validation.py

"""Utilities for input validation"""

# Authors: Olivier Grisel
#          Gael Varoquaux
#          Andreas Mueller
#          Lars Buitinck
#          Alexandre Gramfort
#          Nicolas Tresegnie
#          Sylvain Marie
# License: BSD 3 clause

from functools import wraps
import warnings
import numbers
import operator

import numpy as np
import scipy.sparse as sp
from inspect import signature, isclass, Parameter

# mypy error: Module 'numpy.core.numeric' has no attribute 'ComplexWarning'
from numpy.core.numeric import ComplexWarning  # type: ignore
import joblib

from contextlib import suppress

from .fixes import _object_dtype_isnan
from .. import get_config as _get_config
from ..exceptions import PositiveSpectrumWarning
from ..exceptions import NotFittedError
from ..exceptions import DataConversionWarning
from ..utils._array_api import get_namespace
from ..utils._array_api import _asarray_with_order
from ._isfinite import cy_isfinite, FiniteStatus

FLOAT_DTYPES = (np.float64, np.float32, np.float16)


# This function is not used anymore at this moment in the code base but we keep it in
# case that we merge a new public function without kwarg only by mistake, which would
# require a deprecation cycle to fix.
def _deprecate_positional_args(func=None, *, version="1.3"):
    """Decorator for methods that issues warnings for positional arguments.

    Using the keyword-only argument syntax in pep 3102, arguments after the
    * will issue a warning when passed as a positional argument.

    Parameters
    ----------
    func : callable, default=None
        Function to check arguments on.
    version : callable, default="1.3"
        The version when positional arguments will result in error.
    """

    def _inner_deprecate_positional_args(f):
        sig = signature(f)
        kwonly_args = []
        all_args = []

        for name, param in sig.parameters.items():
            if param.kind == Parameter.POSITIONAL_OR_KEYWORD:
                all_args.append(name)
            elif param.kind == Parameter.KEYWORD_ONLY:
                kwonly_args.append(name)

        @wraps(f)
        def inner_f(*args, **kwargs):
            extra_args = len(args) - len(all_args)
            if extra_args <= 0:
                return f(*args, **kwargs)

            # extra_args > 0
            args_msg = [
                "{}={}".format(name, arg)
                for name, arg in zip(kwonly_args[:extra_args], args[-extra_args:])
            ]
            args_msg = ", ".join(args_msg)
            warnings.warn(
                f"Pass {args_msg} as keyword args. From version "
                f"{version} passing these as positional arguments "
                "will result in an error",
                FutureWarning,
            )
            kwargs.update(zip(sig.parameters, args))
            return f(**kwargs)

        return inner_f

    if func is not None:
        return _inner_deprecate_positional_args(func)

    return _inner_deprecate_positional_args


def _assert_all_finite(
    X, allow_nan=False, msg_dtype=None, estimator_name=None, input_name=""
):
    """Like assert_all_finite, but only for ndarray."""

    xp, _ = get_namespace(X)

    if _get_config()["assume_finite"]:
        return

    X = xp.asarray(X)

    # for object dtype data, we only check for NaNs (GH-13254)
    if X.dtype == np.dtype("object") and not allow_nan:
        if _object_dtype_isnan(X).any():
            raise ValueError("Input contains NaN")

    # We need only consider float arrays, hence can early return for all else.
    if X.dtype.kind not in "fc":
        return

    # First try an O(n) time, O(1) space solution for the common case that
    # everything is finite; fall back to O(n) space `np.isinf/isnan` or custom
    # Cython implementation to prevent false positives and provide a detailed
    # error message.
    with np.errstate(over="ignore"):
        first_pass_isfinite = xp.isfinite(xp.sum(X))
    if first_pass_isfinite:
        return
    # Cython implementation doesn't support FP16 or complex numbers
    use_cython = (
        xp is np and X.data.contiguous and X.dtype.type in {np.float32, np.float64}
    )
    if use_cython:
        out = cy_isfinite(X.reshape(-1), allow_nan=allow_nan)
        has_nan_error = False if allow_nan else out == FiniteStatus.has_nan
        has_inf = out == FiniteStatus.has_infinite
    else:
        has_inf = np.isinf(X).any()
        has_nan_error = False if allow_nan else xp.isnan(X).any()
    if has_inf or has_nan_error:
        if has_nan_error:
            type_err = "NaN"
        else:
            msg_dtype = msg_dtype if msg_dtype is not None else X.dtype
            type_err = f"infinity or a value too large for {msg_dtype!r}"
        padded_input_name = input_name + " " if input_name else ""
        msg_err = f"Input {padded_input_name}contains {type_err}."
        if estimator_name and input_name == "X" and has_nan_error:
            # Improve the error message on how to handle missing values in
            # scikit-learn.
            msg_err += (
                f"\n{estimator_name} does not accept missing values"
                " encoded as NaN natively. For supervised learning, you might want"
                " to consider sklearn.ensemble.HistGradientBoostingClassifier and"
                " Regressor which accept missing values encoded as NaNs natively."
                " Alternatively, it is possible to preprocess the data, for"
                " instance by using an imputer transformer in a pipeline or drop"
                " samples with missing values. See"
                " https://scikit-learn.org/stable/modules/impute.html"
                " You can find a list of all estimators that handle NaN values"
                " at the following page:"
                " https://scikit-learn.org/stable/modules/impute.html"
                "#estimators-that-handle-nan-values"
            )
        raise ValueError(msg_err)


def assert_all_finite(
    X,
    *,
    allow_nan=False,
    estimator_name=None,
    input_name="",
):
    """Throw a ValueError if X contains NaN or infinity.

    Parameters
    ----------
    X : {ndarray, sparse matrix}
        The input data.

    allow_nan : bool, default=False
        If True, do not throw error when `X` contains NaN.

    estimator_name : str, default=None
        The estimator name, used to construct the error message.

    input_name : str, default=""
        The data name used to construct the error message. In particular
        if `input_name` is "X" and the data has NaN values and
        allow_nan is False, the error message will link to the imputer
        documentation.
    """
    _assert_all_finite(
        X.data if sp.issparse(X) else X,
        allow_nan=allow_nan,
        estimator_name=estimator_name,
        input_name=input_name,
    )


def as_float_array(X, *, copy=True, force_all_finite=True):
    """Convert an array-like to an array of floats.

    The new dtype will be np.float32 or np.float64, depending on the original
    type. The function can create a copy or modify the argument depending
    on the argument copy.

    Parameters
    ----------
    X : {array-like, sparse matrix}
        The input data.

    copy : bool, default=True
        If True, a copy of X will be created. If False, a copy may still be
        returned if X's dtype is not a floating point type.

    force_all_finite : bool or 'allow-nan', default=True
        Whether to raise an error on np.inf, np.nan, pd.NA in X. The
        possibilities are:

        - True: Force all values of X to be finite.
        - False: accepts np.inf, np.nan, pd.NA in X.
        - 'allow-nan': accepts only np.nan and pd.NA values in X. Values cannot
          be infinite.

        .. versionadded:: 0.20
           ``force_all_finite`` accepts the string ``'allow-nan'``.

        .. versionchanged:: 0.23
           Accepts `pd.NA` and converts it into `np.nan`

    Returns
    -------
    XT : {ndarray, sparse matrix}
        An array of type float.
    """
    if isinstance(X, np.matrix) or (
        not isinstance(X, np.ndarray) and not sp.issparse(X)
    ):
        return check_array(
            X,
            accept_sparse=["csr", "csc", "coo"],
            dtype=np.float64,
            copy=copy,
            force_all_finite=force_all_finite,
            ensure_2d=False,
        )
    elif sp.issparse(X) and X.dtype in [np.float32, np.float64]:
        return X.copy() if copy else X
    elif X.dtype in [np.float32, np.float64]:  # is numpy array
        return X.copy("F" if X.flags["F_CONTIGUOUS"] else "C") if copy else X
    else:
        if X.dtype.kind in "uib" and X.dtype.itemsize <= 4:
            return_dtype = np.float32
        else:
            return_dtype = np.float64
        return X.astype(return_dtype)


def _is_arraylike(x):
    """Returns whether the input is array-like."""
    return hasattr(x, "__len__") or hasattr(x, "shape") or hasattr(x, "__array__")


def _is_arraylike_not_scalar(array):
    """Return True if array is array-like and not a scalar"""
    return _is_arraylike(array) and not np.isscalar(array)


def _num_features(X):
    """Return the number of features in an array-like X.

