content: """
  The :mod:`sklearn.cross_validation` module includes utilities for cross-
  validation and performance evaluation.
  """
  
  # Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>,
  #         Gael Varoquaux <gael.varoquaux@normalesup.org>,
  #         Olivier Grisel <olivier.grisel@ensta.org>
  # License: BSD 3 clause
  
  from __future__ import print_function
  from __future__ import division
  
  import warnings
  from itertools import chain, combinations
  from math import ceil, floor, factorial
  import numbers
  import time
  from abc import ABCMeta, abstractmethod
  
  import numpy as np
  import scipy.sparse as sp
  
  from .base import is_classifier, clone
  from .utils import indexable, check_random_state, safe_indexing
  from .utils.validation import (_is_arraylike, _num_samples,
                                 check_array, column_or_1d)
  from .utils.multiclass import type_of_target
  from .externals.joblib import Parallel, delayed, logger
  from .externals.six import with_metaclass
  from .externals.six.moves import zip
  from .metrics.scorer import check_scoring
  from .utils.fixes import bincount
  
  __all__ = ['KFold',
             'LeaveOneLabelOut',
             'LeaveOneOut',
             'LeavePLabelOut',
             'LeavePOut',
             'ShuffleSplit',
             'StratifiedKFold',
             'StratifiedShuffleSplit',
             'PredefinedSplit',
             'check_cv',
             'cross_val_score',
             'cross_val_predict',
             'permutation_test_score',
             'train_test_split']
  
  
  class _PartitionIterator(with_metaclass(ABCMeta)):
      """Base class for CV iterators where train_mask = ~test_mask
  
      Implementations must define `_iter_test_masks` or `_iter_test_indices`.
  
      Parameters
      ----------
      n : int
          Total number of elements in dataset.
      """
  
      def __init__(self, n):
          if abs(n - int(n)) >= np.finfo('f').eps:
              raise ValueError("n must be an integer")
          self.n = int(n)
  
      def __iter__(self):
          ind = np.arange(self.n)
          for test_index in self._iter_test_masks():
              train_index = np.logical_not(test_index)
              train_index = ind[train_index]
              test_index = ind[test_index]
              yield train_index, test_index
  
      # Since subclasses must implement either _iter_test_masks or
      # _iter_test_indices, neither can be abstract.
      def _iter_test_masks(self):
          """Generates boolean masks corresponding to test sets.
  
          By default, delegates to _iter_test_indices()
          """
          for test_index in self._iter_test_indices():
              test_mask = self._empty_mask()
              test_mask[test_index] = True
              yield test_mask
  
      def _iter_test_indices(self):
          """Generates integer indices corresponding to test sets."""
          raise NotImplementedError
  
      def _empty_mask(self):
          return np.zeros(self.n, dtype=np.bool)
  
  
  class LeaveOneOut(_PartitionIterator):
      """Leave-One-Out cross validation iterator.
  
      Provides train/test indices to split data in train test sets. Each
      sample is used once as a test set (singleton) while the remaining
      samples form the training set.
  
      Note: ``LeaveOneOut(n)`` is equivalent to ``KFold(n, n_folds=n)`` and
      ``LeavePOut(n, p=1)``.
  
      Due to the high number of test sets (which is the same as the
      number of samples) this cross validation method can be very costly.
      For large datasets one should favor KFold, StratifiedKFold or
      ShuffleSplit.
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      n : int
          Total number of elements in dataset.
  
      Examples
      --------
      >>> from sklearn import cross_validation
      >>> X = np.array([[1, 2], [3, 4]])
      >>> y = np.array([1, 2])
      >>> loo = cross_validation.LeaveOneOut(2)
      >>> len(loo)
      2
      >>> print(loo)
      sklearn.cross_validation.LeaveOneOut(n=2)
      >>> for train_index, test_index in loo:
      ...    print("TRAIN:", train_index, "TEST:", test_index)
      ...    X_train, X_test = X[train_index], X[test_index]
      ...    y_train, y_test = y[train_index], y[test_index]
      ...    print(X_train, X_test, y_train, y_test)
      TRAIN: [1] TEST: [0]
      [[3 4]] [[1 2]] [2] [1]
      TRAIN: [0] TEST: [1]
      [[1 2]] [[3 4]] [1] [2]
  
      See also
      --------
      LeaveOneLabelOut for splitting the data according to explicit,
      domain-specific stratification of the dataset.
      """
  
      def _iter_test_indices(self):
          return range(self.n)
  
      def __repr__(self):
          return '%s.%s(n=%i)' % (
              self.__class__.__module__,
              self.__class__.__name__,
              self.n,
          )
  
      def __len__(self):
          return self.n
  
  
  class LeavePOut(_PartitionIterator):
      """Leave-P-Out cross validation iterator
  
      Provides train/test indices to split data in train test sets. This results
      in testing on all distinct samples of size p, while the remaining n - p
      samples form the training set in each iteration.
  
      Note: ``LeavePOut(n, p)`` is NOT equivalent to ``KFold(n, n_folds=n // p)``
      which creates non-overlapping test sets.
  
      Due to the high number of iterations which grows combinatorically with the
      number of samples this cross validation method can be very costly. For
      large datasets one should favor KFold, StratifiedKFold or ShuffleSplit.
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      n : int
          Total number of elements in dataset.
  
      p : int
          Size of the test sets.
  
      Examples
      --------
      >>> from sklearn import cross_validation
      >>> X = np.array([[1, 2], [3, 4], [5, 6], [7, 8]])
      >>> y = np.array([1, 2, 3, 4])
      >>> lpo = cross_validation.LeavePOut(4, 2)
      >>> len(lpo)
      6
      >>> print(lpo)
      sklearn.cross_validation.LeavePOut(n=4, p=2)
      >>> for train_index, test_index in lpo:
      ...    print("TRAIN:", train_index, "TEST:", test_index)
      ...    X_train, X_test = X[train_index], X[test_index]
      ...    y_train, y_test = y[train_index], y[test_index]
      TRAIN: [2 3] TEST: [0 1]
      TRAIN: [1 3] TEST: [0 2]
      TRAIN: [1 2] TEST: [0 3]
      TRAIN: [0 3] TEST: [1 2]
      TRAIN: [0 2] TEST: [1 3]
      TRAIN: [0 1] TEST: [2 3]
      """
  
      def __init__(self, n, p):
          super(LeavePOut, self).__init__(n)
          self.p = p
  
      def _iter_test_indices(self):
          for comb in combinations(range(self.n), self.p):
              yield np.array(comb)
  
      def __repr__(self):
          return '%s.%s(n=%i, p=%i)' % (
              self.__class__.__module__,
              self.__class__.__name__,
              self.n,
              self.p,
          )
  
      def __len__(self):
          return int(factorial(self.n) / factorial(self.n - self.p)
                     / factorial(self.p))
  
  
  class _BaseKFold(with_metaclass(ABCMeta, _PartitionIterator)):
      """Base class to validate KFold approaches"""
  
