content: """Metrics to assess performance on regression task
  
  Functions named as ``*_score`` return a scalar value to maximize: the higher
  the better
  
  Function named as ``*_error`` or ``*_loss`` return a scalar value to minimize:
  the lower the better
  """
  
  # Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
  #          Mathieu Blondel <mathieu@mblondel.org>
  #          Olivier Grisel <olivier.grisel@ensta.org>
  #          Arnaud Joly <a.joly@ulg.ac.be>
  #          Jochen Wersdorfer <jochen@wersdoerfer.de>
  #          Lars Buitinck <L.J.Buitinck@uva.nl>
  #          Joel Nothman <joel.nothman@gmail.com>
  #          Noel Dawe <noel@dawe.me>
  #          Manoj Kumar <manojkumarsivaraj334@gmail.com>
  #          Michael Eickenberg <michael.eickenberg@gmail.com>
  #          Konstantin Shmelkov <konstantin.shmelkov@polytechnique.edu>
  # License: BSD 3 clause
  
  from __future__ import division
  
  import numpy as np
  
  from ..utils.validation import check_array, check_consistent_length
  from ..utils.validation import column_or_1d
  
  import warnings
  
  __ALL__ = [
      "mean_absolute_error",
      "mean_squared_error",
      "median_absolute_error",
      "r2_score",
      "explained_variance_score"
  ]
  
  
  def _check_reg_targets(y_true, y_pred, multioutput):
      """Check that y_true and y_pred belong to the same regression task
  
      Parameters
      ----------
      y_true : array-like,
  
      y_pred : array-like,
  
      multioutput : array-like or string in ['raw_values', uniform_average',
          'variance_weighted'] or None
          None is accepted due to backward compatibility of r2_score().
  
      Returns
      -------
      type_true : one of {'continuous', continuous-multioutput'}
          The type of the true target data, as output by
          'utils.multiclass.type_of_target'
  
      y_true : array-like of shape = (n_samples, n_outputs)
          Ground truth (correct) target values.
  
      y_pred : array-like of shape = (n_samples, n_outputs)
          Estimated target values.
  
      multioutput : array-like of shape = (n_outputs) or string in ['raw_values',
          uniform_average', 'variance_weighted'] or None
          Custom output weights if ``multioutput`` is array-like or
          just the corresponding argument if ``multioutput`` is a
          correct keyword.
  
      """
      check_consistent_length(y_true, y_pred)
      y_true = check_array(y_true, ensure_2d=False)
      y_pred = check_array(y_pred, ensure_2d=False)
  
      if y_true.ndim == 1:
          y_true = y_true.reshape((-1, 1))
  
      if y_pred.ndim == 1:
          y_pred = y_pred.reshape((-1, 1))
  
      if y_true.shape[1] != y_pred.shape[1]:
          raise ValueError("y_true and y_pred have different number of output "
                           "({0}!={1})".format(y_true.shape[1], y_pred.shape[1]))
  
      n_outputs = y_true.shape[1]
      multioutput_options = (None, 'raw_values', 'uniform_average',
                             'variance_weighted')
      if multioutput not in multioutput_options:
          multioutput = check_array(multioutput, ensure_2d=False)
          if n_outputs == 1:
              raise ValueError("Custom weights are useful only in "
                               "multi-output cases.")
          elif n_outputs != len(multioutput):
              raise ValueError(("There must be equally many custom weights "
                                "(%d) as outputs (%d).") %
                               (len(multioutput), n_outputs))
      y_type = 'continuous' if n_outputs == 1 else 'continuous-multioutput'
  
      return y_type, y_true, y_pred, multioutput
  
  
  def mean_absolute_error(y_true, y_pred,
                          sample_weight=None,
                          multioutput='uniform_average'):
      """Mean absolute error regression loss
  
      Read more in the :ref:`User Guide <mean_absolute_error>`.
  
      Parameters
      ----------
      y_true : array-like of shape = (n_samples) or (n_samples, n_outputs)
          Ground truth (correct) target values.
  
      y_pred : array-like of shape = (n_samples) or (n_samples, n_outputs)
          Estimated target values.
  
      sample_weight : array-like of shape = (n_samples), optional
          Sample weights.
  
      multioutput : string in ['raw_values', 'uniform_average']
          or array-like of shape (n_outputs)
          Defines aggregating of multiple output values.
          Array-like value defines weights used to average errors.
  