    This helper function tries hard to avoid to materialize an array version
    of X unless necessary. For instance, if X is a list of lists,
    this function will return the length of the first element, assuming
    that subsequent elements are all lists of the same length without
    checking.
    Parameters
    ----------
    X : array-like
        array-like to get the number of features.

    Returns
    -------
    features : int
        Number of features
    """
    type_ = type(X)
    if type_.__module__ == "builtins":
        type_name = type_.__qualname__
    else:
        type_name = f"{type_.__module__}.{type_.__qualname__}"
    message = f"Unable to find the number of features from X of type {type_name}"
    if not hasattr(X, "__len__") and not hasattr(X, "shape"):
        if not hasattr(X, "__array__"):
            raise TypeError(message)
        # Only convert X to a numpy array if there is no cheaper, heuristic
        # option.
        X = np.asarray(X)

    if hasattr(X, "shape"):
        if not hasattr(X.shape, "__len__") or len(X.shape) <= 1:
            message += f" with shape {X.shape}"
            raise TypeError(message)
        return X.shape[1]

    first_sample = X[0]

    # Do not consider an array-like of strings or dicts to be a 2D array
    if isinstance(first_sample, (str, bytes, dict)):
        message += f" where the samples are of type {type(first_sample).__qualname__}"
        raise TypeError(message)

    try:
        # If X is a list of lists, for instance, we assume that all nested
        # lists have the same length without checking or converting to
        # a numpy array to keep this function call as cheap as possible.
        return len(first_sample)
    except Exception as err:
        raise TypeError(message) from err


def _num_samples(x):
    """Return number of samples in array-like x."""
    message = "Expected sequence or array-like, got %s" % type(x)
    if hasattr(x, "fit") and callable(x.fit):
        # Don't get num_samples from an ensembles length!
        raise TypeError(message)

    if not hasattr(x, "__len__") and not hasattr(x, "shape"):
        if hasattr(x, "__array__"):
            x = np.asarray(x)
        else:
            raise TypeError(message)

    if hasattr(x, "shape") and x.shape is not None:
        if len(x.shape) == 0:
            raise TypeError(
                "Singleton array %r cannot be considered a valid collection." % x
            )
        # Check that shape is returning an integer or default to len
        # Dask dataframes may not return numeric shape[0] value
        if isinstance(x.shape[0], numbers.Integral):
            return x.shape[0]

    try:
        return len(x)
    except TypeError as type_error:
        raise TypeError(message) from type_error


def check_memory(memory):
    """Check that ``memory`` is joblib.Memory-like.

    joblib.Memory-like means that ``memory`` can be converted into a
    joblib.Memory instance (typically a str denoting the ``location``)
    or has the same interface (has a ``cache`` method).

    Parameters
    ----------
    memory : None, str or object with the joblib.Memory interface
        - If string, the location where to create the `joblib.Memory` interface.
        - If None, no caching is done and the Memory object is completely transparent.

    Returns
    -------
    memory : object with the joblib.Memory interface
        A correct joblib.Memory object.

    Raises
    ------
    ValueError
        If ``memory`` is not joblib.Memory-like.
    """
    if memory is None or isinstance(memory, str):
        memory = joblib.Memory(location=memory, verbose=0)
    elif not hasattr(memory, "cache"):
        raise ValueError(
            "'memory' should be None, a string or have the same"
            " interface as joblib.Memory."
            " Got memory='{}' instead.".format(memory)
        )
    return memory


def check_consistent_length(*arrays):
    """Check that all arrays have consistent first dimensions.

    Checks whether all objects in arrays have the same shape or length.

    Parameters
    ----------
    *arrays : list or tuple of input objects.
        Objects that will be checked for consistent length.
    """

    lengths = [_num_samples(X) for X in arrays if X is not None]
    uniques = np.unique(lengths)
    if len(uniques) > 1:
        raise ValueError(
            "Found input variables with inconsistent numbers of samples: %r"
            % [int(l) for l in lengths]
        )


def _make_indexable(iterable):
    """Ensure iterable supports indexing or convert to an indexable variant.

    Convert sparse matrices to csr and other non-indexable iterable to arrays.
    Let `None` and indexable objects (e.g. pandas dataframes) pass unchanged.

    Parameters
    ----------
    iterable : {list, dataframe, ndarray, sparse matrix} or None
        Object to be converted to an indexable iterable.
    """
    if sp.issparse(iterable):
        return iterable.tocsr()
    elif hasattr(iterable, "__getitem__") or hasattr(iterable, "iloc"):
        return iterable
    elif iterable is None:
        return iterable
    return np.array(iterable)


def indexable(*iterables):
    """Make arrays indexable for cross-validation.

    Checks consistent length, passes through None, and ensures that everything
    can be indexed by converting sparse matrices to csr and converting
    non-interable objects to arrays.

    Parameters
    ----------
    *iterables : {lists, dataframes, ndarrays, sparse matrices}
        List of objects to ensure sliceability.

    Returns
    -------
    result : list of {ndarray, sparse matrix, dataframe} or None
        Returns a list containing indexable arrays (i.e. NumPy array,
        sparse matrix, or dataframe) or `None`.
    """

    result = [_make_indexable(X) for X in iterables]
    check_consistent_length(*result)
    return result


def _ensure_sparse_format(
    spmatrix,
    accept_sparse,
    dtype,
    copy,
    force_all_finite,
    accept_large_sparse,
    estimator_name=None,
    input_name="",
):
    """Convert a sparse matrix to a given format.

    Checks the sparse format of spmatrix and converts if necessary.

    Parameters
    ----------
    spmatrix : sparse matrix
        Input to validate and convert.

    accept_sparse : str, bool or list/tuple of str
        String[s] representing allowed sparse matrix formats ('csc',
        'csr', 'coo', 'dok', 'bsr', 'lil', 'dia'). If the input is sparse but
        not in the allowed format, it will be converted to the first listed
        format. True allows the input to be any format. False means
        that a sparse matrix input will raise an error.

    dtype : str, type or None
        Data type of result. If None, the dtype of the input is preserved.

    copy : bool
        Whether a forced copy will be triggered. If copy=False, a copy might
        be triggered by a conversion.

    force_all_finite : bool or 'allow-nan'
        Whether to raise an error on np.inf, np.nan, pd.NA in X. The
        possibilities are:

        - True: Force all values of X to be finite.
        - False: accepts np.inf, np.nan, pd.NA in X.
        - 'allow-nan': accepts only np.nan and pd.NA values in X. Values cannot
          be infinite.

        .. versionadded:: 0.20
           ``force_all_finite`` accepts the string ``'allow-nan'``.

        .. versionchanged:: 0.23
           Accepts `pd.NA` and converts it into `np.nan`


    estimator_name : str, default=None
        The estimator name, used to construct the error message.

    input_name : str, default=""
        The data name used to construct the error message. In particular
        if `input_name` is "X" and the data has NaN values and
        allow_nan is False, the error message will link to the imputer
        documentation.

