U
    3dN                     @   s  d Z ddlZddlZddlZddlmZ ddlmZ ddl	m
Z
mZmZmZmZmZ ddlmZ dd	d
ddddddddddddgZd7ddZddddd	ZddddddZdddd dZddd!d"d#d
Zddd!d"d$dZddd%d&dZd'd( Zddd!d)d*dZddd!d)d+dZd,d Zd-d. Zddd/d0dZdd1d2dZ dd1d3dZ!ddd/d4dZ"ddddd5dZ#dddd6dZ$dS )8zMetrics 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.
    N)xlogy   )UndefinedMetricWarning)check_arraycheck_consistent_lengthcheck_scalar_num_samplescolumn_or_1d_check_sample_weight)_weighted_percentile	max_errormean_absolute_errormean_squared_errormean_squared_log_errormedian_absolute_errormean_absolute_percentage_errormean_pinball_lossr2_scoreexplained_variance_scoremean_tweedie_deviancemean_poisson_deviancemean_gamma_devianced2_tweedie_scored2_pinball_scored2_absolute_error_scorenumericc                 C   s  t | | t| d|d} t|d|d}| jdkr:| d} |jdkrN|d}| jd |jd kr~td| jd |jd | jd }d}t|tr||krtd||nF|dk	rt|dd	}|dkrtd
n |t	|krtdt	||f |dkrdnd}|| ||fS )aF  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().

    dtype : str or list, default="numeric"
        the dtype argument passed to check_array.

    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.
    F)	ensure_2ddtype   )r   z<y_true and y_pred have different number of output ({0}!={1}))
raw_valuesuniform_averagevariance_weightedzIAllowed 'multioutput' string values are {}. You provided multioutput={!r}N)r   z5Custom weights are useful only in multi-output cases.z?There must be equally many custom weights (%d) as outputs (%d).Z
continuouscontinuous-multioutput)
r   r   ndimZreshapeshape
ValueErrorformat
isinstancestrlen)y_truey_predmultioutputr   	n_outputsZallowed_multioutput_stry_type r0   ?/tmp/pip-unpacked-wheel-zrfo1fqw/sklearn/metrics/_regression.py_check_reg_targetsB   sH    "




 

 

r2   r!   )sample_weightr-   c                C   sj   t | ||\}} }}t| || tjt||  |dd}t|tr\|dkrP|S |dkr\d}tj||dS )a  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,), default=None
        Sample weights.

    multioutput : {'raw_values', 'uniform_average'}  or array-like of shape             (n_outputs,), default='uniform_average'
        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])
    0.85...
    r   weightsaxisr    r!   Nr5   )r2   r   npaverageabsr(   r)   )r+   r,   r3   r-   r/   output_errorsr0   r0   r1   r      s    7  
      ?r3   alphar-   c          
      C   s   t | ||\}} }}t| || | | }|dk|j}|| | d| d|  |  }tj||dd}	t|tr|dkr~|	S |dkrd}ntd| tj|	|dS )	a  Pinball loss for quantile regression.

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

    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.

    alpha : float, slope of the pinball loss, default=0.5,
        This loss is equivalent to :ref:`mean_absolute_error` when `alpha=0.5`,
        `alpha=0.95` is minimized by estimators of the 95th percentile.

    multioutput : {'raw_values', 'uniform_average'}  or array-like of shape             (n_outputs,), default='uniform_average'
        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.

        The pinball loss output is a non-negative floating point. The best
        value is 0.0.