          'raw_values' :
              Returns a full set of errors in case of multioutput input.
  
          'uniform_average' :
              Errors of all outputs are averaged with uniform weight.
  
  
      Returns
      -------
      loss : float or ndarray of floats
          If multioutput is 'raw_values', then mean absolute error is returned
          for each output separately.
          If multioutput is 'uniform_average' or an ndarray of weights, then the
          weighted average of all output errors is returned.
  
          MAE output is non-negative floating point. The best value is 0.0.
  
      Examples
      --------
      >>> from sklearn.metrics import mean_absolute_error
      >>> y_true = [3, -0.5, 2, 7]
      >>> y_pred = [2.5, 0.0, 2, 8]
      >>> mean_absolute_error(y_true, y_pred)
      0.5
      >>> y_true = [[0.5, 1], [-1, 1], [7, -6]]
      >>> y_pred = [[0, 2], [-1, 2], [8, -5]]
      >>> mean_absolute_error(y_true, y_pred)
      0.75
      >>> mean_absolute_error(y_true, y_pred, multioutput='raw_values')
      array([ 0.5,  1. ])
      >>> mean_absolute_error(y_true, y_pred, multioutput=[0.3, 0.7])
      ... # doctest: +ELLIPSIS
      0.849...
      """
      y_type, y_true, y_pred, multioutput = _check_reg_targets(
          y_true, y_pred, multioutput)
      output_errors = np.average(np.abs(y_pred - y_true),
                                 weights=sample_weight, axis=0)
      if multioutput == 'raw_values':
          return output_errors
      elif multioutput == 'uniform_average':
          # pass None as weights to np.average: uniform mean
          multioutput = None
  
      return np.average(output_errors, weights=multioutput)
  
  
  def mean_squared_error(y_true, y_pred,
                         sample_weight=None,
                         multioutput='uniform_average'):
      """Mean squared error regression loss
  
      Read more in the :ref:`User Guide <mean_squared_error>`.
  
      Parameters
      ----------
      y_true : array-like of shape = (n_samples) or (n_samples, n_outputs)
          Ground truth (correct) target values.
  
      y_pred : array-like of shape = (n_samples) or (n_samples, n_outputs)
          Estimated target values.
  
      sample_weight : array-like of shape = (n_samples), optional
          Sample weights.
  
      multioutput : string in ['raw_values', 'uniform_average']
          or array-like of shape (n_outputs)
          Defines aggregating of multiple output values.
          Array-like value defines weights used to average errors.
  
          'raw_values' :
              Returns a full set of errors in case of multioutput input.
  
          'uniform_average' :
              Errors of all outputs are averaged with uniform weight.
  
      Returns
      -------
      loss : float or ndarray of floats
          A non-negative floating point value (the best value is 0.0), or an
          array of floating point values, one for each individual target.
  
      Examples
      --------
      >>> from sklearn.metrics import mean_squared_error
      >>> y_true = [3, -0.5, 2, 7]
      >>> y_pred = [2.5, 0.0, 2, 8]
      >>> mean_squared_error(y_true, y_pred)
      0.375
      >>> y_true = [[0.5, 1],[-1, 1],[7, -6]]
      >>> y_pred = [[0, 2],[-1, 2],[8, -5]]
      >>> mean_squared_error(y_true, y_pred)  # doctest: +ELLIPSIS
      0.708...
      >>> mean_squared_error(y_true, y_pred, multioutput='raw_values')
      ... # doctest: +ELLIPSIS
      array([ 0.416...,  1.        ])
      >>> mean_squared_error(y_true, y_pred, multioutput=[0.3, 0.7])
      ... # doctest: +ELLIPSIS
      0.824...
  
      """
      y_type, y_true, y_pred, multioutput = _check_reg_targets(
          y_true, y_pred, multioutput)
      output_errors = np.average((y_true - y_pred) ** 2, axis=0,
                                 weights=sample_weight)
      if multioutput == 'raw_values':
          return output_errors
      elif multioutput == 'uniform_average':
          # pass None as weights to np.average: uniform mean
          multioutput = None
  
      return np.average(output_errors, weights=multioutput)
  
  
  def median_absolute_error(y_true, y_pred):
      """Median absolute error regression loss
  
      Read more in the :ref:`User Guide <median_absolute_error>`.
  
