_validation.py

"""
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>
# License: BSD 3 clause


import warnings
import numbers
import time
from traceback import format_exception_only
from contextlib import suppress

import numpy as np
import scipy.sparse as sp
from joblib import Parallel, delayed

from ..base import is_classifier, clone
from ..utils import (indexable, check_random_state, safe_indexing,
                     _message_with_time)
from ..utils.validation import _is_arraylike, _num_samples
from ..utils.metaestimators import _safe_split
from ..metrics.scorer import (check_scoring, _check_multimetric_scoring,
                              _MultimetricScorer)
from ..exceptions import FitFailedWarning
from ._split import check_cv
from ..preprocessing import LabelEncoder


__all__ = ['cross_validate', 'cross_val_score', 'cross_val_predict',
           'permutation_test_score', 'learning_curve', 'validation_curve']


def cross_validate(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):
    """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
        The data to fit. Can be for example a list, or an array.

    y : array-like, optional, default: None
        The target variable to try to predict in the case of
        supervised learning.

    groups : array-like, with shape (n_samples,), optional
        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`).

    scoring : string, callable, list/tuple, dict or None, default: None
        A single string (see :ref:`scoring_parameter`) or a callable
        (see :ref:`scoring`) to evaluate the predictions on the test set.

        For evaluating multiple metrics, either give a list of (unique) strings
        or a dict with names as keys and callables as values.

        NOTE that when using custom scorers, each scorer should return a single
        value. Metric functions returning a list/array of values can be wrapped
        into multiple scorers that return one value each.

        See :ref:`multimetric_grid_search` for an example.

        If None, the estimator's score method is used.

    cv : int, cross-validation generator or an iterable, optional
        Determines the cross-validation splitting strategy.
        Possible inputs for cv are:

        - None, to use the default 5-fold cross validation,
        - integer, to specify the number of folds in a `(Stratified)KFold`,
        - :term:`CV splitter`,
        - An iterable yielding (train, test) splits as arrays of indices.

        For integer/None inputs, if the estimator is a classifier and ``y`` is
        either binary or multiclass, :class:`StratifiedKFold` is used. In all
        other cases, :class:`KFold` is used.

        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 or None, optional (default=None)
        The number of CPUs to use to do the computation.
        ``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 : 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'

    return_train_score : boolean, 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.

    return_estimator : boolean, default False
        Whether to return the estimators fitted on each split.

    error_score : 'raise' 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.

    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.
            ``train_score``
                The score array for train scores on each cv split.
                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.scorer 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([0.33150734, 0.08022311, 0.03531764])

    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'])
    [0.28010158 0.39088426 0.22784852]

    See Also
    ---------
    :func:`sklearn.model_selection.cross_val_score`:
        Run cross-validation for single metric evaluation.

    :func:`sklearn.model_selection.cross_val_predict`:
        Get predictions from each split of cross-validation for diagnostic
        purposes.

    :func:`sklearn.metrics.make_scorer`:
        Make a scorer from a performance metric or loss function.

    """
    X, y, groups = indexable(X, y, groups)

    cv = check_cv(cv, y, classifier=is_classifier(estimator))
    scorers, _ = _check_multimetric_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, scorers, train, test, verbose, None,
            fit_params, return_train_score=return_train_score,
            return_times=True, return_estimator=return_estimator,
            error_score=error_score)
        for train, test in cv.split(X, y, groups))

    zipped_scores = list(zip(*scores))
    if return_train_score:
        train_scores = zipped_scores.pop(0)
        train_scores = _aggregate_score_dicts(train_scores)
    if return_estimator:
        fitted_estimators = zipped_scores.pop()
    test_scores, fit_times, score_times = zipped_scores
    test_scores = _aggregate_score_dicts(test_scores)

    ret = {}
    ret['fit_time'] = np.array(fit_times)
    ret['score_time'] = np.array(score_times)

    if return_estimator:
        ret['estimator'] = fitted_estimators

    for name in scorers:
        ret['test_%s' % name] = np.array(test_scores[name])
        if return_train_score:
            key = 'train_%s' % name
            ret[key] = np.array(train_scores[name])

    return ret


def cross_val_score(estimator, X, y=None, groups=None, scoring=None, cv=None,
                    n_jobs=None, verbose=0, fit_params=None,
                    pre_dispatch='2*n_jobs', error_score=np.nan):
    """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.

    y : array-like, optional, default: None
        The target variable to try to predict in the case of
        supervised learning.

    groups : array-like, with shape (n_samples,), optional
        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`).

    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)`` which should return only
        a single value.

