






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  __UpperCAmelCase      (							self       )     ->							Optional[Any]:
							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  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase       )     ->							int:
							# convert to numpy arrays
							UpperCAmelCase_   :				Dict						=						np.array(_UpperCamelCase       )
							UpperCAmelCase_   :				Union[str, Any]						=						np.array(_UpperCamelCase       )

							# 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_   :				Dict						=						X - np.mean(_UpperCamelCase       )
							UpperCAmelCase_   :				Union[str, Any]						=						np.cov(reference_distribution.T       )
							try:
												UpperCAmelCase_   :				List[Any]						=						np.linalg.inv(_UpperCamelCase       )
							except np.linalg.LinAlgError:
												UpperCAmelCase_   :				Tuple						=						np.linalg.pinv(_UpperCamelCase       )
							UpperCAmelCase_   :				Any						=						np.dot(_UpperCamelCase    ,		_UpperCamelCase       )
							UpperCAmelCase_   :				Optional[int]						=						np.dot(_UpperCamelCase    ,		X_minus_mu.T       ).diagonal()

							return {"mahalanobis": mahal_dist}














def 					lowercase__				(					__snake_case   :							List[str]					,	__snake_case   :							List[str]					,	__snake_case   :							Union[str, Any]					,	__snake_case   :							Optional[int]					,	__snake_case   :							str					,	__snake_case   :							Optional[Any]  ):


					'''simple docstring'''


					if index == r:
										for j in range(__snake_case  ):
															print(data[j]					,	end=' '  )
										print(' '  )
										return
					#  When no more elements are there to put in data[]
					if i >= n:
										return
					# current is included, put next at next location
					UpperCAmelCase_   :				int						=						arr[i]
					combination_util(__snake_case					,	__snake_case					,	__snake_case					,	index + 1					,	__snake_case					,	i + 1  )
					# current is excluded, replace it with
					# next (Note that i+1 is passed, but
					# index is not changed)
					combination_util(__snake_case					,	__snake_case					,	__snake_case					,	__snake_case					,	__snake_case					,	i + 1  )
					# The main function that prints all combinations
					# of size r in arr[] of size n. This function
					# mainly uses combinationUtil()




def 					lowercase__				(					__snake_case   :							List[Any]					,	__snake_case   :							List[Any]					,	__snake_case   :							str  ):


					'''simple docstring'''


					UpperCAmelCase_   :				Union[str, Any]						=						[0] * r
					# Print all combination using temporary array 'data[]'
					combination_util(__snake_case					,	__snake_case					,	__snake_case					,	0					,	__snake_case					,	0  )


if __name__ == "__main__":
		# Driver code to check the function above
		__UpperCAmelCase     							=						[10, 20, 30, 40, 50]
		print_combination(arr, len(arr), 3)
		# This code is contributed by Ambuj sahu