    Examples
    --------
    >>> from sklearn.metrics import mean_pinball_loss
    >>> y_true = [1, 2, 3]
    >>> mean_pinball_loss(y_true, [0, 2, 3], alpha=0.1)
    0.03...
    >>> mean_pinball_loss(y_true, [1, 2, 4], alpha=0.1)
    0.3...
    >>> mean_pinball_loss(y_true, [0, 2, 3], alpha=0.9)
    0.3...
    >>> mean_pinball_loss(y_true, [1, 2, 4], alpha=0.9)
    0.03...
    >>> mean_pinball_loss(y_true, y_true, alpha=0.1)
    0.0
    >>> mean_pinball_loss(y_true, y_true, alpha=0.9)
    0.0
    r   r   r4   r    r!   NVmultioutput is expected to be 'raw_values' or 'uniform_average' but we got %r instead.r7   )	r2   r   Zastyper   r8   r9   r(   r)   r&   )
r+   r,   r3   r>   r-   r/   ZdiffsignZlossr;   r0   r0   r1   r      s*    =   
c                C   s   t | ||\}} }}t| || ttjj}t||  tt| | }tj||dd}t	|t
r|dkrt|S |dkrd}tj||dS )ah
  Mean absolute percentage error (MAPE) regression loss.

    Note here that the output is not a percentage in the range [0, 100]
    and a value of 100 does not mean 100% but 1e2. Furthermore, the output
    can be arbitrarily high when `y_true` is small (which is specific to the
    metric) or when `abs(y_true - y_pred)` is large (which is common for most
    regression metrics). Read more in the
    :ref:`User Guide <mean_absolute_percentage_error>`.

    .. versionadded:: 0.24

    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'} or array-like
        Defines aggregating of multiple output values.
        Array-like value defines weights used to average errors.
        If input is list then the shape must be (n_outputs,).

        '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 percentage 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.

        MAPE output is non-negative floating point. The best value is 0.0.
        But note that bad predictions can lead to arbitrarily large
        MAPE values, especially if some `y_true` values are very close to zero.
        Note that we return a large value instead of `inf` when `y_true` is zero.

    Examples
    --------
    >>> from sklearn.metrics import mean_absolute_percentage_error
    >>> y_true = [3, -0.5, 2, 7]
    >>> y_pred = [2.5, 0.0, 2, 8]
    >>> mean_absolute_percentage_error(y_true, y_pred)
    0.3273...
    >>> y_true = [[0.5, 1], [-1, 1], [7, -6]]
    >>> y_pred = [[0, 2], [-1, 2], [8, -5]]
    >>> mean_absolute_percentage_error(y_true, y_pred)
    0.5515...
    >>> mean_absolute_percentage_error(y_true, y_pred, multioutput=[0.3, 0.7])
    0.6198...
    >>> # the value when some element of the y_true is zero is arbitrarily high because
    >>> # of the division by epsilon
    >>> y_true = [1., 0., 2.4, 7.]
    >>> y_pred = [1.2, 0.1, 2.4, 8.]
    >>> mean_absolute_percentage_error(y_true, y_pred)
    112589990684262.48
    r   r4   r    r!   Nr7   )r2   r   r8   Zfinfofloat64Zepsr:   maximumr9   r(   r)   )r+   r,   r3   r-   r/   epsilonZmaper;   r0   r0   r1   r   (  s    E   
Tr3   r-   squaredc                C   sv   t | ||\}} }}t| || tj| | d d|d}|sFt|}t|trh|dkr\|S |dkrhd}tj||dS )a  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,), default=None
        Sample weights.

    multioutput : {'raw_values', 'uniform_average'} or array-like of shape             (n_outputs,), default='uniform_average'
        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.

    squared : bool, default=True
        If True returns MSE value, if False returns RMSE value.

    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 = [3, -0.5, 2, 7]
    >>> y_pred = [2.5, 0.0, 2, 8]
    >>> mean_squared_error(y_true, y_pred, squared=False)
    0.612...
    >>> y_true = [[0.5, 1],[-1, 1],[7, -6]]
    >>> y_pred = [[0, 2],[-1, 2],[8, -5]]
    >>> mean_squared_error(y_true, y_pred)
    0.708...
    >>> mean_squared_error(y_true, y_pred, squared=False)
    0.822...
    >>> mean_squared_error(y_true, y_pred, multioutput='raw_values')
    array([0.41666667, 1.        ])
    >>> mean_squared_error(y_true, y_pred, multioutput=[0.3, 0.7])
    0.825...
    r   r   r6   r5   r    r!   Nr7   )r2   r   r8   r9   sqrtr(   r)   )r+   r,   r3   r-   rE   r/   r;   r0   r0   r1   r   ~  s    <  

c                C   s^   t | ||\}} }}t| || | dk  s8|dk  r@tdtt| t||||dS )a  Mean squared logarithmic error regression loss.