    Returns
    -------
    spmatrix_converted : sparse matrix.
        Matrix that is ensured to have an allowed type.
    """
    if dtype is None:
        dtype = spmatrix.dtype

    changed_format = False

    if isinstance(accept_sparse, str):
        accept_sparse = [accept_sparse]

    # Indices dtype validation
    _check_large_sparse(spmatrix, accept_large_sparse)

    if accept_sparse is False:
        raise TypeError(
            "A sparse matrix was passed, but dense "
            "data is required. Use X.toarray() to "
            "convert to a dense numpy array."
        )
    elif isinstance(accept_sparse, (list, tuple)):
        if len(accept_sparse) == 0:
            raise ValueError(
                "When providing 'accept_sparse' "
                "as a tuple or list, it must contain at "
                "least one string value."
            )
        # ensure correct sparse format
        if spmatrix.format not in accept_sparse:
            # create new with correct sparse
            spmatrix = spmatrix.asformat(accept_sparse[0])
            changed_format = True
    elif accept_sparse is not True:
        # any other type
        raise ValueError(
            "Parameter 'accept_sparse' should be a string, "
            "boolean or list of strings. You provided "
            "'accept_sparse={}'.".format(accept_sparse)
        )

    if dtype != spmatrix.dtype:
        # convert dtype
        spmatrix = spmatrix.astype(dtype)
    elif copy and not changed_format:
        # force copy
        spmatrix = spmatrix.copy()

    if force_all_finite:
        if not hasattr(spmatrix, "data"):
            warnings.warn(
                "Can't check %s sparse matrix for nan or inf." % spmatrix.format,
                stacklevel=2,
            )
        else:
            _assert_all_finite(
                spmatrix.data,
                allow_nan=force_all_finite == "allow-nan",
                estimator_name=estimator_name,
                input_name=input_name,
            )

    return spmatrix


def _ensure_no_complex_data(array):
    if (
        hasattr(array, "dtype")
        and array.dtype is not None
        and hasattr(array.dtype, "kind")
        and array.dtype.kind == "c"
    ):
        raise ValueError("Complex data not supported\n{}\n".format(array))


def _check_estimator_name(estimator):
    if estimator is not None:
        if isinstance(estimator, str):
            return estimator
        else:
            return estimator.__class__.__name__
    return None


def _pandas_dtype_needs_early_conversion(pd_dtype):
    """Return True if pandas extension pd_dtype need to be converted early."""
    # Check these early for pandas versions without extension dtypes
    from pandas.api.types import (
        is_bool_dtype,
        is_sparse,
        is_float_dtype,
        is_integer_dtype,
    )

    if is_bool_dtype(pd_dtype):
        # bool and extension booleans need early converstion because __array__
        # converts mixed dtype dataframes into object dtypes
        return True

    if is_sparse(pd_dtype):
        # Sparse arrays will be converted later in `check_array`
        return False

    try:
        from pandas.api.types import is_extension_array_dtype
    except ImportError:
        return False

    if is_sparse(pd_dtype) or not is_extension_array_dtype(pd_dtype):
        # Sparse arrays will be converted later in `check_array`
        # Only handle extension arrays for integer and floats
        return False
    elif is_float_dtype(pd_dtype):
        # Float ndarrays can normally support nans. They need to be converted
        # first to map pd.NA to np.nan
        return True
    elif is_integer_dtype(pd_dtype):
        # XXX: Warn when converting from a high integer to a float
        return True

    return False


def check_array(
    array,
    accept_sparse=False,
    *,
    accept_large_sparse=True,
    dtype="numeric",
    order=None,
    copy=False,
    force_all_finite=True,
    ensure_2d=True,
    allow_nd=False,
    ensure_min_samples=1,
    ensure_min_features=1,
    estimator=None,
    input_name="",
):

    """Input validation on an array, list, sparse matrix or similar.

    By default, the input is checked to be a non-empty 2D array containing
    only finite values. If the dtype of the array is object, attempt
    converting to float, raising on failure.

    Parameters
    ----------
    array : object
        Input object to check / convert.

    accept_sparse : str, bool or list/tuple of str, default=False
        String[s] representing allowed sparse matrix formats, such as 'csc',
        'csr', etc. If the input is sparse but not in the allowed format,
        it will be converted to the first listed format. True allows the input
        to be any format. False means that a sparse matrix input will
        raise an error.

    accept_large_sparse : bool, default=True
        If a CSR, CSC, COO or BSR sparse matrix is supplied and accepted by
        accept_sparse, accept_large_sparse=False will cause it to be accepted
        only if its indices are stored with a 32-bit dtype.

        .. versionadded:: 0.20

    dtype : 'numeric', type, list of type or None, default='numeric'
        Data type of result. If None, the dtype of the input is preserved.
        If "numeric", dtype is preserved unless array.dtype is object.
        If dtype is a list of types, conversion on the first type is only
        performed if the dtype of the input is not in the list.

    order : {'F', 'C'} or None, default=None
        Whether an array will be forced to be fortran or c-style.
        When order is None (default), then if copy=False, nothing is ensured
        about the memory layout of the output array; otherwise (copy=True)
        the memory layout of the returned array is kept as close as possible
        to the original array.

    copy : bool, default=False
        Whether a forced copy will be triggered. If copy=False, a copy might
        be triggered by a conversion.

    force_all_finite : bool or 'allow-nan', default=True
        Whether to raise an error on np.inf, np.nan, pd.NA in array. The
        possibilities are:

        - True: Force all values of array to be finite.
        - False: accepts np.inf, np.nan, pd.NA in array.
        - 'allow-nan': accepts only np.nan and pd.NA values in array. Values
          cannot be infinite.

        .. versionadded:: 0.20
           ``force_all_finite`` accepts the string ``'allow-nan'``.

        .. versionchanged:: 0.23
           Accepts `pd.NA` and converts it into `np.nan`

    ensure_2d : bool, default=True
        Whether to raise a value error if array is not 2D.

    allow_nd : bool, default=False
        Whether to allow array.ndim > 2.

    ensure_min_samples : int, default=1
        Make sure that the array has a minimum number of samples in its first
        axis (rows for a 2D array). Setting to 0 disables this check.

    ensure_min_features : int, default=1
        Make sure that the 2D array has some minimum number of features
        (columns). The default value of 1 rejects empty datasets.
        This check is only enforced when the input data has effectively 2
        dimensions or is originally 1D and ``ensure_2d`` is True. Setting to 0
        disables this check.

    estimator : str or estimator instance, default=None
        If passed, include the name of the estimator in warning messages.

    input_name : str, default=""
        The data name used to construct the error message. In particular
        if `input_name` is "X" and the data has NaN values and
        allow_nan is False, the error message will link to the imputer
        documentation.

        .. versionadded:: 1.1.0

    Returns
    -------
    array_converted : object
        The converted and validated array.
    """
    if isinstance(array, np.matrix):
        raise TypeError(
            "np.matrix is not supported. Please convert to a numpy array with "
            "np.asarray. For more information see: "
            "https://numpy.org/doc/stable/reference/generated/numpy.matrix.html"
        )

    xp, is_array_api = get_namespace(array)

    # store reference to original array to check if copy is needed when
    # function returns
    array_orig = array

    # store whether originally we wanted numeric dtype
    dtype_numeric = isinstance(dtype, str) and dtype == "numeric"

    dtype_orig = getattr(array, "dtype", None)
    if not hasattr(dtype_orig, "kind"):
        # not a data type (e.g. a column named dtype in a pandas DataFrame)
        dtype_orig = None

    # check if the object contains several dtypes (typically a pandas
    # DataFrame), and store them. If not, store None.
    dtypes_orig = None
    pandas_requires_conversion = False
    if hasattr(array, "dtypes") and hasattr(array.dtypes, "__array__"):
        # throw warning if columns are sparse. If all columns are sparse, then
        # array.sparse exists and sparsity will be preserved (later).
        with suppress(ImportError):
            from pandas.api.types import is_sparse

            if not hasattr(array, "sparse") and array.dtypes.apply(is_sparse).any():
                warnings.warn(
                    "pandas.DataFrame with sparse columns found."
                    "It will be converted to a dense numpy array."
                )

        dtypes_orig = list(array.dtypes)
        pandas_requires_conversion = any(
            _pandas_dtype_needs_early_conversion(i) for i in dtypes_orig
        )
        if all(isinstance(dtype_iter, np.dtype) for dtype_iter in dtypes_orig):
            dtype_orig = np.result_type(*dtypes_orig)

    if dtype_numeric:
        if dtype_orig is not None and dtype_orig.kind == "O":
            # if input is object, convert to float.
            dtype = xp.float64
        else:
            dtype = None

    if isinstance(dtype, (list, tuple)):
        if dtype_orig is not None and dtype_orig in dtype:
            # no dtype conversion required
            dtype = None
        else:
            # dtype conversion required. Let's select the first element of the
            # list of accepted types.
            dtype = dtype[0]

    if pandas_requires_conversion:
        # pandas dataframe requires conversion earlier to handle extension dtypes with
        # nans
        # Use the original dtype for conversion if dtype is None
        new_dtype = dtype_orig if dtype is None else dtype
        array = array.astype(new_dtype)
        # Since we converted here, we do not need to convert again later
        dtype = None

    if force_all_finite not in (True, False, "allow-nan"):
        raise ValueError(
            'force_all_finite should be a bool or "allow-nan". Got {!r} instead'.format(
                force_all_finite
            )
        )

    estimator_name = _check_estimator_name(estimator)
    context = " by %s" % estimator_name if estimator is not None else ""

