
import numpy as np
from numpy import floataa
from numpy.typing import NDArray




def 						A_			(				snake_case				: NDArray[floataa]			,   snake_case				: NDArray[floataa]			)   ->     NDArray[floataa]:



						'''simple docstring'''

						__UpperCamelCase	,				__UpperCamelCase  	=      np.shape(snake_case			)

						__UpperCamelCase  	=      np.zeros((rows, 1)			,   dtype=snake_case			)
						for row in reversed(range(snake_case			)			):
												__UpperCamelCase  	=      0
												for col in range(row + 1			,   snake_case			):
																		total += coefficients[row, col] * x[col]

												__UpperCamelCase  	=      (vector[row] - total) / coefficients[row, row]

						return x




def 						A_			(				snake_case				: NDArray[floataa]			,   snake_case				: NDArray[floataa]			)   ->     NDArray[floataa]:



						'''simple docstring'''

						__UpperCamelCase	,				__UpperCamelCase  	=      np.shape(snake_case			)
						if rows != columns:
												return np.array(()			,   dtype=snake_case			)

						# augmented matrix
						__UpperCamelCase  	=      np.concatenate((coefficients, vector)			,   axis=1			)
						__UpperCamelCase  	=      augmented_mat.astype('''float64'''			)

						# scale the matrix leaving it triangular
						for row in range(rows - 1			):
												__UpperCamelCase  	=      augmented_mat[row, row]
												for col in range(row + 1			,   snake_case			):
																		__UpperCamelCase  	=      augmented_mat[col, row] / pivot
																		augmented_mat[col, :] -= factor * augmented_mat[row, :]

						__UpperCamelCase  	=      retroactive_resolution(
						    augmented_mat[:, 0:columns]			,   augmented_mat[:, columns : columns + 1]			)

						return x


if __name__ == "__main__":
				import doctest

				doctest.testmod()








from typing import Callable




def   snake_case_	(    snake_case	)    ->							Tuple:

       def wrapper(snake_case	):
              lowercase__:  Tuple         =  function_with_docstring.__doc__
              return target_function

       return wrapper


