


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        lowerCamelCase__	(							datasets.Metric      ):






			"""simple docstring"""






			def 				snake_case__				(							self     ):

						'''simple docstring'''


						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 				snake_case__				(							self      ,						snake_case      ,						snake_case     ):

						'''simple docstring'''


						UpperCamelCase__					=       np.array(_lowerCAmelCase     )
						UpperCamelCase__					=       np.array(_lowerCAmelCase     )

						# 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
						UpperCamelCase__					=       X - np.mean(_lowerCAmelCase     )
						UpperCamelCase__					=       np.cov(reference_distribution.T     )
						try:
									UpperCamelCase__					=       np.linalg.inv(_lowerCAmelCase     )
						except np.linalg.LinAlgError:
									UpperCamelCase__					=       np.linalg.pinv(_lowerCAmelCase     )
						UpperCamelCase__					=       np.dot(_lowerCAmelCase      ,						_lowerCAmelCase     )
						UpperCamelCase__					=       np.dot(_lowerCAmelCase      ,						X_minus_mu.T     ).diagonal()

						return {"mahalanobis": mahal_dist}






from __future__ import annotations
def        UpperCamelCase_(				_A   :list[int]				,     _A   :int  )->		list[int]:
			UpperCamelCase__					=       0
			UpperCamelCase__					=       len(_A  ) - 1

			while i < j:
						if nums[i] + nums[j] == target:
									return [i, j]
						elif nums[i] + nums[j] < target:
									UpperCamelCase__					=       i + 1
						else:
									UpperCamelCase__					=       j - 1

			return []


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						print(f'''{two_pointer([2, 7, 1_1, 1_5], 9) = }''')


