
+    Examples
+    --------
+    >>> from sklearn.datasets import load_iris
+    >>> from sklearn.gaussian_process import GaussianProcessClassifier
+    >>> from sklearn.gaussian_process.kernels import RBF
+    >>> X, y = load_iris(return_X_y=True)
+    >>> kernel = 1.0 * RBF(1.0)
+    >>> gpc = GaussianProcessClassifier(kernel=kernel,
+    ...         random_state=0).fit(X, y)
+    >>> gpc.score(X, y)
+    0.9866...
+    >>> gpc.predict_proba(X[:2,:])
+    array([[0.83548752, 0.03228706, 0.13222543],
+           [0.79064206, 0.06525643, 0.14410151]])
+    """
+
+    _parameter_constraints: dict = {
+        "kernel": [Kernel, None],
+        "optimizer": [StrOptions({"fmin_l_bfgs_b"}), callable, None],
+        "n_restarts_optimizer": [Interval(Integral, 0, None, closed="left")],
+        "max_iter_predict": [Interval(Integral, 1, None, closed="left")],
+        "warm_start": ["boolean"],
+        "copy_X_train": ["boolean"],
+        "random_state": ["random_state"],
+        "multi_class": [StrOptions({"one_vs_rest", "one_vs_one"})],
+        "n_jobs": [Integral, None],
+    }
+
+    def __init__(
+        self,
+        kernel=None,
+        *,
+        optimizer="fmin_l_bfgs_b",
+        n_restarts_optimizer=0,
+        max_iter_predict=100,
+        warm_start=False,
+        copy_X_train=True,
+        random_state=None,
+        multi_class="one_vs_rest",
+        n_jobs=None,
+    ):
+        self.kernel = kernel
+        self.optimizer = optimizer
+        self.n_restarts_optimizer = n_restarts_optimizer
+        self.max_iter_predict = max_iter_predict
+        self.warm_start = warm_start
+        self.copy_X_train = copy_X_train
+        self.random_state = random_state
+        self.multi_class = multi_class
+        self.n_jobs = n_jobs
+
+    def fit(self, X, y):
+        """Fit Gaussian process classification model.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features) or list of object
+            Feature vectors or other representations of training data.
+
+        y : array-like of shape (n_samples,)
+            Target values, must be binary.
+
+        Returns
+        -------
+        self : object
+            Returns an instance of self.
+        """
+        self._validate_params()
+
+        if isinstance(self.kernel, CompoundKernel):
+            raise ValueError("kernel cannot be a CompoundKernel")
+
+        if self.kernel is None or self.kernel.requires_vector_input:
+            X, y = self._validate_data(
+                X, y, multi_output=False, ensure_2d=True, dtype="numeric"
+            )
+        else:
+            X, y = self._validate_data(
+                X, y, multi_output=False, ensure_2d=False, dtype=None
+            )
+
+        self.base_estimator_ = _BinaryGaussianProcessClassifierLaplace(
+            kernel=self.kernel,
+            optimizer=self.optimizer,
+            n_restarts_optimizer=self.n_restarts_optimizer,
+            max_iter_predict=self.max_iter_predict,
+            warm_start=self.warm_start,
+            copy_X_train=self.copy_X_train,
+            random_state=self.random_state,
+        )
+
+        self.classes_ = np.unique(y)
+        self.n_classes_ = self.classes_.size
+        if self.n_classes_ == 1:
+            raise ValueError(
+                "GaussianProcessClassifier requires 2 or more "
+                "distinct classes; got %d class (only class %s "
+                "is present)" % (self.n_classes_, self.classes_[0])
+            )
+        if self.n_classes_ > 2:
+            if self.multi_class == "one_vs_rest":
+                self.base_estimator_ = OneVsRestClassifier(
+                    self.base_estimator_, n_jobs=self.n_jobs
+                )
+            elif self.multi_class == "one_vs_one":
+                self.base_estimator_ = OneVsOneClassifier(
+                    self.base_estimator_, n_jobs=self.n_jobs
+                )
+            else:
+                raise ValueError("Unknown multi-class mode %s" % self.multi_class)
+
+        self.base_estimator_.fit(X, y)
+
+        if self.n_classes_ > 2:
+            self.log_marginal_likelihood_value_ = np.mean(
+                [
+                    estimator.log_marginal_likelihood()
+                    for estimator in self.base_estimator_.estimators_
+                ]
+            )
+        else:
+            self.log_marginal_likelihood_value_ = (
+                self.base_estimator_.log_marginal_likelihood()
+            )
+
+        return self
+
+    def predict(self, X):
+        """Perform classification on an array of test vectors X.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features) or list of object
+            Query points where the GP is evaluated for classification.
+
+        Returns
+        -------
+        C : ndarray of shape (n_samples,)
+            Predicted target values for X, values are from ``classes_``.
+        """
+        check_is_fitted(self)
+
+        if self.kernel is None or self.kernel.requires_vector_input:
+            X = self._validate_data(X, ensure_2d=True, dtype="numeric", reset=False)
+        else:
+            X = self._validate_data(X, ensure_2d=False, dtype=None, reset=False)
+
+        return self.base_estimator_.predict(X)
+
+    def predict_proba(self, X):
+        """Return probability estimates for the test vector X.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features) or list of object
+            Query points where the GP is evaluated for classification.
+
+        Returns
+        -------
+        C : array-like of shape (n_samples, n_classes)
+            Returns the probability of the samples for each class in
+            the model. The columns correspond to the classes in sorted
+            order, as they appear in the attribute :term:`classes_`.
+        """
+        check_is_fitted(self)
+        if self.n_classes_ > 2 and self.multi_class == "one_vs_one":
+            raise ValueError(
+                "one_vs_one multi-class mode does not support "
+                "predicting probability estimates. Use "
+                "one_vs_rest mode instead."
+            )
+
+        if self.kernel is None or self.kernel.requires_vector_input:
+            X = self._validate_data(X, ensure_2d=True, dtype="numeric", reset=False)
+        else:
+            X = self._validate_data(X, ensure_2d=False, dtype=None, reset=False)
+
+        return self.base_estimator_.predict_proba(X)
+
+    @property
+    def kernel_(self):
+        """Return the kernel of the base estimator."""
+        if self.n_classes_ == 2:
+            return self.base_estimator_.kernel_
+        else:
+            return CompoundKernel(
+                [estimator.kernel_ for estimator in self.base_estimator_.estimators_]
+            )
+
+    def log_marginal_likelihood(
+        self, theta=None, eval_gradient=False, clone_kernel=True
+    ):
+        """Return log-marginal likelihood of theta for training data.
+
+        In the case of multi-class classification, the mean log-marginal
+        likelihood of the one-versus-rest classifiers are returned.
+
+        Parameters
+        ----------
+        theta : array-like of shape (n_kernel_params,), default=None
+            Kernel hyperparameters for which the log-marginal likelihood is
+            evaluated. In the case of multi-class classification, theta may
+            be the  hyperparameters of the compound kernel or of an individual
+            kernel. In the latter case, all individual kernel get assigned the
+            same theta values. If None, the precomputed log_marginal_likelihood
+            of ``self.kernel_.theta`` is returned.
+
+        eval_gradient : bool, default=False
+            If True, the gradient of the log-marginal likelihood with respect
+            to the kernel hyperparameters at position theta is returned
+            additionally. Note that gradient computation is not supported
+            for non-binary classification. If True, theta must not be None.
+
+        clone_kernel : bool, default=True
+            If True, the kernel attribute is copied. If False, the kernel
+            attribute is modified, but may result in a performance improvement.
+
+        Returns
+        -------
+        log_likelihood : float
+            Log-marginal likelihood of theta for training data.
+
+        log_likelihood_gradient : ndarray of shape (n_kernel_params,), optional
+            Gradient of the log-marginal likelihood with respect to the kernel
+            hyperparameters at position theta.
+            Only returned when `eval_gradient` is True.
+        """
+        check_is_fitted(self)
+
+        if theta is None:
+            if eval_gradient:
+                raise ValueError("Gradient can only be evaluated for theta!=None")
+            return self.log_marginal_likelihood_value_
+
+        theta = np.asarray(theta)
+        if self.n_classes_ == 2:
+            return self.base_estimator_.log_marginal_likelihood(
+                theta, eval_gradient, clone_kernel=clone_kernel
+            )
+        else:
+            if eval_gradient:
+                raise NotImplementedError(
+                    "Gradient of log-marginal-likelihood not implemented for "
+                    "multi-class GPC."
+                )
+            estimators = self.base_estimator_.estimators_
+            n_dims = estimators[0].kernel_.n_dims
+            if theta.shape[0] == n_dims:  # use same theta for all sub-kernels
+                return np.mean(
+                    [
+                        estimator.log_marginal_likelihood(
+                            theta, clone_kernel=clone_kernel
+                        )
+                        for i, estimator in enumerate(estimators)
+                    ]
+                )
+            elif theta.shape[0] == n_dims * self.classes_.shape[0]:
+                # theta for compound kernel
+                return np.mean(
+                    [
+                        estimator.log_marginal_likelihood(
+                            theta[n_dims * i : n_dims * (i + 1)],
+                            clone_kernel=clone_kernel,
+                        )
+                        for i, estimator in enumerate(estimators)
+                    ]
+                )
+            else:
+                raise ValueError(
+                    "Shape of theta must be either %d or %d. "
+                    "Obtained theta with shape %d."
+                    % (n_dims, n_dims * self.classes_.shape[0], theta.shape[0])
+                )

mplug_owl2/lib/python3.10/site-packages/sklearn/gaussian_process/_gpr.py

@@ -0,0 +1,639 @@
+"""Gaussian processes regression."""
+
+# Authors: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
+# Modified by: Pete Green <p.l.green@liverpool.ac.uk>
+# License: BSD 3 clause
+
+import warnings
+from numbers import Integral, Real
+from operator import itemgetter
+
+import numpy as np
+from scipy.linalg import cholesky, cho_solve, solve_triangular
+import scipy.optimize
+
+from ..base import BaseEstimator, RegressorMixin, clone
+from ..base import MultiOutputMixin
+from .kernels import Kernel, RBF, ConstantKernel as C
+from ..preprocessing._data import _handle_zeros_in_scale
+from ..utils import check_random_state
+from ..utils.optimize import _check_optimize_result
+from ..utils._param_validation import Interval, StrOptions
+
+GPR_CHOLESKY_LOWER = True
+
+
+class GaussianProcessRegressor(MultiOutputMixin, RegressorMixin, BaseEstimator):
+    """Gaussian process regression (GPR).
+
+    The implementation is based on Algorithm 2.1 of [RW2006]_.
+
+    In addition to standard scikit-learn estimator API,
+    :class:`GaussianProcessRegressor`:
+
+       * allows prediction without prior fitting (based on the GP prior)
+       * provides an additional method `sample_y(X)`, which evaluates samples
+         drawn from the GPR (prior or posterior) at given inputs
+       * exposes a method `log_marginal_likelihood(theta)`, which can be used
+         externally for other ways of selecting hyperparameters, e.g., via
+         Markov chain Monte Carlo.
+
+    Read more in the :ref:`User Guide <gaussian_process>`.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    kernel : kernel instance, default=None
+        The kernel specifying the covariance function of the GP. If None is
+        passed, the kernel ``ConstantKernel(1.0, constant_value_bounds="fixed")
+        * RBF(1.0, length_scale_bounds="fixed")`` is used as default. Note that
+        the kernel hyperparameters are optimized during fitting unless the
+        bounds are marked as "fixed".
+
+    alpha : float or ndarray of shape (n_samples,), default=1e-10
+        Value added to the diagonal of the kernel matrix during fitting.
+        This can prevent a potential numerical issue during fitting, by
+        ensuring that the calculated values form a positive definite matrix.
+        It can also be interpreted as the variance of additional Gaussian
+        measurement noise on the training observations. Note that this is
+        different from using a `WhiteKernel`. If an array is passed, it must
+        have the same number of entries as the data used for fitting and is
+        used as datapoint-dependent noise level. Allowing to specify the
+        noise level directly as a parameter is mainly for convenience and
+        for consistency with :class:`~sklearn.linear_model.Ridge`.
+
+    optimizer : "fmin_l_bfgs_b", callable or None, default="fmin_l_bfgs_b"
+        Can either be one of the internally supported optimizers for optimizing
+        the kernel's parameters, specified by a string, or an externally
+        defined optimizer passed as a callable. If a callable is passed, it
+        must have the signature::
+
+            def optimizer(obj_func, initial_theta, bounds):
+                # * 'obj_func': the objective function to be minimized, which
+                #   takes the hyperparameters theta as a parameter and an
+                #   optional flag eval_gradient, which determines if the
+                #   gradient is returned additionally to the function value
+                # * 'initial_theta': the initial value for theta, which can be
+                #   used by local optimizers
+                # * 'bounds': the bounds on the values of theta
+                ....
+                # Returned are the best found hyperparameters theta and
+                # the corresponding value of the target function.
+                return theta_opt, func_min
+
+        Per default, the L-BFGS-B algorithm from `scipy.optimize.minimize`
+        is used. If None is passed, the kernel's parameters are kept fixed.
+        Available internal optimizers are: `{'fmin_l_bfgs_b'}`.
+
+    n_restarts_optimizer : int, default=0
+        The number of restarts of the optimizer for finding the kernel's
+        parameters which maximize the log-marginal likelihood. The first run
+        of the optimizer is performed from the kernel's initial parameters,
+        the remaining ones (if any) from thetas sampled log-uniform randomly
+        from the space of allowed theta-values. If greater than 0, all bounds
+        must be finite. Note that `n_restarts_optimizer == 0` implies that one
+        run is performed.
+
+    normalize_y : bool, default=False
+        Whether or not to normalize the target values `y` by removing the mean
+        and scaling to unit-variance. This is recommended for cases where
+        zero-mean, unit-variance priors are used. Note that, in this
+        implementation, the normalisation is reversed before the GP predictions
+        are reported.
+
+        .. versionchanged:: 0.23
+
+    copy_X_train : bool, default=True
+        If True, a persistent copy of the training data is stored in the
+        object. Otherwise, just a reference to the training data is stored,
+        which might cause predictions to change if the data is modified
+        externally.
+
+    random_state : int, RandomState instance or None, default=None
+        Determines random number generation used to initialize the centers.
+        Pass an int for reproducible results across multiple function calls.
+        See :term:`Glossary <random_state>`.
+
+    Attributes
+    ----------
+    X_train_ : array-like of shape (n_samples, n_features) or list of object
+        Feature vectors or other representations of training data (also
+        required for prediction).
+
+    y_train_ : array-like of shape (n_samples,) or (n_samples, n_targets)
+        Target values in training data (also required for prediction).
+
+    kernel_ : kernel instance
+        The kernel used for prediction. The structure of the kernel is the
+        same as the one passed as parameter but with optimized hyperparameters.
+
+    L_ : array-like of shape (n_samples, n_samples)
+        Lower-triangular Cholesky decomposition of the kernel in ``X_train_``.
+
+    alpha_ : array-like of shape (n_samples,)
+        Dual coefficients of training data points in kernel space.
+
+    log_marginal_likelihood_value_ : float
+        The log-marginal-likelihood of ``self.kernel_.theta``.
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+        .. versionadded:: 0.24
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
+    See Also
+    --------
+    GaussianProcessClassifier : Gaussian process classification (GPC)
+        based on Laplace approximation.
+
+    References
+    ----------
+    .. [RW2006] `Carl E. Rasmussen and Christopher K.I. Williams,
+       "Gaussian Processes for Machine Learning",
+       MIT Press 2006 <https://www.gaussianprocess.org/gpml/chapters/RW.pdf>`_
+
+    Examples
+    --------
+    >>> from sklearn.datasets import make_friedman2
+    >>> from sklearn.gaussian_process import GaussianProcessRegressor
+    >>> from sklearn.gaussian_process.kernels import DotProduct, WhiteKernel
+    >>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
+    >>> kernel = DotProduct() + WhiteKernel()
+    >>> gpr = GaussianProcessRegressor(kernel=kernel,
+    ...         random_state=0).fit(X, y)
+    >>> gpr.score(X, y)
+    0.3680...
+    >>> gpr.predict(X[:2,:], return_std=True)
+    (array([653.0..., 592.1...]), array([316.6..., 316.6...]))
+    """
+
+    _parameter_constraints: dict = {
+        "kernel": [None, Kernel],
+        "alpha": [Interval(Real, 0, None, closed="left"), np.ndarray],
+        "optimizer": [StrOptions({"fmin_l_bfgs_b"}), callable, None],
+        "n_restarts_optimizer": [Interval(Integral, 0, None, closed="left")],
+        "normalize_y": ["boolean"],
+        "copy_X_train": ["boolean"],
+        "random_state": ["random_state"],
+    }
+
+    def __init__(
+        self,
+        kernel=None,
+        *,
+        alpha=1e-10,
+        optimizer="fmin_l_bfgs_b",
+        n_restarts_optimizer=0,
+        normalize_y=False,
+        copy_X_train=True,
+        random_state=None,
+    ):
+        self.kernel = kernel
+        self.alpha = alpha
+        self.optimizer = optimizer
+        self.n_restarts_optimizer = n_restarts_optimizer
+        self.normalize_y = normalize_y
+        self.copy_X_train = copy_X_train
+        self.random_state = random_state
+
+    def fit(self, X, y):
+        """Fit Gaussian process regression model.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features) or list of object
+            Feature vectors or other representations of training data.
+
+        y : array-like of shape (n_samples,) or (n_samples, n_targets)
+            Target values.
+
+        Returns
+        -------
+        self : object
+            GaussianProcessRegressor class instance.
+        """
+        self._validate_params()
+
+        if self.kernel is None:  # Use an RBF kernel as default
+            self.kernel_ = C(1.0, constant_value_bounds="fixed") * RBF(
+                1.0, length_scale_bounds="fixed"
+            )
+        else:
+            self.kernel_ = clone(self.kernel)
+
+        self._rng = check_random_state(self.random_state)
+
+        if self.kernel_.requires_vector_input:
+            dtype, ensure_2d = "numeric", True
+        else:
+            dtype, ensure_2d = None, False
+        X, y = self._validate_data(
+            X,
+            y,
+            multi_output=True,
+            y_numeric=True,
+            ensure_2d=ensure_2d,
+            dtype=dtype,
+        )
+
+        # Normalize target value
+        if self.normalize_y:
+            self._y_train_mean = np.mean(y, axis=0)
+            self._y_train_std = _handle_zeros_in_scale(np.std(y, axis=0), copy=False)
+
+            # Remove mean and make unit variance
+            y = (y - self._y_train_mean) / self._y_train_std
+
+        else:
+            shape_y_stats = (y.shape[1],) if y.ndim == 2 else 1
+            self._y_train_mean = np.zeros(shape=shape_y_stats)
+            self._y_train_std = np.ones(shape=shape_y_stats)
+
+        if np.iterable(self.alpha) and self.alpha.shape[0] != y.shape[0]:
+            if self.alpha.shape[0] == 1:
+                self.alpha = self.alpha[0]
+            else:
+                raise ValueError(
+                    "alpha must be a scalar or an array with same number of "
+                    f"entries as y. ({self.alpha.shape[0]} != {y.shape[0]})"
+                )
+
+        self.X_train_ = np.copy(X) if self.copy_X_train else X
+        self.y_train_ = np.copy(y) if self.copy_X_train else y
+
+        if self.optimizer is not None and self.kernel_.n_dims > 0:
+            # Choose hyperparameters based on maximizing the log-marginal
+            # likelihood (potentially starting from several initial values)
+            def obj_func(theta, eval_gradient=True):
+                if eval_gradient:
+                    lml, grad = self.log_marginal_likelihood(
+                        theta, eval_gradient=True, clone_kernel=False
+                    )
+                    return -lml, -grad
+                else:
+                    return -self.log_marginal_likelihood(theta, clone_kernel=False)
+
+            # First optimize starting from theta specified in kernel
+            optima = [
+                (
+                    self._constrained_optimization(
+                        obj_func, self.kernel_.theta, self.kernel_.bounds
+                    )
+                )
+            ]
+
+            # Additional runs are performed from log-uniform chosen initial
+            # theta
+            if self.n_restarts_optimizer > 0:
+                if not np.isfinite(self.kernel_.bounds).all():
+                    raise ValueError(
+                        "Multiple optimizer restarts (n_restarts_optimizer>0) "
+                        "requires that all bounds are finite."
+                    )
+                bounds = self.kernel_.bounds
+                for iteration in range(self.n_restarts_optimizer):
+                    theta_initial = self._rng.uniform(bounds[:, 0], bounds[:, 1])
+                    optima.append(
+                        self._constrained_optimization(obj_func, theta_initial, bounds)
+                    )
+            # Select result from run with minimal (negative) log-marginal
+            # likelihood
+            lml_values = list(map(itemgetter(1), optima))
+            self.kernel_.theta = optima[np.argmin(lml_values)][0]
+            self.kernel_._check_bounds_params()
+
+            self.log_marginal_likelihood_value_ = -np.min(lml_values)
+        else:
+            self.log_marginal_likelihood_value_ = self.log_marginal_likelihood(
+                self.kernel_.theta, clone_kernel=False
+            )
+
+        # Precompute quantities required for predictions which are independent
+        # of actual query points
+        # Alg. 2.1, page 19, line 2 -> L = cholesky(K + sigma^2 I)
+        K = self.kernel_(self.X_train_)
+        K[np.diag_indices_from(K)] += self.alpha
+        try:
+            self.L_ = cholesky(K, lower=GPR_CHOLESKY_LOWER, check_finite=False)
+        except np.linalg.LinAlgError as exc:
+            exc.args = (
+                f"The kernel, {self.kernel_}, is not returning a positive "
+                "definite matrix. Try gradually increasing the 'alpha' "
+                "parameter of your GaussianProcessRegressor estimator.",
+            ) + exc.args
+            raise
+        # Alg 2.1, page 19, line 3 -> alpha = L^T \ (L \ y)
+        self.alpha_ = cho_solve(
+            (self.L_, GPR_CHOLESKY_LOWER),
+            self.y_train_,
+            check_finite=False,
+        )
+        return self
+
+    def predict(self, X, return_std=False, return_cov=False):
+        """Predict using the Gaussian process regression model.
+
+        We can also predict based on an unfitted model by using the GP prior.
+        In addition to the mean of the predictive distribution, optionally also
+        returns its standard deviation (`return_std=True`) or covariance
+        (`return_cov=True`). Note that at most one of the two can be requested.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features) or list of object
+            Query points where the GP is evaluated.
+
+        return_std : bool, default=False
+            If True, the standard-deviation of the predictive distribution at
+            the query points is returned along with the mean.
