
import numpy as np

import datasets


lowercase__		:Dict			  =   "\nCompute the Mahalanobis Distance\n\nMahalonobis distance is the distance between a point and a distribution.\nAnd not between two distinct points. It is effectively a multivariate equivalent of the Euclidean distance.\nIt was introduced by Prof. P. C. Mahalanobis in 1936\nand has been used in various statistical applications ever since\n[source: https://www.machinelearningplus.com/statistics/mahalanobis-distance/]\n"

lowercase__		:List[Any]			  =   "\\n@article{de2000mahalanobis,\n  title={The mahalanobis distance},\n  author={De Maesschalck, Roy and Jouan-Rimbaud, Delphine and Massart, D{\'e}sir{\'e} L},\n  journal={Chemometrics and intelligent laboratory systems},\n  volume={50},\n  number={1},\n  pages={1--18},\n  year={2000},\n  publisher={Elsevier}\n}\n"

lowercase__		:Dict			  =   "\nArgs:\n    X: List of datapoints to be compared with the `reference_distribution`.\n    reference_distribution: List of datapoints from the reference distribution we want to compare to.\nReturns:\n    mahalanobis: The Mahalonobis distance for each datapoint in `X`.\nExamples:\n\n    >>> mahalanobis_metric = datasets.load_metric(\"mahalanobis\")\n    >>> results = mahalanobis_metric.compute(reference_distribution=[[0, 1], [1, 0]], X=[[0, 1]])\n    >>> print(results)\n    {'mahalanobis': array([0.5])}\n"







@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION	,  _KWARGS_DESCRIPTION		)
class     lowercase		( datasets.Metric		):




							def 			A__				(    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 			A__				(    self       ,A__       ,A__):
												# convert to numpy arrays
												lowercase						     =						np.array(A__)
												lowercase						     =						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
												lowercase						     =						X - np.mean(A__)
												lowercase						     =						np.cov(reference_distribution.T)
												try:
																	lowercase						     =						np.linalg.inv(A__)
												except np.linalg.LinAlgError:
																	lowercase						     =						np.linalg.pinv(A__)
												lowercase						     =						np.dot(A__       ,A__)
												lowercase						     =						np.dot(A__       ,X_minus_mu.T).diagonal()

												return {"mahalanobis": mahal_dist}







from __future__ import annotations

from decimal import Decimal

from numpy import array



def 	UpperCamelCase   (							lowerCAmelCase__		):
					'''simple docstring'''
					lowercase						     =						Decimal

					# Check if the provided matrix has 2 rows and 2 columns
					# since this implementation only works for 2x2 matrices
					if len(lowerCAmelCase__		) == 2 and len(matrix[0]		) == 2 and len(matrix[1]		) == 2:
										# Calculate the determinant of the matrix
										lowercase						     =						float(
										    d(matrix[0][0]		) * d(matrix[1][1]		) - d(matrix[1][0]		) * d(matrix[0][1]		)		)
										if determinant == 0:
															raise ValueError('''This matrix has no inverse.'''		)

										# Creates a copy of the matrix with swapped positions of the elements
										lowercase						     =						[[0.0, 0.0], [0.0, 0.0]]
										lowercase     ,						lowercase						     =						matrix[1][1], matrix[0][0]
										lowercase     ,						lowercase						     =						-matrix[1][0], -matrix[0][1]

										# Calculate the inverse of the matrix
										return [
										    [(float(d(lowerCAmelCase__		)		) / determinant) or 0.0 for n in row] for row in swapped_matrix
										]
					elif (
					    len(lowerCAmelCase__		) == 3
					    and len(matrix[0]		) == 3
					    and len(matrix[1]		) == 3
					    and len(matrix[2]		) == 3
					):
										# Calculate the determinant of the matrix using Sarrus rule
										lowercase						     =						float(
										    (
										        (d(matrix[0][0]		) * d(matrix[1][1]		) * d(matrix[2][2]		))
										        + (d(matrix[0][1]		) * d(matrix[1][2]		) * d(matrix[2][0]		))
										        + (d(matrix[0][2]		) * d(matrix[1][0]		) * d(matrix[2][1]		))
										    )
										    - (
										        (d(matrix[0][2]		) * d(matrix[1][1]		) * d(matrix[2][0]		))
										        + (d(matrix[0][1]		) * d(matrix[1][0]		) * d(matrix[2][2]		))
										        + (d(matrix[0][0]		) * d(matrix[1][2]		) * d(matrix[2][1]		))
										    )		)
										if determinant == 0:
															raise ValueError('''This matrix has no inverse.'''		)

										# Creating cofactor matrix
										lowercase						     =						[
										    [d(0.0		), d(0.0		), d(0.0		)],
										    [d(0.0		), d(0.0		), d(0.0		)],
										    [d(0.0		), d(0.0		), d(0.0		)],
										]
										lowercase						     =						(d(matrix[1][1]		) * d(matrix[2][2]		)) - (
										    d(matrix[1][2]		) * d(matrix[2][1]		)
										)
										lowercase						     =						-(
										    (d(matrix[1][0]		) * d(matrix[2][2]		)) - (d(matrix[1][2]		) * d(matrix[2][0]		))
										)
										lowercase						     =						(d(matrix[1][0]		) * d(matrix[2][1]		)) - (
										    d(matrix[1][1]		) * d(matrix[2][0]		)
										)
										lowercase						     =						-(
										    (d(matrix[0][1]		) * d(matrix[2][2]		)) - (d(matrix[0][2]		) * d(matrix[2][1]		))
										)
										lowercase						     =						(d(matrix[0][0]		) * d(matrix[2][2]		)) - (
										    d(matrix[0][2]		) * d(matrix[2][0]		)
										)
										lowercase						     =						-(
										    (d(matrix[0][0]		) * d(matrix[2][1]		)) - (d(matrix[0][1]		) * d(matrix[2][0]		))
										)
										lowercase						     =						(d(matrix[0][1]		) * d(matrix[1][2]		)) - (
										    d(matrix[0][2]		) * d(matrix[1][1]		)
										)
										lowercase						     =						-(
										    (d(matrix[0][0]		) * d(matrix[1][2]		)) - (d(matrix[0][2]		) * d(matrix[1][0]		))
										)
										lowercase						     =						(d(matrix[0][0]		) * d(matrix[1][1]		)) - (
										    d(matrix[0][1]		) * d(matrix[1][0]		)
										)

										# Transpose the cofactor matrix (Adjoint matrix)
										lowercase						     =						array(lowerCAmelCase__		)
										for i in range(3		):
															for j in range(3		):
																				lowercase						     =						cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
										lowercase						     =						array(lowerCAmelCase__		)
										for i in range(3		):
															for j in range(3		):
																				inverse_matrix[i][j] /= d(lowerCAmelCase__		)

        # Calculate the inverse of the matrix
										return [[float(d(lowerCAmelCase__		)		) or 0.0 for n in row] for row in inverse_matrix]
					raise ValueError('''Please provide a matrix of size 2x2 or 3x3.'''		)




