




from scipy.stats import pearsonr

import datasets


SCREAMING_SNAKE_CASE__     :     str		    =       "\nPearson correlation coefficient and p-value for testing non-correlation.\nThe Pearson correlation coefficient measures the linear relationship between two datasets. The calculation of the p-value relies on the assumption that each dataset is normally distributed. Like other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply an exact linear relationship. Positive correlations imply that as x increases, so does y. Negative correlations imply that as x increases, y decreases.\nThe p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets.\n"


SCREAMING_SNAKE_CASE__     :     List[Any]		    =       "\nArgs:\n    predictions (`list` of `int`): Predicted class labels, as returned by a model.\n    references (`list` of `int`): Ground truth labels.\n    return_pvalue (`boolean`): If `True`, returns the p-value, along with the correlation coefficient. If `False`, returns only the correlation coefficient. Defaults to `False`.\n\nReturns:\n    pearsonr (`float`): Pearson correlation coefficient. Minimum possible value is -1. Maximum possible value is 1. Values of 1 and -1 indicate exact linear positive and negative relationships, respectively. A value of 0 implies no correlation.\n    p-value (`float`): P-value, which roughly indicates the probability of an The p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets. Minimum possible value is 0. Maximum possible value is 1. Higher values indicate higher probabilities.\n\nExamples:\n\n    Example 1-A simple example using only predictions and references.\n        >>> pearsonr_metric = datasets.load_metric(\"pearsonr\")\n        >>> results = pearsonr_metric.compute(predictions=[10, 9, 2.5, 6, 4], references=[1, 2, 3, 4, 5])\n        >>> print(round(results['pearsonr'], 2))\n        -0.74\n\n    Example 2-The same as Example 1, but that also returns the `p-value`.\n        >>> pearsonr_metric = datasets.load_metric(\"pearsonr\")\n        >>> results = pearsonr_metric.compute(predictions=[10, 9, 2.5, 6, 4], references=[1, 2, 3, 4, 5], return_pvalue=True)\n        >>> print(sorted(list(results.keys())))\n        ['p-value', 'pearsonr']\n        >>> print(round(results['pearsonr'], 2))\n        -0.74\n        >>> print(round(results['p-value'], 2))\n        0.15\n"


SCREAMING_SNAKE_CASE__     :     List[str]		    =       "\n@article{2020SciPy-NMeth,\nauthor  = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and\n      Haberland, Matt and Reddy, Tyler and Cournapeau, David and\n      Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and\n      Bright, Jonathan and {van der Walt}, St{\'e}fan J. and\n      Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and\n      Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and\n      Kern, Robert and Larson, Eric and Carey, C J and\n      Polat, Ilhan and Feng, Yu and Moore, Eric W. and\n      {VanderPlas}, Jake and Laxalde, Denis and Perktold, Josef and\n      Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and\n      Harris, Charles R. and Archibald, Anne M. and\n      Ribeiro, Antonio H. and Pedregosa, Fabian and\n      {van Mulbregt}, Paul and {SciPy 1.0 Contributors}},\ntitle   = {{{SciPy} 1.0: Fundamental Algorithms for Scientific\n      Computing in Python}},\njournal = {Nature Methods},\nyear    = {2020},\nvolume  = {17},\npages   = {261--272},\nadsurl  = {https://rdcu.be/b08Wh},\ndoi = {10.1038/s41592-019-0686-2},\n}\n"



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





	def 						A_(							self      )  ->					Optional[int]:




				"""simple docstring"""



				return datasets.MetricInfo(
				    description=_DESCRIPTION      ,     citation=_CITATION      ,     inputs_description=_KWARGS_DESCRIPTION      ,     features=datasets.Features(
				        {
				            'predictions': datasets.Value('float'      ),
				            'references': datasets.Value('float'      ),
				        }      )      ,     reference_urls=['https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html']      ,     )





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE=False      )  ->					Optional[int]:




				"""simple docstring"""



				if return_pvalue:
							SCREAMING_SNAKE_CASE_								=						pearsonr(SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      )
							return {"pearsonr": results[0], "p-value": results[1]}
				else:
							return {"pearsonr": float(pearsonr(SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      )[0]      )}






from __future__ import annotations

from decimal import Decimal

from numpy import array

def lowercase    (  SCREAMING_SNAKE_CASE )			->							list[list[float]]:


			'''simple docstring'''







			SCREAMING_SNAKE_CASE_								=						Decimal

			# Check if the provided matrix has 2 rows and 2 columns
			# since this implementation only works for 2x2 matrices
			if len(SCREAMING_SNAKE_CASE ) == 2 and len(matrix[0] ) == 2 and len(matrix[1] ) == 2:
						# Calculate the determinant of the matrix
						SCREAMING_SNAKE_CASE_								=						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
						SCREAMING_SNAKE_CASE_								=						[[0.0, 0.0], [0.0, 0.0]]
						SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_								=						matrix[1][1], matrix[0][0]
						SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_								=						-matrix[1][0], -matrix[0][1]

						# Calculate the inverse of the matrix
						return [
						    [(float(d(SCREAMING_SNAKE_CASE ) ) / determinant) or 0.0 for n in row] for row in swapped_matrix
						]
			elif (
			    len(SCREAMING_SNAKE_CASE ) == 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
						SCREAMING_SNAKE_CASE_								=						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
						SCREAMING_SNAKE_CASE_								=						[
						    [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 )],
						]
						SCREAMING_SNAKE_CASE_								=						(d(matrix[1][1] ) * d(matrix[2][2] )) - (
						    d(matrix[1][2] ) * d(matrix[2][1] )
						)
						SCREAMING_SNAKE_CASE_								=						-(
						    (d(matrix[1][0] ) * d(matrix[2][2] )) - (d(matrix[1][2] ) * d(matrix[2][0] ))
						)
						SCREAMING_SNAKE_CASE_								=						(d(matrix[1][0] ) * d(matrix[2][1] )) - (
						    d(matrix[1][1] ) * d(matrix[2][0] )
						)
						SCREAMING_SNAKE_CASE_								=						-(
						    (d(matrix[0][1] ) * d(matrix[2][2] )) - (d(matrix[0][2] ) * d(matrix[2][1] ))
						)
						SCREAMING_SNAKE_CASE_								=						(d(matrix[0][0] ) * d(matrix[2][2] )) - (
						    d(matrix[0][2] ) * d(matrix[2][0] )
						)
						SCREAMING_SNAKE_CASE_								=						-(
						    (d(matrix[0][0] ) * d(matrix[2][1] )) - (d(matrix[0][1] ) * d(matrix[2][0] ))
						)
						SCREAMING_SNAKE_CASE_								=						(d(matrix[0][1] ) * d(matrix[1][2] )) - (
						    d(matrix[0][2] ) * d(matrix[1][1] )
						)
						SCREAMING_SNAKE_CASE_								=						-(
						    (d(matrix[0][0] ) * d(matrix[1][2] )) - (d(matrix[0][2] ) * d(matrix[1][0] ))
						)
						SCREAMING_SNAKE_CASE_								=						(d(matrix[0][0] ) * d(matrix[1][1] )) - (
						    d(matrix[0][1] ) * d(matrix[1][0] )
						)

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

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

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