text: """Utilities for input validation"""
  
  # Original authors from Sckit-Learn:
  #          Olivier Grisel
  #          Gael Varoquaux
  #          Andreas Mueller
  #          Lars Buitinck
  #          Alexandre Gramfort
  #          Nicolas Tresegnie
  #          Sylvain Marie
  # License: BSD 3 clause
  
  
  # This code originates from the Scikit-Learn library,
  # it was since modified to allow GPU acceleration.
  # This code is under BSD 3 clause license.
  # Authors mentioned above do not endorse or promote this production.
  
  
  from functools import wraps
  import warnings
  import numbers
  
  import numpy as np
  import scipy.sparse as sp
  from distutils.version import LooseVersion
  from inspect import signature, isclass, Parameter
  
  import joblib
  
  from ..exceptions import NonBLASDotWarning, PositiveSpectrumWarning
  from ..exceptions import NotFittedError
  from ..exceptions import DataConversionWarning
  
  from ....thirdparty_adapters import check_array
  
  FLOAT_DTYPES = (np.float64, np.float32, np.float16)
  
  # Silenced by default to reduce verbosity. Turn on at runtime for
  # performance profiling.
  warnings.simplefilter('ignore', NonBLASDotWarning)
  
  
  def _deprecate_positional_args(f):
      """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
      ----------
      f : function
          function to check arguments on
      """
      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:
              # ignore first 'self' argument for instance methods
              args_msg = ['{}={}'.format(name, arg)
                          for name, arg in zip(kwonly_args[:extra_args],
                                               args[-extra_args:])]
              warnings.warn("Pass {} as keyword args. From version 0.25 "
                            "passing these as positional arguments will "
                            "result in an error".format(", ".join(args_msg)),
                            FutureWarning)
          kwargs.update({k: arg for k, arg in zip(sig.parameters, args)})
          return f(**kwargs)
      return inner_f
  
  
  def _assert_all_finite(X, allow_nan=False, msg_dtype=None):
      """Like assert_all_finite, but only for ndarray."""
      # validation is also imported in extmath
      from .extmath import _safe_accumulator_op
  
      X = np.asanyarray(X)
      # 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.isfinite to prevent
      # false positives from overflow in sum method. The sum is also calculated
      # safely to reduce dtype induced overflows.
      is_float = X.dtype.kind in 'fc'
      if is_float and (np.isfinite(_safe_accumulator_op(np.sum, X))):
          pass
      elif is_float:
          msg_err = "Input contains {} or a value too large for {!r}."
          if (allow_nan and np.isinf(X).any() or
                  not allow_nan and not np.isfinite(X).all()):
              type_err = 'infinity' if allow_nan else 'NaN, infinity'
              raise ValueError(
                      msg_err.format
                      (type_err,
                       msg_dtype if msg_dtype is not None else X.dtype)
              )
  
  
  @_deprecate_positional_args
  def assert_all_finite(X, *, allow_nan=False):
      """Throw a ValueError if X contains NaN or infinity.
  
      Parameters
      ----------
      X : array or sparse matrix
  
      allow_nan : bool
      """
      _assert_all_finite(X.data if sp.issparse(X) else X, allow_nan)
  
  
  @_deprecate_positional_args
  def as_float_array(X, *, copy=True, force_all_finite=True):
      """Converts 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}
  
      copy : bool, optional
          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 : boolean 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 : {array, sparse matrix}
          An array of type np.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 _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:
          raise TypeError(message)
  
  
  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
  
      Returns
      -------
      memory : object with the joblib.Memory interface
  
      Raises
      ------
      ValueError
          If ``memory`` is not joblib.Memory-like.
      """
  
      if memory is None or isinstance(memory, str):
          if LooseVersion(joblib.__version__) < '0.12':
              memory = joblib.Memory(cachedir=memory, verbose=0)
          else:
              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")
  
  
  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, array, sparse} 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, arrays, sparse matrices
          List of objects to ensure sliceability.
      """
      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):
      """Convert a sparse matrix to a given format.
  
      Checks the sparse format of spmatrix and converts if necessary.
  
