text: """
  The :mod:`sklearn.model_selection._validation` module includes classes and
  functions to validate the model.
  """
  # Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
  #         Gael Varoquaux <gael.varoquaux@normalesup.org>
  #         Olivier Grisel <olivier.grisel@ensta.org>
  #         Raghav RV <rvraghav93@gmail.com>
  #         Michal Karbownik <michakarbownik@gmail.com>
  # ND adapted by Pedro Ilídio.
  # License: BSD 3 clause
  
  # New imports:
  import sklearn.utils
  import copy
  import itertools
  from sklearn.model_selection._validation import (
      _score,
      _normalize_score_results,
      _warn_about_fit_failures,
      _aggregate_score_dicts,
  )
  from sklearn.utils.validation import (
      _check_fit_params,
      _make_indexable,
      _num_samples,
  )
  from sklearn.utils._tags import _safe_tags
  from ._split import check_cv_nd, _check_train_test_combinations
  
  import warnings
  import numbers
  import time
  from traceback import format_exc
  from contextlib import suppress
  from collections import Counter
  
  import numpy as np
  import scipy.sparse as sp
  from joblib import Parallel, logger
  
  from sklearn.base import is_classifier, clone
  from sklearn.utils import indexable, check_random_state, _safe_indexing
  from sklearn.utils.fixes import delayed
  from sklearn.utils.metaestimators import _safe_split
  from sklearn.metrics import check_scoring
  from sklearn.metrics._scorer import _check_multimetric_scoring, _MultimetricScorer
  from sklearn.exceptions import FitFailedWarning
  from sklearn.model_selection._split import check_cv
  from sklearn.preprocessing import LabelEncoder
  
  
  __all__ = [
      "cross_validate_nd",
  ]
  
  
  def cross_validate_nd(
      estimator,
      X,
      y=None,
      *,
      groups=None,
      scoring=None,
      cv=None,
      n_jobs=None,
      verbose=0,
      fit_params=None,
      pre_dispatch="2*n_jobs",
      return_train_score=False,
      return_estimator=False,
      error_score=np.nan,
      # ND specific:
      diagonal=False,
      train_test_combinations=None,
  ):
      # TODO: ND adapt.
      """Evaluate metric(s) by cross-validation and also record fit/score times.
  
      Read more in the :ref:`User Guide <multimetric_cross_validation>`.
  
      Parameters
      ----------
      estimator : estimator object implementing 'fit'
          The object to use to fit the data.
  
      X : array-like of shape (n_samples, n_features)
          The data to fit. Can be for example a list, or an array.
  
      y : array-like of shape (n_samples,) or (n_samples, n_outputs), \
              default=None
          The target variable to try to predict in the case of
          supervised learning.
  
      groups : array-like of shape (n_samples,), default=None
          Group labels for the samples used while splitting the dataset into
          train/test set. Only used in conjunction with a "Group" :term:`cv`
          instance (e.g., :class:`GroupKFold`).
  
      diagonal : bool, default=False
          Wether to combine each axis splits in a product-manner or zip-manner.
  
      scoring : str, callable, list, tuple, or dict, default=None
          Strategy to evaluate the performance of the cross-validated model on
          the test set.
  
          If `scoring` represents a single score, one can use:
  
          - a single string (see :ref:`scoring_parameter`);
          - a callable (see :ref:`scoring`) that returns a single value.
  
          If `scoring` represents multiple scores, one can use:
  
          - a list or tuple of unique strings;
          - a callable returning a dictionary where the keys are the metric
            names and the values are the metric scores;
          - a dictionary with metric names as keys and callables a values.
  
          See :ref:`multimetric_grid_search` for an example.
  
      cv : int, cross-validation generator or an iterable, default=None
          Determines the cross-validation splitting strategy.
          Possible inputs for cv are:
  
          - None, to use the default 5-fold cross validation,
          - int, to specify the number of folds in a `(Stratified)KFold`,
          - :term:`CV splitter`,
          - An iterable yielding (train, test) splits as arrays of indices.
  
          For int/None inputs, if the estimator is a classifier and ``y`` is
          either binary or multiclass, :class:`StratifiedKFold` is used. In all
          other cases, :class:`.Fold` is used. These splitters are instantiated
          with `shuffle=False` so the splits will be the same across calls.
  
          Refer :ref:`User Guide <cross_validation>` for the various
          cross-validation strategies that can be used here.
  
