



import numpy as np

import datasets


UpperCAmelCase_									=							"\nCompute the Mahalanobis Distance\n\nMahalonobis distance is the distance between a point and a distribution.\nAnd not between two distinct points. It is effectively a multivariate equivalent of the Euclidean distance.\nIt was introduced by Prof. P. C. Mahalanobis in 1936\nand has been used in various statistical applications ever since\n[source: https://www.machinelearningplus.com/statistics/mahalanobis-distance/]\n"

UpperCAmelCase_									=							"\\n@article{de2000mahalanobis,\n  title={The mahalanobis distance},\n  author={De Maesschalck, Roy and Jouan-Rimbaud, Delphine and Massart, D{\'e}sir{\'e} L},\n  journal={Chemometrics and intelligent laboratory systems},\n  volume={50},\n  number={1},\n  pages={1--18},\n  year={2000},\n  publisher={Elsevier}\n}\n"

UpperCAmelCase_									=							"\nArgs:\n    X: List of datapoints to be compared with the `reference_distribution`.\n    reference_distribution: List of datapoints from the reference distribution we want to compare to.\nReturns:\n    mahalanobis: The Mahalonobis distance for each datapoint in `X`.\nExamples:\n\n    >>> mahalanobis_metric = datasets.load_metric(\"mahalanobis\")\n    >>> results = mahalanobis_metric.compute(reference_distribution=[[0, 1], [1, 0]], X=[[0, 1]])\n    >>> print(results)\n    {\'mahalanobis\': array([0.5])}\n"





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





   def 	__lowerCAmelCase							(	self			):
         return datasets.MetricInfo(
             description=_DESCRIPTION       ,     citation=_CITATION       ,     inputs_description=_KWARGS_DESCRIPTION       ,     features=datasets.Features(
                 {
                     '''X''': datasets.Sequence(datasets.Value('''float'''       ,     id='''sequence'''			)       ,     id='''X'''			),
                 }			)       ,     )





   def 	__lowerCAmelCase							(	self       ,     _lowerCAmelCase       ,     _lowerCAmelCase			):
         _lowerCAmelCase 			=  np.array(a_			)
         _lowerCAmelCase 			=  np.array(a_			)

         # Assert that arrays are 2D
         if len(X.shape			) != 2:
               raise ValueError('''Expected `X` to be a 2D vector'''			)
         if len(reference_distribution.shape			) != 2:
               raise ValueError('''Expected `reference_distribution` to be a 2D vector'''			)
         if reference_distribution.shape[0] < 2:
               raise ValueError(
                   '''Expected `reference_distribution` to be a 2D vector with more than one element in the first dimension'''			)

         # Get mahalanobis distance for each prediction
         _lowerCAmelCase 			=  X - np.mean(a_			)
         _lowerCAmelCase 			=  np.cov(reference_distribution.T			)
         try:
               _lowerCAmelCase 			=  np.linalg.inv(a_			)
         except np.linalg.LinAlgError:
               _lowerCAmelCase 			=  np.linalg.pinv(a_			)
         _lowerCAmelCase 			=  np.dot(a_       ,     a_			)
         _lowerCAmelCase 			=  np.dot(a_       ,     X_minus_mu.T			).diagonal()

         return {"mahalanobis": mahal_dist}







from __future__ import annotations
def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	list				)->list:
      if len(_SCREAMING_SNAKE_CASE				) == 0:
            return []
      _lowerCAmelCase			,   _lowerCAmelCase 			=  min(_SCREAMING_SNAKE_CASE				), max(_SCREAMING_SNAKE_CASE				)
      _lowerCAmelCase 			=  int(max_value - min_value				) + 1
      _lowerCAmelCase 			=  [[] for _ in range(_SCREAMING_SNAKE_CASE				)]

      for i in my_list:
            buckets[int(i - min_value				)].append(_SCREAMING_SNAKE_CASE				)

      return [v for bucket in buckets for v in sorted(_SCREAMING_SNAKE_CASE				)]


if __name__ == "__main__":
    from doctest import testmod

    testmod()
    assert bucket_sort([4, 5, 3, 2, 1]) == [1, 2, 3, 4, 5]
    assert bucket_sort([0, 1, -1_0, 1_5, 2, -2]) == [-1_0, -2, 0, 1, 2, 1_5]