+
+        return_cov : bool, default=False
+            If True, the covariance of the joint predictive distribution at
+            the query points is returned along with the mean.
+
+        Returns
+        -------
+        y_mean : ndarray of shape (n_samples,) or (n_samples, n_targets)
+            Mean of predictive distribution a query points.
+
+        y_std : ndarray of shape (n_samples,) or (n_samples, n_targets), optional
+            Standard deviation of predictive distribution at query points.
+            Only returned when `return_std` is True.
+
+        y_cov : ndarray of shape (n_samples, n_samples) or \
+                (n_samples, n_samples, n_targets), optional
+            Covariance of joint predictive distribution a query points.
+            Only returned when `return_cov` is True.
+        """
+        if return_std and return_cov:
+            raise RuntimeError(
+                "At most one of return_std or return_cov can be requested."
+            )
+
+        if self.kernel is None or self.kernel.requires_vector_input:
+            dtype, ensure_2d = "numeric", True
+        else:
+            dtype, ensure_2d = None, False
+
+        X = self._validate_data(X, ensure_2d=ensure_2d, dtype=dtype, reset=False)
+
+        if not hasattr(self, "X_train_"):  # Unfitted;predict based on GP prior
+            if self.kernel is None:
+                kernel = C(1.0, constant_value_bounds="fixed") * RBF(
+                    1.0, length_scale_bounds="fixed"
+                )
+            else:
+                kernel = self.kernel
+            y_mean = np.zeros(X.shape[0])
+            if return_cov:
+                y_cov = kernel(X)
+                return y_mean, y_cov
+            elif return_std:
+                y_var = kernel.diag(X)
+                return y_mean, np.sqrt(y_var)
+            else:
+                return y_mean
+        else:  # Predict based on GP posterior
+            # Alg 2.1, page 19, line 4 -> f*_bar = K(X_test, X_train) . alpha
+            K_trans = self.kernel_(X, self.X_train_)
+            y_mean = K_trans @ self.alpha_
+
+            # undo normalisation
+            y_mean = self._y_train_std * y_mean + self._y_train_mean
+
+            # if y_mean has shape (n_samples, 1), reshape to (n_samples,)
+            if y_mean.ndim > 1 and y_mean.shape[1] == 1:
+                y_mean = np.squeeze(y_mean, axis=1)
+
+            # Alg 2.1, page 19, line 5 -> v = L \ K(X_test, X_train)^T
+            V = solve_triangular(
+                self.L_, K_trans.T, lower=GPR_CHOLESKY_LOWER, check_finite=False
+            )
+
+            if return_cov:
+                # Alg 2.1, page 19, line 6 -> K(X_test, X_test) - v^T. v
+                y_cov = self.kernel_(X) - V.T @ V
+
+                # undo normalisation
+                y_cov = np.outer(y_cov, self._y_train_std**2).reshape(
+                    *y_cov.shape, -1
+                )
+                # if y_cov has shape (n_samples, n_samples, 1), reshape to
+                # (n_samples, n_samples)
+                if y_cov.shape[2] == 1:
+                    y_cov = np.squeeze(y_cov, axis=2)
+
+                return y_mean, y_cov
+            elif return_std:
+                # Compute variance of predictive distribution
+                # Use einsum to avoid explicitly forming the large matrix
+                # V^T @ V just to extract its diagonal afterward.
+                y_var = self.kernel_.diag(X).copy()
+                y_var -= np.einsum("ij,ji->i", V.T, V)
+
+                # Check if any of the variances is negative because of
+                # numerical issues. If yes: set the variance to 0.
+                y_var_negative = y_var < 0
+                if np.any(y_var_negative):
+                    warnings.warn(
+                        "Predicted variances smaller than 0. "
+                        "Setting those variances to 0."
+                    )
+                    y_var[y_var_negative] = 0.0
+
+                # undo normalisation
+                y_var = np.outer(y_var, self._y_train_std**2).reshape(
+                    *y_var.shape, -1
+                )
+
+                # if y_var has shape (n_samples, 1), reshape to (n_samples,)
+                if y_var.shape[1] == 1:
+                    y_var = np.squeeze(y_var, axis=1)
+
+                return y_mean, np.sqrt(y_var)
+            else:
+                return y_mean
+
+    def sample_y(self, X, n_samples=1, random_state=0):
+        """Draw samples from Gaussian process and evaluate at X.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples_X, n_features) or list of object
+            Query points where the GP is evaluated.
+
+        n_samples : int, default=1
+            Number of samples drawn from the Gaussian process per query point.
+
+        random_state : int, RandomState instance or None, default=0
+            Determines random number generation to randomly draw samples.
+            Pass an int for reproducible results across multiple function
+            calls.
+            See :term:`Glossary <random_state>`.
+
+        Returns
+        -------
+        y_samples : ndarray of shape (n_samples_X, n_samples), or \
+            (n_samples_X, n_targets, n_samples)
+            Values of n_samples samples drawn from Gaussian process and
+            evaluated at query points.
+        """
+        rng = check_random_state(random_state)
+
+        y_mean, y_cov = self.predict(X, return_cov=True)
+        if y_mean.ndim == 1:
+            y_samples = rng.multivariate_normal(y_mean, y_cov, n_samples).T
+        else:
+            y_samples = [
+                rng.multivariate_normal(
+                    y_mean[:, target], y_cov[..., target], n_samples
+                ).T[:, np.newaxis]
+                for target in range(y_mean.shape[1])
+            ]
+            y_samples = np.hstack(y_samples)
+        return y_samples
+
+    def log_marginal_likelihood(
+        self, theta=None, eval_gradient=False, clone_kernel=True
+    ):
+        """Return log-marginal likelihood of theta for training data.
+
+        Parameters
+        ----------
+        theta : array-like of shape (n_kernel_params,) default=None
+            Kernel hyperparameters for which the log-marginal likelihood is
+            evaluated. If None, the precomputed log_marginal_likelihood
+            of ``self.kernel_.theta`` is returned.
+
+        eval_gradient : bool, default=False
+            If True, the gradient of the log-marginal likelihood with respect
+            to the kernel hyperparameters at position theta is returned
+            additionally. If True, theta must not be None.
+
+        clone_kernel : bool, default=True
+            If True, the kernel attribute is copied. If False, the kernel
+            attribute is modified, but may result in a performance improvement.
+
+        Returns
+        -------
+        log_likelihood : float
+            Log-marginal likelihood of theta for training data.
+
+        log_likelihood_gradient : ndarray of shape (n_kernel_params,), optional
+            Gradient of the log-marginal likelihood with respect to the kernel
+            hyperparameters at position theta.
+            Only returned when eval_gradient is True.
+        """
+        if theta is None:
+            if eval_gradient:
+                raise ValueError("Gradient can only be evaluated for theta!=None")
+            return self.log_marginal_likelihood_value_
+
+        if clone_kernel:
+            kernel = self.kernel_.clone_with_theta(theta)
+        else:
+            kernel = self.kernel_
+            kernel.theta = theta
+
+        if eval_gradient:
+            K, K_gradient = kernel(self.X_train_, eval_gradient=True)
+        else:
+            K = kernel(self.X_train_)
+
+        # Alg. 2.1, page 19, line 2 -> L = cholesky(K + sigma^2 I)
+        K[np.diag_indices_from(K)] += self.alpha
+        try:
+            L = cholesky(K, lower=GPR_CHOLESKY_LOWER, check_finite=False)
+        except np.linalg.LinAlgError:
+            return (-np.inf, np.zeros_like(theta)) if eval_gradient else -np.inf
+
+        # Support multi-dimensional output of self.y_train_
+        y_train = self.y_train_
+        if y_train.ndim == 1:
+            y_train = y_train[:, np.newaxis]
+
+        # Alg 2.1, page 19, line 3 -> alpha = L^T \ (L \ y)
+        alpha = cho_solve((L, GPR_CHOLESKY_LOWER), y_train, check_finite=False)
+
+        # Alg 2.1, page 19, line 7
+        # -0.5 . y^T . alpha - sum(log(diag(L))) - n_samples / 2 log(2*pi)
+        # y is originally thought to be a (1, n_samples) row vector. However,
+        # in multioutputs, y is of shape (n_samples, 2) and we need to compute
+        # y^T . alpha for each output, independently using einsum. Thus, it
+        # is equivalent to:
+        # for output_idx in range(n_outputs):
+        #     log_likelihood_dims[output_idx] = (
+        #         y_train[:, [output_idx]] @ alpha[:, [output_idx]]
+        #     )
+        log_likelihood_dims = -0.5 * np.einsum("ik,ik->k", y_train, alpha)
+        log_likelihood_dims -= np.log(np.diag(L)).sum()
+        log_likelihood_dims -= K.shape[0] / 2 * np.log(2 * np.pi)
+        # the log likehood is sum-up across the outputs
+        log_likelihood = log_likelihood_dims.sum(axis=-1)
+
+        if eval_gradient:
+            # Eq. 5.9, p. 114, and footnote 5 in p. 114
+            # 0.5 * trace((alpha . alpha^T - K^-1) . K_gradient)
+            # alpha is supposed to be a vector of (n_samples,) elements. With
+            # multioutputs, alpha is a matrix of size (n_samples, n_outputs).
+            # Therefore, we want to construct a matrix of
+            # (n_samples, n_samples, n_outputs) equivalent to
+            # for output_idx in range(n_outputs):
+            #     output_alpha = alpha[:, [output_idx]]
+            #     inner_term[..., output_idx] = output_alpha @ output_alpha.T
+            inner_term = np.einsum("ik,jk->ijk", alpha, alpha)
+            # compute K^-1 of shape (n_samples, n_samples)
+            K_inv = cho_solve(
+                (L, GPR_CHOLESKY_LOWER), np.eye(K.shape[0]), check_finite=False
+            )
+            # create a new axis to use broadcasting between inner_term and
+            # K_inv
+            inner_term -= K_inv[..., np.newaxis]
+            # Since we are interested about the trace of
+            # inner_term @ K_gradient, we don't explicitly compute the
+            # matrix-by-matrix operation and instead use an einsum. Therefore
+            # it is equivalent to:
+            # for param_idx in range(n_kernel_params):
+            #     for output_idx in range(n_output):
+            #         log_likehood_gradient_dims[param_idx, output_idx] = (
+            #             inner_term[..., output_idx] @
+            #             K_gradient[..., param_idx]
+            #         )
+            log_likelihood_gradient_dims = 0.5 * np.einsum(
+                "ijl,jik->kl", inner_term, K_gradient
+            )
+            # the log likehood gradient is the sum-up across the outputs
+            log_likelihood_gradient = log_likelihood_gradient_dims.sum(axis=-1)
+
+        if eval_gradient:
+            return log_likelihood, log_likelihood_gradient
+        else:
+            return log_likelihood
+
+    def _constrained_optimization(self, obj_func, initial_theta, bounds):
+        if self.optimizer == "fmin_l_bfgs_b":
+            opt_res = scipy.optimize.minimize(
+                obj_func,
+                initial_theta,
+                method="L-BFGS-B",
+                jac=True,
+                bounds=bounds,
+            )
+            _check_optimize_result("lbfgs", opt_res)
+            theta_opt, func_min = opt_res.x, opt_res.fun
+        elif callable(self.optimizer):
+            theta_opt, func_min = self.optimizer(obj_func, initial_theta, bounds=bounds)
+        else:
+            raise ValueError(f"Unknown optimizer {self.optimizer}.")
+
+        return theta_opt, func_min
+
+    def _more_tags(self):
+        return {"requires_fit": False}

mplug_owl2/lib/python3.10/site-packages/sklearn/gaussian_process/kernels.py

@@ -0,0 +1,2390 @@
+"""Kernels for Gaussian process regression and classification.
+
+The kernels in this module allow kernel-engineering, i.e., they can be
+combined via the "+" and "*" operators or be exponentiated with a scalar
+via "**". These sum and product expressions can also contain scalar values,
+which are automatically converted to a constant kernel.
+
+All kernels allow (analytic) gradient-based hyperparameter optimization.
+The space of hyperparameters can be specified by giving lower und upper
+boundaries for the value of each hyperparameter (the search space is thus
+rectangular). Instead of specifying bounds, hyperparameters can also be
+declared to be "fixed", which causes these hyperparameters to be excluded from
+optimization.
+"""
+
+# Author: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
+# License: BSD 3 clause
+
+# Note: this module is strongly inspired by the kernel module of the george
+#       package.
+
+from abc import ABCMeta, abstractmethod
+from collections import namedtuple
+import math
+from inspect import signature
+
+import numpy as np
+from scipy.special import kv, gamma
+from scipy.spatial.distance import pdist, cdist, squareform
+
+from ..metrics.pairwise import pairwise_kernels
+from ..base import clone
+from ..utils.validation import _num_samples
+from ..exceptions import ConvergenceWarning
+
+import warnings
+
+
+def _check_length_scale(X, length_scale):
+    length_scale = np.squeeze(length_scale).astype(float)
+    if np.ndim(length_scale) > 1:
+        raise ValueError("length_scale cannot be of dimension greater than 1")
+    if np.ndim(length_scale) == 1 and X.shape[1] != length_scale.shape[0]:
+        raise ValueError(
+            "Anisotropic kernel must have the same number of "
+            "dimensions as data (%d!=%d)" % (length_scale.shape[0], X.shape[1])
+        )
+    return length_scale
+
+
+class Hyperparameter(
+    namedtuple(
+        "Hyperparameter", ("name", "value_type", "bounds", "n_elements", "fixed")
+    )
+):
+    """A kernel hyperparameter's specification in form of a namedtuple.
+
+    .. versionadded:: 0.18
+
+    Attributes
+    ----------
+    name : str
+        The name of the hyperparameter. Note that a kernel using a
+        hyperparameter with name "x" must have the attributes self.x and
+        self.x_bounds
+
+    value_type : str
+        The type of the hyperparameter. Currently, only "numeric"
+        hyperparameters are supported.
+
+    bounds : pair of floats >= 0 or "fixed"
+        The lower and upper bound on the parameter. If n_elements>1, a pair
+        of 1d array with n_elements each may be given alternatively. If
+        the string "fixed" is passed as bounds, the hyperparameter's value
+        cannot be changed.
+
+    n_elements : int, default=1
+        The number of elements of the hyperparameter value. Defaults to 1,
+        which corresponds to a scalar hyperparameter. n_elements > 1
+        corresponds to a hyperparameter which is vector-valued,
+        such as, e.g., anisotropic length-scales.
+
+    fixed : bool, default=None
+        Whether the value of this hyperparameter is fixed, i.e., cannot be
+        changed during hyperparameter tuning. If None is passed, the "fixed" is
+        derived based on the given bounds.
+
+    Examples
+    --------
+    >>> from sklearn.gaussian_process.kernels import ConstantKernel
+    >>> from sklearn.datasets import make_friedman2
+    >>> from sklearn.gaussian_process import GaussianProcessRegressor
+    >>> from sklearn.gaussian_process.kernels import Hyperparameter
+    >>> X, y = make_friedman2(n_samples=50, noise=0, random_state=0)
+    >>> kernel = ConstantKernel(constant_value=1.0,
+    ...    constant_value_bounds=(0.0, 10.0))
+
+    We can access each hyperparameter:
+
+    >>> for hyperparameter in kernel.hyperparameters:
+    ...    print(hyperparameter)
+    Hyperparameter(name='constant_value', value_type='numeric',
+    bounds=array([[ 0., 10.]]), n_elements=1, fixed=False)
+
+    >>> params = kernel.get_params()
+    >>> for key in sorted(params): print(f"{key} : {params[key]}")
+    constant_value : 1.0
+    constant_value_bounds : (0.0, 10.0)
+    """
+
+    # A raw namedtuple is very memory efficient as it packs the attributes
+    # in a struct to get rid of the __dict__ of attributes in particular it
+    # does not copy the string for the keys on each instance.
+    # By deriving a namedtuple class just to introduce the __init__ method we
+    # would also reintroduce the __dict__ on the instance. By telling the
+    # Python interpreter that this subclass uses static __slots__ instead of
+    # dynamic attributes. Furthermore we don't need any additional slot in the
+    # subclass so we set __slots__ to the empty tuple.
+    __slots__ = ()
+
+    def __new__(cls, name, value_type, bounds, n_elements=1, fixed=None):
+        if not isinstance(bounds, str) or bounds != "fixed":
+            bounds = np.atleast_2d(bounds)
+            if n_elements > 1:  # vector-valued parameter
+                if bounds.shape[0] == 1:
+                    bounds = np.repeat(bounds, n_elements, 0)
+                elif bounds.shape[0] != n_elements:
+                    raise ValueError(
+                        "Bounds on %s should have either 1 or "
+                        "%d dimensions. Given are %d"
+                        % (name, n_elements, bounds.shape[0])
+                    )
+
+        if fixed is None:
+            fixed = isinstance(bounds, str) and bounds == "fixed"
+        return super(Hyperparameter, cls).__new__(
+            cls, name, value_type, bounds, n_elements, fixed
+        )
+
+    # This is mainly a testing utility to check that two hyperparameters
+    # are equal.
+    def __eq__(self, other):
+        return (
+            self.name == other.name
+            and self.value_type == other.value_type
+            and np.all(self.bounds == other.bounds)
+            and self.n_elements == other.n_elements
+            and self.fixed == other.fixed
+        )
+
+
+class Kernel(metaclass=ABCMeta):
+    """Base class for all kernels.
+
+    .. versionadded:: 0.18
+    """
+
+    def get_params(self, deep=True):
+        """Get parameters of this kernel.
+
+        Parameters
+        ----------
+        deep : bool, default=True
+            If True, will return the parameters for this estimator and
+            contained subobjects that are estimators.
+
+        Returns
+        -------
+        params : dict
+            Parameter names mapped to their values.
+        """
+        params = dict()
+
+        # introspect the constructor arguments to find the model parameters
+        # to represent
+        cls = self.__class__
+        init = getattr(cls.__init__, "deprecated_original", cls.__init__)
+        init_sign = signature(init)
+        args, varargs = [], []
+        for parameter in init_sign.parameters.values():
+            if parameter.kind != parameter.VAR_KEYWORD and parameter.name != "self":
+                args.append(parameter.name)
+            if parameter.kind == parameter.VAR_POSITIONAL:
+                varargs.append(parameter.name)
+
+        if len(varargs) != 0:
+            raise RuntimeError(
+                "scikit-learn kernels should always "
+                "specify their parameters in the signature"
+                " of their __init__ (no varargs)."
+                " %s doesn't follow this convention." % (cls,)
+            )
+        for arg in args:
+            params[arg] = getattr(self, arg)
+
+        return params
+
+    def set_params(self, **params):
+        """Set the parameters of this kernel.
+
+        The method works on simple kernels as well as on nested kernels.
+        The latter have parameters of the form ``<component>__<parameter>``
+        so that it's possible to update each component of a nested object.
+
+        Returns
+        -------
+        self
+        """
+        if not params:
+            # Simple optimisation to gain speed (inspect is slow)
+            return self
+        valid_params = self.get_params(deep=True)
+        for key, value in params.items():
+            split = key.split("__", 1)
+            if len(split) > 1:
+                # nested objects case
+                name, sub_name = split
+                if name not in valid_params:
+                    raise ValueError(
+                        "Invalid parameter %s for kernel %s. "
+                        "Check the list of available parameters "
+                        "with `kernel.get_params().keys()`." % (name, self)
+                    )
+                sub_object = valid_params[name]
+                sub_object.set_params(**{sub_name: value})
+            else:
+                # simple objects case
+                if key not in valid_params:
+                    raise ValueError(
+                        "Invalid parameter %s for kernel %s. "
+                        "Check the list of available parameters "
+                        "with `kernel.get_params().keys()`."
+                        % (key, self.__class__.__name__)
+                    )
+                setattr(self, key, value)
+        return self
+
+    def clone_with_theta(self, theta):
+        """Returns a clone of self with given hyperparameters theta.
+
+        Parameters
+        ----------
+        theta : ndarray of shape (n_dims,)
+            The hyperparameters
+        """
+        cloned = clone(self)
+        cloned.theta = theta
+        return cloned
+
+    @property
+    def n_dims(self):
+        """Returns the number of non-fixed hyperparameters of the kernel."""
+        return self.theta.shape[0]
+
+    @property
+    def hyperparameters(self):
+        """Returns a list of all hyperparameter specifications."""
+        r = [
+            getattr(self, attr)
+            for attr in dir(self)
+            if attr.startswith("hyperparameter_")
+        ]
+        return r
+
+    @property
+    def theta(self):
+        """Returns the (flattened, log-transformed) non-fixed hyperparameters.
+
+        Note that theta are typically the log-transformed values of the
+        kernel's hyperparameters as this representation of the search space
+        is more amenable for hyperparameter search, as hyperparameters like
+        length-scales naturally live on a log-scale.
+
+        Returns
+        -------
+        theta : ndarray of shape (n_dims,)
+            The non-fixed, log-transformed hyperparameters of the kernel
+        """
+        theta = []
+        params = self.get_params()
+        for hyperparameter in self.hyperparameters:
+            if not hyperparameter.fixed:
+                theta.append(params[hyperparameter.name])
+        if len(theta) > 0:
+            return np.log(np.hstack(theta))
+        else:
+            return np.array([])
+
+    @theta.setter
+    def theta(self, theta):
+        """Sets the (flattened, log-transformed) non-fixed hyperparameters.
+
+        Parameters
+        ----------
+        theta : ndarray of shape (n_dims,)
+            The non-fixed, log-transformed hyperparameters of the kernel
+        """
+        params = self.get_params()
+        i = 0
+        for hyperparameter in self.hyperparameters:
+            if hyperparameter.fixed:
+                continue
+            if hyperparameter.n_elements > 1:
+                # vector-valued parameter
+                params[hyperparameter.name] = np.exp(
+                    theta[i : i + hyperparameter.n_elements]
+                )
+                i += hyperparameter.n_elements
+            else:
+                params[hyperparameter.name] = np.exp(theta[i])
+                i += 1
+
+        if i != len(theta):
+            raise ValueError(
+                "theta has not the correct number of entries."
+                " Should be %d; given are %d" % (i, len(theta))
+            )
+        self.set_params(**params)
+
+    @property
+    def bounds(self):
+        """Returns the log-transformed bounds on the theta.