          .. versionchanged:: 0.22
              ``cv`` default value if None changed from 3-fold to 5-fold.
  
      n_jobs : int, default=None
          Number of jobs to run in parallel. Training the estimator and computing
          the score are parallelized over the cross-validation splits.
          ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
          ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
          for more details.
  
      verbose : int, default=0
          The verbosity level.
  
      fit_params : dict, default=None
          Parameters to pass to the fit method of the estimator.
  
      pre_dispatch : int or str, default='2*n_jobs'
          Controls the number of jobs that get dispatched during parallel
          execution. Reducing this number can be useful to avoid an
          explosion of memory consumption when more jobs get dispatched
          than CPUs can process. This parameter can be:
  
              - None, in which case all the jobs are immediately
                created and spawned. Use this for lightweight and
                fast-running jobs, to avoid delays due to on-demand
                spawning of the jobs
  
              - An int, giving the exact number of total jobs that are
                spawned
  
              - A str, giving an expression as a function of n_jobs,
                as in '2*n_jobs'
  
      return_train_score : bool, default=False
          Whether to include train scores.
          Computing training scores is used to get insights on how different
          parameter settings impact the overfitting/underfitting trade-off.
          However computing the scores on the training set can be computationally
          expensive and is not strictly required to select the parameters that
          yield the best generalization performance.
  
          .. versionadded:: 0.19
  
          .. versionchanged:: 0.21
              Default value was changed from ``True`` to ``False``
  
      return_estimator : bool, default=False
          Whether to return the estimators fitted on each split.
  
          .. versionadded:: 0.20
  
      error_score : 'raise' or numeric, default=np.nan
          Value to assign to the score if an error occurs in estimator fitting.
          If set to 'raise', the error is raised.
          If a numeric value is given, FitFailedWarning is raised.
  
          .. versionadded:: 0.20
  
      Returns
      -------
      scores : dict of float arrays of shape (n_splits,)
          Array of scores of the estimator for each run of the cross validation.
  
          A dict of arrays containing the score/time arrays for each scorer is
          returned. The possible keys for this ``dict`` are:
  
              ``test_score``
                  The score array for test scores on each cv split.
                  Suffix ``_score`` in ``test_score`` changes to a specific
                  metric like ``test_r2`` or ``test_auc`` if there are
                  multiple scoring metrics in the scoring parameter.
              ``train_score``
                  The score array for train scores on each cv split.
                  Suffix ``_score`` in ``train_score`` changes to a specific
                  metric like ``train_r2`` or ``train_auc`` if there are
                  multiple scoring metrics in the scoring parameter.
                  This is available only if ``return_train_score`` parameter
                  is ``True``.
              ``fit_time``
                  The time for fitting the estimator on the train
                  set for each cv split.
              ``score_time``
                  The time for scoring the estimator on the test set for each
                  cv split. (Note time for scoring on the train set is not
                  included even if ``return_train_score`` is set to ``True``
              ``estimator``
                  The estimator objects for each cv split.
                  This is available only if ``return_estimator`` parameter
                  is set to ``True``.
  
      Examples
      --------
      >>> from sklearn import datasets, linear_model
      >>> from sklearn.model_selection import cross_validate
      >>> from sklearn.metrics import make_scorer
      >>> from sklearn.metrics import confusion_matrix
      >>> from sklearn.svm import LinearSVC
      >>> diabetes = datasets.load_diabetes()
      >>> X = diabetes.data[:150]
      >>> y = diabetes.target[:150]
      >>> lasso = linear_model.Lasso()
  
      Single metric evaluation using ``cross_validate``
  
      >>> cv_results = cross_validate(lasso, X, y, cv=3)
      >>> sorted(cv_results.keys())
      ['fit_time', 'score_time', 'test_score']
      >>> cv_results['test_score']
      array([0.3315057 , 0.08022103, 0.03531816])
  
      Multiple metric evaluation using ``cross_validate``
      (please refer the ``scoring`` parameter doc for more information)
  
      >>> scores = cross_validate(lasso, X, y, cv=3,
      ...                         scoring=('r2', 'neg_mean_squared_error'),
      ...                         return_train_score=True)
      >>> print(scores['test_neg_mean_squared_error'])
      [-3635.5... -3573.3... -6114.7...]
      >>> print(scores['train_r2'])
      [0.28009951 0.3908844  0.22784907]
  
      See Also
      --------
      cross_val_score : Run cross-validation for single metric evaluation.
  
      cross_val_predict : Get predictions from each split of cross-validation for
          diagnostic purposes.
  
      sklearn.metrics.make_scorer : Make a scorer from a performance metric or
          loss function.
  
