



'''simple docstring'''

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







def     __UpperCamelCase					(				_lowercase,					_lowercase       )			->      NDArray[floataa]:
	_lowercase	,     _lowercase       :							str  	=		np.shape(_lowercase       )

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

		_lowercase       :							Tuple  	=		(vector[row] - total) / coefficients[row, row]

	return x







def     __UpperCamelCase					(				_lowercase,					_lowercase       )			->      NDArray[floataa]:
	_lowercase	,     _lowercase       :							Optional[Any]  	=		np.shape(_lowercase       )
	if rows != columns:
		return np.array((),					dtype=_lowercase       )

	# augmented matrix
	_lowercase       :							NDArray[floataa]  	=		np.concatenate((coefficients, vector),					axis=1       )
	_lowercase       :							List[str]  	=		augmented_mat.astype('float64'       )

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

	_lowercase       :							Optional[Any]  	=		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


_A					:     List[Any]      ={'''configuration_umt5''': ['''UMT5Config''', '''UMT5OnnxConfig''']}


try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		_A					:     Optional[Any]      =[
		    '''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

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