"""simple docstring"""
from sklearn.metrics import roc_auc_score

import datasets


lowercase__   			=      """
This metric computes the area under the curve (AUC) for the Receiver Operating Characteristic Curve (ROC). The return values represent how well the model used is predicting the correct classes, based on the input data. A score of `0.5` means that the model is predicting exactly at chance, i.e. the model's predictions are correct at the same rate as if the predictions were being decided by the flip of a fair coin or the roll of a fair die. A score above `0.5` indicates that the model is doing better than chance, while a score below `0.5` indicates that the model is doing worse than chance.

This metric has three separate use cases:
    - binary: The case in which there are only two different label classes, and each example gets only one label. This is the default implementation.
    - multiclass: The case in which there can be more than two different label classes, but each example still gets only one label.
    - multilabel: The case in which there can be more than two different label classes, and each example can have more than one label.
"""

lowercase__   			=      """
Args:
- references (array-like of shape (n_samples,) or (n_samples, n_classes)): Ground truth labels. Expects different input based on use case:
    - binary: expects an array-like of shape (n_samples,)
    - multiclass: expects an array-like of shape (n_samples,)
    - multilabel: expects an array-like of shape (n_samples, n_classes)
- prediction_scores (array-like of shape (n_samples,) or (n_samples, n_classes)): Model predictions. Expects different inputs based on use case:
    - binary: expects an array-like of shape (n_samples,)
    - multiclass: expects an array-like of shape (n_samples, n_classes)
    - multilabel: expects an array-like of shape (n_samples, n_classes)
- average (`str`): Type of average, and is ignored in the binary use case. Defaults to 'macro'. Options are:
    - `'micro'`: Calculates metrics globally by considering each element of the label indicator matrix as a label. Only works with the multilabel use case.
    - `'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 (i.e. the number of true instances for each label).
    - `'samples'`: Calculate metrics for each instance, and find their average. Only works with the multilabel use case.
    - `None`:  No average is calculated, and scores for each class are returned. Only works with the multilabels use case.
- sample_weight (array-like of shape (n_samples,)): Sample weights. Defaults to None.
- max_fpr (`float`): If not None, the standardized partial AUC over the range [0, `max_fpr`] is returned. Must be greater than `0` and less than or equal to `1`. Defaults to `None`. Note: For the multiclass use case, `max_fpr` should be either `None` or `1.0` as ROC AUC partial computation is not currently supported for `multiclass`.
- multi_class (`str`): Only used for multiclass targets, where it is required. Determines the type of configuration to use. Options are:
    - `'ovr'`: Stands for One-vs-rest. Computes the AUC of each class against the rest. 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'`: Stands for One-vs-one. Computes the average AUC of all possible pairwise combinations of classes. Insensitive to class imbalance when `average == 'macro'`.
- labels (array-like of shape (n_classes,)): Only used for multiclass targets. List of labels that index the classes in
    `prediction_scores`. If `None`, the numerical or lexicographical order of the labels in
    `prediction_scores` is used. Defaults to `None`.
Returns:
    roc_auc (`float` or array-like of shape (n_classes,)): Returns array if in multilabel use case and `average='None'`. Otherwise, returns `float`.
Examples:
    Example 1:
        >>> roc_auc_score = datasets.load_metric(\"roc_auc\")
        >>> refs = [1, 0, 1, 1, 0, 0]
        >>> pred_scores = [0.5, 0.2, 0.99, 0.3, 0.1, 0.7]
        >>> results = roc_auc_score.compute(references=refs, prediction_scores=pred_scores)
        >>> print(round(results['roc_auc'], 2))
        0.78

    Example 2:
        >>> roc_auc_score = datasets.load_metric(\"roc_auc\", \"multiclass\")
        >>> refs = [1, 0, 1, 2, 2, 0]
        >>> pred_scores = [[0.3, 0.5, 0.2],
        ...                 [0.7, 0.2, 0.1],
        ...                 [0.005, 0.99, 0.005],
        ...                 [0.2, 0.3, 0.5],
        ...                 [0.1, 0.1, 0.8],
        ...                 [0.1, 0.7, 0.2]]
        >>> results = roc_auc_score.compute(references=refs, prediction_scores=pred_scores, multi_class='ovr')
        >>> print(round(results['roc_auc'], 2))
        0.85

