



'''simple docstring'''




import numpy as np

import datasets


UpperCamelCase__       :	str    = '''
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/]
'''

UpperCamelCase__       :	List[Any]    = '''\
@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}
}
'''

UpperCamelCase__       :	List[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 						_UpperCamelCase  (							datasets.Metric    ):


			'''simple docstring'''

			def UpperCamelCase__					(							self     : Dict						):





					"""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     : int							,     lowerCAmelCase__     : Dict							,     lowerCAmelCase__     : int						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		Any           =		np.array(lowerCAmelCase__						)
					__SCREAMING_SNAKE_CASE       :		int           =		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       :		int           =		X - np.mean(lowerCAmelCase__						)
					__SCREAMING_SNAKE_CASE       :		int           =		np.cov(reference_distribution.T						)
					try:
							__SCREAMING_SNAKE_CASE       :		Optional[int]           =		np.linalg.inv(lowerCAmelCase__						)
					except np.linalg.LinAlgError:
							__SCREAMING_SNAKE_CASE       :		Any           =		np.linalg.pinv(lowerCAmelCase__						)
					__SCREAMING_SNAKE_CASE       :		List[str]           =		np.dot(lowerCAmelCase__							,     lowerCAmelCase__						)
					__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		np.dot(lowerCAmelCase__							,     X_minus_mu.T						).diagonal()

					return {"mahalanobis": mahal_dist}




'''simple docstring'''




def 				lowerCAmelCase_   (	_lowerCamelCase:   int					):
		assert (
		    isinstance(_lowerCamelCase       ,      _lowerCamelCase					) and number_of_steps > 0
		), F"number_of_steps needs to be positive integer, your input {number_of_steps}"
		if number_of_steps == 1:
				return 1
		__SCREAMING_SNAKE_CASE       ,						__SCREAMING_SNAKE_CASE       :		Dict           =		1, 1
		for _ in range(number_of_steps - 1					):
				__SCREAMING_SNAKE_CASE       ,						__SCREAMING_SNAKE_CASE       :		Tuple           =		current + previous, current
		return current


if __name__ == "__main__":
						import doctest

						doctest.testmod()