        Similar to :func:`cross_validate`
        but only a single metric is permitted.

        If None, the estimator's default scorer (if available) is used.

    cv : int, cross-validation generator or an iterable, optional
        Determines the cross-validation splitting strategy.
        Possible inputs for cv are:

        - None, to use the default 5-fold cross validation,
        - integer, to specify the number of folds in a `(Stratified)KFold`,
        - :term:`CV splitter`,
        - An iterable yielding (train, test) splits as arrays of indices.

        For integer/None inputs, if the estimator is a classifier and ``y`` is
        either binary or multiclass, :class:`StratifiedKFold` is used. In all
        other cases, :class:`KFold` is used.

        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 or None, optional (default=None)
        The number of CPUs to use to do the computation.
        ``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 : 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'

    error_score : 'raise' 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.

    Returns
    -------
    scores : array of float, shape=(len(list(cv)),)
        Array of scores of the estimator for each run of the cross validation.

    Examples
    --------
    >>> from sklearn import datasets, linear_model
    >>> from sklearn.model_selection import cross_val_score
    >>> diabetes = datasets.load_diabetes()
    >>> X = diabetes.data[:150]
    >>> y = diabetes.target[:150]
    >>> lasso = linear_model.Lasso()
    >>> print(cross_val_score(lasso, X, y, cv=3))
    [0.33150734 0.08022311 0.03531764]

    See Also
    ---------
    :func:`sklearn.model_selection.cross_validate`:
        To run cross-validation on multiple metrics and also to return
        train scores, fit times and score times.

    :func:`sklearn.model_selection.cross_val_predict`:
        Get predictions from each split of cross-validation for diagnostic
        purposes.

    :func:`sklearn.metrics.make_scorer`:
        Make a scorer from a performance metric or loss function.

    """
    # To ensure multimetric format is not supported
    scorer = check_scoring(estimator, scoring=scoring)

    cv_results = cross_validate(estimator=estimator, X=X, y=y, groups=groups,
                                scoring={'score': scorer}, cv=cv,
                                n_jobs=n_jobs, verbose=verbose,
                                fit_params=fit_params,
                                pre_dispatch=pre_dispatch,
                                error_score=error_score)
    return cv_results['test_score']


def _fit_and_score(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,
                   error_score=np.nan):
    """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 : 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, 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' 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.

    return_n_test_samples : boolean, optional, default: False
        Whether to return the ``n_test_samples``

    return_times : boolean, optional, default: False
        Whether to return the fit/score times.

    return_estimator : boolean, optional, default: False
        Whether to return the fitted estimator.

    Returns
    -------
    train_scores : dict of scorer name -> float, optional
        Score on training set (for all the scorers),
        returned only if `return_train_score` is `True`.

    test_scores : dict of scorer name -> float, optional
        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, optional
        The parameters that have been evaluated.

    estimator : estimator object
        The fitted estimator
    """
    if verbose > 1:
        if parameters is None:
            msg = ''
        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 = {k: _index_param_value(X, v, train)
                  for k, v in fit_params.items()}

    train_scores = {}
    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:
        # 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 = {name: error_score for name in scorer}
                if return_train_score:
                    train_scores = test_scores.copy()
            else:
                test_scores = error_score
                if return_train_score:
                    train_scores = error_score
            warnings.warn("Estimator fit failed. The score on this train-test"
                          " partition for these parameters will be set to %f. "
                          "Details: \n%s" %
                          (error_score, format_exception_only(type(e), e)[0]),
                          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:
        fit_time = time.time() - start_time
        test_scores = _score(estimator, X_test, y_test, scorer)
        score_time = time.time() - start_time - fit_time
        if return_train_score:
            train_scores = _score(estimator, X_train, y_train, scorer)
    if verbose > 2:
        if isinstance(test_scores, dict):
            for scorer_name in sorted(test_scores):
                msg += ", %s=" % scorer_name
                if return_train_score:
                    msg += "(train=%.3f," % train_scores[scorer_name]
                    msg += " test=%.3f)" % test_scores[scorer_name]
                else:
                    msg += "%.3f" % test_scores[scorer_name]
        else:
            msg += ", score="
            msg += ("%.3f" % test_scores if not return_train_score else
                    "(train=%.3f, test=%.3f)" % (train_scores, test_scores))

    if verbose > 1:
        total_time = score_time + fit_time
        print(_message_with_time('CV', msg, total_time))

    ret = [train_scores, test_scores] if return_train_score else [test_scores]

    if return_n_test_samples:
        ret.append(_num_samples(X_test))
    if return_times:
        ret.extend([fit_time, score_time])
    if return_parameters:
        ret.append(parameters)
    if return_estimator:
        ret.append(estimator)
    return ret


def _score(estimator, X_test, y_test, scorer):
    """Compute the score(s) of an estimator on a given test set.