      @abstractmethod
      def __init__(self, n, n_folds, shuffle, random_state):
          super(_BaseKFold, self).__init__(n)
  
          if abs(n_folds - int(n_folds)) >= np.finfo('f').eps:
              raise ValueError("n_folds must be an integer")
          self.n_folds = n_folds = int(n_folds)
  
          if n_folds <= 1:
              raise ValueError(
                  "k-fold cross validation requires at least one"
                  " train / test split by setting n_folds=2 or more,"
                  " got n_folds={0}.".format(n_folds))
          if n_folds > self.n:
              raise ValueError(
                  ("Cannot have number of folds n_folds={0} greater"
                   " than the number of samples: {1}.").format(n_folds, n))
  
          if not isinstance(shuffle, bool):
              raise TypeError("shuffle must be True or False;"
                              " got {0}".format(shuffle))
          self.shuffle = shuffle
          self.random_state = random_state
  
  
  class KFold(_BaseKFold):
      """K-Folds cross validation iterator.
  
      Provides train/test indices to split data in train test sets. Split
      dataset into k consecutive folds (without shuffling).
  
      Each fold is then used a validation set once while the k - 1 remaining
      fold form the training set.
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      n : int
          Total number of elements.
  
      n_folds : int, default=3
          Number of folds. Must be at least 2.
  
      shuffle : boolean, optional
          Whether to shuffle the data before splitting into batches.
  
      random_state : None, int or RandomState
          Pseudo-random number generator state used for random
          sampling. If None, use default numpy RNG for shuffling
  
      Examples
      --------
      >>> from sklearn import cross_validation
      >>> X = np.array([[1, 2], [3, 4], [1, 2], [3, 4]])
      >>> y = np.array([1, 2, 3, 4])
      >>> kf = cross_validation.KFold(4, n_folds=2)
      >>> len(kf)
      2
      >>> print(kf)  # doctest: +NORMALIZE_WHITESPACE
      sklearn.cross_validation.KFold(n=4, n_folds=2, shuffle=False,
                                     random_state=None)
      >>> for train_index, test_index in kf:
      ...    print("TRAIN:", train_index, "TEST:", test_index)
      ...    X_train, X_test = X[train_index], X[test_index]
      ...    y_train, y_test = y[train_index], y[test_index]
      TRAIN: [2 3] TEST: [0 1]
      TRAIN: [0 1] TEST: [2 3]
  
      Notes
      -----
      The first n % n_folds folds have size n // n_folds + 1, other folds have
      size n // n_folds.
  
      See also
      --------
      StratifiedKFold: take label information into account to avoid building
      folds with imbalanced class distributions (for binary or multiclass
      classification tasks).
      """
  
      def __init__(self, n, n_folds=3, shuffle=False,
                   random_state=None):
          super(KFold, self).__init__(n, n_folds, shuffle, random_state)
          self.idxs = np.arange(n)
          if shuffle:
              rng = check_random_state(self.random_state)
              rng.shuffle(self.idxs)
  
      def _iter_test_indices(self):
          n = self.n
          n_folds = self.n_folds
          fold_sizes = (n // n_folds) * np.ones(n_folds, dtype=np.int)
          fold_sizes[:n % n_folds] += 1
          current = 0
          for fold_size in fold_sizes:
              start, stop = current, current + fold_size
              yield self.idxs[start:stop]
              current = stop
  
      def __repr__(self):
          return '%s.%s(n=%i, n_folds=%i, shuffle=%s, random_state=%s)' % (
              self.__class__.__module__,
              self.__class__.__name__,
              self.n,
              self.n_folds,
              self.shuffle,
              self.random_state,
          )
  
      def __len__(self):
          return self.n_folds
  
  
  class StratifiedKFold(_BaseKFold):
      """Stratified K-Folds cross validation iterator
  
      Provides train/test indices to split data in train test sets.
  
      This cross-validation object is a variation of KFold that
      returns stratified folds. The folds are made by preserving
      the percentage of samples for each class.
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      y : array-like, [n_samples]
          Samples to split in K folds.
  
      n_folds : int, default=3
          Number of folds. Must be at least 2.
  
      shuffle : boolean, optional
          Whether to shuffle each stratification of the data before splitting
          into batches.
  
      random_state : None, int or RandomState
          Pseudo-random number generator state used for random
          sampling. If None, use default numpy RNG for shuffling
  
      Examples
      --------
      >>> from sklearn import cross_validation
      >>> X = np.array([[1, 2], [3, 4], [1, 2], [3, 4]])
      >>> y = np.array([0, 0, 1, 1])
      >>> skf = cross_validation.StratifiedKFold(y, n_folds=2)
      >>> len(skf)
      2
      >>> print(skf)  # doctest: +NORMALIZE_WHITESPACE
      sklearn.cross_validation.StratifiedKFold(labels=[0 0 1 1], n_folds=2,
                                               shuffle=False, random_state=None)
      >>> for train_index, test_index in skf:
      ...    print("TRAIN:", train_index, "TEST:", test_index)
      ...    X_train, X_test = X[train_index], X[test_index]
      ...    y_train, y_test = y[train_index], y[test_index]
      TRAIN: [1 3] TEST: [0 2]
      TRAIN: [0 2] TEST: [1 3]
  
      Notes
      -----
      All the folds have size trunc(n_samples / n_folds), the last one has the
      complementary.
  
