





'''simple docstring'''




import numpy as np

import datasets


lowercase__       : Optional[int]         =       '''
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/]
'''

lowercase__       : List[str]         =       '''\
@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}
}
'''

lowercase__       : Tuple         =       '''
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 				SCREAMING_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 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase		,      _UpperCAmelCase):

          '''simple docstring'''






          __A		:					Any						=			np.array(_UpperCAmelCase)
          __A		:					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
          __A		:					Union[str, Any]						=			X - np.mean(_UpperCAmelCase)
          __A		:					Tuple						=			np.cov(reference_distribution.T)
          try:
               __A		:					str						=			np.linalg.inv(_UpperCAmelCase)
          except np.linalg.LinAlgError:
               __A		:					List[Any]						=			np.linalg.pinv(_UpperCAmelCase)
          __A		:					int						=			np.dot(_UpperCAmelCase		,      _UpperCAmelCase)
          __A		:					Union[str, Any]						=			np.dot(_UpperCAmelCase		,      X_minus_mu.T).diagonal()

          return {"mahalanobis": mahal_dist}






'''simple docstring'''




def 			_lowerCAmelCase     (    __snake_case    :					int					,				__snake_case    :					int					,				__snake_case    :					int     )	->	float:
     __A		:					Dict						=			(num_of_terms / 2) * (2 * first_term + (num_of_terms - 1) * common_diff)
     # formula for sum of series
     return total






def 			_lowerCAmelCase     (    )	->	Union[str, Any]:
     print(sum_of_series(1					,				1					,				10     )     )


if __name__ == "__main__":
  import doctest

  doctest.testmod()