    Will return a dict of floats if `scorer` is a dict, otherwise a single
    float is returned.
    """
    if isinstance(scorer, dict):
        # will cache method calls if needed. scorer() returns a dict
        scorer = _MultimetricScorer(**scorer)
    if y_test is None:
        scores = scorer(estimator, X_test)
    else:
        scores = scorer(estimator, X_test, y_test)

    error_msg = ("scoring must return a number, got %s (%s) "
                 "instead. (scorer=%s)")
    if isinstance(scores, dict):
        for name, score in scores.items():
            if hasattr(score, 'item'):
                with suppress(ValueError):
                    # e.g. unwrap memmapped scalars
                    score = score.item()
            if not isinstance(score, numbers.Number):
                raise ValueError(error_msg % (score, type(score), name))
            scores[name] = score
    else:  # scalar
        if hasattr(scores, 'item'):
            with suppress(ValueError):
                # e.g. unwrap memmapped scalars
                scores = scores.item()
        if not isinstance(scores, numbers.Number):
            raise ValueError(error_msg % (scores, type(scores), scorer))
    return scores


def cross_val_predict(estimator, X, y=None, groups=None, cv=None,
                      n_jobs=None, verbose=0, fit_params=None,
                      pre_dispatch='2*n_jobs', method='predict'):
    """Generate cross-validated estimates for each input data point

    The data is split according to the cv parameter. Each sample belongs
    to exactly one test set, and its prediction is computed with an
    estimator fitted on the corresponding training set.

    Passing these predictions into an evaluation metric may not be a valid
    way to measure generalization performance. Results can differ from
    :func:`cross_validate` and :func:`cross_val_score` unless all tests sets
    have equal size and the metric decomposes over samples.

    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.

    groups : array-like, with shape (n_samples,), optional
        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`).

    cv : int, cross-validation generator or an iterable, optional
        Determines the cross-validation splitting strategy.
        Possible inputs for cv are:

        - None, to use the default 5-fold cross validation,
        - integer, to specify the number of folds in a `(Stratified)KFold`,
        - :term:`CV splitter`,
        - An iterable yielding (train, test) splits as arrays of indices.

        For integer/None inputs, if the estimator is a classifier and ``y`` is
        either binary or multiclass, :class:`StratifiedKFold` is used. In all
        other cases, :class:`KFold` is used.

        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 or None, optional (default=None)
        The number of CPUs to use to do the computation.
        ``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 : 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'

    method : string, optional, default: 'predict'
        Invokes the passed method name of the passed estimator. For
        method='predict_proba', the columns correspond to the classes
        in sorted order.

    Returns
    -------
    predictions : ndarray
        This is the result of calling ``method``

    See also
    --------
    cross_val_score : calculate score for each CV split

    cross_validate : calculate one or more scores and timings for each CV split

    Notes
    -----
    In the case that one or more classes are absent in a training portion, a
    default score needs to be assigned to all instances for that class if
    ``method`` produces columns per class, as in {'decision_function',
    'predict_proba', 'predict_log_proba'}.  For ``predict_proba`` this value is
    0.  In order to ensure finite output, we approximate negative infinity by
    the minimum finite float value for the dtype in other cases.

    Examples
    --------
    >>> from sklearn import datasets, linear_model
    >>> from sklearn.model_selection import cross_val_predict
    >>> diabetes = datasets.load_diabetes()
    >>> X = diabetes.data[:150]
    >>> y = diabetes.target[:150]
    >>> lasso = linear_model.Lasso()
    >>> y_pred = cross_val_predict(lasso, X, y, cv=3)
    """
    X, y, groups = indexable(X, y, groups)

    cv = check_cv(cv, y, classifier=is_classifier(estimator))

    # If classification methods produce multiple columns of output,
    # we need to manually encode classes to ensure consistent column ordering.
    encode = method in ['decision_function', 'predict_proba',
                        'predict_log_proba']
    if encode:
        y = np.asarray(y)
        if y.ndim == 1:
            le = LabelEncoder()
            y = le.fit_transform(y)
        elif y.ndim == 2:
            y_enc = np.zeros_like(y, dtype=np.int)
            for i_label in range(y.shape[1]):
                y_enc[:, i_label] = LabelEncoder().fit_transform(y[:, i_label])
            y = y_enc