    # When all dataframe columns are sparse, convert to a sparse array
    if hasattr(array, "sparse") and array.ndim > 1:
        with suppress(ImportError):
            from pandas.api.types import is_sparse

            if array.dtypes.apply(is_sparse).all():
                # DataFrame.sparse only supports `to_coo`
                array = array.sparse.to_coo()
                if array.dtype == np.dtype("object"):
                    unique_dtypes = set([dt.subtype.name for dt in array_orig.dtypes])
                    if len(unique_dtypes) > 1:
                        raise ValueError(
                            "Pandas DataFrame with mixed sparse extension arrays "
                            "generated a sparse matrix with object dtype which "
                            "can not be converted to a scipy sparse matrix."
                            "Sparse extension arrays should all have the same "
                            "numeric type."
                        )

    if sp.issparse(array):
        _ensure_no_complex_data(array)
        array = _ensure_sparse_format(
            array,
            accept_sparse=accept_sparse,
            dtype=dtype,
            copy=copy,
            force_all_finite=force_all_finite,
            accept_large_sparse=accept_large_sparse,
            estimator_name=estimator_name,
            input_name=input_name,
        )
    else:
        # If np.array(..) gives ComplexWarning, then we convert the warning
        # to an error. This is needed because specifying a non complex
        # dtype to the function converts complex to real dtype,
        # thereby passing the test made in the lines following the scope
        # of warnings context manager.
        with warnings.catch_warnings():
            try:
                warnings.simplefilter("error", ComplexWarning)
                if dtype is not None and np.dtype(dtype).kind in "iu":
                    # Conversion float -> int should not contain NaN or
                    # inf (numpy#14412). We cannot use casting='safe' because
                    # then conversion float -> int would be disallowed.
                    array = _asarray_with_order(array, order=order, xp=xp)
                    if array.dtype.kind == "f":
                        _assert_all_finite(
                            array,
                            allow_nan=False,
                            msg_dtype=dtype,
                            estimator_name=estimator_name,
                            input_name=input_name,
                        )
                    array = xp.astype(array, dtype, copy=False)
                else:
                    array = _asarray_with_order(array, order=order, dtype=dtype, xp=xp)
            except ComplexWarning as complex_warning:
                raise ValueError(
                    "Complex data not supported\n{}\n".format(array)
                ) from complex_warning

        # It is possible that the np.array(..) gave no warning. This happens
        # when no dtype conversion happened, for example dtype = None. The
        # result is that np.array(..) produces an array of complex dtype
        # and we need to catch and raise exception for such cases.
        _ensure_no_complex_data(array)

        if ensure_2d:
            # If input is scalar raise error
            if array.ndim == 0:
                raise ValueError(
                    "Expected 2D array, got scalar array instead:\narray={}.\n"
                    "Reshape your data either using array.reshape(-1, 1) if "
                    "your data has a single feature or array.reshape(1, -1) "
                    "if it contains a single sample.".format(array)
                )
            # If input is 1D raise error
            if array.ndim == 1:
                raise ValueError(
                    "Expected 2D array, got 1D array instead:\narray={}.\n"
                    "Reshape your data either using array.reshape(-1, 1) if "
                    "your data has a single feature or array.reshape(1, -1) "
                    "if it contains a single sample.".format(array)
                )

        if dtype_numeric and array.dtype.kind in "USV":
            raise ValueError(
                "dtype='numeric' is not compatible with arrays of bytes/strings."
                "Convert your data to numeric values explicitly instead."
            )
        if not allow_nd and array.ndim >= 3:
            raise ValueError(
                "Found array with dim %d. %s expected <= 2."
                % (array.ndim, estimator_name)
            )

        if force_all_finite:
            _assert_all_finite(
                array,
                input_name=input_name,
                estimator_name=estimator_name,
                allow_nan=force_all_finite == "allow-nan",
            )

    if ensure_min_samples > 0:
        n_samples = _num_samples(array)
        if n_samples < ensure_min_samples:
            raise ValueError(
                "Found array with %d sample(s) (shape=%s) while a"
                " minimum of %d is required%s."
                % (n_samples, array.shape, ensure_min_samples, context)
            )

    if ensure_min_features > 0 and array.ndim == 2:
        n_features = array.shape[1]
        if n_features < ensure_min_features:
            raise ValueError(
                "Found array with %d feature(s) (shape=%s) while"
                " a minimum of %d is required%s."
                % (n_features, array.shape, ensure_min_features, context)
            )

    if copy:
        if xp.__name__ in {"numpy", "numpy.array_api"}:
            # only make a copy if `array` and `array_orig` may share memory`
            if np.may_share_memory(array, array_orig):
                array = _asarray_with_order(
                    array, dtype=dtype, order=order, copy=True, xp=xp
                )
        else:
            # always make a copy for non-numpy arrays
            array = _asarray_with_order(
                array, dtype=dtype, order=order, copy=True, xp=xp
            )

    return array


def _check_large_sparse(X, accept_large_sparse=False):
    """Raise a ValueError if X has 64bit indices and accept_large_sparse=False"""
    if not accept_large_sparse:
        supported_indices = ["int32"]
        if X.getformat() == "coo":
            index_keys = ["col", "row"]
        elif X.getformat() in ["csr", "csc", "bsr"]:
            index_keys = ["indices", "indptr"]
        else:
            return
        for key in index_keys:
            indices_datatype = getattr(X, key).dtype
            if indices_datatype not in supported_indices:
                raise ValueError(
                    "Only sparse matrices with 32-bit integer"
                    " indices are accepted. Got %s indices." % indices_datatype
                )


def check_X_y(
    X,
    y,
    accept_sparse=False,
    *,
    accept_large_sparse=True,
    dtype="numeric",
    order=None,
    copy=False,
    force_all_finite=True,
    ensure_2d=True,
    allow_nd=False,
    multi_output=False,
    ensure_min_samples=1,
    ensure_min_features=1,
    y_numeric=False,
    estimator=None,
):
    """Input validation for standard estimators.

    Checks X and y for consistent length, enforces X to be 2D and y 1D. By
    default, X is checked to be non-empty and containing only finite values.
    Standard input checks are also applied to y, such as checking that y
    does not have np.nan or np.inf targets. For multi-label y, set
    multi_output=True to allow 2D and sparse y. If the dtype of X is
    object, attempt converting to float, raising on failure.

    Parameters
    ----------
    X : {ndarray, list, sparse matrix}
        Input data.

    y : {ndarray, list, sparse matrix}
        Labels.

    accept_sparse : str, bool or list of str, default=False
        String[s] representing allowed sparse matrix formats, such as 'csc',
        'csr', etc. If the input is sparse but not in the allowed format,
        it will be converted to the first listed format. True allows the input
        to be any format. False means that a sparse matrix input will
        raise an error.

    accept_large_sparse : bool, default=True
        If a CSR, CSC, COO or BSR sparse matrix is supplied and accepted by
        accept_sparse, accept_large_sparse will cause it to be accepted only
        if its indices are stored with a 32-bit dtype.

        .. versionadded:: 0.20

    dtype : 'numeric', type, list of type or None, default='numeric'
        Data type of result. If None, the dtype of the input is preserved.
        If "numeric", dtype is preserved unless array.dtype is object.
        If dtype is a list of types, conversion on the first type is only
        performed if the dtype of the input is not in the list.

    order : {'F', 'C'}, default=None
        Whether an array will be forced to be fortran or c-style.

    copy : bool, default=False
        Whether a forced copy will be triggered. If copy=False, a copy might
        be triggered by a conversion.

    force_all_finite : bool or 'allow-nan', default=True
        Whether to raise an error on np.inf, np.nan, pd.NA in X. This parameter
        does not influence whether y can have np.inf, np.nan, pd.NA values.
        The possibilities are:

        - True: Force all values of X to be finite.
        - False: accepts np.inf, np.nan, pd.NA in X.
        - 'allow-nan': accepts only np.nan or pd.NA values in X. Values cannot
          be infinite.

