


"""simple docstring"""
import numpy as np
from numpy import floataa
from numpy.typing import NDArray







def     _a					(   _SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					)     ->					NDArray[floataa]:
							snake_case_     							=		np.shape(_lowercase					)

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

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

							return x







def     _a					(   _SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					)     ->					NDArray[floataa]:
							snake_case_     							=		np.shape(_lowercase					)
							if rows != columns:
														return np.array(()					,			dtype=_lowercase					)

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

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

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

							return x


if __name__ == "__main__":
				import doctest

				doctest.testmod()








'''simple docstring'''

import torch

from transformers import PreTrainedModel

from .custom_configuration import CustomConfig, NoSuperInitConfig



class 		lowerCamelCase__   (    A  ):




					'''simple docstring'''



					A_         =    CustomConfig




					def __init__(	self					:						int  ,	UpperCamelCase_					:						List[str]       )	->							int:



						'''simple docstring'''





						super().__init__(UpperCamelCase_       )
						_lowercase       :							List[Any]  	=		torch.nn.Linear(config.hidden_size  ,	config.hidden_size       )




					def     __UpperCAmelCase  (	self					:						Optional[int]  ,	UpperCamelCase_					:						Any       )	->							Union[str, Any]:



						'''simple docstring'''





						return self.linear(UpperCamelCase_       )




					def     __UpperCAmelCase  (	self					:						Optional[int]  ,	UpperCamelCase_					:						Optional[Any]       )	->							str:



						'''simple docstring'''





						pass






class 		lowerCamelCase__   (    A  ):




					'''simple docstring'''



					A_         =    NoSuperInitConfig




					def __init__(	self					:						Optional[int]  ,	UpperCamelCase_					:						Dict       )	->							Optional[Any]:



						'''simple docstring'''





						super().__init__(UpperCamelCase_       )
						_lowercase       :							List[str]  	=		torch.nn.Linear(config.attribute  ,	config.attribute       )




					def     __UpperCAmelCase  (	self					:						Optional[Any]  ,	UpperCamelCase_					:						Optional[int]       )	->							List[Any]:



						'''simple docstring'''





						return self.linear(UpperCamelCase_       )




					def     __UpperCAmelCase  (	self					:						Optional[Any]  ,	UpperCamelCase_					:						int       )	->							List[str]:



						'''simple docstring'''





						pass