    # 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)
    prediction_blocks = parallel(delayed(_fit_and_predict)(
        clone(estimator), X, y, train, test, verbose, fit_params, method)
        for train, test in cv.split(X, y, groups))

    # Concatenate the predictions
    predictions = [pred_block_i for pred_block_i, _ in prediction_blocks]
    test_indices = np.concatenate([indices_i
                                   for _, indices_i in prediction_blocks])

    if not _check_is_permutation(test_indices, _num_samples(X)):
        raise ValueError('cross_val_predict only works for partitions')

    inv_test_indices = np.empty(len(test_indices), dtype=int)
    inv_test_indices[test_indices] = np.arange(len(test_indices))

    if sp.issparse(predictions[0]):
        predictions = sp.vstack(predictions, format=predictions[0].format)
    elif encode and isinstance(predictions[0], list):
        # `predictions` is a list of method outputs from each fold.
        # If each of those is also a list, then treat this as a
        # multioutput-multiclass task. We need to separately concatenate
        # the method outputs for each label into an `n_labels` long list.
        n_labels = y.shape[1]
        concat_pred = []
        for i_label in range(n_labels):
            label_preds = np.concatenate([p[i_label] for p in predictions])
            concat_pred.append(label_preds)
        predictions = concat_pred
    else:
        predictions = np.concatenate(predictions)

    if isinstance(predictions, list):
        return [p[inv_test_indices] for p in predictions]
    else:
        return predictions[inv_test_indices]


def _fit_and_predict(estimator, X, y, train, test, verbose, fit_params,
                     method):
    """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``.

    method : string
        Invokes the passed method name of the passed estimator.

    Returns
    -------
    predictions : sequence
        Result of calling 'estimator.method'

    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 = {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)
    func = getattr(estimator, method)
    predictions = func(X_test)
    if method in ['decision_function', 'predict_proba', 'predict_log_proba']:
        if isinstance(predictions, list):
            predictions = [_enforce_prediction_order(
                estimator.classes_[i_label], predictions[i_label],
                n_classes=len(set(y[:, i_label])), method=method)
                for i_label in range(len(predictions))]
        else:
            # A 2D y array should be a binary label indicator matrix
            n_classes = len(set(y)) if y.ndim == 1 else y.shape[1]
            predictions = _enforce_prediction_order(
                estimator.classes_, predictions, n_classes, method)
    return predictions, test


def _enforce_prediction_order(classes, predictions, n_classes, method):
    """Ensure that prediction arrays have correct column order

    When doing cross-validation, if one or more classes are
    not present in the subset of data used for training,
    then the output prediction array might not have the same
    columns as other folds. Use the list of class names
    (assumed to be integers) to enforce the correct column order.

    Note that `classes` is the list of classes in this fold
    (a subset of the classes in the full training set)
    and `n_classes` is the number of classes in the full training set.
    """
    if n_classes != len(classes):
        recommendation = (
            'To fix this, use a cross-validation '
            'technique resulting in properly '
            'stratified folds')
        warnings.warn('Number of classes in training fold ({}) does '
                      'not match total number of classes ({}). '
                      'Results may not be appropriate for your use case. '
                      '{}'.format(len(classes), n_classes, recommendation),
                      RuntimeWarning)
        if method == 'decision_function':
            if (predictions.ndim == 2 and
                    predictions.shape[1] != len(classes)):
                # This handles the case when the shape of predictions
                # does not match the number of classes used to train
                # it with. This case is found when sklearn.svm.SVC is
                # set to `decision_function_shape='ovo'`.
                raise ValueError('Output shape {} of {} does not match '
                                 'number of classes ({}) in fold. '
                                 'Irregular decision_function outputs '
                                 'are not currently supported by '
                                 'cross_val_predict'.format(
                                    predictions.shape, method, len(classes)))
            if len(classes) <= 2:
                # In this special case, `predictions` contains a 1D array.
                raise ValueError('Only {} class/es in training fold, but {} '
                                 'in overall dataset. This '
                                 'is not supported for decision_function '
                                 'with imbalanced folds. {}'.format(
                                    len(classes), n_classes, recommendation))

        float_min = np.finfo(predictions.dtype).min
        default_values = {'decision_function': float_min,
                          'predict_log_proba': float_min,
                          'predict_proba': 0}
        predictions_for_all_classes = np.full((_num_samples(predictions),
                                               n_classes),
                                              default_values[method],
                                              dtype=predictions.dtype)
        predictions_for_all_classes[:, classes] = predictions
        predictions = predictions_for_all_classes
    return predictions


def _check_is_permutation(indices, n_samples):
    """Check whether indices is a reordering of the array np.arange(n_samples)