+
+        Returns
+        -------
+        bounds : ndarray of shape (n_dims, 2)
+            The log-transformed bounds on the kernel's hyperparameters theta
+        """
+        bounds = [
+            hyperparameter.bounds
+            for hyperparameter in self.hyperparameters
+            if not hyperparameter.fixed
+        ]
+        if len(bounds) > 0:
+            return np.log(np.vstack(bounds))
+        else:
+            return np.array([])
+
+    def __add__(self, b):
+        if not isinstance(b, Kernel):
+            return Sum(self, ConstantKernel(b))
+        return Sum(self, b)
+
+    def __radd__(self, b):
+        if not isinstance(b, Kernel):
+            return Sum(ConstantKernel(b), self)
+        return Sum(b, self)
+
+    def __mul__(self, b):
+        if not isinstance(b, Kernel):
+            return Product(self, ConstantKernel(b))
+        return Product(self, b)
+
+    def __rmul__(self, b):
+        if not isinstance(b, Kernel):
+            return Product(ConstantKernel(b), self)
+        return Product(b, self)
+
+    def __pow__(self, b):
+        return Exponentiation(self, b)
+
+    def __eq__(self, b):
+        if type(self) != type(b):
+            return False
+        params_a = self.get_params()
+        params_b = b.get_params()
+        for key in set(list(params_a.keys()) + list(params_b.keys())):
+            if np.any(params_a.get(key, None) != params_b.get(key, None)):
+                return False
+        return True
+
+    def __repr__(self):
+        return "{0}({1})".format(
+            self.__class__.__name__, ", ".join(map("{0:.3g}".format, self.theta))
+        )
+
+    @abstractmethod
+    def __call__(self, X, Y=None, eval_gradient=False):
+        """Evaluate the kernel."""
+
+    @abstractmethod
+    def diag(self, X):
+        """Returns the diagonal of the kernel k(X, X).
+
+        The result of this method is identical to np.diag(self(X)); however,
+        it can be evaluated more efficiently since only the diagonal is
+        evaluated.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples,)
+            Left argument of the returned kernel k(X, Y)
+
+        Returns
+        -------
+        K_diag : ndarray of shape (n_samples_X,)
+            Diagonal of kernel k(X, X)
+        """
+
+    @abstractmethod
+    def is_stationary(self):
+        """Returns whether the kernel is stationary."""
+
+    @property
+    def requires_vector_input(self):
+        """Returns whether the kernel is defined on fixed-length feature
+        vectors or generic objects. Defaults to True for backward
+        compatibility."""
+        return True
+
+    def _check_bounds_params(self):
+        """Called after fitting to warn if bounds may have been too tight."""
+        list_close = np.isclose(self.bounds, np.atleast_2d(self.theta).T)
+        idx = 0
+        for hyp in self.hyperparameters:
+            if hyp.fixed:
+                continue
+            for dim in range(hyp.n_elements):
+                if list_close[idx, 0]:
+                    warnings.warn(
+                        "The optimal value found for "
+                        "dimension %s of parameter %s is "
+                        "close to the specified lower "
+                        "bound %s. Decreasing the bound and"
+                        " calling fit again may find a "
+                        "better value." % (dim, hyp.name, hyp.bounds[dim][0]),
+                        ConvergenceWarning,
+                    )
+                elif list_close[idx, 1]:
+                    warnings.warn(
+                        "The optimal value found for "
+                        "dimension %s of parameter %s is "
+                        "close to the specified upper "
+                        "bound %s. Increasing the bound and"
+                        " calling fit again may find a "
+                        "better value." % (dim, hyp.name, hyp.bounds[dim][1]),
+                        ConvergenceWarning,
+                    )
+                idx += 1
+
+
+class NormalizedKernelMixin:
+    """Mixin for kernels which are normalized: k(X, X)=1.
+
+    .. versionadded:: 0.18
+    """
+
+    def diag(self, X):
+        """Returns the diagonal of the kernel k(X, X).
+
+        The result of this method is identical to np.diag(self(X)); however,
+        it can be evaluated more efficiently since only the diagonal is
+        evaluated.
+
+        Parameters
+        ----------
+        X : ndarray of shape (n_samples_X, n_features)
+            Left argument of the returned kernel k(X, Y)
+
+        Returns
+        -------
+        K_diag : ndarray of shape (n_samples_X,)
+            Diagonal of kernel k(X, X)
+        """
+        return np.ones(X.shape[0])
+
+
+class StationaryKernelMixin:
+    """Mixin for kernels which are stationary: k(X, Y)= f(X-Y).
+
+    .. versionadded:: 0.18
+    """
+
+    def is_stationary(self):
+        """Returns whether the kernel is stationary."""
+        return True
+
+
+class GenericKernelMixin:
+    """Mixin for kernels which operate on generic objects such as variable-
+    length sequences, trees, and graphs.
+
+    .. versionadded:: 0.22
+    """
+
+    @property
+    def requires_vector_input(self):
+        """Whether the kernel works only on fixed-length feature vectors."""
+        return False
+
+
+class CompoundKernel(Kernel):
+    """Kernel which is composed of a set of other kernels.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    kernels : list of Kernels
+        The other kernels
+
+    Examples
+    --------
+    >>> from sklearn.gaussian_process.kernels import WhiteKernel
+    >>> from sklearn.gaussian_process.kernels import RBF
+    >>> from sklearn.gaussian_process.kernels import CompoundKernel
+    >>> kernel = CompoundKernel(
+    ...     [WhiteKernel(noise_level=3.0), RBF(length_scale=2.0)])
+    >>> print(kernel.bounds)
+    [[-11.51292546  11.51292546]
+     [-11.51292546  11.51292546]]
+    >>> print(kernel.n_dims)
+    2
+    >>> print(kernel.theta)
+    [1.09861229 0.69314718]
+    """
+
+    def __init__(self, kernels):
+        self.kernels = kernels
+
+    def get_params(self, deep=True):
+        """Get parameters of this kernel.
+
+        Parameters
+        ----------
+        deep : bool, default=True
+            If True, will return the parameters for this estimator and
+            contained subobjects that are estimators.
+
+        Returns
+        -------
+        params : dict
+            Parameter names mapped to their values.
+        """
+        return dict(kernels=self.kernels)
+
+    @property
+    def theta(self):
+        """Returns the (flattened, log-transformed) non-fixed hyperparameters.
+
+        Note that theta are typically the log-transformed values of the
+        kernel's hyperparameters as this representation of the search space
+        is more amenable for hyperparameter search, as hyperparameters like
+        length-scales naturally live on a log-scale.
+
+        Returns
+        -------
+        theta : ndarray of shape (n_dims,)
+            The non-fixed, log-transformed hyperparameters of the kernel
+        """
+        return np.hstack([kernel.theta for kernel in self.kernels])
+
+    @theta.setter
+    def theta(self, theta):
+        """Sets the (flattened, log-transformed) non-fixed hyperparameters.
+
+        Parameters
+        ----------
+        theta : array of shape (n_dims,)
+            The non-fixed, log-transformed hyperparameters of the kernel
+        """
+        k_dims = self.k1.n_dims
+        for i, kernel in enumerate(self.kernels):
+            kernel.theta = theta[i * k_dims : (i + 1) * k_dims]
+
+    @property
+    def bounds(self):
+        """Returns the log-transformed bounds on the theta.
+
+        Returns
+        -------
+        bounds : array of shape (n_dims, 2)
+            The log-transformed bounds on the kernel's hyperparameters theta
+        """
+        return np.vstack([kernel.bounds for kernel in self.kernels])
+
+    def __call__(self, X, Y=None, eval_gradient=False):
+        """Return the kernel k(X, Y) and optionally its gradient.
+
+        Note that this compound kernel returns the results of all simple kernel
+        stacked along an additional axis.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples_X, n_features) or list of object, \
+            default=None
+            Left argument of the returned kernel k(X, Y)
+
+        Y : array-like of shape (n_samples_X, n_features) or list of object, \
+            default=None
+            Right argument of the returned kernel k(X, Y). If None, k(X, X)
+            is evaluated instead.
+
+        eval_gradient : bool, default=False
+            Determines whether the gradient with respect to the log of the
+            kernel hyperparameter is computed.
+
+        Returns
+        -------
+        K : ndarray of shape (n_samples_X, n_samples_Y, n_kernels)
+            Kernel k(X, Y)
+
+        K_gradient : ndarray of shape \
+                (n_samples_X, n_samples_X, n_dims, n_kernels), optional
+            The gradient of the kernel k(X, X) with respect to the log of the
+            hyperparameter of the kernel. Only returned when `eval_gradient`
+            is True.
+        """
+        if eval_gradient:
+            K = []
+            K_grad = []
+            for kernel in self.kernels:
+                K_single, K_grad_single = kernel(X, Y, eval_gradient)
+                K.append(K_single)
+                K_grad.append(K_grad_single[..., np.newaxis])
+            return np.dstack(K), np.concatenate(K_grad, 3)
+        else:
+            return np.dstack([kernel(X, Y, eval_gradient) for kernel in self.kernels])
+
+    def __eq__(self, b):
+        if type(self) != type(b) or len(self.kernels) != len(b.kernels):
+            return False
+        return np.all(
+            [self.kernels[i] == b.kernels[i] for i in range(len(self.kernels))]
+        )
+
+    def is_stationary(self):
+        """Returns whether the kernel is stationary."""
+        return np.all([kernel.is_stationary() for kernel in self.kernels])
+
+    @property
+    def requires_vector_input(self):
+        """Returns whether the kernel is defined on discrete structures."""
+        return np.any([kernel.requires_vector_input for kernel in self.kernels])
+
+    def diag(self, X):
+        """Returns the diagonal of the kernel k(X, X).
+
+        The result of this method is identical to `np.diag(self(X))`; however,
+        it can be evaluated more efficiently since only the diagonal is
+        evaluated.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples_X, n_features) or list of object
+            Argument to the kernel.
+
+        Returns
+        -------
+        K_diag : ndarray of shape (n_samples_X, n_kernels)
+            Diagonal of kernel k(X, X)
+        """
+        return np.vstack([kernel.diag(X) for kernel in self.kernels]).T
+
+
+class KernelOperator(Kernel):
+    """Base class for all kernel operators.
+
+    .. versionadded:: 0.18
+    """
+
+    def __init__(self, k1, k2):
+        self.k1 = k1
+        self.k2 = k2
+
+    def get_params(self, deep=True):
+        """Get parameters of this kernel.
+
+        Parameters
+        ----------
+        deep : bool, default=True
+            If True, will return the parameters for this estimator and
+            contained subobjects that are estimators.
+
+        Returns
+        -------
+        params : dict
+            Parameter names mapped to their values.
+        """
+        params = dict(k1=self.k1, k2=self.k2)
+        if deep:
+            deep_items = self.k1.get_params().items()
+            params.update(("k1__" + k, val) for k, val in deep_items)
+            deep_items = self.k2.get_params().items()
+            params.update(("k2__" + k, val) for k, val in deep_items)
+
+        return params
+
+    @property
+    def hyperparameters(self):
+        """Returns a list of all hyperparameter."""
+        r = [
+            Hyperparameter(
+                "k1__" + hyperparameter.name,
+                hyperparameter.value_type,
+                hyperparameter.bounds,
+                hyperparameter.n_elements,
+            )
+            for hyperparameter in self.k1.hyperparameters
+        ]
+
+        for hyperparameter in self.k2.hyperparameters:
+            r.append(
+                Hyperparameter(
+                    "k2__" + hyperparameter.name,
+                    hyperparameter.value_type,
+                    hyperparameter.bounds,
+                    hyperparameter.n_elements,
+                )
+            )
+        return r
+
+    @property
+    def theta(self):
+        """Returns the (flattened, log-transformed) non-fixed hyperparameters.
+
+        Note that theta are typically the log-transformed values of the
+        kernel's hyperparameters as this representation of the search space
+        is more amenable for hyperparameter search, as hyperparameters like
+        length-scales naturally live on a log-scale.
+
+        Returns
+        -------
+        theta : ndarray of shape (n_dims,)
+            The non-fixed, log-transformed hyperparameters of the kernel
+        """
+        return np.append(self.k1.theta, self.k2.theta)
+
+    @theta.setter
+    def theta(self, theta):
+        """Sets the (flattened, log-transformed) non-fixed hyperparameters.
+
+        Parameters
+        ----------
+        theta : ndarray of shape (n_dims,)
+            The non-fixed, log-transformed hyperparameters of the kernel
+        """
+        k1_dims = self.k1.n_dims
+        self.k1.theta = theta[:k1_dims]
+        self.k2.theta = theta[k1_dims:]
+
+    @property
+    def bounds(self):
+        """Returns the log-transformed bounds on the theta.
+
+        Returns
+        -------
+        bounds : ndarray of shape (n_dims, 2)
+            The log-transformed bounds on the kernel's hyperparameters theta
+        """
+        if self.k1.bounds.size == 0:
+            return self.k2.bounds
+        if self.k2.bounds.size == 0:
+            return self.k1.bounds
+        return np.vstack((self.k1.bounds, self.k2.bounds))
+
+    def __eq__(self, b):
+        if type(self) != type(b):
+            return False
+        return (self.k1 == b.k1 and self.k2 == b.k2) or (
+            self.k1 == b.k2 and self.k2 == b.k1
+        )
+
+    def is_stationary(self):
+        """Returns whether the kernel is stationary."""
+        return self.k1.is_stationary() and self.k2.is_stationary()
+
+    @property
+    def requires_vector_input(self):
+        """Returns whether the kernel is stationary."""
+        return self.k1.requires_vector_input or self.k2.requires_vector_input
+
+
+class Sum(KernelOperator):
+    """The `Sum` kernel takes two kernels :math:`k_1` and :math:`k_2`
+    and combines them via
+
+    .. math::
+        k_{sum}(X, Y) = k_1(X, Y) + k_2(X, Y)
+
+    Note that the `__add__` magic method is overridden, so
+    `Sum(RBF(), RBF())` is equivalent to using the + operator
+    with `RBF() + RBF()`.
+
+
+    Read more in the :ref:`User Guide <gp_kernels>`.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    k1 : Kernel
+        The first base-kernel of the sum-kernel
+
+    k2 : Kernel
+        The second base-kernel of the sum-kernel
+
+    Examples
+    --------
+    >>> from sklearn.datasets import make_friedman2
+    >>> from sklearn.gaussian_process import GaussianProcessRegressor
+    >>> from sklearn.gaussian_process.kernels import RBF, Sum, ConstantKernel
+    >>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
+    >>> kernel = Sum(ConstantKernel(2), RBF())
+    >>> gpr = GaussianProcessRegressor(kernel=kernel,
+    ...         random_state=0).fit(X, y)
+    >>> gpr.score(X, y)
+    1.0
+    >>> kernel
+    1.41**2 + RBF(length_scale=1)
+    """
+
+    def __call__(self, X, Y=None, eval_gradient=False):
+        """Return the kernel k(X, Y) and optionally its gradient.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples_X, n_features) or list of object
+            Left argument of the returned kernel k(X, Y)
+
+        Y : array-like of shape (n_samples_X, n_features) or list of object,\
+                default=None
+            Right argument of the returned kernel k(X, Y). If None, k(X, X)
+            is evaluated instead.
+
+        eval_gradient : bool, default=False
+            Determines whether the gradient with respect to the log of
+            the kernel hyperparameter is computed.
+
+        Returns
+        -------
+        K : ndarray of shape (n_samples_X, n_samples_Y)
+            Kernel k(X, Y)
+
+        K_gradient : ndarray of shape (n_samples_X, n_samples_X, n_dims),\
+                optional
+            The gradient of the kernel k(X, X) with respect to the log of the
+            hyperparameter of the kernel. Only returned when `eval_gradient`
+            is True.
+        """
+        if eval_gradient:
+            K1, K1_gradient = self.k1(X, Y, eval_gradient=True)
+            K2, K2_gradient = self.k2(X, Y, eval_gradient=True)
+            return K1 + K2, np.dstack((K1_gradient, K2_gradient))
+        else:
+            return self.k1(X, Y) + self.k2(X, Y)
+
+    def diag(self, X):
+        """Returns the diagonal of the kernel k(X, X).
+
+        The result of this method is identical to `np.diag(self(X))`; however,
+        it can be evaluated more efficiently since only the diagonal is
+        evaluated.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples_X, n_features) or list of object
+            Argument to the kernel.
+
+        Returns
+        -------
+        K_diag : ndarray of shape (n_samples_X,)
+            Diagonal of kernel k(X, X)
+        """
+        return self.k1.diag(X) + self.k2.diag(X)
+
+    def __repr__(self):
+        return "{0} + {1}".format(self.k1, self.k2)
+
+
+class Product(KernelOperator):
+    """The `Product` kernel takes two kernels :math:`k_1` and :math:`k_2`
+    and combines them via
+
+    .. math::
+        k_{prod}(X, Y) = k_1(X, Y) * k_2(X, Y)
+
+    Note that the `__mul__` magic method is overridden, so
+    `Product(RBF(), RBF())` is equivalent to using the * operator
+    with `RBF() * RBF()`.
+
+    Read more in the :ref:`User Guide <gp_kernels>`.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    k1 : Kernel
+        The first base-kernel of the product-kernel
+
+    k2 : Kernel
+        The second base-kernel of the product-kernel
+
+
+    Examples
+    --------
+    >>> from sklearn.datasets import make_friedman2
+    >>> from sklearn.gaussian_process import GaussianProcessRegressor
+    >>> from sklearn.gaussian_process.kernels import (RBF, Product,
+    ...            ConstantKernel)
+    >>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
+    >>> kernel = Product(ConstantKernel(2), RBF())
+    >>> gpr = GaussianProcessRegressor(kernel=kernel,
+    ...         random_state=0).fit(X, y)
+    >>> gpr.score(X, y)
+    1.0
+    >>> kernel
+    1.41**2 * RBF(length_scale=1)
+    """
+
+    def __call__(self, X, Y=None, eval_gradient=False):
+        """Return the kernel k(X, Y) and optionally its gradient.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples_X, n_features) or list of object
+            Left argument of the returned kernel k(X, Y)
+
+        Y : array-like of shape (n_samples_Y, n_features) or list of object,\
+            default=None
+            Right argument of the returned kernel k(X, Y). If None, k(X, X)
+            is evaluated instead.
+
+        eval_gradient : bool, default=False
+            Determines whether the gradient with respect to the log of
+            the kernel hyperparameter is computed.
+
+        Returns
+        -------
+        K : ndarray of shape (n_samples_X, n_samples_Y)
+            Kernel k(X, Y)
+
+        K_gradient : ndarray of shape (n_samples_X, n_samples_X, n_dims), \
+                optional
+            The gradient of the kernel k(X, X) with respect to the log of the
+            hyperparameter of the kernel. Only returned when `eval_gradient`
+            is True.
+        """
+        if eval_gradient:
+            K1, K1_gradient = self.k1(X, Y, eval_gradient=True)
+            K2, K2_gradient = self.k2(X, Y, eval_gradient=True)
+            return K1 * K2, np.dstack(
+                (K1_gradient * K2[:, :, np.newaxis], K2_gradient * K1[:, :, np.newaxis])
+            )
+        else:
+            return self.k1(X, Y) * self.k2(X, Y)
+
+    def diag(self, X):
+        """Returns the diagonal of the kernel k(X, X).
+
+        The result of this method is identical to np.diag(self(X)); however,
+        it can be evaluated more efficiently since only the diagonal is
+        evaluated.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples_X, n_features) or list of object
+            Argument to the kernel.
+
+        Returns
+        -------
+        K_diag : ndarray of shape (n_samples_X,)
+            Diagonal of kernel k(X, X)
+        """
+        return self.k1.diag(X) * self.k2.diag(X)
+
+    def __repr__(self):
+        return "{0} * {1}".format(self.k1, self.k2)
+
+
+class Exponentiation(Kernel):
+    """The Exponentiation kernel takes one base kernel and a scalar parameter
+    :math:`p` and combines them via
+
+    .. math::
+        k_{exp}(X, Y) = k(X, Y) ^p
+
+    Note that the `__pow__` magic method is overridden, so
+    `Exponentiation(RBF(), 2)` is equivalent to using the ** operator
+    with `RBF() ** 2`.
+
+
+    Read more in the :ref:`User Guide <gp_kernels>`.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    kernel : Kernel
+        The base kernel
+
+    exponent : float
+        The exponent for the base kernel
+
+
+    Examples
+    --------
+    >>> from sklearn.datasets import make_friedman2
+    >>> from sklearn.gaussian_process import GaussianProcessRegressor
+    >>> from sklearn.gaussian_process.kernels import (RationalQuadratic,
+    ...            Exponentiation)
+    >>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
+    >>> kernel = Exponentiation(RationalQuadratic(), exponent=2)
+    >>> gpr = GaussianProcessRegressor(kernel=kernel, alpha=5,
+    ...         random_state=0).fit(X, y)
+    >>> gpr.score(X, y)
+    0.419...
+    >>> gpr.predict(X[:1,:], return_std=True)
+    (array([635.5...]), array([0.559...]))
+    """
+
+    def __init__(self, kernel, exponent):
+        self.kernel = kernel
+        self.exponent = exponent
+
+    def get_params(self, deep=True):
+        """Get parameters of this kernel.
+
+        Parameters
+        ----------
+        deep : bool, default=True
+            If True, will return the parameters for this estimator and
+            contained subobjects that are estimators.
+
+        Returns
+        -------
+        params : dict
+            Parameter names mapped to their values.
+        """
+        params = dict(kernel=self.kernel, exponent=self.exponent)
+        if deep:
+            deep_items = self.kernel.get_params().items()
+            params.update(("kernel__" + k, val) for k, val in deep_items)
+        return params
+
+    @property
+    def hyperparameters(self):
+        """Returns a list of all hyperparameter."""
+        r = []
+        for hyperparameter in self.kernel.hyperparameters:
+            r.append(
+                Hyperparameter(
+                    "kernel__" + hyperparameter.name,
+                    hyperparameter.value_type,
+                    hyperparameter.bounds,
+                    hyperparameter.n_elements,
+                )
+            )
+        return r
+
+    @property
+    def theta(self):
+        """Returns the (flattened, log-transformed) non-fixed hyperparameters.
+
+        Note that theta are typically the log-transformed values of the
+        kernel's hyperparameters as this representation of the search space
+        is more amenable for hyperparameter search, as hyperparameters like
+        length-scales naturally live on a log-scale.
+
+        Returns
+        -------
+        theta : ndarray of shape (n_dims,)
+            The non-fixed, log-transformed hyperparameters of the kernel
+        """
+        return self.kernel.theta
+
+    @theta.setter
+    def theta(self, theta):
+        """Sets the (flattened, log-transformed) non-fixed hyperparameters.