    Example 3:
        >>> roc_auc_score = datasets.load_metric(\"roc_auc\", \"multilabel\")
        >>> refs = [[1, 1, 0],
        ...         [1, 1, 0],
        ...         [0, 1, 0],
        ...         [0, 0, 1],
        ...         [0, 1, 1],
        ...         [1, 0, 1]]
        >>> pred_scores = [[0.3, 0.5, 0.2],
        ...                 [0.7, 0.2, 0.1],
        ...                 [0.005, 0.99, 0.005],
        ...                 [0.2, 0.3, 0.5],
        ...                 [0.1, 0.1, 0.8],
        ...                 [0.1, 0.7, 0.2]]
        >>> results = roc_auc_score.compute(references=refs, prediction_scores=pred_scores, average=None)
        >>> print([round(res, 2) for res in results['roc_auc']])
        [0.83, 0.38, 0.94]
"""

lowercase__   			=      """\
@article{doi:10.1177/0272989X8900900307,
author = {Donna Katzman McClish},
title ={Analyzing a Portion of the ROC Curve},
journal = {Medical Decision Making},
volume = {9},
number = {3},
pages = {190-195},
year = {1989},
doi = {10.1177/0272989X8900900307},
    note ={PMID: 2668680},
URL = {https://doi.org/10.1177/0272989X8900900307},
eprint = {https://doi.org/10.1177/0272989X8900900307}
}


@article{10.1023/A:1010920819831,
author = {Hand, David J. and Till, Robert J.},
title = {A Simple Generalisation of the Area Under the ROC Curve for Multiple Class Classification Problems},
year = {2001},
issue_date = {November 2001},
publisher = {Kluwer Academic Publishers},
address = {USA},
volume = {45},
number = {2},
issn = {0885-6125},
url = {https://doi.org/10.1023/A:1010920819831},
doi = {10.1023/A:1010920819831},
journal = {Mach. Learn.},
month = {oct},
pages = {171–186},
numpages = {16},
keywords = {Gini index, AUC, error rate, ROC curve, receiver operating characteristic}
}


@article{scikit-learn,
title={Scikit-learn: Machine Learning in {P}ython},
author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V. and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P. and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},
journal={Journal of Machine Learning Research},
volume={12},
pages={2825--2830},
year={2011}
}
"""




@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION			, _KWARGS_DESCRIPTION							)
class   __snake_case			(	datasets.Metric							):



      def     lowerCamelCase_  (		self)      ->     int:





        '''simple docstring'''





        return datasets.MetricInfo(
            description=_DESCRIPTION       ,     citation=_CITATION       ,     inputs_description=_KWARGS_DESCRIPTION       ,     features=datasets.Features(
                {
                    'prediction_scores': datasets.Sequence(datasets.Value('float')),
                    'references': datasets.Value('int32'),
                }
                if self.config_name == 'multiclass'
                else {
                    'references': datasets.Sequence(datasets.Value('int32')),
                    'prediction_scores': datasets.Sequence(datasets.Value('float')),
                }
                if self.config_name == 'multilabel'
                else {
                    'references': datasets.Value('int32'),
                    'prediction_scores': datasets.Value('float'),
                })       ,     reference_urls=['https://scikit-learn.org/stable/modules/generated/sklearn.metrics.roc_auc_score.html']       ,     )



      def     lowerCamelCase_  (		self       ,     lowercase       ,     lowercase       ,     lowercase="macro"       ,     lowercase=None       ,     lowercase=None       ,     lowercase="raise"       ,     lowercase=None       ,     )      ->     Any:





        '''simple docstring'''





        return {
            "roc_auc": roc_auc_score(
                lowercase       ,     lowercase       ,     average=lowercase       ,     sample_weight=lowercase       ,     max_fpr=lowercase       ,     multi_class=lowercase       ,     labels=lowercase       ,     )
        }