      """
  
      def __init__(self, y, n_folds=3, shuffle=False,
                   random_state=None):
          super(StratifiedKFold, self).__init__(
              len(y), n_folds, shuffle, random_state)
          y = np.asarray(y)
          n_samples = y.shape[0]
          unique_labels, y_inversed = np.unique(y, return_inverse=True)
          label_counts = bincount(y_inversed)
          min_labels = np.min(label_counts)
          if self.n_folds > min_labels:
              warnings.warn(("The least populated class in y has only %d"
                             " members, which is too few. The minimum"
                             " number of labels for any class cannot"
                             " be less than n_folds=%d."
                             % (min_labels, self.n_folds)), Warning)
  
          # don't want to use the same seed in each label's shuffle
          if self.shuffle:
              rng = check_random_state(self.random_state)
          else:
              rng = self.random_state
  
          # pre-assign each sample to a test fold index using individual KFold
          # splitting strategies for each label so as to respect the
          # balance of labels
          per_label_cvs = [
              KFold(max(c, self.n_folds), self.n_folds, shuffle=self.shuffle,
                    random_state=rng) for c in label_counts]
          test_folds = np.zeros(n_samples, dtype=np.int)
          for test_fold_idx, per_label_splits in enumerate(zip(*per_label_cvs)):
              for label, (_, test_split) in zip(unique_labels, per_label_splits):
                  label_test_folds = test_folds[y == label]
                  # the test split can be too big because we used
                  # KFold(max(c, self.n_folds), self.n_folds) instead of
                  # KFold(c, self.n_folds) to make it possible to not crash even
                  # if the data is not 100% stratifiable for all the labels
                  # (we use a warning instead of raising an exception)
                  # If this is the case, let's trim it:
                  test_split = test_split[test_split < len(label_test_folds)]
                  label_test_folds[test_split] = test_fold_idx
                  test_folds[y == label] = label_test_folds
  
          self.test_folds = test_folds
          self.y = y
  
      def _iter_test_masks(self):
          for i in range(self.n_folds):
              yield self.test_folds == i
  
      def __repr__(self):
          return '%s.%s(labels=%s, n_folds=%i, shuffle=%s, random_state=%s)' % (
              self.__class__.__module__,
              self.__class__.__name__,
              self.y,
              self.n_folds,
              self.shuffle,
              self.random_state,
          )
  
      def __len__(self):
          return self.n_folds
  
  
  class LeaveOneLabelOut(_PartitionIterator):
      """Leave-One-Label_Out cross-validation iterator
  
      Provides train/test indices to split data according to a third-party
      provided label. This label information can be used to encode arbitrary
      domain specific stratifications of the samples as integers.
  
      For instance the labels could be the year of collection of the samples
      and thus allow for cross-validation against time-based splits.
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      labels : array-like of int with shape (n_samples,)
          Arbitrary domain-specific stratification of the data to be used
          to draw the splits.
  
      Examples
      --------
      >>> from sklearn import cross_validation
      >>> X = np.array([[1, 2], [3, 4], [5, 6], [7, 8]])
      >>> y = np.array([1, 2, 1, 2])
      >>> labels = np.array([1, 1, 2, 2])
      >>> lol = cross_validation.LeaveOneLabelOut(labels)
      >>> len(lol)
      2
      >>> print(lol)
      sklearn.cross_validation.LeaveOneLabelOut(labels=[1 1 2 2])
      >>> for train_index, test_index in lol:
      ...    print("TRAIN:", train_index, "TEST:", test_index)
      ...    X_train, X_test = X[train_index], X[test_index]
      ...    y_train, y_test = y[train_index], y[test_index]
      ...    print(X_train, X_test, y_train, y_test)
      TRAIN: [2 3] TEST: [0 1]
      [[5 6]
       [7 8]] [[1 2]
       [3 4]] [1 2] [1 2]
      TRAIN: [0 1] TEST: [2 3]
      [[1 2]
       [3 4]] [[5 6]
       [7 8]] [1 2] [1 2]
  
      """
  
      def __init__(self, labels):
          super(LeaveOneLabelOut, self).__init__(len(labels))
          # We make a copy of labels to avoid side-effects during iteration
          self.labels = np.array(labels, copy=True)
          self.unique_labels = np.unique(labels)
          self.n_unique_labels = len(self.unique_labels)
  
      def _iter_test_masks(self):
          for i in self.unique_labels:
              yield self.labels == i
  
      def __repr__(self):
          return '%s.%s(labels=%s)' % (
              self.__class__.__module__,
              self.__class__.__name__,
              self.labels,
          )
  
      def __len__(self):
          return self.n_unique_labels
  
  
  class LeavePLabelOut(_PartitionIterator):
      """Leave-P-Label_Out cross-validation iterator
  
      Provides train/test indices to split data according to a third-party
      provided label. This label information can be used to encode arbitrary
      domain specific stratifications of the samples as integers.
  
      For instance the labels could be the year of collection of the samples
      and thus allow for cross-validation against time-based splits.
  
      The difference between LeavePLabelOut and LeaveOneLabelOut is that
      the former builds the test sets with all the samples assigned to
      ``p`` different values of the labels while the latter uses samples
      all assigned the same labels.
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      labels : array-like of int with shape (n_samples,)
          Arbitrary domain-specific stratification of the data to be used
          to draw the splits.
  
      p : int
          Number of samples to leave out in the test split.
  
      Examples
      --------
      >>> from sklearn import cross_validation
      >>> X = np.array([[1, 2], [3, 4], [5, 6]])
      >>> y = np.array([1, 2, 1])
      >>> labels = np.array([1, 2, 3])
      >>> lpl = cross_validation.LeavePLabelOut(labels, p=2)
      >>> len(lpl)
      3
      >>> print(lpl)
      sklearn.cross_validation.LeavePLabelOut(labels=[1 2 3], p=2)
      >>> for train_index, test_index in lpl:
      ...    print("TRAIN:", train_index, "TEST:", test_index)
      ...    X_train, X_test = X[train_index], X[test_index]
      ...    y_train, y_test = y[train_index], y[test_index]
      ...    print(X_train, X_test, y_train, y_test)
      TRAIN: [2] TEST: [0 1]
      [[5 6]] [[1 2]
       [3 4]] [1] [1 2]
      TRAIN: [1] TEST: [0 2]
      [[3 4]] [[1 2]
       [5 6]] [2] [1 1]
      TRAIN: [0] TEST: [1 2]
      [[1 2]] [[3 4]
       [5 6]] [1] [2 1]
      """
  
      def __init__(self, labels, p):
          # We make a copy of labels to avoid side-effects during iteration
          super(LeavePLabelOut, self).__init__(len(labels))
          self.labels = np.array(labels, copy=True)
          self.unique_labels = np.unique(labels)
          self.n_unique_labels = len(self.unique_labels)
          self.p = p
  
      def _iter_test_masks(self):
          comb = combinations(range(self.n_unique_labels), self.p)
          for idx in comb:
              test_index = self._empty_mask()
              idx = np.array(idx)
              for l in self.unique_labels[idx]:
                  test_index[self.labels == l] = True
              yield test_index
  
      def __repr__(self):
          return '%s.%s(labels=%s, p=%s)' % (
              self.__class__.__module__,
              self.__class__.__name__,
              self.labels,
              self.p,
          )
  
      def __len__(self):
          return int(factorial(self.n_unique_labels) /
                     factorial(self.n_unique_labels - self.p) /
                     factorial(self.p))
  
  
  class BaseShuffleSplit(with_metaclass(ABCMeta)):
      """Base class for ShuffleSplit and StratifiedShuffleSplit"""
  
      def __init__(self, n, n_iter=10, test_size=0.1, train_size=None,
                   random_state=None):
          self.n = n
          self.n_iter = n_iter
          self.test_size = test_size
          self.train_size = train_size
          self.random_state = random_state
          self.n_train, self.n_test = _validate_shuffle_split(n, test_size,
                                                              train_size)
  
      def __iter__(self):
          for train, test in self._iter_indices():
              yield train, test
          return
  
