

"""simple docstring"""






import numpy as np
from numpy import floataa
from numpy.typing import NDArray
def 		A_	(   __UpperCamelCase     :				NDArray[floataa]       ,	__UpperCamelCase     :				NDArray[floataa]				):
		lowercase					,  lowercase										=							np.shape(__UpperCamelCase				)

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

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

		return x
def 		A_	(   __UpperCamelCase     :				NDArray[floataa]       ,	__UpperCamelCase     :				NDArray[floataa]				):
		lowercase					,  lowercase										=							np.shape(__UpperCamelCase				)
		if rows != columns:
				return np.array(()       ,	dtype=__UpperCamelCase				)

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

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

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

		return x


if __name__ == "__main__":
							import doctest

							doctest.testmod()


"""simple docstring"""






from typing import Callable
def 		A_	(   __UpperCamelCase     :				Callable				):

		def wrapper(__UpperCamelCase     :				Optional[Any]				):
				lowercase										=							function_with_docstring.__doc__
				return target_function

		return wrapper