






'''simple docstring'''







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





def 					SCREAMING_SNAKE_CASE_			(UpperCamelCase							,     UpperCamelCase ) ->			NDArray[floataa]:
							lowerCamelCase__    ,						lowerCamelCase__   :      List[Any]			    =			np.shape(UpperCamelCase )

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

														lowerCamelCase__   :      Dict			    =			(vector[row] - total) / coefficients[row, row]

							return x





def 					SCREAMING_SNAKE_CASE_			(UpperCamelCase							,     UpperCamelCase ) ->			NDArray[floataa]:
							lowerCamelCase__    ,						lowerCamelCase__   :      Optional[int]			    =			np.shape(UpperCamelCase )
							if rows != columns:
														return np.array(()							,     dtype=UpperCamelCase )

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

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

							lowerCamelCase__   :      int			    =			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      :     Optional[int]       	={'''configuration_visual_bert''': ['''VISUAL_BERT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''VisualBertConfig''']}

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			_A      :     Optional[int]       	=[
			    '''VISUAL_BERT_PRETRAINED_MODEL_ARCHIVE_LIST''',
			    '''VisualBertForMultipleChoice''',
			    '''VisualBertForPreTraining''',
			    '''VisualBertForQuestionAnswering''',
			    '''VisualBertForRegionToPhraseAlignment''',
			    '''VisualBertForVisualReasoning''',
			    '''VisualBertLayer''',
			    '''VisualBertModel''',
			    '''VisualBertPreTrainedModel''',
			]


if TYPE_CHECKING:
			from .configuration_visual_bert import VISUAL_BERT_PRETRAINED_CONFIG_ARCHIVE_MAP, VisualBertConfig

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_visual_bert import (
						    VISUAL_BERT_PRETRAINED_MODEL_ARCHIVE_LIST,
						    VisualBertForMultipleChoice,
						    VisualBertForPreTraining,
						    VisualBertForQuestionAnswering,
						    VisualBertForRegionToPhraseAlignment,
						    VisualBertForVisualReasoning,
						    VisualBertLayer,
						    VisualBertModel,
						    VisualBertPreTrainedModel,
						)


else:
			import sys

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