    Read more in the :ref:`User Guide <mean_squared_log_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,), default=None
        Sample weights.

    multioutput : {'raw_values', 'uniform_average'} or array-like of shape             (n_outputs,), default='uniform_average'

        Defines aggregating of multiple output values.
        Array-like value defines weights used to average errors.

        'raw_values' :
            Returns a full set of errors when the input is of multioutput
            format.

        'uniform_average' :
            Errors of all outputs are averaged with uniform weight.
    squared : bool, default=True
        If True returns MSLE (mean squared log error) value.
        If False returns RMSLE (root mean squared log error) value.

    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_log_error
    >>> y_true = [3, 5, 2.5, 7]
    >>> y_pred = [2.5, 5, 4, 8]
    >>> mean_squared_log_error(y_true, y_pred)
    0.039...
    >>> mean_squared_log_error(y_true, y_pred, squared=False)
    0.199...
    >>> y_true = [[0.5, 1], [1, 2], [7, 6]]
    >>> y_pred = [[0.5, 2], [1, 2.5], [8, 8]]
    >>> mean_squared_log_error(y_true, y_pred)
    0.044...
    >>> mean_squared_log_error(y_true, y_pred, multioutput='raw_values')
    array([0.00462428, 0.08377444])
    >>> mean_squared_log_error(y_true, y_pred, multioutput=[0.3, 0.7])
    0.060...
    r   zSMean Squared Logarithmic Error cannot be used when targets contain negative values.rD   )r2   r   anyr&   r   r8   log1p)r+   r,   r3   r-   rE   r/   r0   r0   r1   r     s"    :  )r-   r3   c                C   s   t | ||\}} }}|dkr6tjt||  dd}n t||}tt||  |d}t|trx|dkrl|S |dkrxd}tj||dS )a?  Median absolute error regression loss.

    Median absolute error output is non-negative floating point. The best value
    is 0.0. Read more in the :ref:`User Guide <median_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.

    multioutput : {'raw_values', 'uniform_average'} or array-like of shape             (n_outputs,), default='uniform_average'
        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.

    sample_weight : array-like of shape (n_samples,), default=None
        Sample weights.

        .. versionadded:: 0.24

    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.

    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_true = [[0.5, 1], [-1, 1], [7, -6]]
    >>> y_pred = [[0, 2], [-1, 2], [8, -5]]
    >>> median_absolute_error(y_true, y_pred)
    0.75
    >>> median_absolute_error(y_true, y_pred, multioutput='raw_values')
    array([0.5, 1. ])
    >>> median_absolute_error(y_true, y_pred, multioutput=[0.3, 0.7])
    0.85
    Nr   )r6   r3   r    r!   r7   )	r2   r8   Zmedianr:   r
   r   r(   r)   r9   )r+   r,   r-   r3   r/   r;   r0   r0   r1   r     s$    8  
 
c           
      C   s   |dk}|sd| |  }nB| dk}t |g}||@ }d| | ||   ||< d||| @ < t|tr|dkrr|S |dkrd}	q|dkr|}	t |sd}	n|}	t j||	dS )	zCCommon part used by explained variance score and :math:`R^2` score.r   r           r    r!   Nr"   r7   )r8   onesr(   r)   rH   r9   )
	numeratordenominatorr.   r-   force_finitenonzero_denominatoroutput_scoresnonzero_numeratorvalid_scoreavg_weightsr0   r0   r1   _assemble_r2_explained_varianceg  s*    

rU   )r3   r-   rO   c          
      C   s   t | ||\}} }}t| || tj| | |dd}tj| | | d |dd}tj| |dd}tj| | d |dd}	t||	| jd ||dS )a  Explained variance regression score function.

