



"""simple docstring"""
import numpy as np

import datasets


UpperCAmelCase						:		Dict			= "\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						:		Dict			= "\\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						:		Any			= "\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   ):

    def 					_UpperCAmelCase	(				self			:				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_			:				List[str] ,  lowerCAmelCase_			:				str):







      """simple docstring"""







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

      return {"mahalanobis": mahal_dist}






"""simple docstring"""
def 			_SCREAMING_SNAKE_CASE						(__lowerCAmelCase ,  __lowerCAmelCase							) ->						int:







  '''simple docstring'''


  while a != 0:
    lowercase_					,    lowercase_								= b % a, a
  return b


def 			_SCREAMING_SNAKE_CASE						(__lowerCAmelCase ,  __lowerCAmelCase							) ->						int:







  '''simple docstring'''


  if gcd(__lowerCAmelCase ,  __lowerCAmelCase							) != 1:
    lowercase_								= F'''mod inverse of {a!r} and {m!r} does not exist'''
    raise ValueError(__lowerCAmelCase							)
  lowercase_					,    lowercase_					,    lowercase_								= 1, 0, a
  lowercase_					,    lowercase_					,    lowercase_								= 0, 1, m
  while va != 0:
    lowercase_								= ua // va
    lowercase_					,    lowercase_					,    lowercase_					,    lowercase_					,    lowercase_					,    lowercase_								= (ua - q * va), (ua - q * va), (ua - q * va), va, va, va
  return ua % m