        .. versionadded:: 0.20
           ``force_all_finite`` accepts the string ``'allow-nan'``.

        .. versionchanged:: 0.23
           Accepts `pd.NA` and converts it into `np.nan`

    ensure_2d : bool, default=True
        Whether to raise a value error if X is not 2D.

    allow_nd : bool, default=False
        Whether to allow X.ndim > 2.

    multi_output : bool, default=False
        Whether to allow 2D y (array or sparse matrix). If false, y will be
        validated as a vector. y cannot have np.nan or np.inf values if
        multi_output=True.

    ensure_min_samples : int, default=1
        Make sure that X has a minimum number of samples in its first
        axis (rows for a 2D array).

    ensure_min_features : int, default=1
        Make sure that the 2D array has some minimum number of features
        (columns). The default value of 1 rejects empty datasets.
        This check is only enforced when X has effectively 2 dimensions or
        is originally 1D and ``ensure_2d`` is True. Setting to 0 disables
        this check.

    y_numeric : bool, default=False
        Whether to ensure that y has a numeric type. If dtype of y is object,
        it is converted to float64. Should only be used for regression
        algorithms.

    estimator : str or estimator instance, default=None
        If passed, include the name of the estimator in warning messages.

    Returns
    -------
    X_converted : object
        The converted and validated X.

    y_converted : object
        The converted and validated y.
    """
    if y is None:
        if estimator is None:
            estimator_name = "estimator"
        else:
            estimator_name = _check_estimator_name(estimator)
        raise ValueError(
            f"{estimator_name} requires y to be passed, but the target y is None"
        )

    X = check_array(
        X,
        accept_sparse=accept_sparse,
        accept_large_sparse=accept_large_sparse,
        dtype=dtype,
        order=order,
        copy=copy,
        force_all_finite=force_all_finite,
        ensure_2d=ensure_2d,
        allow_nd=allow_nd,
        ensure_min_samples=ensure_min_samples,
        ensure_min_features=ensure_min_features,
        estimator=estimator,
        input_name="X",
    )

    y = _check_y(y, multi_output=multi_output, y_numeric=y_numeric, estimator=estimator)

    check_consistent_length(X, y)

    return X, y


def _check_y(y, multi_output=False, y_numeric=False, estimator=None):
    """Isolated part of check_X_y dedicated to y validation"""
    if multi_output:
        y = check_array(
            y,
            accept_sparse="csr",
            force_all_finite=True,
            ensure_2d=False,
            dtype=None,
            input_name="y",
            estimator=estimator,
        )
    else:
        estimator_name = _check_estimator_name(estimator)
        y = column_or_1d(y, warn=True)
        _assert_all_finite(y, input_name="y", estimator_name=estimator_name)
        _ensure_no_complex_data(y)
    if y_numeric and y.dtype.kind == "O":
        y = y.astype(np.float64)

    return y


def column_or_1d(y, *, dtype=None, warn=False):
    """Ravel column or 1d numpy array, else raises an error.

    Parameters
    ----------
    y : array-like
       Input data.

    dtype : data-type, default=None
        Data type for `y`.

        .. versionadded:: 1.2

    warn : bool, default=False
       To control display of warnings.

    Returns
    -------
    y : ndarray
       Output data.

    Raises
    ------
    ValueError
        If `y` is not a 1D array or a 2D array with a single row or column.
    """
    xp, _ = get_namespace(y)
    y = xp.asarray(y, dtype=dtype)
    shape = y.shape
    if len(shape) == 1:
        return _asarray_with_order(xp.reshape(y, -1), order="C", xp=xp)
    if len(shape) == 2 and shape[1] == 1:
        if warn:
            warnings.warn(
                "A column-vector y was passed when a 1d array was"
                " expected. Please change the shape of y to "
                "(n_samples, ), for example using ravel().",
                DataConversionWarning,
                stacklevel=2,
            )
        return _asarray_with_order(xp.reshape(y, -1), order="C", xp=xp)

    raise ValueError(
        "y should be a 1d array, got an array of shape {} instead.".format(shape)
    )


def check_random_state(seed):
    """Turn seed into a np.random.RandomState instance.

    Parameters
    ----------
    seed : None, int or instance of RandomState
        If seed is None, return the RandomState singleton used by np.random.
        If seed is an int, return a new RandomState instance seeded with seed.
        If seed is already a RandomState instance, return it.
        Otherwise raise ValueError.

    Returns
    -------
    :class:`numpy:numpy.random.RandomState`
        The random state object based on `seed` parameter.
    """
    if seed is None or seed is np.random:
        return np.random.mtrand._rand
    if isinstance(seed, numbers.Integral):
        return np.random.RandomState(seed)
    if isinstance(seed, np.random.RandomState):
        return seed
    raise ValueError(
        "%r cannot be used to seed a numpy.random.RandomState instance" % seed
    )


def has_fit_parameter(estimator, parameter):
    """Check whether the estimator's fit method supports the given parameter.

    Parameters
    ----------
    estimator : object
        An estimator to inspect.

    parameter : str
        The searched parameter.

    Returns
    -------
    is_parameter : bool
        Whether the parameter was found to be a named parameter of the
        estimator's fit method.

    Examples
    --------
    >>> from sklearn.svm import SVC
    >>> from sklearn.utils.validation import has_fit_parameter
    >>> has_fit_parameter(SVC(), "sample_weight")
    True
    """
    return parameter in signature(estimator.fit).parameters


def check_symmetric(array, *, tol=1e-10, raise_warning=True, raise_exception=False):
    """Make sure that array is 2D, square and symmetric.

    If the array is not symmetric, then a symmetrized version is returned.
    Optionally, a warning or exception is raised if the matrix is not
    symmetric.

    Parameters
    ----------
    array : {ndarray, sparse matrix}
        Input object to check / convert. Must be two-dimensional and square,
        otherwise a ValueError will be raised.

    tol : float, default=1e-10
        Absolute tolerance for equivalence of arrays. Default = 1E-10.

    raise_warning : bool, default=True
        If True then raise a warning if conversion is required.

    raise_exception : bool, default=False
        If True then raise an exception if array is not symmetric.

    Returns
    -------
    array_sym : {ndarray, sparse matrix}
        Symmetrized version of the input array, i.e. the average of array
        and array.transpose(). If sparse, then duplicate entries are first
        summed and zeros are eliminated.
    """
    if (array.ndim != 2) or (array.shape[0] != array.shape[1]):
        raise ValueError(
            "array must be 2-dimensional and square. shape = {0}".format(array.shape)
        )

    if sp.issparse(array):
        diff = array - array.T
        # only csr, csc, and coo have `data` attribute
        if diff.format not in ["csr", "csc", "coo"]:
            diff = diff.tocsr()
        symmetric = np.all(abs(diff.data) < tol)
    else:
        symmetric = np.allclose(array, array.T, atol=tol)

    if not symmetric:
        if raise_exception:
            raise ValueError("Array must be symmetric")
        if raise_warning:
            warnings.warn(
                "Array is not symmetric, and will be converted "
                "to symmetric by average with its transpose.",
                stacklevel=2,
            )
        if sp.issparse(array):
            conversion = "to" + array.format
            array = getattr(0.5 * (array + array.T), conversion)()
        else:
            array = 0.5 * (array + array.T)

    return array


def check_is_fitted(estimator, attributes=None, *, msg=None, all_or_any=all):
    """Perform is_fitted validation for estimator.

    Checks if the estimator is fitted by verifying the presence of
    fitted attributes (ending with a trailing underscore) and otherwise
    raises a NotFittedError with the given message.

    If an estimator does not set any attributes with a trailing underscore, it
    can define a ``__sklearn_is_fitted__`` method returning a boolean to specify if the
    estimator is fitted or not.

