"""Metrics to assess performance on classification task given scores

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
#          Joel Nothman <joel.nothman@gmail.com>
#          Noel Dawe <noel@dawe.me>
# License: BSD 3 clause


import warnings
from functools import partial

import numpy as np
from scipy.sparse import csr_matrix
from scipy.stats import rankdata

from ..utils import assert_all_finite
from ..utils import check_consistent_length
from ..utils import column_or_1d, check_array
from ..utils.multiclass import type_of_target
from ..utils.extmath import stable_cumsum
from ..utils.sparsefuncs import count_nonzero
from ..utils.validation import _deprecate_positional_args
from ..exceptions import UndefinedMetricWarning
from ..preprocessing import label_binarize
from ..preprocessing._label import _encode

from ._base import _average_binary_score, _average_multiclass_ovo_score


def auc(x, y):
    """Compute Area Under the Curve (AUC) using the trapezoidal rule

    This is a general function, given points on a curve.  For computing the
    area under the ROC-curve, see :func:`roc_auc_score`.  For an alternative
    way to summarize a precision-recall curve, see
    :func:`average_precision_score`.

    Parameters
    ----------
    x : array, shape = [n]
        x coordinates. These must be either monotonic increasing or monotonic
        decreasing.
    y : array, shape = [n]
        y coordinates.

    Returns
    -------
    auc : float

    Examples
    --------
    >>> import numpy as np
    >>> from sklearn import metrics
    >>> y = np.array([1, 1, 2, 2])
    >>> pred = np.array([0.1, 0.4, 0.35, 0.8])
    >>> fpr, tpr, thresholds = metrics.roc_curve(y, pred, pos_label=2)
    >>> metrics.auc(fpr, tpr)
    0.75

    See also
    --------
    roc_auc_score : Compute the area under the ROC curve
    average_precision_score : Compute average precision from prediction scores
    precision_recall_curve :
        Compute precision-recall pairs for different probability thresholds
    """
    check_consistent_length(x, y)
    x = column_or_1d(x)
    y = column_or_1d(y)

    if x.shape[0] < 2:
        raise ValueError('At least 2 points are needed to compute'
                         ' area under curve, but x.shape = %s' % x.shape)

    direction = 1
    dx = np.diff(x)
    if np.any(dx < 0):
        if np.all(dx <= 0):
            direction = -1
        else:
            raise ValueError("x is neither increasing nor decreasing "
                             ": {}.".format(x))

    area = direction * np.trapz(y, x)
    if isinstance(area, np.memmap):
        # Reductions such as .sum used internally in np.trapz do not return a
        # scalar by default for numpy.memmap instances contrary to
        # regular numpy.ndarray instances.
        area = area.dtype.type(area)
    return area


@_deprecate_positional_args
def average_precision_score(y_true, y_score, *, average="macro", pos_label=1,
                            sample_weight=None):
    """Compute average precision (AP) from prediction scores

    AP summarizes a precision-recall curve as the weighted mean of precisions
    achieved at each threshold, with the increase in recall from the previous
    threshold used as the weight:

    .. math::
        \\text{AP} = \\sum_n (R_n - R_{n-1}) P_n

    where :math:`P_n` and :math:`R_n` are the precision and recall at the nth
    threshold [1]_. This implementation is not interpolated and is different
    from computing the area under the precision-recall curve with the
    trapezoidal rule, which uses linear interpolation and can be too
    optimistic.

    Note: this implementation is restricted to the binary classification task
    or multilabel classification task.

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

    Parameters
    ----------
    y_true : array, shape = [n_samples] or [n_samples, n_classes]
        True binary labels or binary label indicators.

    y_score : array, shape = [n_samples] or [n_samples, n_classes]
        Target scores, can either be probability estimates of the positive
        class, confidence values, or non-thresholded measure of decisions
        (as returned by "decision_function" on some classifiers).

    average : string, [None, 'micro', 'macro' (default), 'samples', 'weighted']
        If ``None``, the scores for each class are returned. Otherwise,
        this determines the type of averaging performed on the data:

        ``'micro'``:
            Calculate metrics globally by considering each element of the label
            indicator matrix as a label.
        ``'macro'``:
            Calculate metrics for each label, and find their unweighted
            mean.  This does not take label imbalance into account.
        ``'weighted'``:
            Calculate metrics for each label, and find their average, weighted
            by support (the number of true instances for each label).
        ``'samples'``:
            Calculate metrics for each instance, and find their average.