      Parameters
      ----------
      y_true : array-like of shape = (n_samples)
          Ground truth (correct) target values.
  
      y_pred : array-like of shape = (n_samples)
          Estimated target values.
  
      Returns
      -------
      loss : float
          A positive floating point value (the best value is 0.0).
  
      Examples
      --------
      >>> from sklearn.metrics import median_absolute_error
      >>> y_true = [3, -0.5, 2, 7]
      >>> y_pred = [2.5, 0.0, 2, 8]
      >>> median_absolute_error(y_true, y_pred)
      0.5
  
      """
      y_type, y_true, y_pred, _ = _check_reg_targets(y_true, y_pred,
                                                     'uniform_average')
      if y_type == 'continuous-multioutput':
          raise ValueError("Multioutput not supported in median_absolute_error")
      return np.median(np.abs(y_pred - y_true))
  
  
  def explained_variance_score(y_true, y_pred,
                               sample_weight=None,
                               multioutput='uniform_average'):
      """Explained variance regression score function
  
      Best possible score is 1.0, lower values are worse.
  
      Read more in the :ref:`User Guide <explained_variance_score>`.
  
      Parameters
      ----------
      y_true : array-like of shape = (n_samples) or (n_samples, n_outputs)
          Ground truth (correct) target values.
  
      y_pred : array-like of shape = (n_samples) or (n_samples, n_outputs)
          Estimated target values.
  
      sample_weight : array-like of shape = (n_samples), optional
          Sample weights.
  
      multioutput : string in ['raw_values', 'uniform_average', \
                  'variance_weighted'] or array-like of shape (n_outputs)
          Defines aggregating of multiple output scores.
          Array-like value defines weights used to average scores.
  
          'raw_values' :
              Returns a full set of scores in case of multioutput input.
  
          'uniform_average' :
              Scores of all outputs are averaged with uniform weight.
  
          'variance_weighted' :
              Scores of all outputs are averaged, weighted by the variances
              of each individual output.
  
      Returns
      -------
      score : float or ndarray of floats
          The explained variance or ndarray if 'multioutput' is 'raw_values'.
  
      Notes
      -----
      This is not a symmetric function.
  
      Examples
      --------
      >>> from sklearn.metrics import explained_variance_score
      >>> y_true = [3, -0.5, 2, 7]
      >>> y_pred = [2.5, 0.0, 2, 8]
      >>> explained_variance_score(y_true, y_pred)  # doctest: +ELLIPSIS
      0.957...
      >>> y_true = [[0.5, 1], [-1, 1], [7, -6]]
      >>> y_pred = [[0, 2], [-1, 2], [8, -5]]
      >>> explained_variance_score(y_true, y_pred, multioutput='uniform_average')
      ... # doctest: +ELLIPSIS
      0.983...
  
      """
      y_type, y_true, y_pred, multioutput = _check_reg_targets(
          y_true, y_pred, multioutput)
  
      y_diff_avg = np.average(y_true - y_pred, weights=sample_weight, axis=0)
      numerator = np.average((y_true - y_pred - y_diff_avg) ** 2,
                             weights=sample_weight, axis=0)
  
      y_true_avg = np.average(y_true, weights=sample_weight, axis=0)
      denominator = np.average((y_true - y_true_avg) ** 2,
                               weights=sample_weight, axis=0)
  
      nonzero_numerator = numerator != 0
      nonzero_denominator = denominator != 0
      valid_score = nonzero_numerator & nonzero_denominator
      output_scores = np.ones(y_true.shape[1])
  
      output_scores[valid_score] = 1 - (numerator[valid_score] /
                                        denominator[valid_score])
      output_scores[nonzero_numerator & ~nonzero_denominator] = 0.
      if multioutput == 'raw_values':
          # return scores individually
          return output_scores
      elif multioutput == 'uniform_average':
          # passing to np.average() None as weights results is uniform mean
          avg_weights = None
      elif multioutput == 'variance_weighted':
          avg_weights = denominator
      else:
          avg_weights = multioutput
  
      return np.average(output_scores, weights=avg_weights)
  
  
  def r2_score(y_true, y_pred,
               sample_weight=None,
               multioutput=None):
      """R^2 (coefficient of determination) regression score function.
  