+
+        Parameters
+        ----------
+        theta : ndarray of shape (n_dims,)
+            The non-fixed, log-transformed hyperparameters of the kernel
+        """
+        self.kernel.theta = theta
+
+    @property
+    def bounds(self):
+        """Returns the log-transformed bounds on the theta.
+
+        Returns
+        -------
+        bounds : ndarray of shape (n_dims, 2)
+            The log-transformed bounds on the kernel's hyperparameters theta
+        """
+        return self.kernel.bounds
+
+    def __eq__(self, b):
+        if type(self) != type(b):
+            return False
+        return self.kernel == b.kernel and self.exponent == b.exponent
+
+    def __call__(self, X, Y=None, eval_gradient=False):
+        """Return the kernel k(X, Y) and optionally its gradient.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples_X, n_features) or list of object
+            Left argument of the returned kernel k(X, Y)
+
+        Y : array-like of shape (n_samples_Y, n_features) or list of object,\
+            default=None
+            Right argument of the returned kernel k(X, Y). If None, k(X, X)
+            is evaluated instead.
+
+        eval_gradient : bool, default=False
+            Determines whether the gradient with respect to the log of
+            the kernel hyperparameter is computed.
+
+        Returns
+        -------
+        K : ndarray of shape (n_samples_X, n_samples_Y)
+            Kernel k(X, Y)
+
+        K_gradient : ndarray of shape (n_samples_X, n_samples_X, n_dims),\
+                optional
+            The gradient of the kernel k(X, X) with respect to the log of the
+            hyperparameter of the kernel. Only returned when `eval_gradient`
+            is True.
+        """
+        if eval_gradient:
+            K, K_gradient = self.kernel(X, Y, eval_gradient=True)
+            K_gradient *= self.exponent * K[:, :, np.newaxis] ** (self.exponent - 1)
+            return K**self.exponent, K_gradient
+        else:
+            K = self.kernel(X, Y, eval_gradient=False)
+            return K**self.exponent
+
+    def diag(self, X):
+        """Returns the diagonal of the kernel k(X, X).
+
+        The result of this method is identical to np.diag(self(X)); however,
+        it can be evaluated more efficiently since only the diagonal is
+        evaluated.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples_X, n_features) or list of object
+            Argument to the kernel.
+
+        Returns
+        -------
+        K_diag : ndarray of shape (n_samples_X,)
+            Diagonal of kernel k(X, X)
+        """
+        return self.kernel.diag(X) ** self.exponent
+
+    def __repr__(self):
+        return "{0} ** {1}".format(self.kernel, self.exponent)
+
+    def is_stationary(self):
+        """Returns whether the kernel is stationary."""
+        return self.kernel.is_stationary()
+
+    @property
+    def requires_vector_input(self):
+        """Returns whether the kernel is defined on discrete structures."""
+        return self.kernel.requires_vector_input
+
+
+class ConstantKernel(StationaryKernelMixin, GenericKernelMixin, Kernel):
+    """Constant kernel.
+
+    Can be used as part of a product-kernel where it scales the magnitude of
+    the other factor (kernel) or as part of a sum-kernel, where it modifies
+    the mean of the Gaussian process.
+
+    .. math::
+        k(x_1, x_2) = constant\\_value \\;\\forall\\; x_1, x_2
+
+    Adding a constant kernel is equivalent to adding a constant::
+
+            kernel = RBF() + ConstantKernel(constant_value=2)
+
+    is the same as::
+
+            kernel = RBF() + 2
+
+
+    Read more in the :ref:`User Guide <gp_kernels>`.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    constant_value : float, default=1.0
+        The constant value which defines the covariance:
+        k(x_1, x_2) = constant_value
+
+    constant_value_bounds : pair of floats >= 0 or "fixed", default=(1e-5, 1e5)
+        The lower and upper bound on `constant_value`.
+        If set to "fixed", `constant_value` cannot be changed during
+        hyperparameter tuning.
+
+    Examples
+    --------
+    >>> from sklearn.datasets import make_friedman2
+    >>> from sklearn.gaussian_process import GaussianProcessRegressor
+    >>> from sklearn.gaussian_process.kernels import RBF, ConstantKernel
+    >>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
+    >>> kernel = RBF() + ConstantKernel(constant_value=2)
+    >>> gpr = GaussianProcessRegressor(kernel=kernel, alpha=5,
+    ...         random_state=0).fit(X, y)
+    >>> gpr.score(X, y)
+    0.3696...
+    >>> gpr.predict(X[:1,:], return_std=True)
+    (array([606.1...]), array([0.24...]))
+    """
+
+    def __init__(self, constant_value=1.0, constant_value_bounds=(1e-5, 1e5)):
+        self.constant_value = constant_value
+        self.constant_value_bounds = constant_value_bounds
+
+    @property
+    def hyperparameter_constant_value(self):
+        return Hyperparameter("constant_value", "numeric", self.constant_value_bounds)
+
+    def __call__(self, X, Y=None, eval_gradient=False):
+        """Return the kernel k(X, Y) and optionally its gradient.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples_X, n_features) or list of object
+            Left argument of the returned kernel k(X, Y)
+
+        Y : array-like of shape (n_samples_X, n_features) or list of object, \
+            default=None
+            Right argument of the returned kernel k(X, Y). If None, k(X, X)
+            is evaluated instead.
+
+        eval_gradient : bool, default=False
+            Determines whether the gradient with respect to the log of
+            the kernel hyperparameter is computed.
+            Only supported when Y is None.
+
+        Returns
+        -------
+        K : ndarray of shape (n_samples_X, n_samples_Y)
+            Kernel k(X, Y)
+
+        K_gradient : ndarray of shape (n_samples_X, n_samples_X, n_dims), \
+            optional
+            The gradient of the kernel k(X, X) with respect to the log of the
+            hyperparameter of the kernel. Only returned when eval_gradient
+            is True.
+        """
+        if Y is None:
+            Y = X
+        elif eval_gradient:
+            raise ValueError("Gradient can only be evaluated when Y is None.")
+
+        K = np.full(
+            (_num_samples(X), _num_samples(Y)),
+            self.constant_value,
+            dtype=np.array(self.constant_value).dtype,
+        )
+        if eval_gradient:
+            if not self.hyperparameter_constant_value.fixed:
+                return (
+                    K,
+                    np.full(
+                        (_num_samples(X), _num_samples(X), 1),
+                        self.constant_value,
+                        dtype=np.array(self.constant_value).dtype,
+                    ),
+                )
+            else:
+                return K, np.empty((_num_samples(X), _num_samples(X), 0))
+        else:
+            return K
+
+    def diag(self, X):
+        """Returns the diagonal of the kernel k(X, X).
+
+        The result of this method is identical to np.diag(self(X)); however,
+        it can be evaluated more efficiently since only the diagonal is
+        evaluated.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples_X, n_features) or list of object
+            Argument to the kernel.
+
+        Returns
+        -------
+        K_diag : ndarray of shape (n_samples_X,)
+            Diagonal of kernel k(X, X)
+        """
+        return np.full(
+            _num_samples(X),
+            self.constant_value,
+            dtype=np.array(self.constant_value).dtype,
+        )
+
+    def __repr__(self):
+        return "{0:.3g}**2".format(np.sqrt(self.constant_value))
+
+
+class WhiteKernel(StationaryKernelMixin, GenericKernelMixin, Kernel):
+    """White kernel.
+
+    The main use-case of this kernel is as part of a sum-kernel where it
+    explains the noise of the signal as independently and identically
+    normally-distributed. The parameter noise_level equals the variance of this
+    noise.
+
+    .. math::
+        k(x_1, x_2) = noise\\_level \\text{ if } x_i == x_j \\text{ else } 0
+
+
+    Read more in the :ref:`User Guide <gp_kernels>`.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    noise_level : float, default=1.0
+        Parameter controlling the noise level (variance)
+
+    noise_level_bounds : pair of floats >= 0 or "fixed", default=(1e-5, 1e5)
+        The lower and upper bound on 'noise_level'.
+        If set to "fixed", 'noise_level' cannot be changed during
+        hyperparameter tuning.
+
+    Examples
+    --------
+    >>> from sklearn.datasets import make_friedman2
+    >>> from sklearn.gaussian_process import GaussianProcessRegressor
+    >>> from sklearn.gaussian_process.kernels import DotProduct, WhiteKernel
+    >>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
+    >>> kernel = DotProduct() + WhiteKernel(noise_level=0.5)
+    >>> gpr = GaussianProcessRegressor(kernel=kernel,
+    ...         random_state=0).fit(X, y)
+    >>> gpr.score(X, y)
+    0.3680...
+    >>> gpr.predict(X[:2,:], return_std=True)
+    (array([653.0..., 592.1... ]), array([316.6..., 316.6...]))
+    """
+
+    def __init__(self, noise_level=1.0, noise_level_bounds=(1e-5, 1e5)):
+        self.noise_level = noise_level
+        self.noise_level_bounds = noise_level_bounds
+
+    @property
+    def hyperparameter_noise_level(self):
+        return Hyperparameter("noise_level", "numeric", self.noise_level_bounds)
+
+    def __call__(self, X, Y=None, eval_gradient=False):
+        """Return the kernel k(X, Y) and optionally its gradient.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples_X, n_features) or list of object
+            Left argument of the returned kernel k(X, Y)
+
+        Y : array-like of shape (n_samples_X, n_features) or list of object,\
+            default=None
+            Right argument of the returned kernel k(X, Y). If None, k(X, X)
+            is evaluated instead.
+
+        eval_gradient : bool, default=False
+            Determines whether the gradient with respect to the log of
+            the kernel hyperparameter is computed.
+            Only supported when Y is None.
+
+        Returns
+        -------
+        K : ndarray of shape (n_samples_X, n_samples_Y)
+            Kernel k(X, Y)
+
+        K_gradient : ndarray of shape (n_samples_X, n_samples_X, n_dims),\
+            optional
+            The gradient of the kernel k(X, X) with respect to the log of the
+            hyperparameter of the kernel. Only returned when eval_gradient
+            is True.
+        """
+        if Y is not None and eval_gradient:
+            raise ValueError("Gradient can only be evaluated when Y is None.")
+
+        if Y is None:
+            K = self.noise_level * np.eye(_num_samples(X))
+            if eval_gradient:
+                if not self.hyperparameter_noise_level.fixed:
+                    return (
+                        K,
+                        self.noise_level * np.eye(_num_samples(X))[:, :, np.newaxis],
+                    )
+                else:
+                    return K, np.empty((_num_samples(X), _num_samples(X), 0))
+            else:
+                return K
+        else:
+            return np.zeros((_num_samples(X), _num_samples(Y)))
+
+    def diag(self, X):
+        """Returns the diagonal of the kernel k(X, X).
+
+        The result of this method is identical to np.diag(self(X)); however,
+        it can be evaluated more efficiently since only the diagonal is
+        evaluated.
+
+        Parameters
+        ----------
+        X : array-like of shape (n_samples_X, n_features) or list of object
+            Argument to the kernel.
+
+        Returns
+        -------
+        K_diag : ndarray of shape (n_samples_X,)
+            Diagonal of kernel k(X, X)
+        """
+        return np.full(
+            _num_samples(X), self.noise_level, dtype=np.array(self.noise_level).dtype
+        )
+
+    def __repr__(self):
+        return "{0}(noise_level={1:.3g})".format(
+            self.__class__.__name__, self.noise_level
+        )
+
+
+class RBF(StationaryKernelMixin, NormalizedKernelMixin, Kernel):
+    """Radial basis function kernel (aka squared-exponential kernel).
+
+    The RBF kernel is a stationary kernel. It is also known as the
+    "squared exponential" kernel. It is parameterized by a length scale
+    parameter :math:`l>0`, which can either be a scalar (isotropic variant
+    of the kernel) or a vector with the same number of dimensions as the inputs
+    X (anisotropic variant of the kernel). The kernel is given by:
+
+    .. math::
+        k(x_i, x_j) = \\exp\\left(- \\frac{d(x_i, x_j)^2}{2l^2} \\right)
+
+    where :math:`l` is the length scale of the kernel and
+    :math:`d(\\cdot,\\cdot)` is the Euclidean distance.
+    For advice on how to set the length scale parameter, see e.g. [1]_.
+
+    This kernel is infinitely differentiable, which implies that GPs with this
+    kernel as covariance function have mean square derivatives of all orders,
+    and are thus very smooth.
+    See [2]_, Chapter 4, Section 4.2, for further details of the RBF kernel.
+
+    Read more in the :ref:`User Guide <gp_kernels>`.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    length_scale : float or ndarray of shape (n_features,), default=1.0
+        The length scale of the kernel. If a float, an isotropic kernel is
+        used. If an array, an anisotropic kernel is used where each dimension
+        of l defines the length-scale of the respective feature dimension.
+
+    length_scale_bounds : pair of floats >= 0 or "fixed", default=(1e-5, 1e5)
+        The lower and upper bound on 'length_scale'.
+        If set to "fixed", 'length_scale' cannot be changed during
+        hyperparameter tuning.
+
+    References
+    ----------
+    .. [1] `David Duvenaud (2014). "The Kernel Cookbook:
+        Advice on Covariance functions".
+        <https://www.cs.toronto.edu/~duvenaud/cookbook/>`_
+
+    .. [2] `Carl Edward Rasmussen, Christopher K. I. Williams (2006).
+        "Gaussian Processes for Machine Learning". The MIT Press.
+        <http://www.gaussianprocess.org/gpml/>`_
+
+    Examples
+    --------
+    >>> from sklearn.datasets import load_iris
+    >>> from sklearn.gaussian_process import GaussianProcessClassifier
+    >>> from sklearn.gaussian_process.kernels import RBF
+    >>> X, y = load_iris(return_X_y=True)
+    >>> kernel = 1.0 * RBF(1.0)
+    >>> gpc = GaussianProcessClassifier(kernel=kernel,
+    ...         random_state=0).fit(X, y)
+    >>> gpc.score(X, y)
+    0.9866...
+    >>> gpc.predict_proba(X[:2,:])
+    array([[0.8354..., 0.03228..., 0.1322...],
+           [0.7906..., 0.0652..., 0.1441...]])
+    """
+
+    def __init__(self, length_scale=1.0, length_scale_bounds=(1e-5, 1e5)):
+        self.length_scale = length_scale
+        self.length_scale_bounds = length_scale_bounds
+
+    @property
+    def anisotropic(self):
+        return np.iterable(self.length_scale) and len(self.length_scale) > 1
+
+    @property
+    def hyperparameter_length_scale(self):
+        if self.anisotropic:
+            return Hyperparameter(
+                "length_scale",
+                "numeric",
+                self.length_scale_bounds,
+                len(self.length_scale),
+            )
+        return Hyperparameter("length_scale", "numeric", self.length_scale_bounds)
+
+    def __call__(self, X, Y=None, eval_gradient=False):
+        """Return the kernel k(X, Y) and optionally its gradient.
+
+        Parameters
+        ----------
+        X : ndarray of shape (n_samples_X, n_features)
+            Left argument of the returned kernel k(X, Y)
+
+        Y : ndarray of shape (n_samples_Y, n_features), default=None
+            Right argument of the returned kernel k(X, Y). If None, k(X, X)
+            if evaluated instead.
+
+        eval_gradient : bool, default=False
+            Determines whether the gradient with respect to the log of
+            the kernel hyperparameter is computed.
+            Only supported when Y is None.
+
+        Returns
+        -------
+        K : ndarray of shape (n_samples_X, n_samples_Y)
+            Kernel k(X, Y)
+
+        K_gradient : ndarray of shape (n_samples_X, n_samples_X, n_dims), \
+                optional
+            The gradient of the kernel k(X, X) with respect to the log of the
+            hyperparameter of the kernel. Only returned when `eval_gradient`
+            is True.
+        """
+        X = np.atleast_2d(X)
+        length_scale = _check_length_scale(X, self.length_scale)
+        if Y is None:
+            dists = pdist(X / length_scale, metric="sqeuclidean")
+            K = np.exp(-0.5 * dists)
+            # convert from upper-triangular matrix to square matrix
+            K = squareform(K)
+            np.fill_diagonal(K, 1)
+        else:
+            if eval_gradient:
+                raise ValueError("Gradient can only be evaluated when Y is None.")
+            dists = cdist(X / length_scale, Y / length_scale, metric="sqeuclidean")
+            K = np.exp(-0.5 * dists)
+
+        if eval_gradient:
+            if self.hyperparameter_length_scale.fixed:
+                # Hyperparameter l kept fixed
+                return K, np.empty((X.shape[0], X.shape[0], 0))
+            elif not self.anisotropic or length_scale.shape[0] == 1:
+                K_gradient = (K * squareform(dists))[:, :, np.newaxis]
+                return K, K_gradient
+            elif self.anisotropic:
+                # We need to recompute the pairwise dimension-wise distances
+                K_gradient = (X[:, np.newaxis, :] - X[np.newaxis, :, :]) ** 2 / (
+                    length_scale**2
+                )
+                K_gradient *= K[..., np.newaxis]
+                return K, K_gradient
+        else:
+            return K
+
+    def __repr__(self):
+        if self.anisotropic:
+            return "{0}(length_scale=[{1}])".format(
+                self.__class__.__name__,
+                ", ".join(map("{0:.3g}".format, self.length_scale)),
+            )
+        else:  # isotropic
+            return "{0}(length_scale={1:.3g})".format(
+                self.__class__.__name__, np.ravel(self.length_scale)[0]
+            )
+
+
+class Matern(RBF):
+    """Matern kernel.
+
+    The class of Matern kernels is a generalization of the :class:`RBF`.
+    It has an additional parameter :math:`\\nu` which controls the
+    smoothness of the resulting function. The smaller :math:`\\nu`,
+    the less smooth the approximated function is.
+    As :math:`\\nu\\rightarrow\\infty`, the kernel becomes equivalent to
+    the :class:`RBF` kernel. When :math:`\\nu = 1/2`, the Matérn kernel
+    becomes identical to the absolute exponential kernel.
+    Important intermediate values are
+    :math:`\\nu=1.5` (once differentiable functions)
+    and :math:`\\nu=2.5` (twice differentiable functions).
+
+    The kernel is given by:
+
+    .. math::
+         k(x_i, x_j) =  \\frac{1}{\\Gamma(\\nu)2^{\\nu-1}}\\Bigg(
+         \\frac{\\sqrt{2\\nu}}{l} d(x_i , x_j )
+         \\Bigg)^\\nu K_\\nu\\Bigg(
+         \\frac{\\sqrt{2\\nu}}{l} d(x_i , x_j )\\Bigg)
+
+
+
+    where :math:`d(\\cdot,\\cdot)` is the Euclidean distance,
+    :math:`K_{\\nu}(\\cdot)` is a modified Bessel function and
+    :math:`\\Gamma(\\cdot)` is the gamma function.
+    See [1]_, Chapter 4, Section 4.2, for details regarding the different
+    variants of the Matern kernel.
+
+    Read more in the :ref:`User Guide <gp_kernels>`.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    length_scale : float or ndarray of shape (n_features,), default=1.0
+        The length scale of the kernel. If a float, an isotropic kernel is
+        used. If an array, an anisotropic kernel is used where each dimension
+        of l defines the length-scale of the respective feature dimension.
+
+    length_scale_bounds : pair of floats >= 0 or "fixed", default=(1e-5, 1e5)
+        The lower and upper bound on 'length_scale'.
+        If set to "fixed", 'length_scale' cannot be changed during
+        hyperparameter tuning.
+
+    nu : float, default=1.5
+        The parameter nu controlling the smoothness of the learned function.
+        The smaller nu, the less smooth the approximated function is.
+        For nu=inf, the kernel becomes equivalent to the RBF kernel and for
+        nu=0.5 to the absolute exponential kernel. Important intermediate
+        values are nu=1.5 (once differentiable functions) and nu=2.5
+        (twice differentiable functions). Note that values of nu not in
+        [0.5, 1.5, 2.5, inf] incur a considerably higher computational cost
+        (appr. 10 times higher) since they require to evaluate the modified
+        Bessel function. Furthermore, in contrast to l, nu is kept fixed to
+        its initial value and not optimized.
+
+    References
+    ----------
+    .. [1] `Carl Edward Rasmussen, Christopher K. I. Williams (2006).
+        "Gaussian Processes for Machine Learning". The MIT Press.
+        <http://www.gaussianprocess.org/gpml/>`_
+
+    Examples
+    --------
+    >>> from sklearn.datasets import load_iris
+    >>> from sklearn.gaussian_process import GaussianProcessClassifier
+    >>> from sklearn.gaussian_process.kernels import Matern
+    >>> X, y = load_iris(return_X_y=True)
+    >>> kernel = 1.0 * Matern(length_scale=1.0, nu=1.5)
+    >>> gpc = GaussianProcessClassifier(kernel=kernel,
+    ...         random_state=0).fit(X, y)
+    >>> gpc.score(X, y)
+    0.9866...
+    >>> gpc.predict_proba(X[:2,:])
+    array([[0.8513..., 0.0368..., 0.1117...],
+            [0.8086..., 0.0693..., 0.1220...]])
+    """
+
+    def __init__(self, length_scale=1.0, length_scale_bounds=(1e-5, 1e5), nu=1.5):
+        super().__init__(length_scale, length_scale_bounds)
+        self.nu = nu
+
+    def __call__(self, X, Y=None, eval_gradient=False):
+        """Return the kernel k(X, Y) and optionally its gradient.
+
+        Parameters
+        ----------
+        X : ndarray of shape (n_samples_X, n_features)
+            Left argument of the returned kernel k(X, Y)
+
+        Y : ndarray of shape (n_samples_Y, n_features), default=None
+            Right argument of the returned kernel k(X, Y). If None, k(X, X)
+            if evaluated instead.
+
+        eval_gradient : bool, default=False
+            Determines whether the gradient with respect to the log of
+            the kernel hyperparameter is computed.
+            Only supported when Y is None.
+
+        Returns
+        -------
+        K : ndarray of shape (n_samples_X, n_samples_Y)
+            Kernel k(X, Y)
+
+        K_gradient : ndarray of shape (n_samples_X, n_samples_X, n_dims), \
+                optional
+            The gradient of the kernel k(X, X) with respect to the log of the
+            hyperparameter of the kernel. Only returned when `eval_gradient`
+            is True.
+        """
+        X = np.atleast_2d(X)
+        length_scale = _check_length_scale(X, self.length_scale)
+        if Y is None:
+            dists = pdist(X / length_scale, metric="euclidean")
+        else:
+            if eval_gradient:
+                raise ValueError("Gradient can only be evaluated when Y is None.")
