"""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
"""


import numpy as np
import warnings

from ..utils.validation import (check_array, check_consistent_length,
                                _num_samples)
from ..utils.validation import column_or_1d
from ..utils.validation import _deprecate_positional_args


def _check_reg_targets(y_true, y_pred, multioutput, dtype="numeric"):
    """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.
    dtype: str or list, default="numeric"
        the dtype argument passed to check_array

    """
    check_consistent_length(y_true, y_pred)
    y_true = check_array(y_true, ensure_2d=False, dtype=dtype)
    y_pred = check_array(y_pred, ensure_2d=False, dtype=dtype)

    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]
    allowed_multioutput_str = ('raw_values', 'uniform_average',
                               'variance_weighted')
    if isinstance(multioutput, str):
        if multioutput not in allowed_multioutput_str:
            raise ValueError("Allowed 'multioutput' string values are {}. "
                             "You provided multioutput={!r}".format(
                                 allowed_multioutput_str,
                                 multioutput))
    elif multioutput is not None:
        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

@_deprecate_positional_args
def r2_score(y_true, y_pred, *, sample_weight=None,
             multioutput="uniform_average"):
    """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,), default=None
        Sample weights.

    multioutput : {'raw_values', 'uniform_average', 'variance_weighted'}, \
            array-like of shape (n_outputs,) or None, default='uniform_average'

        Defines aggregating of multiple output scores.
        Array-like value defines weights used to average scores.
        Default is "uniform_average".

        '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.

        .. versionchanged:: 0.19
            Default value of multioutput is 'uniform_average'.

    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).

    This metric is not well-defined for single samples and will return a NaN
    value if n_samples is less than two.

    References
    ----------
    .. [1] `Wikipedia entry on the Coefficient of determination
            <https://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)
    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')
    0.938...
    >>> y_true = [1, 2, 3]
    >>> y_pred = [1, 2, 3]
    >>> r2_score(y_true, y_pred)
    1.0
    >>> y_true = [1, 2, 3]
    >>> y_pred = [2, 2, 2]
    >>> r2_score(y_true, y_pred)
    0.0
    >>> y_true = [1, 2, 3]
    >>> y_pred = [3, 2, 1]
    >>> r2_score(y_true, y_pred)
    -3.0
    """
    y_type, y_true, y_pred, multioutput = _check_reg_targets(
        y_true, y_pred, multioutput)
    check_consistent_length(y_true, y_pred, sample_weight)

    if _num_samples(y_pred) < 2:
        msg = "R^2 score is not well-defined with less than two samples."
        warnings.warn(msg, UndefinedMetricWarning)
        return float('nan')

    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 isinstance(multioutput, str):
        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)