      @abstractmethod
      def _iter_indices(self):
          """Generate (train, test) indices"""
  
  
  class ShuffleSplit(BaseShuffleSplit):
      """Random permutation cross-validation iterator.
  
      Yields indices to split data into training and test sets.
  
      Note: contrary to other cross-validation strategies, random splits
      do not guarantee that all folds will be different, although this is
      still very likely for sizeable datasets.
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      n : int
          Total number of elements in the dataset.
  
      n_iter : int (default 10)
          Number of re-shuffling & splitting iterations.
  
      test_size : float (default 0.1), int, or None
          If float, should be between 0.0 and 1.0 and represent the
          proportion of the dataset to include in the test split. If
          int, represents the absolute number of test samples. If None,
          the value is automatically set to the complement of the train size.
  
      train_size : float, int, or None (default is None)
          If float, should be between 0.0 and 1.0 and represent the
          proportion of the dataset to include in the train split. If
          int, represents the absolute number of train samples. If None,
          the value is automatically set to the complement of the test size.
  
      random_state : int or RandomState
          Pseudo-random number generator state used for random sampling.
  
      Examples
      --------
      >>> from sklearn import cross_validation
      >>> rs = cross_validation.ShuffleSplit(4, n_iter=3,
      ...     test_size=.25, random_state=0)
      >>> len(rs)
      3
      >>> print(rs)
      ... # doctest: +ELLIPSIS
      ShuffleSplit(4, n_iter=3, test_size=0.25, ...)
      >>> for train_index, test_index in rs:
      ...    print("TRAIN:", train_index, "TEST:", test_index)
      ...
      TRAIN: [3 1 0] TEST: [2]
      TRAIN: [2 1 3] TEST: [0]
      TRAIN: [0 2 1] TEST: [3]
  
      >>> rs = cross_validation.ShuffleSplit(4, n_iter=3,
      ...     train_size=0.5, test_size=.25, random_state=0)
      >>> for train_index, test_index in rs:
      ...    print("TRAIN:", train_index, "TEST:", test_index)
      ...
      TRAIN: [3 1] TEST: [2]
      TRAIN: [2 1] TEST: [0]
      TRAIN: [0 2] TEST: [3]
  
      """
  
      def _iter_indices(self):
          rng = check_random_state(self.random_state)
          for i in range(self.n_iter):
              # random partition
              permutation = rng.permutation(self.n)
              ind_test = permutation[:self.n_test]
              ind_train = permutation[self.n_test:self.n_test + self.n_train]
              yield ind_train, ind_test
  
      def __repr__(self):
          return ('%s(%d, n_iter=%d, test_size=%s, '
                  'random_state=%s)' % (
                      self.__class__.__name__,
                      self.n,
                      self.n_iter,
                      str(self.test_size),
                      self.random_state,
                  ))
  
      def __len__(self):
          return self.n_iter
  
  
  def _validate_shuffle_split(n, test_size, train_size):
      if test_size is None and train_size is None:
          raise ValueError(
              'test_size and train_size can not both be None')
  
      if test_size is not None:
          if np.asarray(test_size).dtype.kind == 'f':
              if test_size >= 1.:
                  raise ValueError(
                      'test_size=%f should be smaller '
                      'than 1.0 or be an integer' % test_size)
          elif np.asarray(test_size).dtype.kind == 'i':
              if test_size >= n:
                  raise ValueError(
                      'test_size=%d should be smaller '
                      'than the number of samples %d' % (test_size, n))
          else:
              raise ValueError("Invalid value for test_size: %r" % test_size)
  
      if train_size is not None:
          if np.asarray(train_size).dtype.kind == 'f':
              if train_size >= 1.:
                  raise ValueError("train_size=%f should be smaller "
                                   "than 1.0 or be an integer" % train_size)
              elif np.asarray(test_size).dtype.kind == 'f' and \
                      train_size + test_size > 1.:
                  raise ValueError('The sum of test_size and train_size = %f, '
                                   'should be smaller than 1.0. Reduce '
                                   'test_size and/or train_size.' %
                                   (train_size + test_size))
          elif np.asarray(train_size).dtype.kind == 'i':
              if train_size >= n:
                  raise ValueError("train_size=%d should be smaller "
                                   "than the number of samples %d" %
                                   (train_size, n))
          else:
              raise ValueError("Invalid value for train_size: %r" % train_size)
  
      if np.asarray(test_size).dtype.kind == 'f':
          n_test = ceil(test_size * n)
      elif np.asarray(test_size).dtype.kind == 'i':
          n_test = float(test_size)
  
      if train_size is None:
          n_train = n - n_test
      else:
          if np.asarray(train_size).dtype.kind == 'f':
              n_train = floor(train_size * n)
          else:
              n_train = float(train_size)
  
      if test_size is None:
          n_test = n - n_train
  
      if n_train + n_test > n:
          raise ValueError('The sum of train_size and test_size = %d, '
                           'should be smaller than the number of '
                           'samples %d. Reduce test_size and/or '
                           'train_size.' % (n_train + n_test, n))
  
      return int(n_train), int(n_test)
  
  
  class StratifiedShuffleSplit(BaseShuffleSplit):
      """Stratified ShuffleSplit cross validation iterator
  
      Provides train/test indices to split data in train test sets.
  
      This cross-validation object is a merge of StratifiedKFold and
      ShuffleSplit, which returns stratified randomized folds. The folds
      are made by preserving the percentage of samples for each class.
  