+            dists = cdist(X / length_scale, Y / length_scale, metric="euclidean")
+
+        if self.nu == 0.5:
+            K = np.exp(-dists)
+        elif self.nu == 1.5:
+            K = dists * math.sqrt(3)
+            K = (1.0 + K) * np.exp(-K)
+        elif self.nu == 2.5:
+            K = dists * math.sqrt(5)
+            K = (1.0 + K + K**2 / 3.0) * np.exp(-K)
+        elif self.nu == np.inf:
+            K = np.exp(-(dists**2) / 2.0)
+        else:  # general case; expensive to evaluate
+            K = dists
+            K[K == 0.0] += np.finfo(float).eps  # strict zeros result in nan
+            tmp = math.sqrt(2 * self.nu) * K
+            K.fill((2 ** (1.0 - self.nu)) / gamma(self.nu))
+            K *= tmp**self.nu
+            K *= kv(self.nu, tmp)
+
+        if Y is None:
+            # convert from upper-triangular matrix to square matrix
+            K = squareform(K)
+            np.fill_diagonal(K, 1)
+
+        if eval_gradient:
+            if self.hyperparameter_length_scale.fixed:
+                # Hyperparameter l kept fixed
+                K_gradient = np.empty((X.shape[0], X.shape[0], 0))
+                return K, K_gradient
+
+            # We need to recompute the pairwise dimension-wise distances
+            if self.anisotropic:
+                D = (X[:, np.newaxis, :] - X[np.newaxis, :, :]) ** 2 / (
+                    length_scale**2
+                )
+            else:
+                D = squareform(dists**2)[:, :, np.newaxis]
+
+            if self.nu == 0.5:
+                denominator = np.sqrt(D.sum(axis=2))[:, :, np.newaxis]
+                divide_result = np.zeros_like(D)
+                np.divide(
+                    D,
+                    denominator,
+                    out=divide_result,
+                    where=denominator != 0,
+                )
+                K_gradient = K[..., np.newaxis] * divide_result
+            elif self.nu == 1.5:
+                K_gradient = 3 * D * np.exp(-np.sqrt(3 * D.sum(-1)))[..., np.newaxis]
+            elif self.nu == 2.5:
+                tmp = np.sqrt(5 * D.sum(-1))[..., np.newaxis]
+                K_gradient = 5.0 / 3.0 * D * (tmp + 1) * np.exp(-tmp)
+            elif self.nu == np.inf:
+                K_gradient = D * K[..., np.newaxis]
+            else:
+                # approximate gradient numerically
+                def f(theta):  # helper function
+                    return self.clone_with_theta(theta)(X, Y)
+
+                return K, _approx_fprime(self.theta, f, 1e-10)
+
+            if not self.anisotropic:
+                return K, K_gradient[:, :].sum(-1)[:, :, np.newaxis]
+            else:
+                return K, K_gradient
+        else:
+            return K
+
+    def __repr__(self):
+        if self.anisotropic:
+            return "{0}(length_scale=[{1}], nu={2:.3g})".format(
+                self.__class__.__name__,
+                ", ".join(map("{0:.3g}".format, self.length_scale)),
+                self.nu,
+            )
+        else:
+            return "{0}(length_scale={1:.3g}, nu={2:.3g})".format(
+                self.__class__.__name__, np.ravel(self.length_scale)[0], self.nu
+            )
+
+
+class RationalQuadratic(StationaryKernelMixin, NormalizedKernelMixin, Kernel):
+    """Rational Quadratic kernel.
+
+    The RationalQuadratic kernel can be seen as a scale mixture (an infinite
+    sum) of RBF kernels with different characteristic length scales. It is
+    parameterized by a length scale parameter :math:`l>0` and a scale
+    mixture parameter :math:`\\alpha>0`. Only the isotropic variant
+    where length_scale :math:`l` is a scalar is supported at the moment.
+    The kernel is given by:
+
+    .. math::
+        k(x_i, x_j) = \\left(
+        1 + \\frac{d(x_i, x_j)^2 }{ 2\\alpha  l^2}\\right)^{-\\alpha}
+
+    where :math:`\\alpha` is the scale mixture parameter, :math:`l` is
+    the length scale of the kernel and :math:`d(\\cdot,\\cdot)` is the
+    Euclidean distance.
+    For advice on how to set the parameters, see e.g. [1]_.
+
+    Read more in the :ref:`User Guide <gp_kernels>`.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    length_scale : float > 0, default=1.0
+        The length scale of the kernel.
+
+    alpha : float > 0, default=1.0
+        Scale mixture parameter
+
+    length_scale_bounds : pair of floats >= 0 or "fixed", default=(1e-5, 1e5)
+        The lower and upper bound on 'length_scale'.
+        If set to "fixed", 'length_scale' cannot be changed during
+        hyperparameter tuning.
+
+    alpha_bounds : pair of floats >= 0 or "fixed", default=(1e-5, 1e5)
+        The lower and upper bound on 'alpha'.
+        If set to "fixed", 'alpha' cannot be changed during
+        hyperparameter tuning.
+
+    References
+    ----------
+    .. [1] `David Duvenaud (2014). "The Kernel Cookbook:
+        Advice on Covariance functions".
+        <https://www.cs.toronto.edu/~duvenaud/cookbook/>`_
+
+    Examples
+    --------
+    >>> from sklearn.datasets import load_iris
+    >>> from sklearn.gaussian_process import GaussianProcessClassifier
+    >>> from sklearn.gaussian_process.kernels import RationalQuadratic
+    >>> X, y = load_iris(return_X_y=True)
+    >>> kernel = RationalQuadratic(length_scale=1.0, alpha=1.5)
+    >>> gpc = GaussianProcessClassifier(kernel=kernel,
+    ...         random_state=0).fit(X, y)
+    >>> gpc.score(X, y)
+    0.9733...
+    >>> gpc.predict_proba(X[:2,:])
+    array([[0.8881..., 0.0566..., 0.05518...],
+            [0.8678..., 0.0707... , 0.0614...]])
+    """
+
+    def __init__(
+        self,
+        length_scale=1.0,
+        alpha=1.0,
+        length_scale_bounds=(1e-5, 1e5),
+        alpha_bounds=(1e-5, 1e5),
+    ):
+        self.length_scale = length_scale
+        self.alpha = alpha
+        self.length_scale_bounds = length_scale_bounds
+        self.alpha_bounds = alpha_bounds
+
+    @property
+    def hyperparameter_length_scale(self):
+        return Hyperparameter("length_scale", "numeric", self.length_scale_bounds)
+
+    @property
+    def hyperparameter_alpha(self):
+        return Hyperparameter("alpha", "numeric", self.alpha_bounds)
+
+    def __call__(self, X, Y=None, eval_gradient=False):
+        """Return the kernel k(X, Y) and optionally its gradient.
+
+        Parameters
+        ----------
+        X : ndarray of shape (n_samples_X, n_features)
+            Left argument of the returned kernel k(X, Y)
+
+        Y : ndarray of shape (n_samples_Y, n_features), default=None
+            Right argument of the returned kernel k(X, Y). If None, k(X, X)
+            if evaluated instead.
+
+        eval_gradient : bool, default=False
+            Determines whether the gradient with respect to the log of
+            the kernel hyperparameter is computed.
+            Only supported when Y is None.
+
+        Returns
+        -------
+        K : ndarray of shape (n_samples_X, n_samples_Y)
+            Kernel k(X, Y)
+
+        K_gradient : ndarray of shape (n_samples_X, n_samples_X, n_dims)
+            The gradient of the kernel k(X, X) with respect to the log of the
+            hyperparameter of the kernel. Only returned when eval_gradient
+            is True.
+        """
+        if len(np.atleast_1d(self.length_scale)) > 1:
+            raise AttributeError(
+                "RationalQuadratic kernel only supports isotropic version, "
+                "please use a single scalar for length_scale"
+            )
+        X = np.atleast_2d(X)
+        if Y is None:
+            dists = squareform(pdist(X, metric="sqeuclidean"))
+            tmp = dists / (2 * self.alpha * self.length_scale**2)
+            base = 1 + tmp
+            K = base**-self.alpha
+            np.fill_diagonal(K, 1)
+        else:
+            if eval_gradient:
+                raise ValueError("Gradient can only be evaluated when Y is None.")
+            dists = cdist(X, Y, metric="sqeuclidean")
+            K = (1 + dists / (2 * self.alpha * self.length_scale**2)) ** -self.alpha
+
+        if eval_gradient:
+            # gradient with respect to length_scale
+            if not self.hyperparameter_length_scale.fixed:
+                length_scale_gradient = dists * K / (self.length_scale**2 * base)
+                length_scale_gradient = length_scale_gradient[:, :, np.newaxis]
+            else:  # l is kept fixed
+                length_scale_gradient = np.empty((K.shape[0], K.shape[1], 0))
+
+            # gradient with respect to alpha
+            if not self.hyperparameter_alpha.fixed:
+                alpha_gradient = K * (
+                    -self.alpha * np.log(base)
+                    + dists / (2 * self.length_scale**2 * base)
+                )
+                alpha_gradient = alpha_gradient[:, :, np.newaxis]
+            else:  # alpha is kept fixed
+                alpha_gradient = np.empty((K.shape[0], K.shape[1], 0))
+
+            return K, np.dstack((alpha_gradient, length_scale_gradient))
+        else:
+            return K
+
+    def __repr__(self):
+        return "{0}(alpha={1:.3g}, length_scale={2:.3g})".format(
+            self.__class__.__name__, self.alpha, self.length_scale
+        )
+
+
+class ExpSineSquared(StationaryKernelMixin, NormalizedKernelMixin, Kernel):
+    r"""Exp-Sine-Squared kernel (aka periodic kernel).
+
+    The ExpSineSquared kernel allows one to model functions which repeat
+    themselves exactly. It is parameterized by a length scale
+    parameter :math:`l>0` and a periodicity parameter :math:`p>0`.
+    Only the isotropic variant where :math:`l` is a scalar is
+    supported at the moment. The kernel is given by:
+
+    .. math::
+        k(x_i, x_j) = \text{exp}\left(-
+        \frac{ 2\sin^2(\pi d(x_i, x_j)/p) }{ l^ 2} \right)
+
+    where :math:`l` is the length scale of the kernel, :math:`p` the
+    periodicity of the kernel and :math:`d(\\cdot,\\cdot)` is the
+    Euclidean distance.
+
+    Read more in the :ref:`User Guide <gp_kernels>`.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+
+    length_scale : float > 0, default=1.0
+        The length scale of the kernel.
+
+    periodicity : float > 0, default=1.0
+        The periodicity of the kernel.
+
+    length_scale_bounds : pair of floats >= 0 or "fixed", default=(1e-5, 1e5)
+        The lower and upper bound on 'length_scale'.
+        If set to "fixed", 'length_scale' cannot be changed during
+        hyperparameter tuning.
+
+    periodicity_bounds : pair of floats >= 0 or "fixed", default=(1e-5, 1e5)
+        The lower and upper bound on 'periodicity'.
+        If set to "fixed", 'periodicity' cannot be changed during
+        hyperparameter tuning.
+
+    Examples
+    --------
+    >>> from sklearn.datasets import make_friedman2
+    >>> from sklearn.gaussian_process import GaussianProcessRegressor
+    >>> from sklearn.gaussian_process.kernels import ExpSineSquared
+    >>> X, y = make_friedman2(n_samples=50, noise=0, random_state=0)
+    >>> kernel = ExpSineSquared(length_scale=1, periodicity=1)
+    >>> gpr = GaussianProcessRegressor(kernel=kernel, alpha=5,
+    ...         random_state=0).fit(X, y)
+    >>> gpr.score(X, y)
+    0.0144...
+    >>> gpr.predict(X[:2,:], return_std=True)
+    (array([425.6..., 457.5...]), array([0.3894..., 0.3467...]))
+    """
+
+    def __init__(
+        self,
+        length_scale=1.0,
+        periodicity=1.0,
+        length_scale_bounds=(1e-5, 1e5),
+        periodicity_bounds=(1e-5, 1e5),
+    ):
+        self.length_scale = length_scale
+        self.periodicity = periodicity
+        self.length_scale_bounds = length_scale_bounds
+        self.periodicity_bounds = periodicity_bounds
+
+    @property
+    def hyperparameter_length_scale(self):
+        """Returns the length scale"""
+        return Hyperparameter("length_scale", "numeric", self.length_scale_bounds)
+
+    @property
+    def hyperparameter_periodicity(self):
+        return Hyperparameter("periodicity", "numeric", self.periodicity_bounds)
+
+    def __call__(self, X, Y=None, eval_gradient=False):
+        """Return the kernel k(X, Y) and optionally its gradient.
+
+        Parameters
+        ----------
+        X : ndarray of shape (n_samples_X, n_features)
+            Left argument of the returned kernel k(X, Y)
+
+        Y : ndarray of shape (n_samples_Y, n_features), default=None
+            Right argument of the returned kernel k(X, Y). If None, k(X, X)
+            if evaluated instead.
+
+        eval_gradient : bool, default=False
+            Determines whether the gradient with respect to the log of
+            the kernel hyperparameter is computed.
+            Only supported when Y is None.
+
+        Returns
+        -------
+        K : ndarray of shape (n_samples_X, n_samples_Y)
+            Kernel k(X, Y)
+
+        K_gradient : ndarray of shape (n_samples_X, n_samples_X, n_dims), \
+                optional
+            The gradient of the kernel k(X, X) with respect to the log of the
+            hyperparameter of the kernel. Only returned when `eval_gradient`
+            is True.
+        """
+        X = np.atleast_2d(X)
+        if Y is None:
+            dists = squareform(pdist(X, metric="euclidean"))
+            arg = np.pi * dists / self.periodicity
+            sin_of_arg = np.sin(arg)
+            K = np.exp(-2 * (sin_of_arg / self.length_scale) ** 2)
+        else:
+            if eval_gradient:
+                raise ValueError("Gradient can only be evaluated when Y is None.")
+            dists = cdist(X, Y, metric="euclidean")
+            K = np.exp(
+                -2 * (np.sin(np.pi / self.periodicity * dists) / self.length_scale) ** 2
+            )
+
+        if eval_gradient:
+            cos_of_arg = np.cos(arg)
+            # gradient with respect to length_scale
+            if not self.hyperparameter_length_scale.fixed:
+                length_scale_gradient = 4 / self.length_scale**2 * sin_of_arg**2 * K
+                length_scale_gradient = length_scale_gradient[:, :, np.newaxis]
+            else:  # length_scale is kept fixed
+                length_scale_gradient = np.empty((K.shape[0], K.shape[1], 0))
+            # gradient with respect to p
+            if not self.hyperparameter_periodicity.fixed:
+                periodicity_gradient = (
+                    4 * arg / self.length_scale**2 * cos_of_arg * sin_of_arg * K
+                )
+                periodicity_gradient = periodicity_gradient[:, :, np.newaxis]
+            else:  # p is kept fixed
+                periodicity_gradient = np.empty((K.shape[0], K.shape[1], 0))
+
+            return K, np.dstack((length_scale_gradient, periodicity_gradient))
+        else:
+            return K
+
+    def __repr__(self):
+        return "{0}(length_scale={1:.3g}, periodicity={2:.3g})".format(
+            self.__class__.__name__, self.length_scale, self.periodicity
+        )
+
+
+class DotProduct(Kernel):
+    r"""Dot-Product kernel.
+
+    The DotProduct kernel is non-stationary and can be obtained from linear
+    regression by putting :math:`N(0, 1)` priors on the coefficients
+    of :math:`x_d (d = 1, . . . , D)` and a prior of :math:`N(0, \sigma_0^2)`
+    on the bias. The DotProduct kernel is invariant to a rotation of
+    the coordinates about the origin, but not translations.
+    It is parameterized by a parameter sigma_0 :math:`\sigma`
+    which controls the inhomogenity of the kernel. For :math:`\sigma_0^2 =0`,
+    the kernel is called the homogeneous linear kernel, otherwise
+    it is inhomogeneous. The kernel is given by
+
+    .. math::
+        k(x_i, x_j) = \sigma_0 ^ 2 + x_i \cdot x_j
+
+    The DotProduct kernel is commonly combined with exponentiation.
+
+    See [1]_, Chapter 4, Section 4.2, for further details regarding the
+    DotProduct kernel.
+
+    Read more in the :ref:`User Guide <gp_kernels>`.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    sigma_0 : float >= 0, default=1.0
+        Parameter controlling the inhomogenity of the kernel. If sigma_0=0,
+        the kernel is homogeneous.
+
+    sigma_0_bounds : pair of floats >= 0 or "fixed", default=(1e-5, 1e5)
+        The lower and upper bound on 'sigma_0'.
+        If set to "fixed", 'sigma_0' cannot be changed during
+        hyperparameter tuning.
+
+    References
+    ----------
+    .. [1] `Carl Edward Rasmussen, Christopher K. I. Williams (2006).
+        "Gaussian Processes for Machine Learning". The MIT Press.
+        <http://www.gaussianprocess.org/gpml/>`_
+
+    Examples
+    --------
+    >>> from sklearn.datasets import make_friedman2
+    >>> from sklearn.gaussian_process import GaussianProcessRegressor
+    >>> from sklearn.gaussian_process.kernels import DotProduct, WhiteKernel
+    >>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
+    >>> kernel = DotProduct() + WhiteKernel()
+    >>> gpr = GaussianProcessRegressor(kernel=kernel,
+    ...         random_state=0).fit(X, y)
+    >>> gpr.score(X, y)
+    0.3680...
+    >>> gpr.predict(X[:2,:], return_std=True)
+    (array([653.0..., 592.1...]), array([316.6..., 316.6...]))
+    """
+
+    def __init__(self, sigma_0=1.0, sigma_0_bounds=(1e-5, 1e5)):
+        self.sigma_0 = sigma_0
+        self.sigma_0_bounds = sigma_0_bounds
+
+    @property
+    def hyperparameter_sigma_0(self):
+        return Hyperparameter("sigma_0", "numeric", self.sigma_0_bounds)
+
+    def __call__(self, X, Y=None, eval_gradient=False):
+        """Return the kernel k(X, Y) and optionally its gradient.
+
+        Parameters
+        ----------
+        X : ndarray of shape (n_samples_X, n_features)
+            Left argument of the returned kernel k(X, Y)
+
+        Y : ndarray of shape (n_samples_Y, n_features), default=None
+            Right argument of the returned kernel k(X, Y). If None, k(X, X)
+            if evaluated instead.
+
+        eval_gradient : bool, default=False
+            Determines whether the gradient with respect to the log of
+            the kernel hyperparameter is computed.
+            Only supported when Y is None.
+
+        Returns
+        -------
+        K : ndarray of shape (n_samples_X, n_samples_Y)
+            Kernel k(X, Y)
+
+        K_gradient : ndarray of shape (n_samples_X, n_samples_X, n_dims),\
+                optional
+            The gradient of the kernel k(X, X) with respect to the log of the
+            hyperparameter of the kernel. Only returned when `eval_gradient`
+            is True.
+        """
+        X = np.atleast_2d(X)
+        if Y is None:
+            K = np.inner(X, X) + self.sigma_0**2
+        else:
+            if eval_gradient:
+                raise ValueError("Gradient can only be evaluated when Y is None.")
+            K = np.inner(X, Y) + self.sigma_0**2
+
+        if eval_gradient:
+            if not self.hyperparameter_sigma_0.fixed:
+                K_gradient = np.empty((K.shape[0], K.shape[1], 1))
+                K_gradient[..., 0] = 2 * self.sigma_0**2
+                return K, K_gradient
+            else:
+                return K, np.empty((X.shape[0], X.shape[0], 0))
+        else:
+            return K
+
+    def diag(self, X):
+        """Returns the diagonal of the kernel k(X, X).
+
+        The result of this method is identical to np.diag(self(X)); however,
+        it can be evaluated more efficiently since only the diagonal is
+        evaluated.
+
+        Parameters
+        ----------
+        X : ndarray of shape (n_samples_X, n_features)
+            Left argument of the returned kernel k(X, Y).
+
+        Returns
+        -------
+        K_diag : ndarray of shape (n_samples_X,)
+            Diagonal of kernel k(X, X).
+        """
+        return np.einsum("ij,ij->i", X, X) + self.sigma_0**2
+
+    def is_stationary(self):
+        """Returns whether the kernel is stationary."""
+        return False
+
+    def __repr__(self):
+        return "{0}(sigma_0={1:.3g})".format(self.__class__.__name__, self.sigma_0)
+
+
+# adapted from scipy/optimize/optimize.py for functions with 2d output
+def _approx_fprime(xk, f, epsilon, args=()):
+    f0 = f(*((xk,) + args))
+    grad = np.zeros((f0.shape[0], f0.shape[1], len(xk)), float)
+    ei = np.zeros((len(xk),), float)
+    for k in range(len(xk)):
+        ei[k] = 1.0
+        d = epsilon * ei
+        grad[:, :, k] = (f(*((xk + d,) + args)) - f0) / d[k]
+        ei[k] = 0.0
+    return grad
+
+
+class PairwiseKernel(Kernel):
+    """Wrapper for kernels in sklearn.metrics.pairwise.
+
+    A thin wrapper around the functionality of the kernels in
+    sklearn.metrics.pairwise.
+
+    Note: Evaluation of eval_gradient is not analytic but numeric and all
+          kernels support only isotropic distances. The parameter gamma is
+          considered to be a hyperparameter and may be optimized. The other
+          kernel parameters are set directly at initialization and are kept
+          fixed.
+
+    .. versionadded:: 0.18
+
+    Parameters
+    ----------
+    gamma : float, default=1.0
+        Parameter gamma of the pairwise kernel specified by metric. It should
+        be positive.
+
+    gamma_bounds : pair of floats >= 0 or "fixed", default=(1e-5, 1e5)
+        The lower and upper bound on 'gamma'.
+        If set to "fixed", 'gamma' cannot be changed during
+        hyperparameter tuning.
+
+    metric : {"linear", "additive_chi2", "chi2", "poly", "polynomial", \
+              "rbf", "laplacian", "sigmoid", "cosine"} or callable, \
+              default="linear"
+        The metric to use when calculating kernel between instances in a
+        feature array. If metric is a string, it must be one of the metrics
+        in pairwise.PAIRWISE_KERNEL_FUNCTIONS.
+        If metric is "precomputed", X is assumed to be a kernel matrix.
+        Alternatively, if metric is a callable function, it is called on each
+        pair of instances (rows) and the resulting value recorded. The callable
+        should take two arrays from X as input and return a value indicating
+        the distance between them.
+
+    pairwise_kernels_kwargs : dict, default=None
+        All entries of this dict (if any) are passed as keyword arguments to
+        the pairwise kernel function.