      """
  
      # *X, y, groups = indexable(*X, y, groups)
      # Call _make_indexable on each one instead of indexable. The only difference
      # being we avoid calling sklear.utils.check_consistent_length this way.
      X = [_make_indexable(a) for a in X]
      y = _make_indexable(y)
  
      ndim = y.ndim
  
      if groups is None:
          groups = [None] * ndim
      groups = [_make_indexable(a) for a in groups]
  
      # Check dimension consistency
      if not (ndim == len(X) == len(groups)):
          # FIXME: multi-output: y would have an extra dimension.
          raise ValueError("Incompatible dimensions. One must ensure "
                           "y.ndim == len(X) == len(groups)")
  
      cv = check_cv_nd(
          cv, y, classifier=is_classifier(estimator), diagonal=diagonal)
  
      train_test_combinations, train_test_names = _check_train_test_combinations(
          ttc=train_test_combinations,
          n_dim=len(X),
          include_train=return_train_score,
      )
  
      if callable(scoring):
          scorers = scoring
      elif scoring is None or isinstance(scoring, str):
          scorers = check_scoring(estimator, scoring)
      else:
          scorers = _check_multimetric_scoring(estimator, scoring)
  
      splits_iter = cv.split(X, y, groups)
      # next(splits_iter) == train_test ==
      #   ((train_ax0, test_ax0), (train_ax1, test_ax1), ...)
  
      # We clone the estimator to make sure that all the folds are
      # independent, and that it is pickle-able.
      parallel = Parallel(n_jobs=n_jobs, verbose=verbose, pre_dispatch=pre_dispatch)
      results = parallel(
          delayed(_fit_and_score_nd)(
              clone(estimator),
              X,
              y,
              scorers,
              train_test,
              verbose,
              None,
              fit_params,
              return_train_score=return_train_score,
              return_times=True,
              return_estimator=return_estimator,
              error_score=error_score,
              train_test_combinations=train_test_combinations,
              train_test_names=train_test_names,
          )
          for train_test in splits_iter
      )
  
      _warn_about_fit_failures(results, error_score)
  
      # For callabe scoring, the return type is only know after calling. If the
      # return type is a dictionary, the error scores can now be inserted with
      # the correct key.
      # 
      # if callable(scoring):  # TODO
      #     _insert_error_scores(results, error_score)
  
      results = _aggregate_score_dicts(results)
  
      ret = {}
      ret["fit_time"] = results["fit_time"]
      ret["score_time"] = results["score_time"]
  
      if return_estimator:
          ret["estimator"] = results["estimator"]
  
      for ttc_name in train_test_names:
          test_scores_dict = _normalize_score_results(
                                  results[f"{ttc_name}_scores"])
  
          for name in test_scores_dict:
              ret[f"{ttc_name}_{name}"] = test_scores_dict[name]
  
      return ret
  
  
  def _fit_and_score_nd(
      estimator,
      X,
      y,
      scorer,
      train_test,
      verbose,
      parameters,
      fit_params,
      return_train_score=False,
      return_parameters=False,
      return_n_test_samples=False,
      return_times=False,
      return_estimator=False,
      split_progress=None,
      candidate_progress=None,
      error_score=np.nan,
      train_test_combinations=None,
      train_test_names=None,
  ):
  
      """Fit estimator and compute scores for a given dataset split.
  
      Parameters
      ----------
      estimator : estimator object implementing 'fit'
          The object to use to fit the data.
  
      X : array-like of shape (n_samples, n_features)
          The data to fit.
  
      y : array-like of shape (n_samples,) or (n_samples, n_outputs) or None
          The target variable to try to predict in the case of
          supervised learning.
  
      scorer : A single callable or dict mapping scorer name to the callable
          If it is a single callable, the return value for ``train_scores`` and
          ``test_scores`` is a single float.
  
          For a dict, it should be one mapping the scorer name to the scorer
          callable object / function.
  
          The callable object / fn should have signature
          ``scorer(estimator, X, y)``.
  
      train : array-like of shape (n_train_samples,)
          Indices of training samples.
  
      test : array-like of shape (n_test_samples,)
          Indices of test samples.
  
      verbose : int
          The verbosity level.
  
      error_score : 'raise' or numeric, default=np.nan
          Value to assign to the score if an error occurs in estimator fitting.
          If set to 'raise', the error is raised.
          If a numeric value is given, FitFailedWarning is raised.
  
      parameters : dict or None
          Parameters to be set on the estimator.
  
      fit_params : dict or None
          Parameters that will be passed to ``estimator.fit``.
  
      return_train_score : bool, default=False
          Compute and return score on training set.
  
      return_parameters : bool, default=False
          Return parameters that has been used for the estimator.
  
      split_progress : {list, tuple} of int, default=None
          A list or tuple of format (<current_split_id>, <total_num_of_splits>).
  
      candidate_progress : {list, tuple} of int, default=None
          A list or tuple of format
          (<current_candidate_id>, <total_number_of_candidates>).
  
      return_n_test_samples : bool, default=False
          Whether to return the ``n_test_samples``.
  
      return_times : bool, default=False
          Whether to return the fit/score times.
  
      return_estimator : bool, default=False
          Whether to return the fitted estimator.
  
