



import numpy as np

import datasets


lowerCamelCase__			= """
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/]
"""

lowerCamelCase__			= """\
@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}
}
"""

lowerCamelCase__			= """
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    SCREAMING_SNAKE_CASE			(							datasets.Metric					):





							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		:		List[str]      ,				__lowercase		:		Any      ,				__lowercase		:		int	):

											'''simple docstring'''
											__a       =		np.array(__lowercase	)
											__a       =		np.array(__lowercase	)

											# 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(__lowercase	)
											__a       =		np.cov(reference_distribution.T	)
											try:
															__a       =		np.linalg.inv(__lowercase	)
											except np.linalg.LinAlgError:
															__a       =		np.linalg.pinv(__lowercase	)
											__a       =		np.dot(__lowercase      ,				__lowercase	)
											__a       =		np.dot(__lowercase      ,				X_minus_mu.T	).diagonal()

											return {"mahalanobis": mahal_dist}





from __future__ import annotations

from collections import Counter
from random import random






class    SCREAMING_SNAKE_CASE			:





							def __init__(   self		:		Optional[Any]	):

											'''simple docstring'''
											__a       =		{}





							def 						UpperCamelCase_					(   self		:		Dict      ,				__lowercase		:		str	):

											'''simple docstring'''
											__a       =		{}





							def 						UpperCamelCase_					(   self		:		List[str]      ,				__lowercase		:		str      ,				__lowercase		:		str      ,				__lowercase		:		float	):

											'''simple docstring'''
											if nodea not in self.connections:
															self.add_node(__lowercase	)
											if nodea not in self.connections:
															self.add_node(__lowercase	)
											__a       =		probability





							def 						UpperCamelCase_					(   self		:		Union[str, Any]	):

											'''simple docstring'''
											return list(self.connections	)







							def 						UpperCamelCase_					(   self		:		Tuple      ,				__lowercase		:		str	):

											'''simple docstring'''
											__a       =		0
											__a       =		random()

											for dest in self.connections[node]:
															current_probability += self.connections[node][dest]
															if current_probability > random_value:
																			return dest
											return ""



def   lowerCAmelCase__						(							_SCREAMING_SNAKE_CASE       :			str				,     _SCREAMING_SNAKE_CASE       :			list[tuple[str, str, float]]				,     _SCREAMING_SNAKE_CASE       :			int    ):
				"""simple docstring"""







				__a       =		MarkovChainGraphUndirectedUnweighted()

				for nodea, nodea, probability in transitions:
								graph.add_transition_probability(_SCREAMING_SNAKE_CASE				,     _SCREAMING_SNAKE_CASE				,     _SCREAMING_SNAKE_CASE    )

				__a       =		Counter(graph.get_nodes()    )
				__a       =		start

				for _ in range(_SCREAMING_SNAKE_CASE    ):
								__a       =		graph.transition(_SCREAMING_SNAKE_CASE    )
								visited[node] += 1

				return visited


if __name__ == "__main__":
						import doctest

						doctest.testmod()