+
+    Examples
+    --------
+    >>> from sklearn.datasets import load_iris
+    >>> from sklearn.gaussian_process import GaussianProcessClassifier
+    >>> from sklearn.gaussian_process.kernels import PairwiseKernel
+    >>> X, y = load_iris(return_X_y=True)
+    >>> kernel = PairwiseKernel(metric='rbf')
+    >>> gpc = GaussianProcessClassifier(kernel=kernel,
+    ...         random_state=0).fit(X, y)
+    >>> gpc.score(X, y)
+    0.9733...
+    >>> gpc.predict_proba(X[:2,:])
+    array([[0.8880..., 0.05663..., 0.05532...],
+           [0.8676..., 0.07073..., 0.06165...]])
+    """
+
+    def __init__(
+        self,
+        gamma=1.0,
+        gamma_bounds=(1e-5, 1e5),
+        metric="linear",
+        pairwise_kernels_kwargs=None,
+    ):
+        self.gamma = gamma
+        self.gamma_bounds = gamma_bounds
+        self.metric = metric
+        self.pairwise_kernels_kwargs = pairwise_kernels_kwargs
+
+    @property
+    def hyperparameter_gamma(self):
+        return Hyperparameter("gamma", "numeric", self.gamma_bounds)
+
+    def __call__(self, X, Y=None, eval_gradient=False):
+        """Return the kernel k(X, Y) and optionally its gradient.
+
+        Parameters
+        ----------
+        X : ndarray of shape (n_samples_X, n_features)
+            Left argument of the returned kernel k(X, Y)
+
+        Y : ndarray of shape (n_samples_Y, n_features), default=None
+            Right argument of the returned kernel k(X, Y). If None, k(X, X)
+            if evaluated instead.
+
+        eval_gradient : bool, default=False
+            Determines whether the gradient with respect to the log of
+            the kernel hyperparameter is computed.
+            Only supported when Y is None.
+
+        Returns
+        -------
+        K : ndarray of shape (n_samples_X, n_samples_Y)
+            Kernel k(X, Y)
+
+        K_gradient : ndarray of shape (n_samples_X, n_samples_X, n_dims),\
+                optional
+            The gradient of the kernel k(X, X) with respect to the log of the
+            hyperparameter of the kernel. Only returned when `eval_gradient`
+            is True.
+        """
+        pairwise_kernels_kwargs = self.pairwise_kernels_kwargs
+        if self.pairwise_kernels_kwargs is None:
+            pairwise_kernels_kwargs = {}
+
+        X = np.atleast_2d(X)
+        K = pairwise_kernels(
+            X,
+            Y,
+            metric=self.metric,
+            gamma=self.gamma,
+            filter_params=True,
+            **pairwise_kernels_kwargs,
+        )
+        if eval_gradient:
+            if self.hyperparameter_gamma.fixed:
+                return K, np.empty((X.shape[0], X.shape[0], 0))
+            else:
+                # approximate gradient numerically
+                def f(gamma):  # helper function
+                    return pairwise_kernels(
+                        X,
+                        Y,
+                        metric=self.metric,
+                        gamma=np.exp(gamma),
+                        filter_params=True,
+                        **pairwise_kernels_kwargs,
+                    )
+
+                return K, _approx_fprime(self.theta, f, 1e-10)
+        else:
+            return K
+
+    def diag(self, X):
+        """Returns the diagonal of the kernel k(X, X).
+
+        The result of this method is identical to np.diag(self(X)); however,
+        it can be evaluated more efficiently since only the diagonal is
+        evaluated.
+
+        Parameters
+        ----------
+        X : ndarray of shape (n_samples_X, n_features)
+            Left argument of the returned kernel k(X, Y)
+
+        Returns
+        -------
+        K_diag : ndarray of shape (n_samples_X,)
+            Diagonal of kernel k(X, X)
+        """
+        # We have to fall back to slow way of computing diagonal
+        return np.apply_along_axis(self, 1, X).ravel()
+
+    def is_stationary(self):
+        """Returns whether the kernel is stationary."""
+        return self.metric in ["rbf"]
+
+    def __repr__(self):
+        return "{0}(gamma={1}, metric={2})".format(
+            self.__class__.__name__, self.gamma, self.metric
+        )

mplug_owl2/lib/python3.10/site-packages/sklearn/gaussian_process/tests/_mini_sequence_kernel.py

@@ -0,0 +1,50 @@
+from sklearn.gaussian_process.kernels import Kernel, Hyperparameter
+from sklearn.gaussian_process.kernels import GenericKernelMixin
+from sklearn.gaussian_process.kernels import StationaryKernelMixin
+import numpy as np
+from sklearn.base import clone
+
+
+class MiniSeqKernel(GenericKernelMixin, StationaryKernelMixin, Kernel):
+    """
+    A minimal (but valid) convolutional kernel for sequences of variable
+    length.
+    """
+
+    def __init__(self, baseline_similarity=0.5, baseline_similarity_bounds=(1e-5, 1)):
+        self.baseline_similarity = baseline_similarity
+        self.baseline_similarity_bounds = baseline_similarity_bounds
+
+    @property
+    def hyperparameter_baseline_similarity(self):
+        return Hyperparameter(
+            "baseline_similarity", "numeric", self.baseline_similarity_bounds
+        )
+
+    def _f(self, s1, s2):
+        return sum(
+            [1.0 if c1 == c2 else self.baseline_similarity for c1 in s1 for c2 in s2]
+        )
+
+    def _g(self, s1, s2):
+        return sum([0.0 if c1 == c2 else 1.0 for c1 in s1 for c2 in s2])
+
+    def __call__(self, X, Y=None, eval_gradient=False):
+        if Y is None:
+            Y = X
+
+        if eval_gradient:
+            return (
+                np.array([[self._f(x, y) for y in Y] for x in X]),
+                np.array([[[self._g(x, y)] for y in Y] for x in X]),
+            )
+        else:
+            return np.array([[self._f(x, y) for y in Y] for x in X])
+
+    def diag(self, X):
+        return np.array([self._f(x, x) for x in X])
+
+    def clone_with_theta(self, theta):
+        cloned = clone(self)
+        cloned.theta = theta
+        return cloned

mplug_owl2/lib/python3.10/site-packages/sklearn/gaussian_process/tests/test_gpc.py

@@ -0,0 +1,286 @@
+"""Testing for Gaussian process classification """
+
+# Author: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
+# License: BSD 3 clause
+
+import warnings
+import numpy as np
+
+from scipy.optimize import approx_fprime
+
+import pytest
+
+from sklearn.gaussian_process import GaussianProcessClassifier
+from sklearn.gaussian_process.kernels import (
+    RBF,
+    CompoundKernel,
+    ConstantKernel as C,
+    WhiteKernel,
+)
+from sklearn.gaussian_process.tests._mini_sequence_kernel import MiniSeqKernel
+from sklearn.exceptions import ConvergenceWarning
+
+from sklearn.utils._testing import assert_almost_equal, assert_array_equal
+
+
+def f(x):
+    return np.sin(x)
+
+
+X = np.atleast_2d(np.linspace(0, 10, 30)).T
+X2 = np.atleast_2d([2.0, 4.0, 5.5, 6.5, 7.5]).T
+y = np.array(f(X).ravel() > 0, dtype=int)
+fX = f(X).ravel()
+y_mc = np.empty(y.shape, dtype=int)  # multi-class
+y_mc[fX < -0.35] = 0
+y_mc[(fX >= -0.35) & (fX < 0.35)] = 1
+y_mc[fX > 0.35] = 2
+
+
+fixed_kernel = RBF(length_scale=1.0, length_scale_bounds="fixed")
+kernels = [
+    RBF(length_scale=0.1),
+    fixed_kernel,
+    RBF(length_scale=1.0, length_scale_bounds=(1e-3, 1e3)),
+    C(1.0, (1e-2, 1e2)) * RBF(length_scale=1.0, length_scale_bounds=(1e-3, 1e3)),
+]
+non_fixed_kernels = [kernel for kernel in kernels if kernel != fixed_kernel]
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_predict_consistent(kernel):
+    # Check binary predict decision has also predicted probability above 0.5.
+    gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
+    assert_array_equal(gpc.predict(X), gpc.predict_proba(X)[:, 1] >= 0.5)
+
+
+def test_predict_consistent_structured():
+    # Check binary predict decision has also predicted probability above 0.5.
+    X = ["A", "AB", "B"]
+    y = np.array([True, False, True])
+    kernel = MiniSeqKernel(baseline_similarity_bounds="fixed")
+    gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
+    assert_array_equal(gpc.predict(X), gpc.predict_proba(X)[:, 1] >= 0.5)
+
+
+@pytest.mark.parametrize("kernel", non_fixed_kernels)
+def test_lml_improving(kernel):
+    # Test that hyperparameter-tuning improves log-marginal likelihood.
+    gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
+    assert gpc.log_marginal_likelihood(gpc.kernel_.theta) > gpc.log_marginal_likelihood(
+        kernel.theta
+    )
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_lml_precomputed(kernel):
+    # Test that lml of optimized kernel is stored correctly.
+    gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
+    assert_almost_equal(
+        gpc.log_marginal_likelihood(gpc.kernel_.theta), gpc.log_marginal_likelihood(), 7
+    )
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_lml_without_cloning_kernel(kernel):
+    # Test that clone_kernel=False has side-effects of kernel.theta.
+    gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
+    input_theta = np.ones(gpc.kernel_.theta.shape, dtype=np.float64)
+
+    gpc.log_marginal_likelihood(input_theta, clone_kernel=False)
+    assert_almost_equal(gpc.kernel_.theta, input_theta, 7)
+
+
+@pytest.mark.parametrize("kernel", non_fixed_kernels)
+def test_converged_to_local_maximum(kernel):
+    # Test that we are in local maximum after hyperparameter-optimization.
+    gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
+
+    lml, lml_gradient = gpc.log_marginal_likelihood(gpc.kernel_.theta, True)
+
+    assert np.all(
+        (np.abs(lml_gradient) < 1e-4)
+        | (gpc.kernel_.theta == gpc.kernel_.bounds[:, 0])
+        | (gpc.kernel_.theta == gpc.kernel_.bounds[:, 1])
+    )
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_lml_gradient(kernel):
+    # Compare analytic and numeric gradient of log marginal likelihood.
+    gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
+
+    lml, lml_gradient = gpc.log_marginal_likelihood(kernel.theta, True)
+    lml_gradient_approx = approx_fprime(
+        kernel.theta, lambda theta: gpc.log_marginal_likelihood(theta, False), 1e-10
+    )
+
+    assert_almost_equal(lml_gradient, lml_gradient_approx, 3)
+
+
+def test_random_starts():
+    # Test that an increasing number of random-starts of GP fitting only
+    # increases the log marginal likelihood of the chosen theta.
+    n_samples, n_features = 25, 2
+    rng = np.random.RandomState(0)
+    X = rng.randn(n_samples, n_features) * 2 - 1
+    y = (np.sin(X).sum(axis=1) + np.sin(3 * X).sum(axis=1)) > 0
+
+    kernel = C(1.0, (1e-2, 1e2)) * RBF(
+        length_scale=[1e-3] * n_features, length_scale_bounds=[(1e-4, 1e2)] * n_features
+    )
+    last_lml = -np.inf
+    for n_restarts_optimizer in range(5):
+        gp = GaussianProcessClassifier(
+            kernel=kernel, n_restarts_optimizer=n_restarts_optimizer, random_state=0
+        ).fit(X, y)
+        lml = gp.log_marginal_likelihood(gp.kernel_.theta)
+        assert lml > last_lml - np.finfo(np.float32).eps
+        last_lml = lml
+
+
+@pytest.mark.parametrize("kernel", non_fixed_kernels)
+def test_custom_optimizer(kernel):
+    # Test that GPC can use externally defined optimizers.
+    # Define a dummy optimizer that simply tests 10 random hyperparameters
+    def optimizer(obj_func, initial_theta, bounds):
+        rng = np.random.RandomState(0)
+        theta_opt, func_min = initial_theta, obj_func(
+            initial_theta, eval_gradient=False
+        )
+        for _ in range(10):
+            theta = np.atleast_1d(
+                rng.uniform(np.maximum(-2, bounds[:, 0]), np.minimum(1, bounds[:, 1]))
+            )
+            f = obj_func(theta, eval_gradient=False)
+            if f < func_min:
+                theta_opt, func_min = theta, f
+        return theta_opt, func_min
+
+    gpc = GaussianProcessClassifier(kernel=kernel, optimizer=optimizer)
+    gpc.fit(X, y_mc)
+    # Checks that optimizer improved marginal likelihood
+    assert gpc.log_marginal_likelihood(gpc.kernel_.theta) > gpc.log_marginal_likelihood(
+        kernel.theta
+    )
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_multi_class(kernel):
+    # Test GPC for multi-class classification problems.
+    gpc = GaussianProcessClassifier(kernel=kernel)
+    gpc.fit(X, y_mc)
+
+    y_prob = gpc.predict_proba(X2)
+    assert_almost_equal(y_prob.sum(1), 1)
+
+    y_pred = gpc.predict(X2)
+    assert_array_equal(np.argmax(y_prob, 1), y_pred)
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_multi_class_n_jobs(kernel):
+    # Test that multi-class GPC produces identical results with n_jobs>1.
+    gpc = GaussianProcessClassifier(kernel=kernel)
+    gpc.fit(X, y_mc)
+
+    gpc_2 = GaussianProcessClassifier(kernel=kernel, n_jobs=2)
+    gpc_2.fit(X, y_mc)
+
+    y_prob = gpc.predict_proba(X2)
+    y_prob_2 = gpc_2.predict_proba(X2)
+    assert_almost_equal(y_prob, y_prob_2)
+
+
+def test_warning_bounds():
+    kernel = RBF(length_scale_bounds=[1e-5, 1e-3])
+    gpc = GaussianProcessClassifier(kernel=kernel)
+    warning_message = (
+        "The optimal value found for dimension 0 of parameter "
+        "length_scale is close to the specified upper bound "
+        "0.001. Increasing the bound and calling fit again may "
+        "find a better value."
+    )
+    with pytest.warns(ConvergenceWarning, match=warning_message):
+        gpc.fit(X, y)
+
+    kernel_sum = WhiteKernel(noise_level_bounds=[1e-5, 1e-3]) + RBF(
+        length_scale_bounds=[1e3, 1e5]
+    )
+    gpc_sum = GaussianProcessClassifier(kernel=kernel_sum)
+    with warnings.catch_warnings(record=True) as record:
+        warnings.simplefilter("always")
+        gpc_sum.fit(X, y)
+
+        assert len(record) == 2
+
+        assert issubclass(record[0].category, ConvergenceWarning)
+        assert (
+            record[0].message.args[0]
+            == "The optimal value found for "
+            "dimension 0 of parameter "
+            "k1__noise_level is close to the "
+            "specified upper bound 0.001. "
+            "Increasing the bound and calling "
+            "fit again may find a better value."
+        )
+
+        assert issubclass(record[1].category, ConvergenceWarning)
+        assert (
+            record[1].message.args[0]
+            == "The optimal value found for "
+            "dimension 0 of parameter "
+            "k2__length_scale is close to the "
+            "specified lower bound 1000.0. "
+            "Decreasing the bound and calling "
+            "fit again may find a better value."
+        )
+
+    X_tile = np.tile(X, 2)
+    kernel_dims = RBF(length_scale=[1.0, 2.0], length_scale_bounds=[1e1, 1e2])
+    gpc_dims = GaussianProcessClassifier(kernel=kernel_dims)
+
+    with warnings.catch_warnings(record=True) as record:
+        warnings.simplefilter("always")
+        gpc_dims.fit(X_tile, y)
+
+        assert len(record) == 2
+
+        assert issubclass(record[0].category, ConvergenceWarning)
+        assert (
+            record[0].message.args[0]
+            == "The optimal value found for "
+            "dimension 0 of parameter "
+            "length_scale is close to the "
+            "specified upper bound 100.0. "
+            "Increasing the bound and calling "
+            "fit again may find a better value."
+        )
+
+        assert issubclass(record[1].category, ConvergenceWarning)
+        assert (
+            record[1].message.args[0]
+            == "The optimal value found for "
+            "dimension 1 of parameter "
+            "length_scale is close to the "
+            "specified upper bound 100.0. "
+            "Increasing the bound and calling "
+            "fit again may find a better value."
+        )
+
+
+@pytest.mark.parametrize(
+    "params, error_type, err_msg",
+    [
+        (
+            {"kernel": CompoundKernel(0)},
+            ValueError,
+            "kernel cannot be a CompoundKernel",
+        )
+    ],
+)
+def test_gpc_fit_error(params, error_type, err_msg):
+    """Check that expected error are raised during fit."""
+    gpc = GaussianProcessClassifier(**params)
+    with pytest.raises(error_type, match=err_msg):
+        gpc.fit(X, y)

mplug_owl2/lib/python3.10/site-packages/sklearn/gaussian_process/tests/test_gpr.py

@@ -0,0 +1,800 @@
+"""Testing for Gaussian process regression """
+
+# Author: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
+# Modified by: Pete Green <p.l.green@liverpool.ac.uk>
+# License: BSD 3 clause
+
+import warnings
+import sys
+import re
+import numpy as np
+
+from scipy.optimize import approx_fprime
+
+import pytest
+
+from sklearn.gaussian_process import GaussianProcessRegressor
+from sklearn.gaussian_process.kernels import (
+    RBF,
+    ConstantKernel as C,
+    WhiteKernel,
+)
+from sklearn.gaussian_process.kernels import DotProduct, ExpSineSquared
+from sklearn.gaussian_process.tests._mini_sequence_kernel import MiniSeqKernel
+from sklearn.exceptions import ConvergenceWarning
+from sklearn.utils._testing import (
+    assert_array_less,
+    assert_almost_equal,
+    assert_array_almost_equal,
+    assert_allclose,
+)
+
+
+def f(x):
+    return x * np.sin(x)
+
+
+X = np.atleast_2d([1.0, 3.0, 5.0, 6.0, 7.0, 8.0]).T
+X2 = np.atleast_2d([2.0, 4.0, 5.5, 6.5, 7.5]).T
+y = f(X).ravel()
+
+fixed_kernel = RBF(length_scale=1.0, length_scale_bounds="fixed")
+kernels = [
+    RBF(length_scale=1.0),
+    fixed_kernel,
+    RBF(length_scale=1.0, length_scale_bounds=(1e-3, 1e3)),
+    C(1.0, (1e-2, 1e2)) * RBF(length_scale=1.0, length_scale_bounds=(1e-3, 1e3)),
+    C(1.0, (1e-2, 1e2)) * RBF(length_scale=1.0, length_scale_bounds=(1e-3, 1e3))
+    + C(1e-5, (1e-5, 1e2)),
+    C(0.1, (1e-2, 1e2)) * RBF(length_scale=1.0, length_scale_bounds=(1e-3, 1e3))
+    + C(1e-5, (1e-5, 1e2)),
+]
+non_fixed_kernels = [kernel for kernel in kernels if kernel != fixed_kernel]
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_gpr_interpolation(kernel):
+    if sys.maxsize <= 2**32:
+        pytest.xfail("This test may fail on 32 bit Python")
+
+    # Test the interpolating property for different kernels.
+    gpr = GaussianProcessRegressor(kernel=kernel).fit(X, y)
+    y_pred, y_cov = gpr.predict(X, return_cov=True)
+
+    assert_almost_equal(y_pred, y)
+    assert_almost_equal(np.diag(y_cov), 0.0)
+
+
+def test_gpr_interpolation_structured():
+    # Test the interpolating property for different kernels.
+    kernel = MiniSeqKernel(baseline_similarity_bounds="fixed")
+    X = ["A", "B", "C"]
+    y = np.array([1, 2, 3])
+    gpr = GaussianProcessRegressor(kernel=kernel).fit(X, y)
+    y_pred, y_cov = gpr.predict(X, return_cov=True)
+
+    assert_almost_equal(
+        kernel(X, eval_gradient=True)[1].ravel(), (1 - np.eye(len(X))).ravel()
+    )
+    assert_almost_equal(y_pred, y)
+    assert_almost_equal(np.diag(y_cov), 0.0)
+
+
+@pytest.mark.parametrize("kernel", non_fixed_kernels)
+def test_lml_improving(kernel):
+    if sys.maxsize <= 2**32:
+        pytest.xfail("This test may fail on 32 bit Python")
+
+    # Test that hyperparameter-tuning improves log-marginal likelihood.
+    gpr = GaussianProcessRegressor(kernel=kernel).fit(X, y)
+    assert gpr.log_marginal_likelihood(gpr.kernel_.theta) > gpr.log_marginal_likelihood(
+        kernel.theta
+    )
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_lml_precomputed(kernel):
+    # Test that lml of optimized kernel is stored correctly.
+    gpr = GaussianProcessRegressor(kernel=kernel).fit(X, y)
+    assert gpr.log_marginal_likelihood(gpr.kernel_.theta) == pytest.approx(
+        gpr.log_marginal_likelihood()
+    )
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_lml_without_cloning_kernel(kernel):
+    # Test that lml of optimized kernel is stored correctly.
+    gpr = GaussianProcessRegressor(kernel=kernel).fit(X, y)
+    input_theta = np.ones(gpr.kernel_.theta.shape, dtype=np.float64)
+
+    gpr.log_marginal_likelihood(input_theta, clone_kernel=False)
+    assert_almost_equal(gpr.kernel_.theta, input_theta, 7)
+
+
+@pytest.mark.parametrize("kernel", non_fixed_kernels)
+def test_converged_to_local_maximum(kernel):
+    # Test that we are in local maximum after hyperparameter-optimization.
+    gpr = GaussianProcessRegressor(kernel=kernel).fit(X, y)
+
+    lml, lml_gradient = gpr.log_marginal_likelihood(gpr.kernel_.theta, True)
+
+    assert np.all(
+        (np.abs(lml_gradient) < 1e-4)
+        | (gpr.kernel_.theta == gpr.kernel_.bounds[:, 0])
+        | (gpr.kernel_.theta == gpr.kernel_.bounds[:, 1])
+    )
+
+
+@pytest.mark.parametrize("kernel", non_fixed_kernels)
+def test_solution_inside_bounds(kernel):
+    # Test that hyperparameter-optimization remains in bounds#
+    gpr = GaussianProcessRegressor(kernel=kernel).fit(X, y)
+
+    bounds = gpr.kernel_.bounds
+    max_ = np.finfo(gpr.kernel_.theta.dtype).max
+    tiny = 1e-10
+    bounds[~np.isfinite(bounds[:, 1]), 1] = max_
+
+    assert_array_less(bounds[:, 0], gpr.kernel_.theta + tiny)
+    assert_array_less(gpr.kernel_.theta, bounds[:, 1] + tiny)
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_lml_gradient(kernel):
+    # Compare analytic and numeric gradient of log marginal likelihood.
