




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






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




	'''simple docstring'''


	lowerCamelCase_       ,      lowerCamelCase_							:		Union[str, Any]							       =							np.shape(_A      )

	lowerCamelCase_							:		List[Any]							       =							np.zeros((rows, 1)						,       dtype=_A      )
	for row in reversed(range(_A      )      ):
		lowerCamelCase_							:		Union[str, Any]							       =							0
		for col in range(row + 1						,       _A      ):
			total += coefficients[row, col] * x[col]

		lowerCamelCase_							:		int							       =							(vector[row] - total) / coefficients[row, row]

	return x






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




	'''simple docstring'''


	lowerCamelCase_       ,      lowerCamelCase_							:		Optional[Any]							       =							np.shape(_A      )
	if rows != columns:
		return np.array(()						,       dtype=_A      )

	# augmented matrix
	lowerCamelCase_							:		Any							       =							np.concatenate((coefficients, vector)						,       axis=1      )
	lowerCamelCase_							:		int							       =							augmented_mat.astype('float64'      )

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

	lowerCamelCase_							:		Any							       =							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 (							A      )							->							List[str]:




	'''simple docstring'''


	def wrapper(A      ):
		lowerCamelCase_							:		Dict							       =							function_with_docstring.__doc__
		return target_function

	return wrapper