    Best possible score is 1.0, lower values are worse.

    In the particular case when ``y_true`` is constant, the explained variance
    score is not finite: it is either ``NaN`` (perfect predictions) or
    ``-Inf`` (imperfect predictions). To prevent such non-finite numbers to
    pollute higher-level experiments such as a grid search cross-validation,
    by default these cases are replaced with 1.0 (perfect predictions) or 0.0
    (imperfect predictions) respectively. If ``force_finite``
    is set to ``False``, this score falls back on the original :math:`R^2`
    definition.

    .. note::
       The Explained Variance score is similar to the
       :func:`R^2 score <r2_score>`, with the notable difference that it
       does not account for systematic offsets in the prediction. Most often
       the :func:`R^2 score <r2_score>` should be preferred.

    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,), default=None
        Sample weights.

    multioutput : {'raw_values', 'uniform_average', 'variance_weighted'} or             array-like of shape (n_outputs,), default='uniform_average'
        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.

    force_finite : bool, default=True
        Flag indicating if ``NaN`` and ``-Inf`` scores resulting from constant
        data should be replaced with real numbers (``1.0`` if prediction is
        perfect, ``0.0`` otherwise). Default is ``True``, a convenient setting
        for hyperparameters' search procedures (e.g. grid search
        cross-validation).

        .. versionadded:: 1.1

    Returns
    -------
    score : float or ndarray of floats
        The explained variance or ndarray if 'multioutput' is 'raw_values'.

    See Also
    --------
    r2_score :
        Similar metric, but accounting for systematic offsets in
        prediction.

    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)
    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')
    0.983...
    >>> y_true = [-2, -2, -2]
    >>> y_pred = [-2, -2, -2]
    >>> explained_variance_score(y_true, y_pred)
    1.0
    >>> explained_variance_score(y_true, y_pred, force_finite=False)
    nan
    >>> y_true = [-2, -2, -2]
    >>> y_pred = [-2, -2, -2 + 1e-8]
    >>> explained_variance_score(y_true, y_pred)
    0.0
    >>> explained_variance_score(y_true, y_pred, force_finite=False)
    -inf
    r   r4   r   r   rM   rN   r.   r-   rO   )r2   r   r8   r9   rU   r%   )
r+   r,   r3   r-   rO   r/   Z
y_diff_avgrM   Z
y_true_avgrN   r0   r0   r1   r     s*    g    c          
      C   s   t | ||\}} }}t| || t|dk rDd}t|t tdS |dk	rht|}|ddtj	f }nd}|| | d  j
dtjd}|| tj| d|d d  j
dtjd}	t||	| jd	 ||d
S )aX  :math:`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). In the general case when the true y is
    non-constant, a constant model that always predicts the average y
    disregarding the input features would get a :math:`R^2` score of 0.0.

    In the particular case when ``y_true`` is constant, the :math:`R^2` score
    is not finite: it is either ``NaN`` (perfect predictions) or ``-Inf``
    (imperfect predictions). To prevent such non-finite numbers to pollute
    higher-level experiments such as a grid search cross-validation, by default
    these cases are replaced with 1.0 (perfect predictions) or 0.0 (imperfect
    predictions) respectively. You can set ``force_finite`` to ``False`` to
    prevent this fix from happening.

    Note: when the prediction residuals have zero mean, the :math:`R^2` score
    is identical to the
    :func:`Explained Variance score <explained_variance_score>`.

    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'.

    force_finite : bool, default=True
        Flag indicating if ``NaN`` and ``-Inf`` scores resulting from constant
        data should be replaced with real numbers (``1.0`` if prediction is
        perfect, ``0.0`` otherwise). Default is ``True``, a convenient setting
        for hyperparameters' search procedures (e.g. grid search
        cross-validation).