    Parameters
    ----------
    estimator : estimator instance
        Estimator instance for which the check is performed.

    attributes : str, list or tuple of str, default=None
        Attribute name(s) given as string or a list/tuple of strings
        Eg.: ``["coef_", "estimator_", ...], "coef_"``

        If `None`, `estimator` is considered fitted if there exist an
        attribute that ends with a underscore and does not start with double
        underscore.

    msg : str, default=None
        The default error message is, "This %(name)s instance is not fitted
        yet. Call 'fit' with appropriate arguments before using this
        estimator."

        For custom messages if "%(name)s" is present in the message string,
        it is substituted for the estimator name.

        Eg. : "Estimator, %(name)s, must be fitted before sparsifying".

    all_or_any : callable, {all, any}, default=all
        Specify whether all or any of the given attributes must exist.

    Raises
    ------
    TypeError
        If the estimator is a class or not an estimator instance

    NotFittedError
        If the attributes are not found.
    """
    if isclass(estimator):
        raise TypeError("{} is a class, not an instance.".format(estimator))
    if msg is None:
        msg = (
            "This %(name)s instance is not fitted yet. Call 'fit' with "
            "appropriate arguments before using this estimator."
        )

    if not hasattr(estimator, "fit"):
        raise TypeError("%s is not an estimator instance." % (estimator))

    if attributes is not None:
        if not isinstance(attributes, (list, tuple)):
            attributes = [attributes]
        fitted = all_or_any([hasattr(estimator, attr) for attr in attributes])
    elif hasattr(estimator, "__sklearn_is_fitted__"):
        fitted = estimator.__sklearn_is_fitted__()
    else:
        fitted = [
            v for v in vars(estimator) if v.endswith("_") and not v.startswith("__")
        ]

    if not fitted:
        raise NotFittedError(msg % {"name": type(estimator).__name__})


def check_non_negative(X, whom):
    """
    Check if there is any negative value in an array.

    Parameters
    ----------
    X : {array-like, sparse matrix}
        Input data.

    whom : str
        Who passed X to this function.
    """
    xp, _ = get_namespace(X)
    # avoid X.min() on sparse matrix since it also sorts the indices
    if sp.issparse(X):
        if X.format in ["lil", "dok"]:
            X = X.tocsr()
        if X.data.size == 0:
            X_min = 0
        else:
            X_min = X.data.min()
    else:
        X_min = xp.min(X)

    if X_min < 0:
        raise ValueError("Negative values in data passed to %s" % whom)


def check_scalar(
    x,
    name,
    target_type,
    *,
    min_val=None,
    max_val=None,
    include_boundaries="both",
):
    """Validate scalar parameters type and value.

    Parameters
    ----------
    x : object
        The scalar parameter to validate.

    name : str
        The name of the parameter to be printed in error messages.

    target_type : type or tuple
        Acceptable data types for the parameter.

    min_val : float or int, default=None
        The minimum valid value the parameter can take. If None (default) it
        is implied that the parameter does not have a lower bound.

    max_val : float or int, default=None
        The maximum valid value the parameter can take. If None (default) it
        is implied that the parameter does not have an upper bound.

    include_boundaries : {"left", "right", "both", "neither"}, default="both"
        Whether the interval defined by `min_val` and `max_val` should include
        the boundaries. Possible choices are:

        - `"left"`: only `min_val` is included in the valid interval.
          It is equivalent to the interval `[ min_val, max_val )`.
        - `"right"`: only `max_val` is included in the valid interval.
          It is equivalent to the interval `( min_val, max_val ]`.
        - `"both"`: `min_val` and `max_val` are included in the valid interval.
          It is equivalent to the interval `[ min_val, max_val ]`.
        - `"neither"`: neither `min_val` nor `max_val` are included in the
          valid interval. It is equivalent to the interval `( min_val, max_val )`.

    Returns
    -------
    x : numbers.Number
        The validated number.

    Raises
    ------
    TypeError
        If the parameter's type does not match the desired type.

    ValueError
        If the parameter's value violates the given bounds.
        If `min_val`, `max_val` and `include_boundaries` are inconsistent.
    """

    def type_name(t):
        """Convert type into humman readable string."""
        module = t.__module__
        qualname = t.__qualname__
        if module == "builtins":
            return qualname
        elif t == numbers.Real:
            return "float"
        elif t == numbers.Integral:
            return "int"
        return f"{module}.{qualname}"

    if not isinstance(x, target_type):
        if isinstance(target_type, tuple):
            types_str = ", ".join(type_name(t) for t in target_type)
            target_type_str = f"{{{types_str}}}"
        else:
            target_type_str = type_name(target_type)

        raise TypeError(
            f"{name} must be an instance of {target_type_str}, not"
            f" {type(x).__qualname__}."
        )

    expected_include_boundaries = ("left", "right", "both", "neither")
    if include_boundaries not in expected_include_boundaries:
        raise ValueError(
            f"Unknown value for `include_boundaries`: {repr(include_boundaries)}. "
            f"Possible values are: {expected_include_boundaries}."
        )

    if max_val is None and include_boundaries == "right":
        raise ValueError(
            "`include_boundaries`='right' without specifying explicitly `max_val` "
            "is inconsistent."
        )

    if min_val is None and include_boundaries == "left":
        raise ValueError(
            "`include_boundaries`='left' without specifying explicitly `min_val` "
            "is inconsistent."
        )

    comparison_operator = (
        operator.lt if include_boundaries in ("left", "both") else operator.le
    )
    if min_val is not None and comparison_operator(x, min_val):
        raise ValueError(
            f"{name} == {x}, must be"
            f" {'>=' if include_boundaries in ('left', 'both') else '>'} {min_val}."
        )

    comparison_operator = (
        operator.gt if include_boundaries in ("right", "both") else operator.ge
    )
    if max_val is not None and comparison_operator(x, max_val):
        raise ValueError(
            f"{name} == {x}, must be"
            f" {'<=' if include_boundaries in ('right', 'both') else '<'} {max_val}."
        )

    return x


def _check_psd_eigenvalues(lambdas, enable_warnings=False):
    """Check the eigenvalues of a positive semidefinite (PSD) matrix.

    Checks the provided array of PSD matrix eigenvalues for numerical or
    conditioning issues and returns a fixed validated version. This method
    should typically be used if the PSD matrix is user-provided (e.g. a
    Gram matrix) or computed using a user-provided dissimilarity metric
    (e.g. kernel function), or if the decomposition process uses approximation
    methods (randomized SVD, etc.).

    It checks for three things:

    - that there are no significant imaginary parts in eigenvalues (more than
      1e-5 times the maximum real part). If this check fails, it raises a
      ``ValueError``. Otherwise all non-significant imaginary parts that may
      remain are set to zero. This operation is traced with a
      ``PositiveSpectrumWarning`` when ``enable_warnings=True``.

    - that eigenvalues are not all negative. If this check fails, it raises a
      ``ValueError``

    - that there are no significant negative eigenvalues with absolute value
      more than 1e-10 (1e-6) and more than 1e-5 (5e-3) times the largest
      positive eigenvalue in double (simple) precision. If this check fails,
      it raises a ``ValueError``. Otherwise all negative eigenvalues that may
      remain are set to zero. This operation is traced with a
      ``PositiveSpectrumWarning`` when ``enable_warnings=True``.

    Finally, all the positive eigenvalues that are too small (with a value
    smaller than the maximum eigenvalue multiplied by 1e-12 (2e-7)) are set to
    zero. This operation is traced with a ``PositiveSpectrumWarning`` when
    ``enable_warnings=True``.

    Parameters
    ----------
    lambdas : array-like of shape (n_eigenvalues,)
        Array of eigenvalues to check / fix.

    enable_warnings : bool, default=False
        When this is set to ``True``, a ``PositiveSpectrumWarning`` will be
        raised when there are imaginary parts, negative eigenvalues, or
        extremely small non-zero eigenvalues. Otherwise no warning will be
        raised. In both cases, imaginary parts, negative eigenvalues, and
        extremely small non-zero eigenvalues will be set to zero.

    Returns
    -------
    lambdas_fixed : ndarray of shape (n_eigenvalues,)
        A fixed validated copy of the array of eigenvalues.