+    gpr = GaussianProcessRegressor(kernel=kernel).fit(X, y)
+
+    lml, lml_gradient = gpr.log_marginal_likelihood(kernel.theta, True)
+    lml_gradient_approx = approx_fprime(
+        kernel.theta, lambda theta: gpr.log_marginal_likelihood(theta, False), 1e-10
+    )
+
+    assert_almost_equal(lml_gradient, lml_gradient_approx, 3)
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_prior(kernel):
+    # Test that GP prior has mean 0 and identical variances.
+    gpr = GaussianProcessRegressor(kernel=kernel)
+
+    y_mean, y_cov = gpr.predict(X, return_cov=True)
+
+    assert_almost_equal(y_mean, 0, 5)
+    if len(gpr.kernel.theta) > 1:
+        # XXX: quite hacky, works only for current kernels
+        assert_almost_equal(np.diag(y_cov), np.exp(kernel.theta[0]), 5)
+    else:
+        assert_almost_equal(np.diag(y_cov), 1, 5)
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_sample_statistics(kernel):
+    # Test that statistics of samples drawn from GP are correct.
+    gpr = GaussianProcessRegressor(kernel=kernel).fit(X, y)
+
+    y_mean, y_cov = gpr.predict(X2, return_cov=True)
+
+    samples = gpr.sample_y(X2, 300000)
+
+    # More digits accuracy would require many more samples
+    assert_almost_equal(y_mean, np.mean(samples, 1), 1)
+    assert_almost_equal(
+        np.diag(y_cov) / np.diag(y_cov).max(),
+        np.var(samples, 1) / np.diag(y_cov).max(),
+        1,
+    )
+
+
+def test_no_optimizer():
+    # Test that kernel parameters are unmodified when optimizer is None.
+    kernel = RBF(1.0)
+    gpr = GaussianProcessRegressor(kernel=kernel, optimizer=None).fit(X, y)
+    assert np.exp(gpr.kernel_.theta) == 1.0
+
+
+@pytest.mark.parametrize("kernel", kernels)
+@pytest.mark.parametrize("target", [y, np.ones(X.shape[0], dtype=np.float64)])
+def test_predict_cov_vs_std(kernel, target):
+    if sys.maxsize <= 2**32:
+        pytest.xfail("This test may fail on 32 bit Python")
+
+    # Test that predicted std.-dev. is consistent with cov's diagonal.
+    gpr = GaussianProcessRegressor(kernel=kernel).fit(X, y)
+    y_mean, y_cov = gpr.predict(X2, return_cov=True)
+    y_mean, y_std = gpr.predict(X2, return_std=True)
+    assert_almost_equal(np.sqrt(np.diag(y_cov)), y_std)
+
+
+def test_anisotropic_kernel():
+    # Test that GPR can identify meaningful anisotropic length-scales.
+    # We learn a function which varies in one dimension ten-times slower
+    # than in the other. The corresponding length-scales should differ by at
+    # least a factor 5
+    rng = np.random.RandomState(0)
+    X = rng.uniform(-1, 1, (50, 2))
+    y = X[:, 0] + 0.1 * X[:, 1]
+
+    kernel = RBF([1.0, 1.0])
+    gpr = GaussianProcessRegressor(kernel=kernel).fit(X, y)
+    assert np.exp(gpr.kernel_.theta[1]) > np.exp(gpr.kernel_.theta[0]) * 5
+
+
+def test_random_starts():
+    # Test that an increasing number of random-starts of GP fitting only
+    # increases the log marginal likelihood of the chosen theta.
+    n_samples, n_features = 25, 2
+    rng = np.random.RandomState(0)
+    X = rng.randn(n_samples, n_features) * 2 - 1
+    y = (
+        np.sin(X).sum(axis=1)
+        + np.sin(3 * X).sum(axis=1)
+        + rng.normal(scale=0.1, size=n_samples)
+    )
+
+    kernel = C(1.0, (1e-2, 1e2)) * RBF(
+        length_scale=[1.0] * n_features, length_scale_bounds=[(1e-4, 1e2)] * n_features
+    ) + WhiteKernel(noise_level=1e-5, noise_level_bounds=(1e-5, 1e1))
+    last_lml = -np.inf
+    for n_restarts_optimizer in range(5):
+        gp = GaussianProcessRegressor(
+            kernel=kernel,
+            n_restarts_optimizer=n_restarts_optimizer,
+            random_state=0,
+        ).fit(X, y)
+        lml = gp.log_marginal_likelihood(gp.kernel_.theta)
+        assert lml > last_lml - np.finfo(np.float32).eps
+        last_lml = lml
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_y_normalization(kernel):
+    """
+    Test normalization of the target values in GP
+
+    Fitting non-normalizing GP on normalized y and fitting normalizing GP
+    on unnormalized y should yield identical results. Note that, here,
+    'normalized y' refers to y that has been made zero mean and unit
+    variance.
+
+    """
+
+    y_mean = np.mean(y)
+    y_std = np.std(y)
+    y_norm = (y - y_mean) / y_std
+
+    # Fit non-normalizing GP on normalized y
+    gpr = GaussianProcessRegressor(kernel=kernel)
+    gpr.fit(X, y_norm)
+
+    # Fit normalizing GP on unnormalized y
+    gpr_norm = GaussianProcessRegressor(kernel=kernel, normalize_y=True)
+    gpr_norm.fit(X, y)
+
+    # Compare predicted mean, std-devs and covariances
+    y_pred, y_pred_std = gpr.predict(X2, return_std=True)
+    y_pred = y_pred * y_std + y_mean
+    y_pred_std = y_pred_std * y_std
+    y_pred_norm, y_pred_std_norm = gpr_norm.predict(X2, return_std=True)
+
+    assert_almost_equal(y_pred, y_pred_norm)
+    assert_almost_equal(y_pred_std, y_pred_std_norm)
+
+    _, y_cov = gpr.predict(X2, return_cov=True)
+    y_cov = y_cov * y_std**2
+    _, y_cov_norm = gpr_norm.predict(X2, return_cov=True)
+
+    assert_almost_equal(y_cov, y_cov_norm)
+
+
+def test_large_variance_y():
+    """
+    Here we test that, when noramlize_y=True, our GP can produce a
+    sensible fit to training data whose variance is significantly
+    larger than unity. This test was made in response to issue #15612.
+
+    GP predictions are verified against predictions that were made
+    using GPy which, here, is treated as the 'gold standard'. Note that we
+    only investigate the RBF kernel here, as that is what was used in the
+    GPy implementation.
+
+    The following code can be used to recreate the GPy data:
+
+    --------------------------------------------------------------------------
+    import GPy
+
+    kernel_gpy = GPy.kern.RBF(input_dim=1, lengthscale=1.)
+    gpy = GPy.models.GPRegression(X, np.vstack(y_large), kernel_gpy)
+    gpy.optimize()
+    y_pred_gpy, y_var_gpy = gpy.predict(X2)
+    y_pred_std_gpy = np.sqrt(y_var_gpy)
+    --------------------------------------------------------------------------
+    """
+
+    # Here we utilise a larger variance version of the training data
+    y_large = 10 * y
+
+    # Standard GP with normalize_y=True
+    RBF_params = {"length_scale": 1.0}
+    kernel = RBF(**RBF_params)
+    gpr = GaussianProcessRegressor(kernel=kernel, normalize_y=True)
+    gpr.fit(X, y_large)
+    y_pred, y_pred_std = gpr.predict(X2, return_std=True)
+
+    # 'Gold standard' mean predictions from GPy
+    y_pred_gpy = np.array(
+        [15.16918303, -27.98707845, -39.31636019, 14.52605515, 69.18503589]
+    )
+
+    # 'Gold standard' std predictions from GPy
+    y_pred_std_gpy = np.array(
+        [7.78860962, 3.83179178, 0.63149951, 0.52745188, 0.86170042]
+    )
+
+    # Based on numerical experiments, it's reasonable to expect our
+    # GP's mean predictions to get within 7% of predictions of those
+    # made by GPy.
+    assert_allclose(y_pred, y_pred_gpy, rtol=0.07, atol=0)
+
+    # Based on numerical experiments, it's reasonable to expect our
+    # GP's std predictions to get within 15% of predictions of those
+    # made by GPy.
+    assert_allclose(y_pred_std, y_pred_std_gpy, rtol=0.15, atol=0)
+
+
+def test_y_multioutput():
+    # Test that GPR can deal with multi-dimensional target values
+    y_2d = np.vstack((y, y * 2)).T
+
+    # Test for fixed kernel that first dimension of 2d GP equals the output
+    # of 1d GP and that second dimension is twice as large
+    kernel = RBF(length_scale=1.0)
+
+    gpr = GaussianProcessRegressor(kernel=kernel, optimizer=None, normalize_y=False)
+    gpr.fit(X, y)
+
+    gpr_2d = GaussianProcessRegressor(kernel=kernel, optimizer=None, normalize_y=False)
+    gpr_2d.fit(X, y_2d)
+
+    y_pred_1d, y_std_1d = gpr.predict(X2, return_std=True)
+    y_pred_2d, y_std_2d = gpr_2d.predict(X2, return_std=True)
+    _, y_cov_1d = gpr.predict(X2, return_cov=True)
+    _, y_cov_2d = gpr_2d.predict(X2, return_cov=True)
+
+    assert_almost_equal(y_pred_1d, y_pred_2d[:, 0])
+    assert_almost_equal(y_pred_1d, y_pred_2d[:, 1] / 2)
+
+    # Standard deviation and covariance do not depend on output
+    for target in range(y_2d.shape[1]):
+        assert_almost_equal(y_std_1d, y_std_2d[..., target])
+        assert_almost_equal(y_cov_1d, y_cov_2d[..., target])
+
+    y_sample_1d = gpr.sample_y(X2, n_samples=10)
+    y_sample_2d = gpr_2d.sample_y(X2, n_samples=10)
+
+    assert y_sample_1d.shape == (5, 10)
+    assert y_sample_2d.shape == (5, 2, 10)
+    # Only the first target will be equal
+    assert_almost_equal(y_sample_1d, y_sample_2d[:, 0, :])
+
+    # Test hyperparameter optimization
+    for kernel in kernels:
+        gpr = GaussianProcessRegressor(kernel=kernel, normalize_y=True)
+        gpr.fit(X, y)
+
+        gpr_2d = GaussianProcessRegressor(kernel=kernel, normalize_y=True)
+        gpr_2d.fit(X, np.vstack((y, y)).T)
+
+        assert_almost_equal(gpr.kernel_.theta, gpr_2d.kernel_.theta, 4)
+
+
+@pytest.mark.parametrize("kernel", non_fixed_kernels)
+def test_custom_optimizer(kernel):
+    # Test that GPR can use externally defined optimizers.
+    # Define a dummy optimizer that simply tests 50 random hyperparameters
+    def optimizer(obj_func, initial_theta, bounds):
+        rng = np.random.RandomState(0)
+        theta_opt, func_min = initial_theta, obj_func(
+            initial_theta, eval_gradient=False
+        )
+        for _ in range(50):
+            theta = np.atleast_1d(
+                rng.uniform(np.maximum(-2, bounds[:, 0]), np.minimum(1, bounds[:, 1]))
+            )
+            f = obj_func(theta, eval_gradient=False)
+            if f < func_min:
+                theta_opt, func_min = theta, f
+        return theta_opt, func_min
+
+    gpr = GaussianProcessRegressor(kernel=kernel, optimizer=optimizer)
+    gpr.fit(X, y)
+    # Checks that optimizer improved marginal likelihood
+    assert gpr.log_marginal_likelihood(gpr.kernel_.theta) > gpr.log_marginal_likelihood(
+        gpr.kernel.theta
+    )
+
+
+def test_gpr_correct_error_message():
+    X = np.arange(12).reshape(6, -1)
+    y = np.ones(6)
+    kernel = DotProduct()
+    gpr = GaussianProcessRegressor(kernel=kernel, alpha=0.0)
+    message = (
+        "The kernel, %s, is not returning a "
+        "positive definite matrix. Try gradually increasing "
+        "the 'alpha' parameter of your "
+        "GaussianProcessRegressor estimator." % kernel
+    )
+    with pytest.raises(np.linalg.LinAlgError, match=re.escape(message)):
+        gpr.fit(X, y)
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_duplicate_input(kernel):
+    # Test GPR can handle two different output-values for the same input.
+    gpr_equal_inputs = GaussianProcessRegressor(kernel=kernel, alpha=1e-2)
+    gpr_similar_inputs = GaussianProcessRegressor(kernel=kernel, alpha=1e-2)
+
+    X_ = np.vstack((X, X[0]))
+    y_ = np.hstack((y, y[0] + 1))
+    gpr_equal_inputs.fit(X_, y_)
+
+    X_ = np.vstack((X, X[0] + 1e-15))
+    y_ = np.hstack((y, y[0] + 1))
+    gpr_similar_inputs.fit(X_, y_)
+
+    X_test = np.linspace(0, 10, 100)[:, None]
+    y_pred_equal, y_std_equal = gpr_equal_inputs.predict(X_test, return_std=True)
+    y_pred_similar, y_std_similar = gpr_similar_inputs.predict(X_test, return_std=True)
+
+    assert_almost_equal(y_pred_equal, y_pred_similar)
+    assert_almost_equal(y_std_equal, y_std_similar)
+
+
+def test_no_fit_default_predict():
+    # Test that GPR predictions without fit does not break by default.
+    default_kernel = C(1.0, constant_value_bounds="fixed") * RBF(
+        1.0, length_scale_bounds="fixed"
+    )
+    gpr1 = GaussianProcessRegressor()
+    _, y_std1 = gpr1.predict(X, return_std=True)
+    _, y_cov1 = gpr1.predict(X, return_cov=True)
+
+    gpr2 = GaussianProcessRegressor(kernel=default_kernel)
+    _, y_std2 = gpr2.predict(X, return_std=True)
+    _, y_cov2 = gpr2.predict(X, return_cov=True)
+
+    assert_array_almost_equal(y_std1, y_std2)
+    assert_array_almost_equal(y_cov1, y_cov2)
+
+
+def test_warning_bounds():
+    kernel = RBF(length_scale_bounds=[1e-5, 1e-3])
+    gpr = GaussianProcessRegressor(kernel=kernel)
+    warning_message = (
+        "The optimal value found for dimension 0 of parameter "
+        "length_scale is close to the specified upper bound "
+        "0.001. Increasing the bound and calling fit again may "
+        "find a better value."
+    )
+    with pytest.warns(ConvergenceWarning, match=warning_message):
+        gpr.fit(X, y)
+
+    kernel_sum = WhiteKernel(noise_level_bounds=[1e-5, 1e-3]) + RBF(
+        length_scale_bounds=[1e3, 1e5]
+    )
+    gpr_sum = GaussianProcessRegressor(kernel=kernel_sum)
+    with warnings.catch_warnings(record=True) as record:
+        warnings.simplefilter("always")
+        gpr_sum.fit(X, y)
+
+        assert len(record) == 2
+
+        assert issubclass(record[0].category, ConvergenceWarning)
+        assert (
+            record[0].message.args[0]
+            == "The optimal value found for "
+            "dimension 0 of parameter "
+            "k1__noise_level is close to the "
+            "specified upper bound 0.001. "
+            "Increasing the bound and calling "
+            "fit again may find a better value."
+        )
+
+        assert issubclass(record[1].category, ConvergenceWarning)
+        assert (
+            record[1].message.args[0]
+            == "The optimal value found for "
+            "dimension 0 of parameter "
+            "k2__length_scale is close to the "
+            "specified lower bound 1000.0. "
+            "Decreasing the bound and calling "
+            "fit again may find a better value."
+        )
+
+    X_tile = np.tile(X, 2)
+    kernel_dims = RBF(length_scale=[1.0, 2.0], length_scale_bounds=[1e1, 1e2])
+    gpr_dims = GaussianProcessRegressor(kernel=kernel_dims)
+
+    with warnings.catch_warnings(record=True) as record:
+        warnings.simplefilter("always")
+        gpr_dims.fit(X_tile, y)
+
+        assert len(record) == 2
+
+        assert issubclass(record[0].category, ConvergenceWarning)
+        assert (
+            record[0].message.args[0]
+            == "The optimal value found for "
+            "dimension 0 of parameter "
+            "length_scale is close to the "
+            "specified lower bound 10.0. "
+            "Decreasing the bound and calling "
+            "fit again may find a better value."
+        )
+
+        assert issubclass(record[1].category, ConvergenceWarning)
+        assert (
+            record[1].message.args[0]
+            == "The optimal value found for "
+            "dimension 1 of parameter "
+            "length_scale is close to the "
+            "specified lower bound 10.0. "
+            "Decreasing the bound and calling "
+            "fit again may find a better value."
+        )
+
+
+def test_bound_check_fixed_hyperparameter():
+    # Regression test for issue #17943
+    # Check that having a hyperparameter with fixed bounds doesn't cause an
+    # error
+    k1 = 50.0**2 * RBF(length_scale=50.0)  # long term smooth rising trend
+    k2 = ExpSineSquared(
+        length_scale=1.0, periodicity=1.0, periodicity_bounds="fixed"
+    )  # seasonal component
+    kernel = k1 + k2
+    GaussianProcessRegressor(kernel=kernel).fit(X, y)
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_constant_target(kernel):
+    """Check that the std. dev. is affected to 1 when normalizing a constant
+    feature.
+    Non-regression test for:
+    https://github.com/scikit-learn/scikit-learn/issues/18318
+    NaN where affected to the target when scaling due to null std. dev. with
+    constant target.
+    """
+    y_constant = np.ones(X.shape[0], dtype=np.float64)
+
+    gpr = GaussianProcessRegressor(kernel=kernel, normalize_y=True)
+    gpr.fit(X, y_constant)
+    assert gpr._y_train_std == pytest.approx(1.0)
+
+    y_pred, y_cov = gpr.predict(X, return_cov=True)
+    assert_allclose(y_pred, y_constant)
+    # set atol because we compare to zero
+    assert_allclose(np.diag(y_cov), 0.0, atol=1e-9)
+
+    # Test multi-target data
+    n_samples, n_targets = X.shape[0], 2
+    rng = np.random.RandomState(0)
+    y = np.concatenate(
+        [
+            rng.normal(size=(n_samples, 1)),  # non-constant target
+            np.full(shape=(n_samples, 1), fill_value=2),  # constant target
+        ],
+        axis=1,
+    )
+
+    gpr.fit(X, y)
+    Y_pred, Y_cov = gpr.predict(X, return_cov=True)
+
+    assert_allclose(Y_pred[:, 1], 2)
+    assert_allclose(np.diag(Y_cov[..., 1]), 0.0, atol=1e-9)
+
+    assert Y_pred.shape == (n_samples, n_targets)
+    assert Y_cov.shape == (n_samples, n_samples, n_targets)
+
+
+def test_gpr_consistency_std_cov_non_invertible_kernel():
+    """Check the consistency between the returned std. dev. and the covariance.
+    Non-regression test for:
+    https://github.com/scikit-learn/scikit-learn/issues/19936
+    Inconsistencies were observed when the kernel cannot be inverted (or
+    numerically stable).
+    """
+    kernel = C(8.98576054e05, (1e-12, 1e12)) * RBF(
+        [5.91326520e02, 1.32584051e03], (1e-12, 1e12)
+    ) + WhiteKernel(noise_level=1e-5)
+    gpr = GaussianProcessRegressor(kernel=kernel, alpha=0, optimizer=None)
+    X_train = np.array(
+        [
+            [0.0, 0.0],
+            [1.54919334, -0.77459667],
+            [-1.54919334, 0.0],
+            [0.0, -1.54919334],
+            [0.77459667, 0.77459667],
+            [-0.77459667, 1.54919334],
+        ]
+    )
+    y_train = np.array(
+        [
+            [-2.14882017e-10],
+            [-4.66975823e00],
+            [4.01823986e00],
+            [-1.30303674e00],
+            [-1.35760156e00],
+            [3.31215668e00],
+        ]
+    )
+    gpr.fit(X_train, y_train)
+    X_test = np.array(
+        [
+            [-1.93649167, -1.93649167],
+            [1.93649167, -1.93649167],
+            [-1.93649167, 1.93649167],
+            [1.93649167, 1.93649167],
+        ]
+    )
+    pred1, std = gpr.predict(X_test, return_std=True)
+    pred2, cov = gpr.predict(X_test, return_cov=True)
+    assert_allclose(std, np.sqrt(np.diagonal(cov)), rtol=1e-5)
+
+
+@pytest.mark.parametrize(
+    "params, TypeError, err_msg",
+    [
+        (
+            {"alpha": np.zeros(100)},
+            ValueError,
+            "alpha must be a scalar or an array with same number of entries as y",
+        ),
+        (
+            {
+                "kernel": WhiteKernel(noise_level_bounds=(-np.inf, np.inf)),
+                "n_restarts_optimizer": 2,
+            },
+            ValueError,
+            "requires that all bounds are finite",
+        ),
+    ],
+)
+def test_gpr_fit_error(params, TypeError, err_msg):
+    """Check that expected error are raised during fit."""
+    gpr = GaussianProcessRegressor(**params)
+    with pytest.raises(TypeError, match=err_msg):
+        gpr.fit(X, y)
+
+
+def test_gpr_lml_error():
+    """Check that we raise the proper error in the LML method."""
+    gpr = GaussianProcessRegressor(kernel=RBF()).fit(X, y)
+
+    err_msg = "Gradient can only be evaluated for theta!=None"
+    with pytest.raises(ValueError, match=err_msg):
+        gpr.log_marginal_likelihood(eval_gradient=True)
+
+
+def test_gpr_predict_error():
+    """Check that we raise the proper error during predict."""
+    gpr = GaussianProcessRegressor(kernel=RBF()).fit(X, y)
+
+    err_msg = "At most one of return_std or return_cov can be requested."
+    with pytest.raises(RuntimeError, match=err_msg):
+        gpr.predict(X, return_cov=True, return_std=True)
+
+
+@pytest.mark.parametrize("normalize_y", [True, False])
+@pytest.mark.parametrize("n_targets", [None, 1, 10])
+def test_predict_shapes(normalize_y, n_targets):
+    """Check the shapes of y_mean, y_std, and y_cov in single-output
+    (n_targets=None) and multi-output settings, including the edge case when
+    n_targets=1, where the sklearn convention is to squeeze the predictions.