        .. versionadded:: 1.1

    Returns
    -------
    z : float or ndarray of floats
        The :math:`R^2` score or ndarray of scores if 'multioutput' is
        'raw_values'.

    Notes
    -----
    This is not a symmetric function.

    Unlike most other scores, :math:`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_true = [-2, -2, -2]
    >>> y_pred = [-2, -2, -2]
    >>> r2_score(y_true, y_pred)
    1.0
    >>> r2_score(y_true, y_pred, force_finite=False)
    nan
    >>> y_true = [-2, -2, -2]
    >>> y_pred = [-2, -2, -2 + 1e-8]
    >>> r2_score(y_true, y_pred)
    0.0
    >>> r2_score(y_true, y_pred, force_finite=False)
    -inf
    r   z9R^2 score is not well-defined with less than two samples.nanNg      ?r   )r6   r   rF   r   rV   )r2   r   r   warningswarnr   floatr	   r8   newaxissumrA   r9   rU   r%   )
r+   r,   r3   r-   rO   r/   msgZweightrM   rN   r0   r0   r1   r     s6       c                 C   s8   t | |d\}} }}|dkr$tdtt| | S )ab  
    The max_error metric calculates the maximum residual error.

    Read more in the :ref:`User Guide <max_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
    -------
    max_error : float
        A positive floating point value (the best value is 0.0).

    Examples
    --------
    >>> from sklearn.metrics import max_error
    >>> y_true = [3, 2, 7, 1]
    >>> y_pred = [4, 2, 7, 1]
    >>> max_error(y_true, y_pred)
    1
    Nr#   z&Multioutput not supported in max_error)r2   r&   r8   maxr:   )r+   r,   r/   _r0   r0   r1   r     s    c                 C   s6  |}|dk rndt t | dd| d| d|   | t |d|  d|   t |d| d|    }n|dkr| | d }n|dkrdt| | | |  |  }n|dkrdt ||  | |  d  }nXdt | d| d| d|   | t |d|  d|   t |d| d|    }t j||dS )z&Mean Tweedie deviance regression loss.r   r   r   r7   )r8   powerrB   r   logr9   )r+   r,   r3   r`   pdevr0   r0   r1   _mean_tweedie_deviance  s.    & rd   r3   r`   c                C   sR  t | |dtjtjgd\}} }}|dkr0tdt| || |dk	r^t|}|ddtjf }t|dt	j
d}d| d}|d	k r|d	k rt|d
 n|d	krnd	|  k rdk rn n
tdnzd|  krdk r
n n(| d	k  s|d	k rBt|d n8|dkr>| d	k s0|d	k rBt|d ntt| |||dS )a[  Mean Tweedie deviance regression loss.

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

    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.

    sample_weight : array-like of shape (n_samples,), default=None
        Sample weights.

    power : float, default=0
        Tweedie power parameter. Either power <= 0 or power >= 1.

        The higher `p` the less weight is given to extreme
        deviations between true and predicted targets.

        - power < 0: Extreme stable distribution. Requires: y_pred > 0.
        - power = 0 : Normal distribution, output corresponds to
          mean_squared_error. y_true and y_pred can be any real numbers.
        - power = 1 : Poisson distribution. Requires: y_true >= 0 and
          y_pred > 0.
        - 1 < p < 2 : Compound Poisson distribution. Requires: y_true >= 0
          and y_pred > 0.
        - power = 2 : Gamma distribution. Requires: y_true > 0 and y_pred > 0.
        - power = 3 : Inverse Gaussian distribution. Requires: y_true > 0
          and y_pred > 0.
        - otherwise : Positive stable distribution. Requires: y_true > 0
          and y_pred > 0.

    Returns
    -------
    loss : float
        A non-negative floating point value (the best value is 0.0).