      Returns
      -------
      result : dict with the following attributes
          train_scores : dict of scorer name -> float
              Score on training set (for all the scorers),
              returned only if `return_train_score` is `True`.
          test_scores : dict of scorer name -> float
              Score on testing set (for all the scorers).
          n_test_samples : int
              Number of test samples.
          fit_time : float
              Time spent for fitting in seconds.
          score_time : float
              Time spent for scoring in seconds.
          parameters : dict or None
              The parameters that have been evaluated.
          estimator : estimator object
              The fitted estimator.
          fit_error : str or None
              Traceback str if the fit failed, None if the fit succeeded.
      """
      if not isinstance(error_score, numbers.Number) and error_score != "raise":
          raise ValueError(
              "error_score must be the string 'raise' or a numeric value. "
              "(Hint: if using 'raise', please make sure that it has been "
              "spelled correctly.)"
          )
  
      progress_msg = ""
      if verbose > 2:
          if split_progress is not None:
              progress_msg = f" {split_progress[0]+1}/{split_progress[1]}"
          if candidate_progress and verbose > 9:
              progress_msg += f"; {candidate_progress[0]+1}/{candidate_progress[1]}"
  
      if verbose > 1:
          if parameters is None:
              params_msg = ""
          else:
              sorted_keys = sorted(parameters)  # Ensure deterministic o/p
              params_msg = ", ".join(f"{k}={parameters[k]}" for k in sorted_keys)
      if verbose > 9:
          start_msg = f"[CV{progress_msg}] START {params_msg}"
          print(f"{start_msg}{(80 - len(start_msg)) * '.'}")
  
      # Adjust length of sample weights
      fit_params = fit_params if fit_params is not None else {}
      # fit_params = _check_fit_params(X, fit_params, train)  # FIXME
  
      if parameters is not None:
          # clone after setting parameters in case any parameters
          # are estimators (like pipeline steps)
          # because pipeline doesn't clone steps in fit
          cloned_parameters = {}
          for k, v in parameters.items():
              cloned_parameters[k] = clone(v, safe=False)
  
          estimator = estimator.set_params(**cloned_parameters)
  
      start_time = time.time()
  
      ####################### MODFIED SECTION ##########################
  
      test_splits = {}
  
      # NOTE: ttc stands for train-test combinations
      for is_test_tuple, ttc_name in zip(train_test_combinations, train_test_names):
          # is_test_tuple ~= (0, 1, 1, 0)
          test_indices = [ax_train_test[is_test] for is_test, ax_train_test in
                          zip(is_test_tuple, train_test)]
          test_splits[ttc_name] = _safe_split_nd(estimator, X, y, test_indices)
  
  
      train_indices = [i[0] for i in train_test]
      X_train, y_train = _safe_split_nd(estimator, X, y, train_indices)
  
      result = {}
      try:
          if y_train is None:
              estimator.fit(X_train, **fit_params)
          else:
              estimator.fit(X_train, y_train, **fit_params)
  
      except Exception:
          # Note fit time as time until error
          fit_time = time.time() - start_time
          score_time = 0.0
          if error_score == "raise":
              raise
          elif isinstance(error_score, numbers.Number):
              if isinstance(scorer, dict):
                  test_scores = {
                      ttc_name+'_scores': {name: error_score for name in scorer}
                      for ttc_name in test_splits.keys()
                  }
                  # NOTE: train_score is automatically included by
                  # _check_train_test_combinations, if requested.
              else:
                  test_scores = {
                      ttc_name+'_scores': error_score
                      for ttc_name in test_splits.keys()
                  }
          result["fit_error"] = format_exc()
      else:
          result["fit_error"] = None
  
          fit_time = time.time() - start_time
          test_scores = {}
          for ttc_name, (X_test, y_test) in test_splits.items():
              test_scores[ttc_name+'_scores'] = _score(estimator, X_test, y_test.flatten(),
                                                       scorer, error_score)
          score_time = time.time() - start_time - fit_time
  
      if verbose > 1:
          total_time = score_time + fit_time
          end_msg = f"[CV{progress_msg}] END "
          result_msg = params_msg + (";" if params_msg else "")
          if verbose > 2:
              #if isinstance(test_scores, dict):
              for scorer_name in sorted(test_scores):
                  result_msg += f" {scorer_name}: ("
                  result_msg += f"test={test_scores})"  # FIXME
          result_msg += f" total time={logger.short_format_time(total_time)}"
  