        Will be ignored when ``y_true`` is binary.

    pos_label : int or str (default=1)
        The label of the positive class. Only applied to binary ``y_true``.
        For multilabel-indicator ``y_true``, ``pos_label`` is fixed to 1.

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

    Returns
    -------
    average_precision : float

    References
    ----------
    .. [1] `Wikipedia entry for the Average precision
           <https://en.wikipedia.org/w/index.php?title=Information_retrieval&
           oldid=793358396#Average_precision>`_

    See also
    --------
    roc_auc_score : Compute the area under the ROC curve

    precision_recall_curve :
        Compute precision-recall pairs for different probability thresholds

    Examples
    --------
    >>> import numpy as np
    >>> from sklearn.metrics import average_precision_score
    >>> y_true = np.array([0, 0, 1, 1])
    >>> y_scores = np.array([0.1, 0.4, 0.35, 0.8])
    >>> average_precision_score(y_true, y_scores)
    0.83...

    Notes
    -----
    .. versionchanged:: 0.19
      Instead of linearly interpolating between operating points, precisions
      are weighted by the change in recall since the last operating point.
    """
    def _binary_uninterpolated_average_precision(
            y_true, y_score, pos_label=1, sample_weight=None):
        precision, recall, _ = precision_recall_curve(
            y_true, y_score, pos_label=pos_label, sample_weight=sample_weight)
        # Return the step function integral
        # The following works because the last entry of precision is
        # guaranteed to be 1, as returned by precision_recall_curve
        return -np.sum(np.diff(recall) * np.array(precision)[:-1])

    y_type = type_of_target(y_true)
    if y_type == "multilabel-indicator" and pos_label != 1:
        raise ValueError("Parameter pos_label is fixed to 1 for "
                         "multilabel-indicator y_true. Do not set "
                         "pos_label or set pos_label to 1.")
    elif y_type == "binary":
        present_labels = np.unique(y_true)
        if len(present_labels) == 2 and pos_label not in present_labels:
            raise ValueError("pos_label=%r is invalid. Set it to a label in "
                             "y_true." % pos_label)
    average_precision = partial(_binary_uninterpolated_average_precision,
                                pos_label=pos_label)
    return _average_binary_score(average_precision, y_true, y_score,
                                 average, sample_weight=sample_weight)


def _binary_roc_auc_score(y_true, y_score, sample_weight=None, max_fpr=None):
    """Binary roc auc score"""
    if len(np.unique(y_true)) != 2:
        raise ValueError("Only one class present in y_true. ROC AUC score "
                         "is not defined in that case.")

    fpr, tpr, _ = roc_curve(y_true, y_score,
                            sample_weight=sample_weight)
    if max_fpr is None or max_fpr == 1:
        return auc(fpr, tpr)
    if max_fpr <= 0 or max_fpr > 1:
        raise ValueError("Expected max_fpr in range (0, 1], got: %r" % max_fpr)

    # Add a single point at max_fpr by linear interpolation
    stop = np.searchsorted(fpr, max_fpr, 'right')
    x_interp = [fpr[stop - 1], fpr[stop]]
    y_interp = [tpr[stop - 1], tpr[stop]]
    tpr = np.append(tpr[:stop], np.interp(max_fpr, x_interp, y_interp))
    fpr = np.append(fpr[:stop], max_fpr)
    partial_auc = auc(fpr, tpr)

    # McClish correction: standardize result to be 0.5 if non-discriminant
    # and 1 if maximal
    min_area = 0.5 * max_fpr**2
    max_area = max_fpr
    return 0.5 * (1 + (partial_auc - min_area) / (max_area - min_area))


@_deprecate_positional_args
def roc_auc_score(y_true, y_score, *, average="macro", sample_weight=None,
                  max_fpr=None, multi_class="raise", labels=None):
    """Compute Area Under the Receiver Operating Characteristic Curve (ROC AUC)
    from prediction scores.