      Note: like the ShuffleSplit strategy, stratified random splits
      do not guarantee that all folds will be different, although this is
      still very likely for sizeable datasets.
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      y : array, [n_samples]
          Labels of samples.
  
      n_iter : int (default 10)
          Number of re-shuffling & splitting iterations.
  
      test_size : float (default 0.1), int, or None
          If float, should be between 0.0 and 1.0 and represent the
          proportion of the dataset to include in the test split. If
          int, represents the absolute number of test samples. If None,
          the value is automatically set to the complement of the train size.
  
      train_size : float, int, or None (default is None)
          If float, should be between 0.0 and 1.0 and represent the
          proportion of the dataset to include in the train split. If
          int, represents the absolute number of train samples. If None,
          the value is automatically set to the complement of the test size.
  
      random_state : int or RandomState
          Pseudo-random number generator state used for random sampling.
  
      Examples
      --------
      >>> from sklearn.cross_validation import StratifiedShuffleSplit
      >>> X = np.array([[1, 2], [3, 4], [1, 2], [3, 4]])
      >>> y = np.array([0, 0, 1, 1])
      >>> sss = StratifiedShuffleSplit(y, 3, test_size=0.5, random_state=0)
      >>> len(sss)
      3
      >>> print(sss)       # doctest: +ELLIPSIS
      StratifiedShuffleSplit(labels=[0 0 1 1], n_iter=3, ...)
      >>> for train_index, test_index in sss:
      ...    print("TRAIN:", train_index, "TEST:", test_index)
      ...    X_train, X_test = X[train_index], X[test_index]
      ...    y_train, y_test = y[train_index], y[test_index]
      TRAIN: [1 2] TEST: [3 0]
      TRAIN: [0 2] TEST: [1 3]
      TRAIN: [0 2] TEST: [3 1]
      """
  
      def __init__(self, y, n_iter=10, test_size=0.1, train_size=None,
                   random_state=None):
  
          super(StratifiedShuffleSplit, self).__init__(
              len(y), n_iter, test_size, train_size, random_state)
  
          self.y = np.array(y)
          self.classes, self.y_indices = np.unique(y, return_inverse=True)
          n_cls = self.classes.shape[0]
  
          if np.min(bincount(self.y_indices)) < 2:
              raise ValueError("The least populated class in y has only 1"
                               " member, which is too few. The minimum"
                               " number of labels for any class cannot"
                               " be less than 2.")
  
          if self.n_train < n_cls:
              raise ValueError('The train_size = %d should be greater or '
                               'equal to the number of classes = %d' %
                               (self.n_train, n_cls))
          if self.n_test < n_cls:
              raise ValueError('The test_size = %d should be greater or '
                               'equal to the number of classes = %d' %
                               (self.n_test, n_cls))
  
      def _iter_indices(self):
          rng = check_random_state(self.random_state)
          cls_count = bincount(self.y_indices)
          p_i = cls_count / float(self.n)
          n_i = np.round(self.n_train * p_i).astype(int)
          t_i = np.minimum(cls_count - n_i,
                           np.round(self.n_test * p_i).astype(int))
  
          for n in range(self.n_iter):
              train = []
              test = []
  
              for i, cls in enumerate(self.classes):
                  permutation = rng.permutation(cls_count[i])
                  cls_i = np.where((self.y == cls))[0][permutation]
  
                  train.extend(cls_i[:n_i[i]])
                  test.extend(cls_i[n_i[i]:n_i[i] + t_i[i]])
  
              # Because of rounding issues (as n_train and n_test are not
              # dividers of the number of elements per class), we may end
              # up here with less samples in train and test than asked for.
              if len(train) < self.n_train or len(test) < self.n_test:
                  # We complete by affecting randomly the missing indexes
                  missing_idx = np.where(bincount(train + test,
                                                  minlength=len(self.y)) == 0,
                                         )[0]
                  missing_idx = rng.permutation(missing_idx)
                  train.extend(missing_idx[:(self.n_train - len(train))])
                  test.extend(missing_idx[-(self.n_test - len(test)):])
  
              train = rng.permutation(train)
              test = rng.permutation(test)
  
              yield train, test
  
      def __repr__(self):
          return ('%s(labels=%s, n_iter=%d, test_size=%s, '
                  'random_state=%s)' % (
                      self.__class__.__name__,
                      self.y,
                      self.n_iter,
                      str(self.test_size),
                      self.random_state,
                  ))
  
      def __len__(self):
          return self.n_iter
  
  
  class PredefinedSplit(_PartitionIterator):
      """Predefined split cross validation iterator
  
      Splits the data into training/test set folds according to a predefined
      scheme. Each sample can be assigned to at most one test set fold, as
      specified by the user through the ``test_fold`` parameter.
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      test_fold : "array-like, shape (n_samples,)
          test_fold[i] gives the test set fold of sample i. A value of -1
          indicates that the corresponding sample is not part of any test set
          folds, but will instead always be put into the training fold.
  
      Examples
      --------
      >>> from sklearn.cross_validation import PredefinedSplit
      >>> X = np.array([[1, 2], [3, 4], [1, 2], [3, 4]])
      >>> y = np.array([0, 0, 1, 1])
      >>> ps = PredefinedSplit(test_fold=[0, 1, -1, 1])
      >>> len(ps)
      2
      >>> print(ps)       # doctest: +NORMALIZE_WHITESPACE +ELLIPSIS
      sklearn.cross_validation.PredefinedSplit(test_fold=[ 0  1 -1  1])
      >>> for train_index, test_index in ps:
      ...    print("TRAIN:", train_index, "TEST:", test_index)
      ...    X_train, X_test = X[train_index], X[test_index]
      ...    y_train, y_test = y[train_index], y[test_index]
      TRAIN: [1 2 3] TEST: [0]
      TRAIN: [0 2] TEST: [1 3]
      """
  
      def __init__(self, test_fold):
          super(PredefinedSplit, self).__init__(len(test_fold))
          self.test_fold = np.array(test_fold, dtype=np.int)
          self.test_fold = column_or_1d(self.test_fold)
          self.unique_folds = np.unique(self.test_fold)
          self.unique_folds = self.unique_folds[self.unique_folds != -1]
  
      def _iter_test_indices(self):
          for f in self.unique_folds:
              yield np.where(self.test_fold == f)[0]
  
      def __repr__(self):
          return '%s.%s(test_fold=%s)' % (
              self.__class__.__module__,
              self.__class__.__name__,
              self.test_fold)
  
      def __len__(self):
          return len(self.unique_folds)
  
  
  ##############################################################################
  def _index_param_value(X, v, indices):
      """Private helper function for parameter value indexing."""
      if not _is_arraylike(v) or _num_samples(v) != _num_samples(X):
          # pass through: skip indexing
          return v
      if sp.issparse(v):
          v = v.tocsr()
      return safe_indexing(v, indices)
  
  
  def cross_val_predict(estimator, X, y=None, cv=None, n_jobs=1,
                        verbose=0, fit_params=None, pre_dispatch='2*n_jobs'):
      """Generate cross-validated estimates for each input data point
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      estimator : estimator object implementing 'fit' and 'predict'
          The object to use to fit the data.
  