    Examples
    --------
    >>> from sklearn.utils.validation import _check_psd_eigenvalues
    >>> _check_psd_eigenvalues([1, 2])      # nominal case
    array([1, 2])
    >>> _check_psd_eigenvalues([5, 5j])     # significant imag part
    Traceback (most recent call last):
        ...
    ValueError: There are significant imaginary parts in eigenvalues (1
        of the maximum real part). Either the matrix is not PSD, or there was
        an issue while computing the eigendecomposition of the matrix.
    >>> _check_psd_eigenvalues([5, 5e-5j])  # insignificant imag part
    array([5., 0.])
    >>> _check_psd_eigenvalues([-5, -1])    # all negative
    Traceback (most recent call last):
        ...
    ValueError: All eigenvalues are negative (maximum is -1). Either the
        matrix is not PSD, or there was an issue while computing the
        eigendecomposition of the matrix.
    >>> _check_psd_eigenvalues([5, -1])     # significant negative
    Traceback (most recent call last):
        ...
    ValueError: There are significant negative eigenvalues (0.2 of the
        maximum positive). Either the matrix is not PSD, or there was an issue
        while computing the eigendecomposition of the matrix.
    >>> _check_psd_eigenvalues([5, -5e-5])  # insignificant negative
    array([5., 0.])
    >>> _check_psd_eigenvalues([5, 4e-12])  # bad conditioning (too small)
    array([5., 0.])

    """

    lambdas = np.array(lambdas)
    is_double_precision = lambdas.dtype == np.float64

    # note: the minimum value available is
    #  - single-precision: np.finfo('float32').eps = 1.2e-07
    #  - double-precision: np.finfo('float64').eps = 2.2e-16

    # the various thresholds used for validation
    # we may wish to change the value according to precision.
    significant_imag_ratio = 1e-5
    significant_neg_ratio = 1e-5 if is_double_precision else 5e-3
    significant_neg_value = 1e-10 if is_double_precision else 1e-6
    small_pos_ratio = 1e-12 if is_double_precision else 2e-7

    # Check that there are no significant imaginary parts
    if not np.isreal(lambdas).all():
        max_imag_abs = np.abs(np.imag(lambdas)).max()
        max_real_abs = np.abs(np.real(lambdas)).max()
        if max_imag_abs > significant_imag_ratio * max_real_abs:
            raise ValueError(
                "There are significant imaginary parts in eigenvalues (%g "
                "of the maximum real part). Either the matrix is not PSD, or "
                "there was an issue while computing the eigendecomposition "
                "of the matrix." % (max_imag_abs / max_real_abs)
            )

        # warn about imaginary parts being removed
        if enable_warnings:
            warnings.warn(
                "There are imaginary parts in eigenvalues (%g "
                "of the maximum real part). Either the matrix is not"
                " PSD, or there was an issue while computing the "
                "eigendecomposition of the matrix. Only the real "
                "parts will be kept." % (max_imag_abs / max_real_abs),
                PositiveSpectrumWarning,
            )

    # Remove all imaginary parts (even if zero)
    lambdas = np.real(lambdas)

    # Check that there are no significant negative eigenvalues
    max_eig = lambdas.max()
    if max_eig < 0:
        raise ValueError(
            "All eigenvalues are negative (maximum is %g). "
            "Either the matrix is not PSD, or there was an "
            "issue while computing the eigendecomposition of "
            "the matrix." % max_eig
        )

    else:
        min_eig = lambdas.min()
        if (
            min_eig < -significant_neg_ratio * max_eig
            and min_eig < -significant_neg_value
        ):
            raise ValueError(
                "There are significant negative eigenvalues (%g"
                " of the maximum positive). Either the matrix is "
                "not PSD, or there was an issue while computing "
                "the eigendecomposition of the matrix." % (-min_eig / max_eig)
            )
        elif min_eig < 0:
            # Remove all negative values and warn about it
            if enable_warnings:
                warnings.warn(
                    "There are negative eigenvalues (%g of the "
                    "maximum positive). Either the matrix is not "
                    "PSD, or there was an issue while computing the"
                    " eigendecomposition of the matrix. Negative "
                    "eigenvalues will be replaced with 0." % (-min_eig / max_eig),
                    PositiveSpectrumWarning,
                )
            lambdas[lambdas < 0] = 0

    # Check for conditioning (small positive non-zeros)
    too_small_lambdas = (0 < lambdas) & (lambdas < small_pos_ratio * max_eig)
    if too_small_lambdas.any():
        if enable_warnings:
            warnings.warn(
                "Badly conditioned PSD matrix spectrum: the largest "
                "eigenvalue is more than %g times the smallest. "
                "Small eigenvalues will be replaced with 0."
                "" % (1 / small_pos_ratio),
                PositiveSpectrumWarning,
            )
        lambdas[too_small_lambdas] = 0

    return lambdas


def _check_sample_weight(
    sample_weight, X, dtype=None, copy=False, only_non_negative=False
):
    """Validate sample weights.

    Note that passing sample_weight=None will output an array of ones.
    Therefore, in some cases, you may want to protect the call with:
    if sample_weight is not None:
        sample_weight = _check_sample_weight(...)

    Parameters
    ----------
    sample_weight : {ndarray, Number or None}, shape (n_samples,)
        Input sample weights.

    X : {ndarray, list, sparse matrix}
        Input data.

    only_non_negative : bool, default=False,
        Whether or not the weights are expected to be non-negative.

        .. versionadded:: 1.0

    dtype : dtype, default=None
        dtype of the validated `sample_weight`.
        If None, and the input `sample_weight` is an array, the dtype of the
        input is preserved; otherwise an array with the default numpy dtype
        is be allocated.  If `dtype` is not one of `float32`, `float64`,
        `None`, the output will be of dtype `float64`.

    copy : bool, default=False
        If True, a copy of sample_weight will be created.

    Returns
    -------
    sample_weight : ndarray of shape (n_samples,)
        Validated sample weight. It is guaranteed to be "C" contiguous.
    """
    n_samples = _num_samples(X)

    if dtype is not None and dtype not in [np.float32, np.float64]:
        dtype = np.float64

    if sample_weight is None:
        sample_weight = np.ones(n_samples, dtype=dtype)
    elif isinstance(sample_weight, numbers.Number):
        sample_weight = np.full(n_samples, sample_weight, dtype=dtype)
    else:
        if dtype is None:
            dtype = [np.float64, np.float32]
        sample_weight = check_array(
            sample_weight,
            accept_sparse=False,
            ensure_2d=False,
            dtype=dtype,
            order="C",
            copy=copy,
            input_name="sample_weight",
        )
        if sample_weight.ndim != 1:
            raise ValueError("Sample weights must be 1D array or scalar")

        if sample_weight.shape != (n_samples,):
            raise ValueError(
                "sample_weight.shape == {}, expected {}!".format(
                    sample_weight.shape, (n_samples,)
                )
            )

    if only_non_negative:
        check_non_negative(sample_weight, "`sample_weight`")

    return sample_weight


def _allclose_dense_sparse(x, y, rtol=1e-7, atol=1e-9):
    """Check allclose for sparse and dense data.

    Both x and y need to be either sparse or dense, they
    can't be mixed.

    Parameters
    ----------
    x : {array-like, sparse matrix}
        First array to compare.

    y : {array-like, sparse matrix}
        Second array to compare.

    rtol : float, default=1e-7
        Relative tolerance; see numpy.allclose.

    atol : float, default=1e-9
        absolute tolerance; see numpy.allclose. Note that the default here is
        more tolerant than the default for numpy.testing.assert_allclose, where
        atol=0.
    """
    if sp.issparse(x) and sp.issparse(y):
        x = x.tocsr()
        y = y.tocsr()
        x.sum_duplicates()
        y.sum_duplicates()
        return (
            np.array_equal(x.indices, y.indices)
            and np.array_equal(x.indptr, y.indptr)
            and np.allclose(x.data, y.data, rtol=rtol, atol=atol)
        )
    elif not sp.issparse(x) and not sp.issparse(y):
        return np.allclose(x, y, rtol=rtol, atol=atol)
    raise ValueError(
        "Can only compare two sparse matrices, not a sparse matrix and an array"
    )


def _check_fit_params(X, fit_params, indices=None):
    """Check and validate the parameters passed during `fit`.

