

def 					__lowerCamelCase	( UpperCamelCase__   ,							UpperCamelCase__ = " "      ):







							'''simple docstring'''






							snake_case_							=    []

							snake_case_							=    0
							for index, char in enumerate(UpperCamelCase__      ):
														if char == separator:
																					split_words.append(string[last_index:index]      )
																					snake_case_							=    index + 1
														elif index + 1 == len(UpperCamelCase__      ):
																					split_words.append(string[last_index : index + 1]      )
							return split_words


if __name__ == "__main__":
					from doctest import testmod

					testmod()







from __future__ import annotations

import numpy as np





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							snake_case_				,    snake_case_							=    np.shape(UpperCamelCase__      )
							if rows != columns:
														snake_case_							=    (
														    '\'table\' has to be of square shaped array but got a '
														    F'''{rows}x{columns} array:\n{table}'''
														)
														raise ValueError(UpperCamelCase__      )

							snake_case_							=    np.zeros((rows, columns)      )
							snake_case_							=    np.zeros((rows, columns)      )
							for i in range(UpperCamelCase__      ):
														for j in range(UpperCamelCase__      ):
																					snake_case_							=    sum(lower[i][k] * upper[k][j] for k in range(UpperCamelCase__      )      )
																					if upper[j][j] == 0:
																												raise ArithmeticError('No LU decomposition exists'      )
																					snake_case_							=    (table[i][j] - total) / upper[j][j]
														snake_case_							=    1
														for j in range(UpperCamelCase__   ,							UpperCamelCase__      ):
																					snake_case_							=    sum(lower[i][k] * upper[k][j] for k in range(UpperCamelCase__      )      )
																					snake_case_							=    table[i][j] - total
							return lower, upper


if __name__ == "__main__":
					import doctest

					doctest.testmod()