      Best possible score is 1.0 and it can be negative (because the
      model can be arbitrarily worse). A constant model that always
      predicts the expected value of y, disregarding the input features,
      would get a R^2 score of 0.0.
  
      Read more in the :ref:`User Guide <r2_score>`.
  
      Parameters
      ----------
      y_true : array-like of shape = (n_samples) or (n_samples, n_outputs)
          Ground truth (correct) target values.
  
      y_pred : array-like of shape = (n_samples) or (n_samples, n_outputs)
          Estimated target values.
  
      sample_weight : array-like of shape = (n_samples), optional
          Sample weights.
  
      multioutput : string in ['raw_values', 'uniform_average',
                  'variance_weighted'] or None or array-like of shape (n_outputs)
          Defines aggregating of multiple output scores.
          Array-like value defines weights used to average scores.
          Default value correponds to 'variance_weighted', but
          will be changed to 'uniform_average' in next versions.
  
          'raw_values' :
              Returns a full set of scores in case of multioutput input.
  
          'uniform_average' :
              Scores of all outputs are averaged with uniform weight.
  
          'variance_weighted' :
              Scores of all outputs are averaged, weighted by the variances
              of each individual output.
  
      Returns
      -------
      z : float or ndarray of floats
          The R^2 score or ndarray of scores if 'multioutput' is
          'raw_values'.
  
      Notes
      -----
      This is not a symmetric function.
  
      Unlike most other scores, R^2 score may be negative (it need not actually
      be the square of a quantity R).
  
      References
      ----------
      .. [1] `Wikipedia entry on the Coefficient of determination
              <http://en.wikipedia.org/wiki/Coefficient_of_determination>`_
  
      Examples
      --------
      >>> from sklearn.metrics import r2_score
      >>> y_true = [3, -0.5, 2, 7]
      >>> y_pred = [2.5, 0.0, 2, 8]
      >>> r2_score(y_true, y_pred)  # doctest: +ELLIPSIS
      0.948...
      >>> y_true = [[0.5, 1], [-1, 1], [7, -6]]
      >>> y_pred = [[0, 2], [-1, 2], [8, -5]]
      >>> r2_score(y_true, y_pred, multioutput='variance_weighted')  # doctest: +ELLIPSIS
      0.938...
  
      """
      y_type, y_true, y_pred, multioutput = _check_reg_targets(
          y_true, y_pred, multioutput)
  
      if sample_weight is not None:
          sample_weight = column_or_1d(sample_weight)
          weight = sample_weight[:, np.newaxis]
      else:
          weight = 1.
  
      numerator = (weight * (y_true - y_pred) ** 2).sum(axis=0,
                                                        dtype=np.float64)
      denominator = (weight * (y_true - np.average(
          y_true, axis=0, weights=sample_weight)) ** 2).sum(axis=0,
                                                            dtype=np.float64)
      nonzero_denominator = denominator != 0
      nonzero_numerator = numerator != 0
      valid_score = nonzero_denominator & nonzero_numerator
      output_scores = np.ones([y_true.shape[1]])
      output_scores[valid_score] = 1 - (numerator[valid_score] /
                                        denominator[valid_score])
      # arbitrary set to zero to avoid -inf scores, having a constant
      # y_true is not interesting for scoring a regression anyway
      output_scores[nonzero_numerator & ~nonzero_denominator] = 0.
      if multioutput is None and y_true.shape[1] != 1:
          # @FIXME change in 0.18
          warnings.warn("Default 'multioutput' behavior now corresponds to "
                        "'variance_weighted' value, it will be changed "
                        "to 'uniform_average' in 0.18.",
                        DeprecationWarning)
          multioutput = 'variance_weighted'
      if multioutput == 'raw_values':
          # return scores individually
          return output_scores
      elif multioutput == 'uniform_average':
          # passing None as weights results is uniform mean
          avg_weights = None
      elif multioutput == 'variance_weighted':
          avg_weights = denominator
          # avoid fail on constant y or one-element arrays
          if not np.any(nonzero_denominator):
              if not np.any(nonzero_numerator):
                  return 1.0
              else:
                  return 0.0
      else:
          avg_weights = multioutput
  
      return np.average(output_scores, weights=avg_weights)
  