"""simple docstring"""







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 				A__ (			datasets.Metric):

		def 							__lowerCamelCase							(   self				):
			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 ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
			# convert to numpy arrays
			__lowerCAmelCase    :		Any		    =   np.array(a_				)
			__lowerCAmelCase    :		str		    =   np.array(a_				)

			# 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
			__lowerCAmelCase    :		Optional[int]		    =   X - np.mean(a_				)
			__lowerCAmelCase    :		Dict		    =   np.cov(reference_distribution.T				)
			try:
				__lowerCAmelCase    :		Dict		    =   np.linalg.inv(a_				)
			except np.linalg.LinAlgError:
				__lowerCAmelCase    :		Optional[int]		    =   np.linalg.pinv(a_				)
			__lowerCAmelCase    :		Optional[Any]		    =   np.dot(a_ ,	a_				)
			__lowerCAmelCase    :		Tuple		    =   np.dot(a_ ,	X_minus_mu.T				).diagonal()

			return {"mahalanobis": mahal_dist}

"""simple docstring"""







class 				A__ :

		def __init__(   self				):
			__lowerCAmelCase    :		Optional[int]		    =   0
			__lowerCAmelCase    :		Any		    =   0
			__lowerCAmelCase    :		List[Any]		    =   {}

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE				):
			if vertex not in self.adjacency:
				__lowerCAmelCase    :		Dict		    =   {}
				self.num_vertices += 1

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
			self.add_vertex(_SCREAMING_SNAKE_CASE				)
			self.add_vertex(_SCREAMING_SNAKE_CASE				)

			if head == tail:
				return

			__lowerCAmelCase    :		Union[str, Any]		    =   weight
			__lowerCAmelCase    :		str		    =   weight

		def 							__lowerCamelCase							(   self				):
			__lowerCAmelCase    :		int		    =   self.get_edges()
			for edge in edges:
				__lowerCAmelCase    ,     __lowerCAmelCase    ,     __lowerCAmelCase    :		Optional[Any]		    =   edge
				edges.remove((tail, head, weight)				)
			for i in range(len(_SCREAMING_SNAKE_CASE				)				):
				__lowerCAmelCase    :		List[str]		    =   list(edges[i]				)

			edges.sort(key=lambda _SCREAMING_SNAKE_CASE				: e[2]				)
			for i in range(len(_SCREAMING_SNAKE_CASE				) - 1				):
				if edges[i][2] >= edges[i + 1][2]:
					__lowerCAmelCase    :		Dict		    =   edges[i][2] + 1
			for edge in edges:
				__lowerCAmelCase    ,     __lowerCAmelCase    ,     __lowerCAmelCase    :		str		    =   edge
				__lowerCAmelCase    :		Union[str, Any]		    =   weight
				__lowerCAmelCase    :		Optional[int]		    =   weight

		def __str__(   self				):
			__lowerCAmelCase    :		List[Any]		    =   ''
			for tail in self.adjacency:
				for head in self.adjacency[tail]:
					__lowerCAmelCase    :		str		    =   self.adjacency[head][tail]
					string += f"{head} -> {tail} == {weight}\n"
			return string.rstrip('\n'				)

		def 							__lowerCamelCase							(   self				):
			__lowerCAmelCase    :		Tuple		    =   []
			for tail in self.adjacency:
				for head in self.adjacency[tail]:
					output.append((tail, head, self.adjacency[head][tail])				)
			return output

		def 							__lowerCamelCase							(   self				):
			return self.adjacency.keys()

		@staticmethod
		def 							__lowerCamelCase							(   _SCREAMING_SNAKE_CASE=None ,	_SCREAMING_SNAKE_CASE=None				):
			__lowerCAmelCase    :		List[str]		    =   Graph()
			if vertices is None:
				__lowerCAmelCase    :		int		    =   []
			if edges is None:
				__lowerCAmelCase    :		Optional[int]		    =   []
			for vertex in vertices:
				g.add_vertex(_SCREAMING_SNAKE_CASE				)
			for edge in edges:
				g.add_edge(*_SCREAMING_SNAKE_CASE				)
			return g




		class 				A__ :

				def __init__(   self				):
					__lowerCAmelCase    :		Dict		    =   {}
					__lowerCAmelCase    :		Optional[int]		    =   {}

				def __len__(   self				):
					return len(self.parent				)

				def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE				):
					if item in self.parent:
						return self.find(_SCREAMING_SNAKE_CASE				)

					__lowerCAmelCase    :		Dict		    =   item
					__lowerCAmelCase    :		int		    =   0
					return item

				def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE				):
					if item not in self.parent:
						return self.make_set(_SCREAMING_SNAKE_CASE				)
					if item != self.parent[item]:
						__lowerCAmelCase    :		Dict		    =   self.find(self.parent[item]				)
					return self.parent[item]







				def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
					__lowerCAmelCase    :		Any		    =   self.find(_SCREAMING_SNAKE_CASE				)
					__lowerCAmelCase    :		List[str]		    =   self.find(_SCREAMING_SNAKE_CASE				)

					if roota == roota:
						return roota

					if self.rank[roota] > self.rank[roota]:
						__lowerCAmelCase    :		Tuple		    =   roota
						return roota

					if self.rank[roota] < self.rank[roota]:
						__lowerCAmelCase    :		str		    =   roota
						return roota

					if self.rank[roota] == self.rank[roota]:
						self.rank[roota] += 1
						__lowerCAmelCase    :		Optional[int]		    =   roota
						return roota
					return None



		@staticmethod
		def 							__lowerCamelCase							(   _SCREAMING_SNAKE_CASE				):
			__lowerCAmelCase    :		Union[str, Any]		    =   graph.num_vertices

			__lowerCAmelCase    :		List[Any]		    =   Graph.UnionFind()
			__lowerCAmelCase    :		Tuple		    =   []
			while num_components > 1:
				__lowerCAmelCase    :		str		    =   {}
				for vertex in graph.get_vertices():
					__lowerCAmelCase    :		Union[str, Any]		    =   -1

				__lowerCAmelCase    :		int		    =   graph.get_edges()
				for edge in edges:
					__lowerCAmelCase    ,     __lowerCAmelCase    ,     __lowerCAmelCase    :		Union[str, Any]		    =   edge
					edges.remove((tail, head, weight)				)
				for edge in edges:
					__lowerCAmelCase    ,     __lowerCAmelCase    ,     __lowerCAmelCase    :		Any		    =   edge
					__lowerCAmelCase    :		Optional[int]		    =   union_find.find(_SCREAMING_SNAKE_CASE				)
					__lowerCAmelCase    :		str		    =   union_find.find(_SCREAMING_SNAKE_CASE				)
					if seta != seta:
						if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
							__lowerCAmelCase    :		List[str]		    =   [head, tail, weight]

						if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
							__lowerCAmelCase    :		List[str]		    =   [head, tail, weight]
				for vertex in cheap_edge:
					if cheap_edge[vertex] != -1:
						__lowerCAmelCase    ,     __lowerCAmelCase    ,     __lowerCAmelCase    :		str		    =   cheap_edge[vertex]
						if union_find.find(_SCREAMING_SNAKE_CASE				) != union_find.find(_SCREAMING_SNAKE_CASE				):
							union_find.union(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				)
							mst_edges.append(cheap_edge[vertex]				)
							__lowerCAmelCase    :		List[str]		    =   num_components - 1
			__lowerCAmelCase    :		Union[str, Any]		    =   Graph.build(edges=_SCREAMING_SNAKE_CASE				)
			return mst