






import numpy as np

import datasets


snake_case__      :	int       	=      '\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'

snake_case__      :	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'

snake_case__      :	Union[str, 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 						_a       (  datasets.Metric    ):






  """simple docstring"""





  def    _UpperCAmelCase     (     self )			-> List[str]:
     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		,		_UpperCAmelCase		,		_UpperCAmelCase )			-> int:
     UpperCamelCase_									=     np.array(UpperCamelCase__ )
     UpperCamelCase_									=     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
     UpperCamelCase_									=     X - np.mean(UpperCamelCase__ )
     UpperCamelCase_									=     np.cov(reference_distribution.T )
     try:
        UpperCamelCase_									=     np.linalg.inv(UpperCamelCase__ )
     except np.linalg.LinAlgError:
        UpperCamelCase_									=     np.linalg.pinv(UpperCamelCase__ )
     UpperCamelCase_									=     np.dot(UpperCamelCase__		,		UpperCamelCase__ )
     UpperCamelCase_									=     np.dot(UpperCamelCase__		,		X_minus_mu.T ).diagonal()

     return {"mahalanobis": mahal_dist}













from typing import Any






def     _snake_case    (__lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase    ,      ):
   _validation(
       __lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase    ,      )
   # Creates data structures and fill initial step
   UpperCamelCase_									=     {}
   UpperCamelCase_									=     {}
   for state in states_space:
      UpperCamelCase_									=     observations_space[0]
      UpperCamelCase_									=     (
          initial_probabilities[state] * emission_probabilities[state][observation]
      )
      UpperCamelCase_									=     None

   # Fills the data structure with the probabilities of
   # different transitions and pointers to previous states
   for o in range(1    ,      len(__lowercase)):
      UpperCamelCase_									=     observations_space[o]
      UpperCamelCase_									=     observations_space[o - 1]
      for state in states_space:
         # Calculates the argmax for probability function
         UpperCamelCase_									=     ''
         UpperCamelCase_									=     -1
         for k_state in states_space:
            UpperCamelCase_									=     (
                probabilities[(k_state, prior_observation)]
                * transition_probabilities[k_state][state]
                * emission_probabilities[state][observation]
            )
            if probability > max_probability:
               UpperCamelCase_									=     probability
               UpperCamelCase_									=     k_state

            # Update probabilities and pointers dicts
         UpperCamelCase_									=     (
             probabilities[(arg_max, prior_observation)]
             * transition_probabilities[arg_max][state]
             * emission_probabilities[state][observation]
         )

         UpperCamelCase_									=     arg_max

    # The final observation
   UpperCamelCase_									=     observations_space[len(__lowercase) - 1]

   # argmax for given final observation
   UpperCamelCase_									=     ''
   UpperCamelCase_									=     -1
   for k_state in states_space:
      UpperCamelCase_									=     probabilities[(k_state, final_observation)]
      if probability > max_probability:
         UpperCamelCase_									=     probability
         UpperCamelCase_									=     k_state
   UpperCamelCase_									=     arg_max

   # Process pointers backwards
   UpperCamelCase_									=     last_state
   UpperCamelCase_									=     []
   for o in range(len(__lowercase) - 1    ,      -1    ,      -1):
      result.append(__lowercase)
      UpperCamelCase_									=     pointers[previous, observations_space[o]]
   result.reverse()

   return result






def     _snake_case    (__lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase    ,      ):
   _validate_not_empty(
       __lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase    ,      )
   _validate_lists(__lowercase    ,      __lowercase)
   _validate_dicts(
       __lowercase    ,      __lowercase    ,      __lowercase)






def     _snake_case    (__lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase    ,      ):
   if not all(
       [
           observations_space,
           states_space,
           initial_probabilities,
           transition_probabilities,
           emission_probabilities,
       ]):
      raise ValueError('There\'s an empty parameter')






def     _snake_case    (__lowercase    ,      __lowercase):
   _validate_list(__lowercase    ,      'observations_space')
   _validate_list(__lowercase    ,      'states_space')






def     _snake_case    (__lowercase    ,      __lowercase):
   if not isinstance(_object    ,      __lowercase):
      UpperCamelCase_									=     f"""{var_name} must be a list"""
      raise ValueError(__lowercase)
   else:
      for x in _object:
         if not isinstance(__lowercase    ,      __lowercase):
            UpperCamelCase_									=     f"""{var_name} must be a list of strings"""
            raise ValueError(__lowercase)






def     _snake_case    (__lowercase    ,      __lowercase    ,      __lowercase    ,      ):
   _validate_dict(__lowercase    ,      'initial_probabilities'    ,      __lowercase)
   _validate_nested_dict(__lowercase    ,      'transition_probabilities')
   _validate_nested_dict(__lowercase    ,      'emission_probabilities')






def     _snake_case    (__lowercase    ,      __lowercase):
   _validate_dict(_object    ,      __lowercase    ,      __lowercase)
   for x in _object.values():
      _validate_dict(__lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase)






def     _snake_case    (__lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase = False):
   if not isinstance(_object    ,      __lowercase):
      UpperCamelCase_									=     f"""{var_name} must be a dict"""
      raise ValueError(__lowercase)
   if not all(isinstance(__lowercase    ,      __lowercase) for x in _object):
      UpperCamelCase_									=     f"""{var_name} all keys must be strings"""
      raise ValueError(__lowercase)
   if not all(isinstance(__lowercase    ,      __lowercase) for x in _object.values()):
      UpperCamelCase_									=     'nested dictionary ' if nested else ''
      UpperCamelCase_									=     f"""{var_name} {nested_text}all values must be {value_type.__name__}"""
      raise ValueError(__lowercase)


if __name__ == "__main__":
 from doctest import testmod

 testmod()