    Examples
    --------
    >>> from sklearn.metrics import mean_tweedie_deviance
    >>> y_true = [2, 0, 1, 4]
    >>> y_pred = [0.5, 0.5, 2., 2.]
    >>> mean_tweedie_deviance(y_true, y_pred, power=1)
    1.4260...
    Nr   r#   z2Multioutput not supported in mean_tweedie_deviancer`   )nameZtarget_typez'Mean Tweedie deviance error with power=z can only be used on r   zstrictly positive y_pred.r   z;Tweedie deviance is only defined for power<=0 and power>=1.r   z,non-negative y and strictly positive y_pred.zstrictly positive y and y_pred.re   )r2   r8   rA   float32r&   r   r	   r[   r   numbersRealrH   rd   )r+   r,   r3   r`   r/   r_   rb   messager0   r0   r1   r     sL    0   


   rJ   c                C   s   t | ||ddS )ad  Mean Poisson deviance regression loss.

    Poisson deviance is equivalent to the Tweedie deviance with
    the power parameter `power=1`.

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

    Parameters
    ----------
    y_true : array-like of shape (n_samples,)
        Ground truth (correct) target values. Requires y_true >= 0.

    y_pred : array-like of shape (n_samples,)
        Estimated target values. Requires y_pred > 0.

    sample_weight : array-like of shape (n_samples,), default=None
        Sample weights.

    Returns
    -------
    loss : float
        A non-negative floating point value (the best value is 0.0).

    Examples
    --------
    >>> from sklearn.metrics import mean_poisson_deviance
    >>> y_true = [2, 0, 1, 4]
    >>> y_pred = [0.5, 0.5, 2., 2.]
    >>> mean_poisson_deviance(y_true, y_pred)
    1.4260...
    r   re   r   r+   r,   r3   r0   r0   r1   r   G  s     c                C   s   t | ||ddS )a  Mean Gamma deviance regression loss.

    Gamma deviance is equivalent to the Tweedie deviance with
    the power parameter `power=2`. It is invariant to scaling of
    the target variable, and measures relative errors.

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

    Parameters
    ----------
    y_true : array-like of shape (n_samples,)
        Ground truth (correct) target values. Requires y_true > 0.

    y_pred : array-like of shape (n_samples,)
        Estimated target values. Requires y_pred > 0.

    sample_weight : array-like of shape (n_samples,), default=None
        Sample weights.

    Returns
    -------
    loss : float
        A non-negative floating point value (the best value is 0.0).

    Examples
    --------
    >>> from sklearn.metrics import mean_gamma_deviance
    >>> y_true = [2, 0.5, 1, 4]
    >>> y_pred = [0.5, 0.5, 2., 2.]
    >>> mean_gamma_deviance(y_true, y_pred)
    1.0568...
    r   re   rl   rm   r0   r0   r1   r   j  s    !c          
      C   s   t | |dtjtjgd\}} }}|dkr0tdt|dk rTd}t|t t	dS t
| t
| } }t| |||d}tj| |d	}t| |||d}	d
||	  S )a
  D^2 regression score function, fraction of Tweedie deviance explained.

    Best possible score is 1.0 and it can be negative (because the model can be
    arbitrarily worse). A model that always uses the empirical mean of `y_true` as
    constant prediction, disregarding the input features, gets a D^2 score of 0.0.

    Read more in the :ref:`User Guide <d2_score>`.

    .. versionadded:: 1.0

    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.

    sample_weight : array-like of shape (n_samples,), optional
        Sample weights.

    power : float, default=0
        Tweedie power parameter. Either power <= 0 or power >= 1.

        The higher `p` the less weight is given to extreme
        deviations between true and predicted targets.

        - power < 0: Extreme stable distribution. Requires: y_pred > 0.
        - power = 0 : Normal distribution, output corresponds to r2_score.
          y_true and y_pred can be any real numbers.
        - power = 1 : Poisson distribution. Requires: y_true >= 0 and
          y_pred > 0.
        - 1 < p < 2 : Compound Poisson distribution. Requires: y_true >= 0
          and y_pred > 0.
        - power = 2 : Gamma distribution. Requires: y_true > 0 and y_pred > 0.
        - power = 3 : Inverse Gaussian distribution. Requires: y_true > 0
          and y_pred > 0.
        - otherwise : Positive stable distribution. Requires: y_true > 0
          and y_pred > 0.