+
+    Non-regression test for:
+    https://github.com/scikit-learn/scikit-learn/issues/17394
+    https://github.com/scikit-learn/scikit-learn/issues/18065
+    https://github.com/scikit-learn/scikit-learn/issues/22174
+    """
+    rng = np.random.RandomState(1234)
+
+    n_features, n_samples_train, n_samples_test = 6, 9, 7
+
+    y_train_shape = (n_samples_train,)
+    if n_targets is not None:
+        y_train_shape = y_train_shape + (n_targets,)
+
+    # By convention single-output data is squeezed upon prediction
+    y_test_shape = (n_samples_test,)
+    if n_targets is not None and n_targets > 1:
+        y_test_shape = y_test_shape + (n_targets,)
+
+    X_train = rng.randn(n_samples_train, n_features)
+    X_test = rng.randn(n_samples_test, n_features)
+    y_train = rng.randn(*y_train_shape)
+
+    model = GaussianProcessRegressor(normalize_y=normalize_y)
+    model.fit(X_train, y_train)
+
+    y_pred, y_std = model.predict(X_test, return_std=True)
+    _, y_cov = model.predict(X_test, return_cov=True)
+
+    assert y_pred.shape == y_test_shape
+    assert y_std.shape == y_test_shape
+    assert y_cov.shape == (n_samples_test,) + y_test_shape
+
+
+@pytest.mark.parametrize("normalize_y", [True, False])
+@pytest.mark.parametrize("n_targets", [None, 1, 10])
+def test_sample_y_shapes(normalize_y, n_targets):
+    """Check the shapes of y_samples in single-output (n_targets=0) and
+    multi-output settings, including the edge case when n_targets=1, where the
+    sklearn convention is to squeeze the predictions.
+
+    Non-regression test for:
+    https://github.com/scikit-learn/scikit-learn/issues/22175
+    """
+    rng = np.random.RandomState(1234)
+
+    n_features, n_samples_train = 6, 9
+    # Number of spatial locations to predict at
+    n_samples_X_test = 7
+    # Number of sample predictions per test point
+    n_samples_y_test = 5
+
+    y_train_shape = (n_samples_train,)
+    if n_targets is not None:
+        y_train_shape = y_train_shape + (n_targets,)
+
+    # By convention single-output data is squeezed upon prediction
+    if n_targets is not None and n_targets > 1:
+        y_test_shape = (n_samples_X_test, n_targets, n_samples_y_test)
+    else:
+        y_test_shape = (n_samples_X_test, n_samples_y_test)
+
+    X_train = rng.randn(n_samples_train, n_features)
+    X_test = rng.randn(n_samples_X_test, n_features)
+    y_train = rng.randn(*y_train_shape)
+
+    model = GaussianProcessRegressor(normalize_y=normalize_y)
+
+    # FIXME: before fitting, the estimator does not have information regarding
+    # the number of targets and default to 1. This is inconsistent with the shape
+    # provided after `fit`. This assert should be made once the following issue
+    # is fixed:
+    # https://github.com/scikit-learn/scikit-learn/issues/22430
+    # y_samples = model.sample_y(X_test, n_samples=n_samples_y_test)
+    # assert y_samples.shape == y_test_shape
+
+    model.fit(X_train, y_train)
+
+    y_samples = model.sample_y(X_test, n_samples=n_samples_y_test)
+    assert y_samples.shape == y_test_shape
+
+
+class CustomKernel(C):
+    """
+    A custom kernel that has a diag method that returns the first column of the
+    input matrix X. This is a helper for the test to check that the input
+    matrix X is not mutated.
+    """
+
+    def diag(self, X):
+        return X[:, 0]
+
+
+def test_gpr_predict_input_not_modified():
+    """
+    Check that the input X is not modified by the predict method of the
+    GaussianProcessRegressor when setting return_std=True.
+
+    Non-regression test for:
+    https://github.com/scikit-learn/scikit-learn/issues/24340
+    """
+    gpr = GaussianProcessRegressor(kernel=CustomKernel()).fit(X, y)
+
+    X2_copy = np.copy(X2)
+    _, _ = gpr.predict(X2, return_std=True)
+
+    assert_allclose(X2, X2_copy)

mplug_owl2/lib/python3.10/site-packages/sklearn/gaussian_process/tests/test_kernels.py

@@ -0,0 +1,390 @@
+"""Testing for kernels for Gaussian processes."""
+
+# Author: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
+# License: BSD 3 clause
+
+import pytest
+import numpy as np
+from inspect import signature
+
+from sklearn.gaussian_process.kernels import _approx_fprime
+
+from sklearn.metrics.pairwise import (
+    PAIRWISE_KERNEL_FUNCTIONS,
+    euclidean_distances,
+    pairwise_kernels,
+)
+from sklearn.gaussian_process.kernels import (
+    RBF,
+    Matern,
+    RationalQuadratic,
+    ExpSineSquared,
+    DotProduct,
+    ConstantKernel,
+    WhiteKernel,
+    PairwiseKernel,
+    KernelOperator,
+    Exponentiation,
+    CompoundKernel,
+)
+from sklearn.base import clone
+
+from sklearn.utils._testing import (
+    assert_almost_equal,
+    assert_array_equal,
+    assert_array_almost_equal,
+    assert_allclose,
+)
+
+
+X = np.random.RandomState(0).normal(0, 1, (5, 2))
+Y = np.random.RandomState(0).normal(0, 1, (6, 2))
+
+kernel_rbf_plus_white = RBF(length_scale=2.0) + WhiteKernel(noise_level=3.0)
+kernels = [
+    RBF(length_scale=2.0),
+    RBF(length_scale_bounds=(0.5, 2.0)),
+    ConstantKernel(constant_value=10.0),
+    2.0 * RBF(length_scale=0.33, length_scale_bounds="fixed"),
+    2.0 * RBF(length_scale=0.5),
+    kernel_rbf_plus_white,
+    2.0 * RBF(length_scale=[0.5, 2.0]),
+    2.0 * Matern(length_scale=0.33, length_scale_bounds="fixed"),
+    2.0 * Matern(length_scale=0.5, nu=0.5),
+    2.0 * Matern(length_scale=1.5, nu=1.5),
+    2.0 * Matern(length_scale=2.5, nu=2.5),
+    2.0 * Matern(length_scale=[0.5, 2.0], nu=0.5),
+    3.0 * Matern(length_scale=[2.0, 0.5], nu=1.5),
+    4.0 * Matern(length_scale=[0.5, 0.5], nu=2.5),
+    RationalQuadratic(length_scale=0.5, alpha=1.5),
+    ExpSineSquared(length_scale=0.5, periodicity=1.5),
+    DotProduct(sigma_0=2.0),
+    DotProduct(sigma_0=2.0) ** 2,
+    RBF(length_scale=[2.0]),
+    Matern(length_scale=[2.0]),
+]
+for metric in PAIRWISE_KERNEL_FUNCTIONS:
+    if metric in ["additive_chi2", "chi2"]:
+        continue
+    kernels.append(PairwiseKernel(gamma=1.0, metric=metric))
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_kernel_gradient(kernel):
+    # Compare analytic and numeric gradient of kernels.
+    K, K_gradient = kernel(X, eval_gradient=True)
+
+    assert K_gradient.shape[0] == X.shape[0]
+    assert K_gradient.shape[1] == X.shape[0]
+    assert K_gradient.shape[2] == kernel.theta.shape[0]
+
+    def eval_kernel_for_theta(theta):
+        kernel_clone = kernel.clone_with_theta(theta)
+        K = kernel_clone(X, eval_gradient=False)
+        return K
+
+    K_gradient_approx = _approx_fprime(kernel.theta, eval_kernel_for_theta, 1e-10)
+
+    assert_almost_equal(K_gradient, K_gradient_approx, 4)
+
+
+@pytest.mark.parametrize(
+    "kernel",
+    [
+        kernel
+        for kernel in kernels
+        # skip non-basic kernels
+        if not (isinstance(kernel, (KernelOperator, Exponentiation)))
+    ],
+)
+def test_kernel_theta(kernel):
+    # Check that parameter vector theta of kernel is set correctly.
+    theta = kernel.theta
+    _, K_gradient = kernel(X, eval_gradient=True)
+
+    # Determine kernel parameters that contribute to theta
+    init_sign = signature(kernel.__class__.__init__).parameters.values()
+    args = [p.name for p in init_sign if p.name != "self"]
+    theta_vars = map(
+        lambda s: s[0 : -len("_bounds")], filter(lambda s: s.endswith("_bounds"), args)
+    )
+    assert set(hyperparameter.name for hyperparameter in kernel.hyperparameters) == set(
+        theta_vars
+    )
+
+    # Check that values returned in theta are consistent with
+    # hyperparameter values (being their logarithms)
+    for i, hyperparameter in enumerate(kernel.hyperparameters):
+        assert theta[i] == np.log(getattr(kernel, hyperparameter.name))
+
+    # Fixed kernel parameters must be excluded from theta and gradient.
+    for i, hyperparameter in enumerate(kernel.hyperparameters):
+        # create copy with certain hyperparameter fixed
+        params = kernel.get_params()
+        params[hyperparameter.name + "_bounds"] = "fixed"
+        kernel_class = kernel.__class__
+        new_kernel = kernel_class(**params)
+        # Check that theta and K_gradient are identical with the fixed
+        # dimension left out
+        _, K_gradient_new = new_kernel(X, eval_gradient=True)
+        assert theta.shape[0] == new_kernel.theta.shape[0] + 1
+        assert K_gradient.shape[2] == K_gradient_new.shape[2] + 1
+        if i > 0:
+            assert theta[:i] == new_kernel.theta[:i]
+            assert_array_equal(K_gradient[..., :i], K_gradient_new[..., :i])
+        if i + 1 < len(kernel.hyperparameters):
+            assert theta[i + 1 :] == new_kernel.theta[i:]
+            assert_array_equal(K_gradient[..., i + 1 :], K_gradient_new[..., i:])
+
+    # Check that values of theta are modified correctly
+    for i, hyperparameter in enumerate(kernel.hyperparameters):
+        theta[i] = np.log(42)
+        kernel.theta = theta
+        assert_almost_equal(getattr(kernel, hyperparameter.name), 42)
+
+        setattr(kernel, hyperparameter.name, 43)
+        assert_almost_equal(kernel.theta[i], np.log(43))
+
+
+@pytest.mark.parametrize(
+    "kernel",
+    [
+        kernel
+        for kernel in kernels
+        # Identity is not satisfied on diagonal
+        if kernel != kernel_rbf_plus_white
+    ],
+)
+def test_auto_vs_cross(kernel):
+    # Auto-correlation and cross-correlation should be consistent.
+    K_auto = kernel(X)
+    K_cross = kernel(X, X)
+    assert_almost_equal(K_auto, K_cross, 5)
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_kernel_diag(kernel):
+    # Test that diag method of kernel returns consistent results.
+    K_call_diag = np.diag(kernel(X))
+    K_diag = kernel.diag(X)
+    assert_almost_equal(K_call_diag, K_diag, 5)
+
+
+def test_kernel_operator_commutative():
+    # Adding kernels and multiplying kernels should be commutative.
+    # Check addition
+    assert_almost_equal((RBF(2.0) + 1.0)(X), (1.0 + RBF(2.0))(X))
+
+    # Check multiplication
+    assert_almost_equal((3.0 * RBF(2.0))(X), (RBF(2.0) * 3.0)(X))
+
+
+def test_kernel_anisotropic():
+    # Anisotropic kernel should be consistent with isotropic kernels.
+    kernel = 3.0 * RBF([0.5, 2.0])
+
+    K = kernel(X)
+    X1 = np.array(X)
+    X1[:, 0] *= 4
+    K1 = 3.0 * RBF(2.0)(X1)
+    assert_almost_equal(K, K1)
+
+    X2 = np.array(X)
+    X2[:, 1] /= 4
+    K2 = 3.0 * RBF(0.5)(X2)
+    assert_almost_equal(K, K2)
+
+    # Check getting and setting via theta
+    kernel.theta = kernel.theta + np.log(2)
+    assert_array_equal(kernel.theta, np.log([6.0, 1.0, 4.0]))
+    assert_array_equal(kernel.k2.length_scale, [1.0, 4.0])
+
+
+@pytest.mark.parametrize(
+    "kernel", [kernel for kernel in kernels if kernel.is_stationary()]
+)
+def test_kernel_stationary(kernel):
+    # Test stationarity of kernels.
+    K = kernel(X, X + 1)
+    assert_almost_equal(K[0, 0], np.diag(K))
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_kernel_input_type(kernel):
+    # Test whether kernels is for vectors or structured data
+    if isinstance(kernel, Exponentiation):
+        assert kernel.requires_vector_input == kernel.kernel.requires_vector_input
+    if isinstance(kernel, KernelOperator):
+        assert kernel.requires_vector_input == (
+            kernel.k1.requires_vector_input or kernel.k2.requires_vector_input
+        )
+
+
+def test_compound_kernel_input_type():
+    kernel = CompoundKernel([WhiteKernel(noise_level=3.0)])
+    assert not kernel.requires_vector_input
+
+    kernel = CompoundKernel([WhiteKernel(noise_level=3.0), RBF(length_scale=2.0)])
+    assert kernel.requires_vector_input
+
+
+def check_hyperparameters_equal(kernel1, kernel2):
+    # Check that hyperparameters of two kernels are equal
+    for attr in set(dir(kernel1) + dir(kernel2)):
+        if attr.startswith("hyperparameter_"):
+            attr_value1 = getattr(kernel1, attr)
+            attr_value2 = getattr(kernel2, attr)
+            assert attr_value1 == attr_value2
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_kernel_clone(kernel):
+    # Test that sklearn's clone works correctly on kernels.
+    kernel_cloned = clone(kernel)
+
+    # XXX: Should this be fixed?
+    # This differs from the sklearn's estimators equality check.
+    assert kernel == kernel_cloned
+    assert id(kernel) != id(kernel_cloned)
+
+    # Check that all constructor parameters are equal.
+    assert kernel.get_params() == kernel_cloned.get_params()
+
+    # Check that all hyperparameters are equal.
+    check_hyperparameters_equal(kernel, kernel_cloned)
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_kernel_clone_after_set_params(kernel):
+    # This test is to verify that using set_params does not
+    # break clone on kernels.
+    # This used to break because in kernels such as the RBF, non-trivial
+    # logic that modified the length scale used to be in the constructor
+    # See https://github.com/scikit-learn/scikit-learn/issues/6961
+    # for more details.
+    bounds = (1e-5, 1e5)
+    kernel_cloned = clone(kernel)
+    params = kernel.get_params()
+    # RationalQuadratic kernel is isotropic.
+    isotropic_kernels = (ExpSineSquared, RationalQuadratic)
+    if "length_scale" in params and not isinstance(kernel, isotropic_kernels):
+        length_scale = params["length_scale"]
+        if np.iterable(length_scale):
+            # XXX unreached code as of v0.22
+            params["length_scale"] = length_scale[0]
+            params["length_scale_bounds"] = bounds
+        else:
+            params["length_scale"] = [length_scale] * 2
+            params["length_scale_bounds"] = bounds * 2
+        kernel_cloned.set_params(**params)
+        kernel_cloned_clone = clone(kernel_cloned)
+        assert kernel_cloned_clone.get_params() == kernel_cloned.get_params()
+        assert id(kernel_cloned_clone) != id(kernel_cloned)
+        check_hyperparameters_equal(kernel_cloned, kernel_cloned_clone)
+
+
+def test_matern_kernel():
+    # Test consistency of Matern kernel for special values of nu.
+    K = Matern(nu=1.5, length_scale=1.0)(X)
+    # the diagonal elements of a matern kernel are 1
+    assert_array_almost_equal(np.diag(K), np.ones(X.shape[0]))
+    # matern kernel for coef0==0.5 is equal to absolute exponential kernel
+    K_absexp = np.exp(-euclidean_distances(X, X, squared=False))
+    K = Matern(nu=0.5, length_scale=1.0)(X)
+    assert_array_almost_equal(K, K_absexp)
+    # matern kernel with coef0==inf is equal to RBF kernel
+    K_rbf = RBF(length_scale=1.0)(X)
+    K = Matern(nu=np.inf, length_scale=1.0)(X)
+    assert_array_almost_equal(K, K_rbf)
+    assert_allclose(K, K_rbf)
+    # test that special cases of matern kernel (coef0 in [0.5, 1.5, 2.5])
+    # result in nearly identical results as the general case for coef0 in
+    # [0.5 + tiny, 1.5 + tiny, 2.5 + tiny]
+    tiny = 1e-10
+    for nu in [0.5, 1.5, 2.5]:
+        K1 = Matern(nu=nu, length_scale=1.0)(X)
+        K2 = Matern(nu=nu + tiny, length_scale=1.0)(X)
+        assert_array_almost_equal(K1, K2)
+    # test that coef0==large is close to RBF
+    large = 100
+    K1 = Matern(nu=large, length_scale=1.0)(X)
+    K2 = RBF(length_scale=1.0)(X)
+    assert_array_almost_equal(K1, K2, decimal=2)
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_kernel_versus_pairwise(kernel):
+    # Check that GP kernels can also be used as pairwise kernels.
+
+    # Test auto-kernel
+    if kernel != kernel_rbf_plus_white:
+        # For WhiteKernel: k(X) != k(X,X). This is assumed by
+        # pairwise_kernels
+        K1 = kernel(X)
+        K2 = pairwise_kernels(X, metric=kernel)
+        assert_array_almost_equal(K1, K2)
+
+    # Test cross-kernel
+    K1 = kernel(X, Y)
+    K2 = pairwise_kernels(X, Y, metric=kernel)
+    assert_array_almost_equal(K1, K2)
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_set_get_params(kernel):
+    # Check that set_params()/get_params() is consistent with kernel.theta.
+
+    # Test get_params()
+    index = 0
+    params = kernel.get_params()
+    for hyperparameter in kernel.hyperparameters:
+        if isinstance("string", type(hyperparameter.bounds)):
+            if hyperparameter.bounds == "fixed":
+                continue
+        size = hyperparameter.n_elements
+        if size > 1:  # anisotropic kernels
+            assert_almost_equal(
+                np.exp(kernel.theta[index : index + size]), params[hyperparameter.name]
+            )
+            index += size
+        else:
+            assert_almost_equal(
+                np.exp(kernel.theta[index]), params[hyperparameter.name]
+            )
+            index += 1
+    # Test set_params()
+    index = 0
+    value = 10  # arbitrary value
+    for hyperparameter in kernel.hyperparameters:
+        if isinstance("string", type(hyperparameter.bounds)):
+            if hyperparameter.bounds == "fixed":
+                continue
+        size = hyperparameter.n_elements
+        if size > 1:  # anisotropic kernels
+            kernel.set_params(**{hyperparameter.name: [value] * size})
+            assert_almost_equal(
+                np.exp(kernel.theta[index : index + size]), [value] * size
+            )
+            index += size
+        else:
+            kernel.set_params(**{hyperparameter.name: value})
+            assert_almost_equal(np.exp(kernel.theta[index]), value)
+            index += 1
+
+
+@pytest.mark.parametrize("kernel", kernels)
+def test_repr_kernels(kernel):
+    # Smoke-test for repr in kernels.
+
+    repr(kernel)
+
+
+def test_rational_quadratic_kernel():
+    kernel = RationalQuadratic(length_scale=[1.0, 1.0])
+    message = (
+        "RationalQuadratic kernel only supports isotropic "
+        "version, please use a single "
+        "scalar for length_scale"
+    )
+    with pytest.raises(AttributeError, match=message):
+        kernel(X)

mplug_owl2/lib/python3.10/site-packages/sklearn/model_selection/__init__.py

@@ -0,0 +1,89 @@
+import typing
+
+from ._split import BaseCrossValidator
+from ._split import BaseShuffleSplit
+from ._split import KFold
+from ._split import GroupKFold
+from ._split import StratifiedKFold
+from ._split import TimeSeriesSplit
+from ._split import LeaveOneGroupOut
+from ._split import LeaveOneOut
+from ._split import LeavePGroupsOut
+from ._split import LeavePOut
+from ._split import RepeatedKFold
+from ._split import RepeatedStratifiedKFold
+from ._split import ShuffleSplit
+from ._split import GroupShuffleSplit
+from ._split import StratifiedShuffleSplit
+from ._split import StratifiedGroupKFold
+from ._split import PredefinedSplit
+from ._split import train_test_split
+from ._split import check_cv
+
+from ._validation import cross_val_score
+from ._validation import cross_val_predict
+from ._validation import cross_validate
+from ._validation import learning_curve
+from ._validation import permutation_test_score
+from ._validation import validation_curve
+
+from ._search import GridSearchCV
+from ._search import RandomizedSearchCV
+from ._search import ParameterGrid
+from ._search import ParameterSampler
+
+from ._plot import LearningCurveDisplay
+
+if typing.TYPE_CHECKING:
+    # Avoid errors in type checkers (e.g. mypy) for experimental estimators.
+    # TODO: remove this check once the estimator is no longer experimental.
+    from ._search_successive_halving import (  # noqa
+        HalvingGridSearchCV,
+        HalvingRandomSearchCV,
+    )
+
+
+__all__ = [
+    "BaseCrossValidator",
+    "BaseShuffleSplit",
+    "GridSearchCV",
+    "TimeSeriesSplit",
+    "KFold",
+    "GroupKFold",
+    "GroupShuffleSplit",
+    "LeaveOneGroupOut",
+    "LeaveOneOut",
+    "LeavePGroupsOut",
+    "LeavePOut",
+    "RepeatedKFold",
+    "RepeatedStratifiedKFold",
+    "ParameterGrid",
+    "ParameterSampler",
+    "PredefinedSplit",
+    "RandomizedSearchCV",
+    "ShuffleSplit",
+    "StratifiedKFold",
+    "StratifiedGroupKFold",
+    "StratifiedShuffleSplit",
+    "check_cv",
+    "cross_val_predict",
+    "cross_val_score",
+    "cross_validate",
+    "learning_curve",
+    "LearningCurveDisplay",
+    "permutation_test_score",
+    "train_test_split",
+    "validation_curve",
+]
+
+
+# TODO: remove this check once the estimator is no longer experimental.
+def __getattr__(name):
+    if name in {"HalvingGridSearchCV", "HalvingRandomSearchCV"}:
+        raise ImportError(
+            f"{name} is experimental and the API might change without any "
+            "deprecation cycle. To use it, you need to explicitly import "
+            "enable_halving_search_cv:\n"
+            "from sklearn.experimental import enable_halving_search_cv"
+        )
+    raise AttributeError(f"module {__name__} has no attribute {name}")