



"""simple docstring"""






import numpy as np

import datasets


_lowercase : Tuple      						=						"\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"

_lowercase : Optional[Any]      						=						"\\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"

_lowercase : Optional[int]      						=						"\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        __SCREAMING_SNAKE_CASE	(      datasets.Metric   ):


					'''simple docstring'''





					def 		snake_case       (       self							:  Tuple     )->					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 		snake_case       (       self							:  Dict,  lowerCamelCase							:  Union[str, Any],  lowerCamelCase							:  Dict     )->					List[Any]:
								# convert to numpy arrays
								lowerCamelCase__		:		int			=np.array(SCREAMING_SNAKE_CASE__     )
								lowerCamelCase__		:		List[Any]			=np.array(SCREAMING_SNAKE_CASE__     )

								# 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__		:		List[str]			=X - np.mean(SCREAMING_SNAKE_CASE__     )
								lowerCamelCase__		:		Optional[Any]			=np.cov(reference_distribution.T     )
								try:
											lowerCamelCase__		:		str			=np.linalg.inv(SCREAMING_SNAKE_CASE__     )
								except np.linalg.LinAlgError:
											lowerCamelCase__		:		Any			=np.linalg.pinv(SCREAMING_SNAKE_CASE__     )
								lowerCamelCase__		:		Dict			=np.dot(SCREAMING_SNAKE_CASE__,  SCREAMING_SNAKE_CASE__     )
								lowerCamelCase__		:		Any			=np.dot(SCREAMING_SNAKE_CASE__,  X_minus_mu.T     ).diagonal()

								return {"mahalanobis": mahal_dist}






from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors




def  __magic_name__ (   __lowerCAmelCase	:						int							)			->   int:
				__lowerCamelCase    					=	prime_factors(__lowerCAmelCase							)
				if is_square_free(__lowerCAmelCase							):
								return -1 if len(__lowerCAmelCase							) % 2 else 1
				return 0


if __name__ == "__main__":
					import doctest

					doctest.testmod()