    Returns
    -------
    z : float or ndarray of floats
        The D^2 score.

    Notes
    -----
    This is not a symmetric function.

    Like R^2, D^2 score may be negative (it need not actually be the square of
    a quantity D).

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

    References
    ----------
    .. [1] Eq. (3.11) of Hastie, Trevor J., Robert Tibshirani and Martin J.
           Wainwright. "Statistical Learning with Sparsity: The Lasso and
           Generalizations." (2015). https://hastie.su.domains/StatLearnSparsity/

    Examples
    --------
    >>> from sklearn.metrics import d2_tweedie_score
    >>> y_true = [0.5, 1, 2.5, 7]
    >>> y_pred = [1, 1, 5, 3.5]
    >>> d2_tweedie_score(y_true, y_pred)
    0.285...
    >>> d2_tweedie_score(y_true, y_pred, power=1)
    0.487...
    >>> d2_tweedie_score(y_true, y_pred, power=2)
    0.630...
    >>> d2_tweedie_score(y_true, y_true, power=2)
    1.0
    Nrf   r#   z-Multioutput not supported in d2_tweedie_scorer   9D^2 score is not well-defined with less than two samples.rW   re   r7   r   )r2   r8   rA   rh   r&   r   rX   rY   r   rZ   Zsqueezer   r9   rd   )
r+   r,   r3   r`   r/   r_   r]   rM   Zy_avgrN   r0   r0   r1   r     s6    L   
      c                C   sZ  t | ||\}} }}t| || t|dk rDd}t|t tdS t| |||dd}|dkrt	tj
| |d dd	t| d
f}n,t|| }t	t| ||d dt| d
f}t| |||dd}	|dk}
|	dk}|
|@ }t| jd
 }d
|| |	|   ||< d||
| @ < t|trH|dkr*|S |dkr:d}ntd| n|}tj||dS )u
  
    :math:`D^2` regression score function, fraction of pinball loss explained.

    Best possible score is 1.0 and it can be negative (because the model can be
    arbitrarily worse). A model that always uses the empirical alpha-quantile of
    `y_true` as constant prediction, disregarding the input features,
    gets a :math:`D^2` score of 0.0.

    Read more in the :ref:`User Guide <d2_score>`.

    .. versionadded:: 1.1

    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.

    alpha : float, default=0.5
        Slope of the pinball deviance. It determines the quantile level alpha
        for which the pinball deviance and also D2 are optimal.
        The default `alpha=0.5` is equivalent to `d2_absolute_error_score`.

    multioutput : {'raw_values', 'uniform_average'} or array-like of shape             (n_outputs,), default='uniform_average'
        Defines aggregating of multiple output values.
        Array-like value defines weights used to average scores.

        'raw_values' :
            Returns a full set of errors in case of multioutput input.

        'uniform_average' :
            Scores of all outputs are averaged with uniform weight.

    Returns
    -------
    score : float or ndarray of floats
        The :math:`D^2` score with a pinball deviance
        or ndarray of scores if `multioutput='raw_values'`.

    Notes
    -----
    Like :math:`R^2`, :math:`D^2` score may be negative
    (it need not actually be the square of a quantity D).

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

     References
    ----------
    .. [1] Eq. (7) of `Koenker, Roger; Machado, José A. F. (1999).
           "Goodness of Fit and Related Inference Processes for Quantile Regression"
           <http://dx.doi.org/10.1080/01621459.1999.10473882>`_
    .. [2] Eq. (3.11) of Hastie, Trevor J., Robert Tibshirani and Martin J.
           Wainwright. "Statistical Learning with Sparsity: The Lasso and
           Generalizations." (2015). https://hastie.su.domains/StatLearnSparsity/

