





'''simple docstring'''

import numpy as np

import datasets


a        =						"\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"

a        =						"\\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"

a        =						"\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 __a (   datasets.Metric			):





   def      UpperCAmelCase__     (					self				:			Union[str, Any]    ):

      '''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      UpperCAmelCase__     (					self				:			Optional[int]				,lowerCamelCase				:			str				,lowerCamelCase				:			List[Any]    ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE      							=       np.array(lowerCamelCase    )
      __SCREAMING_SNAKE_CASE      							=       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
      __SCREAMING_SNAKE_CASE      							=       X - np.mean(lowerCamelCase    )
      __SCREAMING_SNAKE_CASE      							=       np.cov(reference_distribution.T    )
      try:
         __SCREAMING_SNAKE_CASE      							=       np.linalg.inv(lowerCamelCase    )
      except np.linalg.LinAlgError:
         __SCREAMING_SNAKE_CASE      							=       np.linalg.pinv(lowerCamelCase    )
      __SCREAMING_SNAKE_CASE      							=       np.dot(lowerCamelCase				,lowerCamelCase    )
      __SCREAMING_SNAKE_CASE      							=       np.dot(lowerCamelCase				,X_minus_mu.T    ).diagonal()

      return {"mahalanobis": mahal_dist}












'''simple docstring'''

def 						__magic_name__       (							__UpperCAmelCase = 1							,	__UpperCAmelCase = 1000      )						->					int:

   '''simple docstring'''







   __SCREAMING_SNAKE_CASE      							=       1
   __SCREAMING_SNAKE_CASE      							=       0

   for divide_by_number in range(__UpperCAmelCase							,	digit + 1      ):
      __SCREAMING_SNAKE_CASE      							=       []
      __SCREAMING_SNAKE_CASE      							=       numerator
      for _ in range(1							,	digit + 1      ):
         if now_divide in has_been_divided:
            if longest_list_length < len(__UpperCAmelCase      ):
               __SCREAMING_SNAKE_CASE      							=       len(__UpperCAmelCase      )
               __SCREAMING_SNAKE_CASE      							=       divide_by_number
         else:
            has_been_divided.append(__UpperCAmelCase      )
            __SCREAMING_SNAKE_CASE      							=       now_divide * 10 % divide_by_number

   return the_digit


# Tests
if __name__ == "__main__":
    import doctest

    doctest.testmod()





