



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

def      A_ (		__a       :			NDArray[floataa]	,						__a       :			NDArray[floataa]						):

				"""simple docstring"""
				a__ ,     a__			 =						np.shape(__a						)

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

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

				return x

def      A_ (		__a       :			NDArray[floataa]	,						__a       :			NDArray[floataa]						):

				"""simple docstring"""
				a__ ,     a__			 =						np.shape(__a						)
				if rows != columns:
								return np.array(()	,						dtype=__a						)

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

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

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

				return x


if __name__ == "__main__":
	import doctest

	doctest.testmod()






def      A_ (		__a       :			float						):

				"""simple docstring"""
				return int(__a						) if x - int(__a						) >= 0 else int(__a						) - 1


if __name__ == "__main__":
	import doctest

	doctest.testmod()