      Parameters
      ----------
      spmatrix : scipy sparse matrix
          Input to validate and convert.
  
      accept_sparse : string, boolean or list/tuple of strings
          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 : string, type or None
          Data type of result. If None, the dtype of the input is preserved.
  
      copy : boolean
          Whether a forced copy will be triggered. If copy=False, a copy might
          be triggered by a conversion.
  
      force_all_finite : boolean 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
      -------
      spmatrix_converted : scipy 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')
  
      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_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)
  
  
  @_deprecate_positional_args
  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 : nd-array, list or sparse matrix
          Input data.
  
      y : nd-array, list or sparse matrix
          Labels.
  
      accept_sparse : string, boolean or list of string (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 : string, type, list of types 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.
  
      copy : boolean (default=False)
          Whether a forced copy will be triggered. If copy=False, a copy might
          be triggered by a conversion.
  
      force_all_finite : boolean 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 : boolean (default=True)
          Whether to raise a value error if X is not 2D.
  
      allow_nd : boolean (default=False)
          Whether to allow X.ndim > 2.
  
      multi_output : boolean (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 : boolean (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:
          raise ValueError("y cannot be 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)
      if multi_output:
          y = check_array(y, accept_sparse='csr', force_all_finite=True,
                          ensure_2d=False, dtype=None)
      else:
          y = column_or_1d(y, warn=True)
          _assert_all_finite(y)
      if y_numeric and y.dtype.kind == 'O':
          y = y.astype(np.float64)
  
      check_consistent_length(X, y)
  
      return X, y
  
  
  @_deprecate_positional_args
  def column_or_1d(y, *, warn=False):
      """ Ravel column or 1d numpy array, else raises an error
  
      Parameters
      ----------
      y : array-like
  
      warn : boolean, default False
         To control display of warnings.
  
      Returns
      -------
      y : array
  
      """
      y = np.asarray(y)
      shape = np.shape(y)
      if len(shape) == 1:
          return np.ravel(y)
      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 np.ravel(y)
  
      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 | 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.
      """
      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):
      """Checks 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
      >>> has_fit_parameter(SVC(), "sample_weight")
      True
  
      """
      return parameter in signature(estimator.fit).parameters
  
  
  @_deprecate_positional_args
  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 : nd-array or sparse matrix
          Input object to check / convert. Must be two-dimensional and square,
          otherwise a ValueError will be raised.
      tol : float
          Absolute tolerance for equivalence of arrays. Default = 1E-10.
      raise_warning : boolean (default=True)
          If True then raise a warning if conversion is required.
      raise_exception : boolean (default=False)
          If True then raise an exception if array is not symmetric.
  
      Returns
      -------
      array_sym : ndarray or 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
  
  
  @_deprecate_positional_args
  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.
  
      This utility is meant to be used internally by estimators themselves,
      typically in their own predict / transform methods.
  
      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 : string
          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.
  
      Returns
      -------
      None
  
      Raises
      ------
      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]
          attrs = all_or_any([hasattr(estimator, attr) for attr in attributes])
      else:
          attrs = [v for v in vars(estimator)
                   if v.endswith("_") and not v.startswith("__")]
  
      if not attrs:
          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 or sparse matrix
          Input data.
  
      whom : string
          Who passed X to this function.
      """
      # 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 = X.min()
  
      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):
      """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, optional (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, optional (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.
  
      Raises
      -------
      TypeError
          If the parameter's type does not match the desired type.
  
      ValueError
          If the parameter's value violates the given bounds.
      """
  
      if not isinstance(x, target_type):
          raise TypeError('`{}` must be an instance of {}, not {}.'
                          .format(name, target_type, type(x)))
  
      if min_val is not None and x < min_val:
          raise ValueError('`{}`= {}, must be >= {}.'.format(name, x, min_val))
  
      if max_val is not None and x > max_val:
          raise ValueError('`{}`= {}, must be <= {}.'.format(name, x, max_val))
  
  
  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 divided by 1e12) 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
      --------
      >>> _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
  
      # 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):
      """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 : nd-array, list or sparse matrix
          Input data.
  
      dtype: dtype
         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`.
  
      Returns
      -------
      sample_weight : ndarray, 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"
          )
          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,)))
      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 or sparse matrix
          First array to compare.
  
      y : array-like or sparse matrix
          Second array to compare.
  
      rtol : float, optional
          relative tolerance; see numpy.allclose
  
      atol : float, optional
          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
  