'''simple docstring'''




from __future__ import annotations

from collections.abc import Iterable

class      UpperCamelCase_					:





	def __init__(    self						,						A						,						A       )     ->     int:
								UpperCAmelCase	,	UpperCAmelCase	:						Any					=						float(A       ), float(A       )





	def __eq__(    self						,						A       )     ->     str:
								return self.x == other.x and self.y == other.y





	def __ne__(    self						,						A       )     ->     Dict:
								return not self == other





	def __gt__(    self						,						A       )     ->     Dict:
								if self.x > other.x:
															return True
								elif self.x == other.x:
															return self.y > other.y
								return False





	def __lt__(    self						,						A       )     ->     str:
								return not self > other





	def __ge__(    self						,						A       )     ->     Union[str, Any]:
								if self.x > other.x:
															return True
								elif self.x == other.x:
															return self.y >= other.y
								return False





	def __le__(    self						,						A       )     ->     List[str]:
								if self.x < other.x:
															return True
								elif self.x == other.x:
															return self.y <= other.y
								return False





	def __repr__(    self       )     ->     Tuple:
								return f'''({self.x}, {self.y})'''






	def __hash__(    self       )     ->     List[str]:
								return hash(self.x       )




def  __lowerCamelCase    (   _lowercase      ,							) ->     list[Point]:
							UpperCAmelCase	:						list[Point]					=						[]
							if list_of_tuples:
														for p in list_of_tuples:
																					if isinstance(_lowercase      ,							_lowercase						):
																												points.append(_lowercase						)
																					else:
																												try:
																																			points.append(Point(p[0]      ,							p[1]						)						)
																												except (IndexError, TypeError):
																																			print(
																																			    F'''Ignoring deformed point {p}. All points'''
																																			    """ must have at least 2 coordinates."""						)
							return points



def  __lowerCamelCase    (   _lowercase						) ->     list[Point]:

							if not hasattr(_lowercase      ,							"""__iter__"""						):
														UpperCAmelCase	:						List[str]					=						F'''Expecting an iterable object but got an non-iterable type {points}'''
														raise ValueError(_lowercase						)

							if not points:
														UpperCAmelCase	:						Optional[int]					=						F'''Expecting a list of points but got {points}'''
														raise ValueError(_lowercase						)

							return _construct_points(_lowercase						)



def  __lowerCamelCase    (   _lowercase      ,							_lowercase      ,							_lowercase						) ->     float:
							UpperCAmelCase	:						Dict					=						(a.x * b.y + b.x * c.y + c.x * a.y) - (a.y * b.x + b.y * c.x + c.y * a.x)
							return det



def  __lowerCamelCase    (   _lowercase						) ->     list[Point]:
							UpperCAmelCase	:						Optional[int]					=						sorted(_validate_input(_lowercase						)						)
							UpperCAmelCase	:						int					=						len(_lowercase						)
							UpperCAmelCase	:						Any					=						set()

							for i in range(n - 1						):
														for j in range(i + 1      ,							_lowercase						):
																					UpperCAmelCase	:						Optional[Any]					=						False
																					UpperCAmelCase	:						Optional[int]					=						True
																					for k in range(_lowercase						):
																												if k != i and k != j:
																																			UpperCAmelCase	:						Union[str, Any]					=						_det(points[i]      ,							points[j]      ,							points[k]						)

																																			if det_k > 0:
																																										UpperCAmelCase	:						Optional[int]					=						True
																																			elif det_k < 0:
																																										UpperCAmelCase	:						int					=						True
																																			else:
																																										# point[i], point[j], point[k] all lie on a straight line
																																										# if point[k] is to the left of point[i] or it's to the
																																										# right of point[j], then point[i], point[j] cannot be
																																										# part of the convex hull of A
																																										if points[k] < points[i] or points[k] > points[j]:
																																																	UpperCAmelCase	:						List[Any]					=						False
																																																	break

																												if points_left_of_ij and points_right_of_ij:
																																			UpperCAmelCase	:						Union[str, Any]					=						False
																																			break

																					if ij_part_of_convex_hull:
																												convex_set.update([points[i], points[j]]						)

							return sorted(_lowercase						)



def  __lowerCamelCase    (   _lowercase						) ->     list[Point]:
							UpperCAmelCase	:						List[str]					=						sorted(_validate_input(_lowercase						)						)
							UpperCAmelCase	:						Optional[Any]					=						len(_lowercase						)

							# divide all the points into an upper hull and a lower hull
							# the left most point and the right most point are definitely
							# members of the convex hull by definition.
							# use these two anchors to divide all the points into two hulls,
							# an upper hull and a lower hull.