      X : array-like
          The data to fit. Can be, for example a list, or an array at least 2d.
  
      y : array-like, optional, default: None
          The target variable to try to predict in the case of
          supervised learning.
  
      cv : cross-validation generator or int, optional, default: None
          A cross-validation generator to use. If int, determines
          the number of folds in StratifiedKFold if y is binary
          or multiclass and estimator is a classifier, or the number
          of folds in KFold otherwise. If None, it is equivalent to cv=3.
          This generator must include all elements in the test set exactly once.
          Otherwise, a ValueError is raised.
  
      n_jobs : integer, optional
          The number of CPUs to use to do the computation. -1 means
          'all CPUs'.
  
      verbose : integer, optional
          The verbosity level.
  
      fit_params : dict, optional
          Parameters to pass to the fit method of the estimator.
  
      pre_dispatch : int, or string, optional
          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 string, giving an expression as a function of n_jobs,
                as in '2*n_jobs'
  
      Returns
      -------
      preds : ndarray
          This is the result of calling 'predict'
      """
      X, y = indexable(X, y)
  
      cv = check_cv(cv, X, y, classifier=is_classifier(estimator))
      # 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)
      preds_blocks = parallel(delayed(_fit_and_predict)(clone(estimator), X, y,
                                                        train, test, verbose,
                                                        fit_params)
                              for train, test in cv)
      p = np.concatenate([p for p, _ in preds_blocks])
      locs = np.concatenate([loc for _, loc in preds_blocks])
      if not _check_is_partition(locs, _num_samples(X)):
          raise ValueError('cross_val_predict only works for partitions')
      preds = p.copy()
      preds[locs] = p
      return preds
  
  
  def _fit_and_predict(estimator, X, y, train, test, verbose, fit_params):
      """Fit estimator and predict values for a given dataset split.
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      estimator : estimator object implementing 'fit' and 'predict'
          The object to use to fit the data.
  
      X : array-like of shape at least 2D
          The data to fit.
  
      y : array-like, optional, default: None
          The target variable to try to predict in the case of
          supervised learning.
  
      train : array-like, shape (n_train_samples,)
          Indices of training samples.
  
      test : array-like, shape (n_test_samples,)
          Indices of test samples.
  
      verbose : integer
          The verbosity level.
  
      fit_params : dict or None
          Parameters that will be passed to ``estimator.fit``.
  
      Returns
      -------
      preds : sequence
          Result of calling 'estimator.predict'
  
      test : array-like
          This is the value of the test parameter
      """
      # Adjust length of sample weights
      fit_params = fit_params if fit_params is not None else {}
      fit_params = dict([(k, _index_param_value(X, v, train))
                        for k, v in fit_params.items()])
  
      X_train, y_train = _safe_split(estimator, X, y, train)
      X_test, _ = _safe_split(estimator, X, y, test, train)
  
      if y_train is None:
          estimator.fit(X_train, **fit_params)
      else:
          estimator.fit(X_train, y_train, **fit_params)
      preds = estimator.predict(X_test)
      return preds, test
  
  
  def _check_is_partition(locs, n):
      """Check whether locs is a reordering of the array np.arange(n)
  
      Parameters
      ----------
      locs : ndarray
          integer array to test
      n : int
          number of expected elements
  
      Returns
      -------
      is_partition : bool
          True iff sorted(locs) is range(n)
      """
      if len(locs) != n:
          return False
      hit = np.zeros(n, bool)
      hit[locs] = True
      if not np.all(hit):
          return False
      return True
  
  
  def cross_val_score(estimator, X, y=None, scoring=None, cv=None, n_jobs=1,
                      verbose=0, fit_params=None, pre_dispatch='2*n_jobs'):
      """Evaluate a score by cross-validation
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      estimator : estimator object implementing 'fit'
          The object to use to fit the data.
  
      X : array-like
          The data to fit. Can be, for example a list, or an array at least 2d.
  
      y : array-like, optional, default: None
          The target variable to try to predict in the case of
          supervised learning.
  
      scoring : string, callable or None, optional, default: None
          A string (see model evaluation documentation) or
          a scorer callable object / function with signature
          ``scorer(estimator, X, y)``.
  
      cv : cross-validation generator or int, optional, default: None
          A cross-validation generator to use. If int, determines
          the number of folds in StratifiedKFold if y is binary
          or multiclass and estimator is a classifier, or the number
          of folds in KFold otherwise. If None, it is equivalent to cv=3.
  
      n_jobs : integer, optional
          The number of CPUs to use to do the computation. -1 means
          'all CPUs'.
  
      verbose : integer, optional
          The verbosity level.
  
      fit_params : dict, optional
          Parameters to pass to the fit method of the estimator.
  
      pre_dispatch : int, or string, optional
          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 string, giving an expression as a function of n_jobs,
                as in '2*n_jobs'
  
      Returns
      -------
      scores : array of float, shape=(len(list(cv)),)
          Array of scores of the estimator for each run of the cross validation.
      """
      X, y = indexable(X, y)
  
      cv = check_cv(cv, X, y, classifier=is_classifier(estimator))
      scorer = check_scoring(estimator, scoring=scoring)
      # 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)
      scores = parallel(delayed(_fit_and_score)(clone(estimator), X, y, scorer,
                                                train, test, verbose, None,
                                                fit_params)
                        for train, test in cv)
      return np.array(scores)[:, 0]
  
  
  class FitFailedWarning(RuntimeWarning):
      pass
  
  
  def _fit_and_score(estimator, X, y, scorer, train, test, verbose,
                     parameters, fit_params, return_train_score=False,
                     return_parameters=False, error_score='raise'):
      """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 at least 2D
          The data to fit.
  
      y : array-like, optional, default: None
          The target variable to try to predict in the case of
          supervised learning.
  
      scorer : callable
          A scorer callable object / function with signature
          ``scorer(estimator, X, y)``.
  
      train : array-like, shape (n_train_samples,)
          Indices of training samples.
  
      test : array-like, shape (n_test_samples,)
          Indices of test samples.
  
      verbose : integer
          The verbosity level.
  
      error_score : 'raise' (default) or numeric
          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. This parameter does not affect the refit
          step, which will always raise the error.
  
