

'''simple docstring'''





import numpy as np

import datasets


UpperCamelCase_							=					"""
Compute the Mahalanobis Distance

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

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

UpperCamelCase_							=					"""
Args:
    X: List of datapoints to be compared with the `reference_distribution`.
    reference_distribution: List of datapoints from the reference distribution we want to compare to.
Returns:
    mahalanobis: The Mahalonobis distance for each datapoint in `X`.
Examples:

    >>> mahalanobis_metric = datasets.load_metric(\"mahalanobis\")
    >>> results = mahalanobis_metric.compute(reference_distribution=[[0, 1], [1, 0]], X=[[0, 1]])
    >>> print(results)
    {'mahalanobis': array([0.5])}
"""





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







				def    lowerCamelCase_  (					self    :		Optional[int]      ):
										'''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    lowerCamelCase_  (					self    :		int		,				UpperCAmelCase__    :		int		,				UpperCAmelCase__    :		List[Any]      ):
										'''simple docstring'''
										lowercase   :       Optional[int]								=np.array(UpperCAmelCase__      )
										lowercase   :       Dict								=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
										lowercase   :       Optional[int]								=X - np.mean(UpperCAmelCase__      )
										lowercase   :       str								=np.cov(reference_distribution.T      )
										try:
																lowercase   :       Union[str, Any]								=np.linalg.inv(UpperCAmelCase__      )
										except np.linalg.LinAlgError:
																lowercase   :       Optional[int]								=np.linalg.pinv(UpperCAmelCase__      )
										lowercase   :       Any								=np.dot(UpperCAmelCase__		,				UpperCAmelCase__      )
										lowercase   :       List[str]								=np.dot(UpperCAmelCase__		,				X_minus_mu.T      ).diagonal()

										return {"mahalanobis": mahal_dist}








'''simple docstring'''





import math






def 							_lowerCAmelCase (      __magic_name__	:    float      ,   __magic_name__	:    float	)							->     float:
						if (
						    not isinstance(__magic_name__      ,   (int, float)	)
						    or power_factor < -1
						    or power_factor > 1
						):
												raise ValueError('''power_factor must be a valid float value between -1 and 1.'''	)
						return apparent_power * power_factor






def 							_lowerCAmelCase (      __magic_name__	:    float      ,   __magic_name__	:    float	)							->     float:
						if (
						    not isinstance(__magic_name__      ,   (int, float)	)
						    or power_factor < -1
						    or power_factor > 1
						):
												raise ValueError('''power_factor must be a valid float value between -1 and 1.'''	)
						return apparent_power * math.sqrt(1 - power_factor**2	)


if __name__ == "__main__":
							import doctest

							doctest.testmod()