    Parameters
    ----------
    X : array-like of shape (n_samples, n_features)
        Data array.

    fit_params : dict
        Dictionary containing the parameters passed at fit.

    indices : array-like of shape (n_samples,), default=None
        Indices to be selected if the parameter has the same size as `X`.

    Returns
    -------
    fit_params_validated : dict
        Validated parameters. We ensure that the values support indexing.
    """
    from . import _safe_indexing

    fit_params_validated = {}
    for param_key, param_value in fit_params.items():
        if not _is_arraylike(param_value) or _num_samples(param_value) != _num_samples(
            X
        ):
            # Non-indexable pass-through (for now for backward-compatibility).
            # https://github.com/scikit-learn/scikit-learn/issues/15805
            fit_params_validated[param_key] = param_value
        else:
            # Any other fit_params should support indexing
            # (e.g. for cross-validation).
            fit_params_validated[param_key] = _make_indexable(param_value)
            fit_params_validated[param_key] = _safe_indexing(
                fit_params_validated[param_key], indices
            )

    return fit_params_validated


def _get_feature_names(X):
    """Get feature names from X.

    Support for other array containers should place its implementation here.

    Parameters
    ----------
    X : {ndarray, dataframe} of shape (n_samples, n_features)
        Array container to extract feature names.

        - pandas dataframe : The columns will be considered to be feature
          names. If the dataframe contains non-string feature names, `None` is
          returned.
        - All other array containers will return `None`.

    Returns
    -------
    names: ndarray or None
        Feature names of `X`. Unrecognized array containers will return `None`.
    """
    feature_names = None

    # extract feature names for support array containers
    if hasattr(X, "columns"):
        feature_names = np.asarray(X.columns, dtype=object)

    if feature_names is None or len(feature_names) == 0:
        return

    types = sorted(t.__qualname__ for t in set(type(v) for v in feature_names))

    # mixed type of string and non-string is not supported
    if len(types) > 1 and "str" in types:
        raise TypeError(
            "Feature names only support column names that are all strings, but got"
            f" dtypes: {types}. If you want support for feature names, convert the"
            " columns to strings. For example, by using X.columns ="
            " X.columns.astype(str)."
        )

    # Only feature names of all strings are supported
    if len(types) == 1 and types[0] == "str":
        return feature_names


def _check_feature_names_in(estimator, input_features=None, *, generate_names=True):
    """Check `input_features` and generate names if needed.

    Commonly used in :term:`get_feature_names_out`.

    Parameters
    ----------
    input_features : array-like of str or None, default=None
        Input features.

        - If `input_features` is `None`, then `feature_names_in_` is
          used as feature names in. If `feature_names_in_` is not defined,
          then the following input feature names are generated:
          `["x0", "x1", ..., "x(n_features_in_ - 1)"]`.
        - If `input_features` is an array-like, then `input_features` must
          match `feature_names_in_` if `feature_names_in_` is defined.

    generate_names : bool, default=True
        Whether to generate names when `input_features` is `None` and
        `estimator.feature_names_in_` is not defined. This is useful for transformers
        that validates `input_features` but do not require them in
        :term:`get_feature_names_out` e.g. `PCA`.

    Returns
    -------
    feature_names_in : ndarray of str or `None`
        Feature names in.
    """

    feature_names_in_ = getattr(estimator, "feature_names_in_", None)
    n_features_in_ = getattr(estimator, "n_features_in_", None)

    if input_features is not None:
        input_features = np.asarray(input_features, dtype=object)
        if feature_names_in_ is not None and not np.array_equal(
            feature_names_in_, input_features
        ):
            raise ValueError("input_features is not equal to feature_names_in_")

        if n_features_in_ is not None and len(input_features) != n_features_in_:
            raise ValueError(
                "input_features should have length equal to number of "
                f"features ({n_features_in_}), got {len(input_features)}"
            )
        return input_features

    if feature_names_in_ is not None:
        return feature_names_in_

    if not generate_names:
        return

    # Generates feature names if `n_features_in_` is defined
    if n_features_in_ is None:
        raise ValueError("Unable to generate feature names without n_features_in_")

    return np.asarray([f"x{i}" for i in range(n_features_in_)], dtype=object)


def _generate_get_feature_names_out(estimator, n_features_out, input_features=None):
    """Generate feature names out for estimator using the estimator name as the prefix.

    The input_feature names are validated but not used. This function is useful
    for estimators that generate their own names based on `n_features_out`, i.e. PCA.

    Parameters
    ----------
    estimator : estimator instance
        Estimator producing output feature names.

    n_feature_out : int
        Number of feature names out.

    input_features : array-like of str or None, default=None
        Only used to validate feature names with `estimator.feature_names_in_`.

    Returns
    -------
    feature_names_in : ndarray of str or `None`
        Feature names in.
    """
    _check_feature_names_in(estimator, input_features, generate_names=False)
    estimator_name = estimator.__class__.__name__.lower()
    return np.asarray(
        [f"{estimator_name}{i}" for i in range(n_features_out)], dtype=object
    )


def _check_monotonic_cst(estimator, monotonic_cst=None):
    """Check the monotonic constraints and return the corresponding array.

    This helper function should be used in the `fit` method of an estimator
    that supports monotonic constraints and called after the estimator has
    introspected input data to set the `n_features_in_` and optionally the
    `feature_names_in_` attributes.

    .. versionadded:: 1.2

    Parameters
    ----------
    estimator : estimator instance

    monotonic_cst : array-like of int, dict of str or None, default=None
        Monotonic constraints for the features.

        - If array-like, then it should contain only -1, 0 or 1. Each value
            will be checked to be in [-1, 0, 1]. If a value is -1, then the
            corresponding feature is required to be monotonically decreasing.
        - If dict, then it the keys should be the feature names occurring in
            `estimator.feature_names_in_` and the values should be -1, 0 or 1.
        - If None, then an array of 0s will be allocated.

    Returns
    -------
    monotonic_cst : ndarray of int
        Monotonic constraints for each feature.
    """
    original_monotonic_cst = monotonic_cst
    if monotonic_cst is None or isinstance(monotonic_cst, dict):
        monotonic_cst = np.full(
            shape=estimator.n_features_in_,
            fill_value=0,
            dtype=np.int8,
        )
        if isinstance(original_monotonic_cst, dict):
            if not hasattr(estimator, "feature_names_in_"):
                raise ValueError(
                    f"{estimator.__class__.__name__} was not fitted on data "
                    "with feature names. Pass monotonic_cst as an integer "
                    "array instead."
                )
            unexpected_feature_names = list(
                set(original_monotonic_cst) - set(estimator.feature_names_in_)
            )
            unexpected_feature_names.sort()  # deterministic error message
            n_unexpeced = len(unexpected_feature_names)
            if unexpected_feature_names:
                if len(unexpected_feature_names) > 5:
                    unexpected_feature_names = unexpected_feature_names[:5]
                    unexpected_feature_names.append("...")
                raise ValueError(
                    f"monotonic_cst contains {n_unexpeced} unexpected feature "
                    f"names: {unexpected_feature_names}."
                )
            for feature_idx, feature_name in enumerate(estimator.feature_names_in_):
                if feature_name in original_monotonic_cst:
                    cst = original_monotonic_cst[feature_name]
                    if cst not in [-1, 0, 1]:
                        raise ValueError(
                            f"monotonic_cst['{feature_name}'] must be either "
                            f"-1, 0 or 1. Got {cst!r}."
                        )
                    monotonic_cst[feature_idx] = cst
    else:
        unexpected_cst = np.setdiff1d(monotonic_cst, [-1, 0, 1])
        if unexpected_cst.shape[0]:
            raise ValueError(
                "monotonic_cst must be an array-like of -1, 0 or 1. Observed "
                f"values: {unexpected_cst.tolist()}."
            )

        monotonic_cst = np.asarray(monotonic_cst, dtype=np.int8)
        if monotonic_cst.shape[0] != estimator.n_features_in_:
            raise ValueError(
                f"monotonic_cst has shape {monotonic_cst.shape} but the input data "
                f"X has {estimator.n_features_in_} features."
            )
    return monotonic_cst