
def 	UpperCamelCase   (							lowerCAmelCase__			,      lowerCAmelCase__		):
					'''simple docstring'''

					def get_matched_characters(lowerCAmelCase__			,      lowerCAmelCase__		) -> str:
										lowercase						     =						[]
										lowercase						     =						min(len(_stra		)			,      len(_stra		)		) // 2
										for i, l in enumerate(_stra		):
															lowercase						     =						int(max(0			,      i - limit		)		)
															lowercase						     =						int(min(i + limit + 1			,      len(_stra		)		)		)
															if l in _stra[left:right]:
																				matched.append(a_		)
																				lowercase						     =						f'{_stra[0:_stra.index(a_		)]} {_stra[_stra.index(a_		) + 1:]}'

										return "".join(a_		)

					# matching characters
					lowercase						     =						get_matched_characters(a_			,      a_		)
					lowercase						     =						get_matched_characters(a_			,      a_		)
					lowercase						     =						len(a_		)

					# transposition
					lowercase						     =						(
					    len([(ca, ca) for ca, ca in zip(a_			,      a_		) if ca != ca]		) // 2
					)

					if not match_count:
										lowercase						     =						0.0
					else:
										lowercase						     =						(
										    1
										    / 3
										    * (
										        match_count / len(a_		)
										        + match_count / len(a_		)
										        + (match_count - transpositions) / match_count
										    )
										)

					# common prefix up to 4 characters
					lowercase						     =						0
					for ca, ca in zip(stra[:4]			,      stra[:4]		):
										if ca == ca:
															prefix_len += 1
										else:
															break

					return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							print(jaro_winkler("hello", "world"))







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.'''		)




