



'''simple docstring'''





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





def 						__lowerCamelCase       (      __magic_name__	:  NDArray[floataa]     , __magic_name__	:  NDArray[floataa]						):
							a__:       Tuple											=np.shape(__magic_name__						)

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

														a__:       str											=(vector[row] - total) / coefficients[row, row]

							return x





def 						__lowerCamelCase       (      __magic_name__	:  NDArray[floataa]     , __magic_name__	:  NDArray[floataa]						):
							a__:       int											=np.shape(__magic_name__						)
							if rows != columns:
														return np.array(()     , dtype=__magic_name__						)

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

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

							a__:       List[Any]											=retroactive_resolution(
							    augmented_mat[:, 0:columns]     , augmented_mat[:, columns : columns + 1]						)

							return x


if __name__ == "__main__":
		import doctest

		doctest.testmod()










from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


__UpperCAmelCase						  =     {
    '''configuration_splinter''': ['''SPLINTER_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''SplinterConfig'''],
    '''tokenization_splinter''': ['''SplinterTokenizer'''],
}

try:
		if not is_tokenizers_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		__UpperCAmelCase						  =     ['''SplinterTokenizerFast''']

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		__UpperCAmelCase						  =     [
		    '''SPLINTER_PRETRAINED_MODEL_ARCHIVE_LIST''',
		    '''SplinterForQuestionAnswering''',
		    '''SplinterForPreTraining''',
		    '''SplinterLayer''',
		    '''SplinterModel''',
		    '''SplinterPreTrainedModel''',
		]


if TYPE_CHECKING:
		from .configuration_splinter import SPLINTER_PRETRAINED_CONFIG_ARCHIVE_MAP, SplinterConfig
		from .tokenization_splinter import SplinterTokenizer

		try:
				if not is_tokenizers_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .tokenization_splinter_fast import SplinterTokenizerFast

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_splinter import (
				    SPLINTER_PRETRAINED_MODEL_ARCHIVE_LIST,
				    SplinterForPreTraining,
				    SplinterForQuestionAnswering,
				    SplinterLayer,
				    SplinterModel,
				    SplinterPreTrainedModel,
				)


else:
		import sys

		__UpperCAmelCase						  =     _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)





