





import numpy as np

import datasets


A       :   Dict					= '''
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/]
'''

A       :   Dict					= '''\
@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}
}
'''

A       :   Optional[Any]					= '''
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     A     (datasets.Metric       ):
			'''simple docstring'''




			def   a_			(     self  :       Optional[Any]  )      ->      Optional[int]:







					"""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   a_			(     self  :       Union[str, Any]				,      __lowerCAmelCase  :       str				,      __lowerCAmelCase  :       Union[str, Any]  )      ->      Dict:







					"""simple docstring"""






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

					return {"mahalanobis": mahal_dist}










def   __lowerCamelCase   (				__a  :int       )						->							Dict:






		"""simple docstring"""

		A__     =  len(__a       )
		A__     =  sum(__a       )

		A__     =  [[False for x in range(s + 1       )] for y in range(n + 1       )]

		for i in range(1       ,	n + 1       ):
				A__     =  True

		for i in range(1       ,	s + 1       ):
				A__     =  False

		for i in range(1       ,	n + 1       ):
				for j in range(1       ,	s + 1       ):
						A__     =  dp[i][j - 1]

						if arr[i - 1] <= j:
								A__     =  dp[i][j] or dp[i - 1][j - arr[i - 1]]

		for j in range(int(s / 2       )       ,	-1       ,	-1       ):
				if dp[n][j] is True:
						A__     =  s - 2 * j
						break

		return diff