    Note: this implementation can be used with binary, multiclass and
    multilabel classification, but some restrictions apply (see Parameters).

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

    Parameters
    ----------
    y_true : array-like of shape (n_samples,) or (n_samples, n_classes)
        True labels or binary label indicators. The binary and multiclass cases
        expect labels with shape (n_samples,) while the multilabel case expects
        binary label indicators with shape (n_samples, n_classes).

    y_score : array-like of shape (n_samples,) or (n_samples, n_classes)
        Target scores. In the binary and multilabel cases, these can be either
        probability estimates or non-thresholded decision values (as returned
        by `decision_function` on some classifiers). In the multiclass case,
        these must be probability estimates which sum to 1. The binary
        case expects a shape (n_samples,), and the scores must be the scores of
        the class with the greater label. The multiclass and multilabel
        cases expect a shape (n_samples, n_classes). In the multiclass case,
        the order of the class scores must correspond to the order of
        ``labels``, if provided, or else to the numerical or lexicographical
        order of the labels in ``y_true``.

    average : {'micro', 'macro', 'samples', 'weighted'} or None, \
            default='macro'
        If ``None``, the scores for each class are returned. Otherwise,
        this determines the type of averaging performed on the data:
        Note: multiclass ROC AUC currently only handles the 'macro' and
        'weighted' averages.

        ``'micro'``:
            Calculate metrics globally by considering each element of the label
            indicator matrix as a label.
        ``'macro'``:
            Calculate metrics for each label, and find their unweighted
            mean.  This does not take label imbalance into account.
        ``'weighted'``:
            Calculate metrics for each label, and find their average, weighted
            by support (the number of true instances for each label).
        ``'samples'``:
            Calculate metrics for each instance, and find their average.

        Will be ignored when ``y_true`` is binary.

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

    max_fpr : float > 0 and <= 1, default=None
        If not ``None``, the standardized partial AUC [2]_ over the range
        [0, max_fpr] is returned. For the multiclass case, ``max_fpr``,
        should be either equal to ``None`` or ``1.0`` as AUC ROC partial
        computation currently is not supported for multiclass.

    multi_class : {'raise', 'ovr', 'ovo'}, default='raise'
        Multiclass only. Determines the type of configuration to use. The
        default value raises an error, so either ``'ovr'`` or ``'ovo'`` must be
        passed explicitly.

        ``'ovr'``:
            Computes the AUC of each class against the rest [3]_ [4]_. This
            treats the multiclass case in the same way as the multilabel case.
            Sensitive to class imbalance even when ``average == 'macro'``,
            because class imbalance affects the composition of each of the
            'rest' groupings.
        ``'ovo'``:
            Computes the average AUC of all possible pairwise combinations of
            classes [5]_. Insensitive to class imbalance when
            ``average == 'macro'``.

    labels : array-like of shape (n_classes,), default=None
        Multiclass only. List of labels that index the classes in ``y_score``.
        If ``None``, the numerical or lexicographical order of the labels in
        ``y_true`` is used.

    Returns
    -------
    auc : float

    References
    ----------
    .. [1] `Wikipedia entry for the Receiver operating characteristic
            <https://en.wikipedia.org/wiki/Receiver_operating_characteristic>`_

    .. [2] `Analyzing a portion of the ROC curve. McClish, 1989
            <https://www.ncbi.nlm.nih.gov/pubmed/2668680>`_

    .. [3] Provost, F., Domingos, P. (2000). Well-trained PETs: Improving
           probability estimation trees (Section 6.2), CeDER Working Paper
           #IS-00-04, Stern School of Business, New York University.

    .. [4] `Fawcett, T. (2006). An introduction to ROC analysis. Pattern