    Parameters
    ----------
    indices : ndarray
        integer array to test
    n_samples : int
        number of expected elements

    Returns
    -------
    is_partition : bool
        True iff sorted(indices) is np.arange(n)
    """
    if len(indices) != n_samples:
        return False
    hit = np.zeros(n_samples, dtype=bool)
    hit[indices] = True
    if not np.all(hit):
        return False
    return True


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 permutation_test_score(estimator, X, y, groups=None, cv=None,
                           n_permutations=100, n_jobs=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.

    groups : array-like, with shape (n_samples,), optional
        Labels to constrain permutation within groups, i.e. ``y`` values
        are permuted among samples with the same group identifier.
        When not specified, ``y`` values are permuted among all samples.

        When a grouped cross-validator is used, the group labels are
        also passed on to the ``split`` method of the cross-validator. The
        cross-validator uses them for grouping the samples  while splitting
        the dataset into train/test set.

    scoring : string, callable or None, optional, default: None
        A single string (see :ref:`scoring_parameter`) or a callable
        (see :ref:`scoring`) to evaluate the predictions on the test set.

        If None the estimator's score method is used.

    cv : int, cross-validation generator or an iterable, optional
        Determines the cross-validation splitting strategy.
        Possible inputs for cv are:

        - None, to use the default 5-fold cross validation,
        - integer, to specify the number of folds in a `(Stratified)KFold`,
        - :term:`CV splitter`,
        - An iterable yielding (train, test) splits as arrays of indices.

        For integer/None inputs, if the estimator is a classifier and ``y`` is
        either binary or multiclass, :class:`StratifiedKFold` is used. In all
        other cases, :class:`KFold` is used.

        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_permutations : integer, optional
        Number of times to permute ``y``.

    n_jobs : int or None, optional (default=None)
        The number of CPUs to use to do the computation.
        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
        ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
        for more details.

    random_state : int, RandomState instance or None, optional (default=0)
        If int, random_state is the seed used by the random number generator;
        If RandomState instance, random_state is the random number generator;
        If None, the random number generator is the RandomState instance used
        by `np.random`.

    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 p-value, which approximates the probability that the score would
        be obtained by chance. This is calculated as:

        `(C + 1) / (n_permutations + 1)`

        Where C is the number of permutations whose score >= the true score.

        The best possible p-value is 1/(n_permutations + 1), the worst is 1.0.

    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, groups = indexable(X, y, groups)

    cv = check_cv(cv, 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, groups, cv, scorer)
    permutation_scores = Parallel(n_jobs=n_jobs, verbose=verbose)(
        delayed(_permutation_test_score)(
            clone(estimator), X, _shuffle(y, groups, random_state),
            groups, 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


def _permutation_test_score(estimator, X, y, groups, cv, scorer):
    """Auxiliary function for permutation_test_score"""
    avg_score = []
    for train, test in cv.split(X, y, groups):
        X_train, y_train = _safe_split(estimator, X, y, train)
        X_test, y_test = _safe_split(estimator, X, y, test, train)
        estimator.fit(X_train, y_train)
        avg_score.append(scorer(estimator, X_test, y_test))
    return np.mean(avg_score)


def _shuffle(y, groups, random_state):
    """Return a shuffled copy of y eventually shuffle among same groups."""
    if groups is None:
        indices = random_state.permutation(len(y))
    else:
        indices = np.arange(len(groups))
        for group in np.unique(groups):
            this_mask = (groups == group)
            indices[this_mask] = random_state.permutation(indices[this_mask])
    return safe_indexing(y, indices)


def learning_curve(estimator, X, y, groups=None,
                   train_sizes=np.linspace(0.1, 1.0, 5), cv=None,
                   scoring=None, exploit_incremental_learning=False,
                   n_jobs=None, pre_dispatch="all", verbose=0, shuffle=False,
                   random_state=None, error_score=np.nan, return_times=False):
    """Learning curve.

    Determines cross-validated training and test scores for different training
    set sizes.

    A cross-validation generator splits the whole dataset k times in training
    and test data. Subsets of the training set with varying sizes will be used
    to train the estimator and a score for each training subset size and the
    test set will be computed. Afterwards, the scores will be averaged over
    all k runs for each training subset size.

    Read more in the :ref:`User Guide <learning_curve>`.

    Parameters
    ----------
    estimator : object type that implements the "fit" and "predict" methods
        An object of that type which is cloned for each validation.

