


'''simple docstring'''
import numpy as np

import datasets


__snake_case							      =     '''
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/]
'''

__snake_case							      =     '''\
@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}
}
'''

__snake_case							      =     '''
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    lowercase	(							datasets.Metric					):

		"""simple docstring"""

		def     lowerCAmelCase__				(		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     lowerCAmelCase__				(		self    ,   UpperCamelCase_    ,   UpperCamelCase_							):

							'''simple docstring'''


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

							return {"mahalanobis": mahal_dist}






def 		lowerCAmelCase_    (  __UpperCAmelCase:			int      )      ->	bool:
    return str(__UpperCAmelCase      ) == str(__UpperCAmelCase      )[::-1]




def 		lowerCAmelCase_    (  __UpperCAmelCase:			int      )      ->	int:
    return int(__UpperCAmelCase      ) + int(str(__UpperCAmelCase      )[::-1]      )




def 		lowerCAmelCase_    (  __UpperCAmelCase:			int = 1_0000      )      ->	int:
    UpperCamelCase__							:				Optional[Any]          =      []
    for num in range(1		,   __UpperCAmelCase      ):
        UpperCamelCase__							:				str          =      0
        UpperCamelCase__							:				Any          =      num
        while iterations < 50:
            UpperCamelCase__							:				List[Any]          =      sum_reverse(__UpperCAmelCase      )
            iterations += 1
            if is_palindrome(__UpperCAmelCase      ):
                break
        else:
            lychrel_nums.append(__UpperCAmelCase      )
    return len(__UpperCAmelCase      )


if __name__ == "__main__":
  print(F'''{solution() = }''')