      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 : boolean, optional, default: False
          Compute and return score on training set.
  
      return_parameters : boolean, optional, default: False
          Return parameters that has been used for the estimator.
  
      Returns
      -------
      train_score : float, optional
          Score on training set, returned only if `return_train_score` is `True`.
  
      test_score : float
          Score on test set.
  
      n_test_samples : int
          Number of test samples.
  
      scoring_time : float
          Time spent for fitting and scoring in seconds.
  
      parameters : dict or None, optional
          The parameters that have been evaluated.
      """
      if verbose > 1:
          if parameters is None:
              msg = "no parameters to be set"
          else:
              msg = '%s' % (', '.join('%s=%s' % (k, v)
                            for k, v in parameters.items()))
          print("[CV] %s %s" % (msg, (64 - len(msg)) * '.'))
  
      # Adjust length of sample weights
      fit_params = fit_params if fit_params is not None else {}
      fit_params = dict([(k, _index_param_value(X, v, train))
                        for k, v in fit_params.items()])
  
      if parameters is not None:
          estimator.set_params(**parameters)
  
      start_time = time.time()
  
      X_train, y_train = _safe_split(estimator, X, y, train)
      X_test, y_test = _safe_split(estimator, X, y, test, train)
  
      try:
          if y_train is None:
              estimator.fit(X_train, **fit_params)
          else:
              estimator.fit(X_train, y_train, **fit_params)
  
      except Exception as e:
          if error_score == 'raise':
              raise
          elif isinstance(error_score, numbers.Number):
              test_score = error_score
              if return_train_score:
                  train_score = error_score
              warnings.warn("Classifier fit failed. The score on this train-test"
                            " partition for these parameters will be set to %f. "
                            "Details: \n%r" % (error_score, e), FitFailedWarning)
          else:
              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.)"
                               )
  
      else:
          test_score = _score(estimator, X_test, y_test, scorer)
          if return_train_score:
              train_score = _score(estimator, X_train, y_train, scorer)
  
      scoring_time = time.time() - start_time
  
      if verbose > 2:
          msg += ", score=%f" % test_score
      if verbose > 1:
          end_msg = "%s -%s" % (msg, logger.short_format_time(scoring_time))
          print("[CV] %s %s" % ((64 - len(end_msg)) * '.', end_msg))
  
      ret = [train_score] if return_train_score else []
      ret.extend([test_score, _num_samples(X_test), scoring_time])
      if return_parameters:
          ret.append(parameters)
      return ret
  
  
  def _safe_split(estimator, X, y, indices, train_indices=None):
      """Create subset of dataset and properly handle kernels."""
      if hasattr(estimator, 'kernel') and callable(estimator.kernel):
          # cannot compute the kernel values with custom function
          raise ValueError("Cannot use a custom kernel function. "
                           "Precompute the kernel matrix instead.")
  
      if not hasattr(X, "shape"):
          if getattr(estimator, "_pairwise", False):
              raise ValueError("Precomputed kernels or affinity matrices have "
                               "to be passed as arrays or sparse matrices.")
          X_subset = [X[idx] for idx in indices]
      else:
          if getattr(estimator, "_pairwise", False):
              # X is a precomputed square kernel matrix
              if X.shape[0] != X.shape[1]:
                  raise ValueError("X should be a square kernel matrix")
              if train_indices is None:
                  X_subset = X[np.ix_(indices, indices)]
              else:
                  X_subset = X[np.ix_(indices, train_indices)]
          else:
              X_subset = safe_indexing(X, indices)
  
      if y is not None:
          y_subset = safe_indexing(y, indices)
      else:
          y_subset = None
  
      return X_subset, y_subset
  
  
  def _score(estimator, X_test, y_test, scorer):
      """Compute the score of an estimator on a given test set."""
      if y_test is None:
          score = scorer(estimator, X_test)
      else:
          score = scorer(estimator, X_test, y_test)
      if not isinstance(score, numbers.Number):
          raise ValueError("scoring must return a number, got %s (%s) instead."
                           % (str(score), type(score)))
      return score
  
  
  def _permutation_test_score(estimator, X, y, cv, scorer):
      """Auxiliary function for permutation_test_score"""
      avg_score = []
      for train, test in cv:
          estimator.fit(X[train], y[train])
          avg_score.append(scorer(estimator, X[test], y[test]))
      return np.mean(avg_score)
  
  
  def _shuffle(y, labels, random_state):
      """Return a shuffled copy of y eventually shuffle among same labels."""
      if labels is None:
          ind = random_state.permutation(len(y))
      else:
          ind = np.arange(len(labels))
          for label in np.unique(labels):
              this_mask = (labels == label)
              ind[this_mask] = random_state.permutation(ind[this_mask])
      return y[ind]
  
  
  def check_cv(cv, X=None, y=None, classifier=False):
      """Input checker utility for building a CV in a user friendly way.
  
      Parameters
      ----------
      cv : int, a cv generator instance, or None
          The input specifying which cv generator to use. It can be an
          integer, in which case it is the number of folds in a KFold,
          None, in which case 3 fold is used, or another object, that
          will then be used as a cv generator.
  
      X : array-like
          The data the cross-val object will be applied on.
  
      y : array-like
          The target variable for a supervised learning problem.
  
      classifier : boolean optional
          Whether the task is a classification task, in which case
          stratified KFold will be used.
  
      Returns
      -------
      checked_cv: a cross-validation generator instance.
          The return value is guaranteed to be a cv generator instance, whatever
          the input type.
      """
      is_sparse = sp.issparse(X)
      if cv is None:
          cv = 3
      if isinstance(cv, numbers.Integral):
          if classifier:
              if type_of_target(y) in ['binary', 'multiclass']:
                  cv = StratifiedKFold(y, cv)
              else:
                  cv = KFold(_num_samples(y), cv)
          else:
              if not is_sparse:
                  n_samples = len(X)
              else:
                  n_samples = X.shape[0]
              cv = KFold(n_samples, cv)
      return cv
  
  
  def permutation_test_score(estimator, X, y, cv=None,
                             n_permutations=100, n_jobs=1, labels=None,
                             random_state=0, verbose=0, scoring=None):
      """Evaluate the significance of a cross-validated score with permutations
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      estimator : estimator object implementing 'fit'
          The object to use to fit the data.
  