    Examples
    --------
    >>> from sklearn.metrics import d2_pinball_score
    >>> y_true = [1, 2, 3]
    >>> y_pred = [1, 3, 3]
    >>> d2_pinball_score(y_true, y_pred)
    0.5
    >>> d2_pinball_score(y_true, y_pred, alpha=0.9)
    0.772...
    >>> d2_pinball_score(y_true, y_pred, alpha=0.1)
    -1.045...
    >>> d2_pinball_score(y_true, y_true, alpha=0.1)
    1.0
    r   rn   rW   r    r=   Nd   r   )qr6   r   )r3   
percentilerK   r!   r?   r7   )r2   r   r   rX   rY   r   rZ   r   r8   Ztilerq   r*   r
   r   rL   r%   r(   r)   r&   r9   )r+   r,   r3   r>   r-   r/   r]   rM   Z
y_quantilerN   rR   rP   rS   rQ   rT   r0   r0   r1   r     sp    O   

  


c                C   s   t | ||d|dS )a
  
    :math:`D^2` regression score function,     fraction of absolute error explained.

    Best possible score is 1.0 and it can be negative (because the model can be
    arbitrarily worse). A model that always uses the empirical median of `y_true`
    as constant prediction, disregarding the input features,
    gets a :math:`D^2` score of 0.0.

    Read more in the :ref:`User Guide <d2_score>`.

    .. versionadded:: 1.1

    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 : {'raw_values', 'uniform_average'} or array-like of shape             (n_outputs,), default='uniform_average'
        Defines aggregating of multiple output values.
        Array-like value defines weights used to average scores.

        'raw_values' :
            Returns a full set of errors in case of multioutput input.

        'uniform_average' :
            Scores of all outputs are averaged with uniform weight.

    Returns
    -------
    score : float or ndarray of floats
        The :math:`D^2` score with an absolute error deviance
        or ndarray of scores if 'multioutput' is 'raw_values'.

    Notes
    -----
    Like :math:`R^2`, :math:`D^2` score may be negative
    (it need not actually be the square of a quantity D).

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

     References
    ----------
    .. [1] Eq. (3.11) of Hastie, Trevor J., Robert Tibshirani and Martin J.
           Wainwright. "Statistical Learning with Sparsity: The Lasso and
           Generalizations." (2015). https://hastie.su.domains/StatLearnSparsity/

    Examples
    --------
    >>> from sklearn.metrics import d2_absolute_error_score
    >>> y_true = [3, -0.5, 2, 7]
    >>> y_pred = [2.5, 0.0, 2, 8]
    >>> d2_absolute_error_score(y_true, y_pred)
    0.764...
    >>> y_true = [[0.5, 1], [-1, 1], [7, -6]]
    >>> y_pred = [[0, 2], [-1, 2], [8, -5]]
    >>> d2_absolute_error_score(y_true, y_pred, multioutput='uniform_average')
    0.691...
    >>> d2_absolute_error_score(y_true, y_pred, multioutput='raw_values')
    array([0.8125    , 0.57142857])
    >>> y_true = [1, 2, 3]
    >>> y_pred = [1, 2, 3]
    >>> d2_absolute_error_score(y_true, y_pred)
    1.0
    >>> y_true = [1, 2, 3]
    >>> y_pred = [2, 2, 2]
    >>> d2_absolute_error_score(y_true, y_pred)
    0.0
    >>> y_true = [1, 2, 3]
    >>> y_pred = [3, 2, 1]
    >>> d2_absolute_error_score(y_true, y_pred)
    -1.0
    r<   r=   )r   )r+   r,   r3   r-   r0   r0   r1   r     s    T    )r   )%__doc__ri   rX   Znumpyr8   Zscipy.specialr   
exceptionsr   Zutils.validationr   r   r   r   r	   r
   Zutils.statsr   Z__ALL__r2   r   r   r   r   r   r   rU   r   r   r   rd   r   r   r   r   r   r   r0   r0   r0   r1   <module>   s    
L G  V W  P  O L0  !\#$e    