							# all points to the left (above) the line joining the extreme points belong to the
							# upper hull
							# all points to the right (below) the line joining the extreme points below to the
							# lower hull
							# ignore all points on the line joining the extreme points since they cannot be
							# part of the convex hull

							UpperCAmelCase	:						List[str]					=						points[0]
							UpperCAmelCase	:						Union[str, Any]					=						points[n - 1]

							UpperCAmelCase	:						int					=						{left_most_point, right_most_point}
							UpperCAmelCase	:						Dict					=						[]
							UpperCAmelCase	:						Any					=						[]

							for i in range(1      ,							n - 1						):
														UpperCAmelCase	:						Any					=						_det(_lowercase      ,							_lowercase      ,							points[i]						)

														if det > 0:
																					upper_hull.append(points[i]						)
														elif det < 0:
																					lower_hull.append(points[i]						)

							_construct_hull(_lowercase      ,							_lowercase      ,							_lowercase      ,							_lowercase						)
							_construct_hull(_lowercase      ,							_lowercase      ,							_lowercase      ,							_lowercase						)

							return sorted(_lowercase						)



def  __lowerCamelCase    (   _lowercase      ,							_lowercase      ,							_lowercase      ,							_lowercase						) ->     None:
							if points:
														UpperCAmelCase	:						Union[str, Any]					=						None
														UpperCAmelCase	:						int					=						float("""-inf"""						)
														UpperCAmelCase	:						Tuple					=						[]

														for p in points:
																					UpperCAmelCase	:						List[Any]					=						_det(_lowercase      ,							_lowercase      ,							_lowercase						)

																					if det > 0:
																												candidate_points.append(_lowercase						)

																												if det > extreme_point_distance:
																																			UpperCAmelCase	:						List[str]					=						det
																																			UpperCAmelCase	:						Optional[Any]					=						p

														if extreme_point:
																					_construct_hull(_lowercase      ,							_lowercase      ,							_lowercase      ,							_lowercase						)
																					convex_set.add(_lowercase						)
																					_construct_hull(_lowercase      ,							_lowercase      ,							_lowercase      ,							_lowercase						)



def  __lowerCamelCase    (   _lowercase						) ->     list[Point]:
							UpperCAmelCase	:						Any					=						sorted(_validate_input(_lowercase						)						)
							UpperCAmelCase	:						Union[str, Any]					=						len(_lowercase						)

							UpperCAmelCase	:						Dict					=						points[:2]
							for i in range(2      ,							_lowercase						):
														UpperCAmelCase	:						Dict					=						_det(convex_hull[1]      ,							convex_hull[0]      ,							points[i]						)
														if det > 0:
																					convex_hull.insert(0      ,							points[i]						)
																					break
														elif det < 0:
																					convex_hull.append(points[i]						)
																					break
														else:
																					UpperCAmelCase	:						Dict					=						points[i]
							i += 1

							for j in range(_lowercase      ,							_lowercase						):
														if (
														    _det(convex_hull[0]      ,							convex_hull[-1]      ,							points[j]						) > 0
														    and _det(convex_hull[-1]      ,							convex_hull[0]      ,							points[1]						) < 0
														):
																					# The point lies within the convex hull
																					continue

														convex_hull.insert(0      ,							points[j]						)
														convex_hull.append(points[j]						)
														while _det(convex_hull[0]      ,							convex_hull[1]      ,							convex_hull[2]						) >= 0:
																					del convex_hull[1]
														while _det(convex_hull[-1]      ,							convex_hull[-2]      ,							convex_hull[-3]						) <= 0:
																					del convex_hull[-2]

    # `convex_hull` is contains the convex hull in circular order
							return sorted(convex_hull[1:] if len(_lowercase						) > 3 else convex_hull						)



def  __lowerCamelCase    (   ) ->     Tuple:
							UpperCAmelCase	:						Tuple					=						[
							    (0, 3),
							    (2, 2),
							    (1, 1),
							    (2, 1),
							    (3, 0),
							    (0, 0),
							    (3, 3),
							    (2, -1),
							    (2, -4),
							    (1, -3),
							]
							# the convex set of points is
							# [(0, 0), (0, 3), (1, -3), (2, -4), (3, 0), (3, 3)]
							UpperCAmelCase	:						Tuple					=						convex_hull_bf(_lowercase						)

							UpperCAmelCase	:						List[Any]					=						convex_hull_recursive(_lowercase						)
							assert results_bf == results_recursive

							UpperCAmelCase	:						Union[str, Any]					=						convex_hull_melkman(_lowercase						)
							assert results_bf == results_melkman

							print(_lowercase						)


if __name__ == "__main__":
							main()

