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

def lowercase_  (       _snake_case       ,_snake_case						):
							SCREAMING_SNAKE_CASE__						:	Optional[int]									=       np.shape(_snake_case						)

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

														SCREAMING_SNAKE_CASE__						:	Union[str, Any]									=       (vector[row] - total) / coefficients[row, row]

							return x

def lowercase_  (       _snake_case       ,_snake_case						):
							SCREAMING_SNAKE_CASE__						:	str									=       np.shape(_snake_case						)
							if rows != columns:
														return np.array(()       ,dtype=_snake_case						)

							# augmented matrix
							SCREAMING_SNAKE_CASE__						:	NDArray[floataa]									=       np.concatenate((coefficients, vector)       ,axis=1						)
							SCREAMING_SNAKE_CASE__						:	Optional[Any]									=       augmented_mat.astype("""float64"""						)

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

							SCREAMING_SNAKE_CASE__						:	str									=       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 TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCAmelCase__				:   Optional[Any]   							=			{'configuration_umt5': ['UMT5Config', 'UMT5OnnxConfig']}


try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCAmelCase__				:   Tuple   							=			[
					    'UMT5EncoderModel',
					    'UMT5ForConditionalGeneration',
					    'UMT5ForQuestionAnswering',
					    'UMT5Model',
					    'UMT5PreTrainedModel',
					]

if TYPE_CHECKING:
					from .configuration_umta import UMTaConfig, UMTaOnnxConfig

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_umta import (
										    UMTaEncoderModel,
										    UMTaForConditionalGeneration,
										    UMTaForQuestionAnswering,
										    UMTaModel,
										    UMTaPreTrainedModel,
										)
else:
					import sys

					UpperCAmelCase__				:   Optional[Any]   							=			_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