    X : array-like, shape (n_samples, n_features)
        Training vector, where n_samples is the number of samples and
        n_features is the number of features.

    y : array-like, shape (n_samples) or (n_samples, n_features), optional
        Target relative to X for classification or regression;
        None for unsupervised learning.

    groups : array-like, with shape (n_samples,), optional
        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`).

    train_sizes : array-like, shape (n_ticks,), dtype float or int
        Relative or absolute numbers of training examples that will be used to
        generate the learning curve. If the dtype is float, it is regarded as a
        fraction of the maximum size of the training set (that is determined
        by the selected validation method), i.e. it has to be within (0, 1].
        Otherwise it is interpreted as absolute sizes of the training sets.
        Note that for classification the number of samples usually have to
        be big enough to contain at least one sample from each class.
        (default: np.linspace(0.1, 1.0, 5))

    cv : int, cross-validation generator or an iterable, optional
        Determines the cross-validation splitting strategy.
        Possible inputs for cv are:

        - None, to use the default 5-fold cross validation,
        - integer, to specify the number of folds in a `(Stratified)KFold`,
        - :term:`CV splitter`,
        - An iterable yielding (train, test) splits as arrays of indices.

        For integer/None inputs, if the estimator is a classifier and ``y`` is
        either binary or multiclass, :class:`StratifiedKFold` is used. In all
        other cases, :class:`KFold` is used.

        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.

    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)``.

    exploit_incremental_learning : boolean, optional, default: False
        If the estimator supports incremental learning, this will be
        used to speed up fitting for different training set sizes.

    n_jobs : int or None, optional (default=None)
        Number of jobs to run in parallel.
        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
        ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
        for more details.

    pre_dispatch : integer or string, optional
        Number of predispatched jobs for parallel execution (default is
        all). The option can reduce the allocated memory. The string can
        be an expression like '2*n_jobs'.

    verbose : integer, optional
        Controls the verbosity: the higher, the more messages.

    shuffle : boolean, optional
        Whether to shuffle training data before taking prefixes of it
        based on``train_sizes``.

    random_state : int, RandomState instance or None, optional (default=None)
        If int, random_state is the seed used by the random number generator;
        If RandomState instance, random_state is the random number generator;
        If None, the random number generator is the RandomState instance used
        by `np.random`. Used when ``shuffle`` is True.

    error_score : 'raise' 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.

    return_times : boolean, optional (default: False)
        Whether to return the fit and score times.

    Returns
    -------
    train_sizes_abs : array, shape (n_unique_ticks,), dtype int
        Numbers of training examples that has been used to generate the
        learning curve. Note that the number of ticks might be less
        than n_ticks because duplicate entries will be removed.

    train_scores : array, shape (n_ticks, n_cv_folds)
        Scores on training sets.

    test_scores : array, shape (n_ticks, n_cv_folds)
        Scores on test set.

    fit_times : array, shape (n_ticks, n_cv_folds)
        Times spent for fitting in seconds. Only present if ``return_times``
        is True.

    score_times : array, shape (n_ticks, n_cv_folds)
        Times spent for scoring in seconds. Only present if ``return_times``
        is True.

    Notes
    -----
    See :ref:`examples/model_selection/plot_learning_curve.py
    <sphx_glr_auto_examples_model_selection_plot_learning_curve.py>`
    """
    if exploit_incremental_learning and not hasattr(estimator, "partial_fit"):
        raise ValueError("An estimator must support the partial_fit interface "
                         "to exploit incremental learning")
    X, y, groups = indexable(X, y, groups)

    cv = check_cv(cv, y, classifier=is_classifier(estimator))
    # Store it as list as we will be iterating over the list multiple times
    cv_iter = list(cv.split(X, y, groups))

    scorer = check_scoring(estimator, scoring=scoring)

    n_max_training_samples = len(cv_iter[0][0])
    # Because the lengths of folds can be significantly different, it is
    # not guaranteed that we use all of the available training data when we
    # use the first 'n_max_training_samples' samples.
    train_sizes_abs = _translate_train_sizes(train_sizes,
                                             n_max_training_samples)
    n_unique_ticks = train_sizes_abs.shape[0]
    if verbose > 0:
        print("[learning_curve] Training set sizes: " + str(train_sizes_abs))

    parallel = Parallel(n_jobs=n_jobs, pre_dispatch=pre_dispatch,
                        verbose=verbose)

    if shuffle:
        rng = check_random_state(random_state)
        cv_iter = ((rng.permutation(train), test) for train, test in cv_iter)