          # Right align the result_msg
          end_msg += "." * (80 - len(end_msg) - len(result_msg))
          end_msg += result_msg
          print(end_msg)
  
      result.update(test_scores)
  
      if return_n_test_samples:
          for ttc_name, (X_test, _) in test_splits.items():
              result[f"n_{ttc_name}_samples"] = tuple(x.shape[0] for x in X_test)
      if return_times:
          result["fit_time"] = fit_time
          result["score_time"] = score_time
      if return_parameters:
          result["parameters"] = parameters
      if return_estimator:
          result["estimator"] = estimator
      return result
  
  
  # NOTE: Originally in sklearn.utils.metaestimators
  def _safe_split_nd(estimator, X, y, indices, train_indices=None):
      """Create subset of n-dimensional dataset.
  
      Slice X, y according to indices for n-dimensional cross-validation.
  
      .. versionchanged:: hypertree
          No ``estimator`` or ``train_indices`` parameters are necessary by now.
  
      Parameters
      ----------
      X : list-like of array-like, sparse matrix or iterable
          The feature matrices for each axis.
  
      y : array-like, sparse matrix or iterable
          Targets to be indexed.
  
      indices : iterator of array of int
          Slice to select from X and y.
  
      Returns
      -------
      X_subset : list of array-like, sparse matrix or list
          Indexed data.
  
      y_subset : array-like, sparse matrix or list
          Indexed targets.
  
      """
      n_dim = y.ndim
      # TODO: further checking in another function may be adeuqate.
      # X_subset = _safe_indexing(X, indices)
      if not (len(X) == len(indices) == n_dim):
          raise ValueError("Incompatible dimensions. One must ensure "
                           "len(X) == len(indices) == y.ndim")
  
      if _safe_tags(estimator, key="pairwise"):
          X_subset = []
          for i in range(n_dim):
              Xi, ind = X[i], indices[i]
              if not hasattr(Xi, "shape"):
                  raise ValueError(
                      "Precomputed kernels or affinity matrices have "
                      "to be passed as arrays or sparse matrices."
                  )
              # Xi is a precomputed square kernel matrix
              if Xi.shape[0] != Xi.shape[1]:
                  raise ValueError("Xi should be a square kernel matrix")
              if train_indices is None:
                  X_subset.append(Xi[np.ix_(ind, ind)])
              else:
                  X_subset.append(Xi[np.ix_(ind, train_indices[i])])
      else:
          X_subset = [Xax[i] for Xax, i in zip(X, indices)]
  
      if y is not None:
          y_subset = y[np.ix_(*indices)]
      else:
          y_subset = None
  
      return X_subset, y_subset
  
  
  # NOTE: Originally in sklearn.utils.__init__
  # FIXME: unused by now.
  def _safe_indexing_nd(X, indices):
      """Return rows, items or columns of X using indices.
  
      .. warning::
  
          This utility is documented, but **private**. This means that
          backward compatibility might be broken without any deprecation
          cycle.
  
      .. versionchanged:: hypertree
          The original sklearn function has an additional argument to specifying
          the axis of indexing, with it being required to be 0 or 1. Since we are
          in the n-dimensional domain, this restriction is eliminated and the axis
          information must be implicit in the `indices`' format, such as
          (slice(None), [3, 4, 5]) to get the columns 3, 4 and 5 of an ndarray (e-
          quivalent to np.s_[:, [3, 4, 5]]).
  
      Parameters
      ----------
      X : array-like, sparse-matrix, list, pandas.DataFrame, pandas.Series
          Data from which to sample rows, items or columns. `list` are only
          supported when `axis=0`.
      indices : bool, int, str, slice, array-like
  
      Returns
      -------
      subset
          Subset of X on axis 0 or 1.
  
      Notes
      -----
      CSR, CSC, and LIL sparse matrices are supported. COO sparse matrices are
      not supported.
      """
      if indices is None:
          return X
  
      # TODO: use isinstance.
      # if hasattr(X, "iloc"):
      #     return _pandas_indexing(X, indices, indices_dtype, axis=axis)
      # elif hasattr(X, "shape"):
      #     return _array_indexing(X, indices, indices_dtype, axis=axis)
      if isinstance(X, list):
          return sklearn.utils._list_indexing(X, indices, indices_dtype)
      else:
          return X[indices]
  