      X : array-like of shape at least 2D
          The data to fit.
  
      y : array-like
          The target variable to try to predict in the case of
          supervised learning.
  
      scoring : string, callable or None, optional, default: None
          A string (see model evaluation documentation) or
          a scorer callable object / function with signature
          ``scorer(estimator, X, y)``.
  
      cv : integer or cross-validation generator, optional
          If an integer is passed, it is the number of fold (default 3).
          Specific cross-validation objects can be passed, see
          sklearn.cross_validation module for the list of possible objects.
  
      n_permutations : integer, optional
          Number of times to permute ``y``.
  
      n_jobs : integer, optional
          The number of CPUs to use to do the computation. -1 means
          'all CPUs'.
  
      labels : array-like of shape [n_samples] (optional)
          Labels constrain the permutation among groups of samples with
          a same label.
  
      random_state : RandomState or an int seed (0 by default)
          A random number generator instance to define the state of the
          random permutations generator.
  
      verbose : integer, optional
          The verbosity level.
  
      Returns
      -------
      score : float
          The true score without permuting targets.
  
      permutation_scores : array, shape (n_permutations,)
          The scores obtained for each permutations.
  
      pvalue : float
          The returned value equals p-value if `scoring` returns bigger
          numbers for better scores (e.g., accuracy_score). If `scoring` is
          rather a loss function (i.e. when lower is better such as with
          `mean_squared_error`) then this is actually the complement of the
          p-value:  1 - p-value.
  
      Notes
      -----
      This function implements Test 1 in:
  
          Ojala and Garriga. Permutation Tests for Studying Classifier
          Performance.  The Journal of Machine Learning Research (2010)
          vol. 11
  
      """
      X, y = indexable(X, y)
      cv = check_cv(cv, X, y, classifier=is_classifier(estimator))
      scorer = check_scoring(estimator, scoring=scoring)
      random_state = check_random_state(random_state)
  
      # We clone the estimator to make sure that all the folds are
      # independent, and that it is pickle-able.
      score = _permutation_test_score(clone(estimator), X, y, cv, scorer)
      permutation_scores = Parallel(n_jobs=n_jobs, verbose=verbose)(
          delayed(_permutation_test_score)(
              clone(estimator), X, _shuffle(y, labels, random_state), cv,
              scorer)
          for _ in range(n_permutations))
      permutation_scores = np.array(permutation_scores)
      pvalue = (np.sum(permutation_scores >= score) + 1.0) / (n_permutations + 1)
      return score, permutation_scores, pvalue
  
  
  permutation_test_score.__test__ = False  # to avoid a pb with nosetests
  
  
  def train_test_split(*arrays, **options):
      """Split arrays or matrices into random train and test subsets
  
      Quick utility that wraps input validation and
      ``next(iter(ShuffleSplit(n_samples)))`` and application to input
      data into a single call for splitting (and optionally subsampling)
      data in a oneliner.
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      *arrays : sequence of arrays or scipy.sparse matrices with same shape[0]
          Python lists or tuples occurring in arrays are converted to 1D numpy
          arrays.
  
      test_size : float, int, or None (default is None)
          If float, should be between 0.0 and 1.0 and represent the
          proportion of the dataset to include in the test split. If
          int, represents the absolute number of test samples. If None,
          the value is automatically set to the complement of the train size.
          If train size is also None, test size is set to 0.25.
  
      train_size : float, int, or None (default is None)
          If float, should be between 0.0 and 1.0 and represent the
          proportion of the dataset to include in the train split. If
          int, represents the absolute number of train samples. If None,
          the value is automatically set to the complement of the test size.
  
      random_state : int or RandomState
          Pseudo-random number generator state used for random sampling.
  
      stratify : array-like or None (default is None)
          If not None, data is split in a stratified fashion, using this as
          the labels array.
  
      Returns
      -------
      splitting : list of arrays, length=2 * len(arrays)
          List containing train-test split of input array.
  
      Examples
      --------
      >>> import numpy as np
      >>> from sklearn.cross_validation import train_test_split
      >>> X, y = np.arange(10).reshape((5, 2)), range(5)
      >>> X
      array([[0, 1],
             [2, 3],
             [4, 5],
             [6, 7],
             [8, 9]])
      >>> list(y)
      [0, 1, 2, 3, 4]
  
      >>> X_train, X_test, y_train, y_test = train_test_split(
      ...     X, y, test_size=0.33, random_state=42)
      ...
      >>> X_train
      array([[4, 5],
             [0, 1],
             [6, 7]])
      >>> y_train
      [2, 0, 3]
      >>> X_test
      array([[2, 3],
             [8, 9]])
      >>> y_test
      [1, 4]
  
      """
      n_arrays = len(arrays)
      if n_arrays == 0:
          raise ValueError("At least one array required as input")
  
      test_size = options.pop('test_size', None)
      train_size = options.pop('train_size', None)
      random_state = options.pop('random_state', None)
      dtype = options.pop('dtype', None)
      if dtype is not None:
          warnings.warn("dtype option is ignored and will be removed in 0.18.",
                        DeprecationWarning)
  
      allow_nd = options.pop('allow_nd', None)
      allow_lists = options.pop('allow_lists', None)
      stratify = options.pop('stratify', None)
  
      if allow_lists is not None:
          warnings.warn("The allow_lists option is deprecated and will be "
                        "assumed True in 0.18 and removed.", DeprecationWarning)
  
      if options:
          raise TypeError("Invalid parameters passed: %s" % str(options))
      if allow_nd is not None:
          warnings.warn("The allow_nd option is deprecated and will be "
                        "assumed True in 0.18 and removed.", DeprecationWarning)
      if allow_lists is False or allow_nd is False:
          arrays = [check_array(x, 'csr', allow_nd=allow_nd,
                                force_all_finite=False, ensure_2d=False)
                    if x is not None else x
                    for x in arrays]
  
      if test_size is None and train_size is None:
          test_size = 0.25
      arrays = indexable(*arrays)
      if stratify is not None:
          cv = StratifiedShuffleSplit(stratify, test_size=test_size,
                                      train_size=train_size,
                                      random_state=random_state)
      else:
          n_samples = _num_samples(arrays[0])
          cv = ShuffleSplit(n_samples, test_size=test_size,
                            train_size=train_size,
                            random_state=random_state)
  
      train, test = next(iter(cv))
      return list(chain.from_iterable((safe_indexing(a, train),
                                       safe_indexing(a, test)) for a in arrays))
  
  
  train_test_split.__test__ = False  # to avoid a pb with nosetests
  