    if exploit_incremental_learning:
        classes = np.unique(y) if is_classifier(estimator) else None
        out = parallel(delayed(_incremental_fit_estimator)(
            clone(estimator), X, y, classes, train, test, train_sizes_abs,
            scorer, verbose, return_times) for train, test in cv_iter)
    else:
        train_test_proportions = []
        for train, test in cv_iter:
            for n_train_samples in train_sizes_abs:
                train_test_proportions.append((train[:n_train_samples], test))

        out = parallel(delayed(_fit_and_score)(
            clone(estimator), X, y, scorer, train, test, verbose,
            parameters=None, fit_params=None, return_train_score=True,
            error_score=error_score, return_times=return_times)
            for train, test in train_test_proportions)
        out = np.array(out)
        n_cv_folds = out.shape[0] // n_unique_ticks
        dim = 4 if return_times else 2
        out = out.reshape(n_cv_folds, n_unique_ticks, dim)

    out = np.asarray(out).transpose((2, 1, 0))

    ret = train_sizes_abs, out[0], out[1]

    if return_times:
        ret = ret + (out[2], out[3])

    return ret


def _translate_train_sizes(train_sizes, n_max_training_samples):
    """Determine absolute sizes of training subsets and validate 'train_sizes'.

    Examples:
        _translate_train_sizes([0.5, 1.0], 10) -> [5, 10]
        _translate_train_sizes([5, 10], 10) -> [5, 10]

    Parameters
    ----------
    train_sizes : array-like, shape (n_ticks,), dtype float or int
        Numbers of training examples that will be used to generate the
        learning curve. If the dtype is float, it is regarded as a
        fraction of 'n_max_training_samples', i.e. it has to be within (0, 1].

    n_max_training_samples : int
        Maximum number of training samples (upper bound of 'train_sizes').

    Returns
    -------
    train_sizes_abs : array, shape (n_unique_ticks,), dtype int
        Numbers of training examples that will be used to generate the
        learning curve. Note that the number of ticks might be less
        than n_ticks because duplicate entries will be removed.
    """
    train_sizes_abs = np.asarray(train_sizes)
    n_ticks = train_sizes_abs.shape[0]
    n_min_required_samples = np.min(train_sizes_abs)
    n_max_required_samples = np.max(train_sizes_abs)
    if np.issubdtype(train_sizes_abs.dtype, np.floating):
        if n_min_required_samples <= 0.0 or n_max_required_samples > 1.0:
            raise ValueError("train_sizes has been interpreted as fractions "
                             "of the maximum number of training samples and "
                             "must be within (0, 1], but is within [%f, %f]."
                             % (n_min_required_samples,
                                n_max_required_samples))
        train_sizes_abs = (train_sizes_abs * n_max_training_samples).astype(
                             dtype=np.int, copy=False)
        train_sizes_abs = np.clip(train_sizes_abs, 1,
                                  n_max_training_samples)
    else:
        if (n_min_required_samples <= 0 or
                n_max_required_samples > n_max_training_samples):
            raise ValueError("train_sizes has been interpreted as absolute "
                             "numbers of training samples and must be within "
                             "(0, %d], but is within [%d, %d]."
                             % (n_max_training_samples,
                                n_min_required_samples,
                                n_max_required_samples))

    train_sizes_abs = np.unique(train_sizes_abs)
    if n_ticks > train_sizes_abs.shape[0]:
        warnings.warn("Removed duplicate entries from 'train_sizes'. Number "
                      "of ticks will be less than the size of "
                      "'train_sizes' %d instead of %d)."
                      % (train_sizes_abs.shape[0], n_ticks), RuntimeWarning)

    return train_sizes_abs


def _incremental_fit_estimator(estimator, X, y, classes, train, test,
                               train_sizes, scorer, verbose, return_times):
    """Train estimator on training subsets incrementally and compute scores."""
    train_scores, test_scores, fit_times, score_times = [], [], [], []
    partitions = zip(train_sizes, np.split(train, train_sizes)[:-1])
    for n_train_samples, partial_train in partitions:
        train_subset = train[:n_train_samples]
        X_train, y_train = _safe_split(estimator, X, y, train_subset)
        X_partial_train, y_partial_train = _safe_split(estimator, X, y,
                                                       partial_train)
        X_test, y_test = _safe_split(estimator, X, y, test, train_subset)
        start_fit = time.time()
        if y_partial_train is None:
            estimator.partial_fit(X_partial_train, classes=classes)
        else:
            estimator.partial_fit(X_partial_train, y_partial_train,
                                  classes=classes)
        fit_time = time.time() - start_fit
        fit_times.append(fit_time)

        start_score = time.time()

        test_scores.append(_score(estimator, X_test, y_test, scorer))
        train_scores.append(_score(estimator, X_train, y_train, scorer))

        score_time = time.time() - start_score
        score_times.append(score_time)

    ret = ((train_scores, test_scores, fit_times, score_times)
           if return_times else (train_scores, test_scores))

    return np.array(ret).T


def validation_curve(estimator, X, y, param_name, param_range, groups=None,
                     cv=None, scoring=None, n_jobs=None, pre_dispatch="all",
                     verbose=0, error_score=np.nan):
    """Validation curve.

    Determine training and test scores for varying parameter values.

    Compute scores for an estimator with different values of a specified
    parameter. This is similar to grid search with one parameter. However, this
    will also compute training scores and is merely a utility for plotting the
    results.

    Read more in the :ref:`User Guide <learning_curve>`.

    Parameters
    ----------
    estimator : object type that implements the "fit" and "predict" methods
        An object of that type which is cloned for each validation.

    X : array-like, shape (n_samples, n_features)
        Training vector, where n_samples is the number of samples and
        n_features is the number of features.

    y : array-like, shape (n_samples) or (n_samples, n_features), optional
        Target relative to X for classification or regression;
        None for unsupervised learning.

    param_name : string
        Name of the parameter that will be varied.

    param_range : array-like, shape (n_values,)
        The values of the parameter that will be evaluated.

    groups : array-like, with shape (n_samples,), optional
        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`).

    cv : int, cross-validation generator or an iterable, optional
        Determines the cross-validation splitting strategy.
        Possible inputs for cv are:

        - None, to use the default 5-fold cross validation,
        - integer, to specify the number of folds in a `(Stratified)KFold`,
        - :term:`CV splitter`,
        - An iterable yielding (train, test) splits as arrays of indices.

        For integer/None inputs, if the estimator is a classifier and ``y`` is
        either binary or multiclass, :class:`StratifiedKFold` is used. In all
        other cases, :class:`KFold` is used.

        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.

    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)``.

    n_jobs : int or None, optional (default=None)
        Number of jobs to run in parallel.
        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
        ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
        for more details.

    pre_dispatch : integer or string, optional
        Number of predispatched jobs for parallel execution (default is
        all). The option can reduce the allocated memory. The string can
        be an expression like '2*n_jobs'.

    verbose : integer, optional
        Controls the verbosity: the higher, the more messages.

    error_score : 'raise' 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.

    Returns
    -------
    train_scores : array, shape (n_ticks, n_cv_folds)
        Scores on training sets.

    test_scores : array, shape (n_ticks, n_cv_folds)
        Scores on test set.

    Notes
    -----
    See :ref:`sphx_glr_auto_examples_model_selection_plot_validation_curve.py`

    """
    X, y, groups = indexable(X, y, groups)

    cv = check_cv(cv, y, classifier=is_classifier(estimator))
    scorer = check_scoring(estimator, scoring=scoring)

    parallel = Parallel(n_jobs=n_jobs, pre_dispatch=pre_dispatch,
                        verbose=verbose)
    out = parallel(delayed(_fit_and_score)(
        clone(estimator), X, y, scorer, train, test, verbose,
        parameters={param_name: v}, fit_params=None, return_train_score=True,
        error_score=error_score)
        # NOTE do not change order of iteration to allow one time cv splitters
        for train, test in cv.split(X, y, groups) for v in param_range)
    out = np.asarray(out)
    n_params = len(param_range)
    n_cv_folds = out.shape[0] // n_params
    out = out.reshape(n_cv_folds, n_params, 2).transpose((2, 1, 0))

    return out[0], out[1]


def _aggregate_score_dicts(scores):
    """Aggregate the list of dict to dict of np ndarray

    The aggregated output of _fit_and_score will be a list of dict
    of form [{'prec': 0.1, 'acc':1.0}, {'prec': 0.1, 'acc':1.0}, ...]
    Convert it to a dict of array {'prec': np.array([0.1 ...]), ...}

    Parameters
    ----------

    scores : list of dict
        List of dicts of the scores for all scorers. This is a flat list,
        assumed originally to be of row major order.

    Example
    -------

    >>> scores = [{'a': 1, 'b':10}, {'a': 2, 'b':2}, {'a': 3, 'b':3},
    ...           {'a': 10, 'b': 10}]                         # doctest: +SKIP
    >>> _aggregate_score_dicts(scores)                        # doctest: +SKIP
    {'a': array([1, 2, 3, 10]),
     'b': array([10, 2, 3, 10])}
    """
    return {key: np.asarray([score[key] for score in scores])
            for key in scores[0]}