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



def      _a     (   __UpperCamelCase       :  NDArray[floataa]	,__UpperCamelCase       :  NDArray[floataa]    ):
			lowerCAmelCase__      ,				lowerCAmelCase__ :    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__ :    int				      =			(vector[row] - total) / coefficients[row, row]

			return x



def      _a     (   __UpperCamelCase       :  NDArray[floataa]	,__UpperCamelCase       :  NDArray[floataa]    ):
			lowerCAmelCase__      ,				lowerCAmelCase__ :    str				      =			np.shape(__UpperCamelCase    )
			if rows != columns:
						return np.array(()	,dtype=__UpperCamelCase    )

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

			# scale the matrix leaving it triangular
			for row in range(rows - 1    ):
						lowerCAmelCase__ :    str				      =			augmented_mat[row, row]
						for col in range(row + 1	,__UpperCamelCase    ):
									lowerCAmelCase__ :    Optional[int]				      =			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()





import unittest
from pathlib import Path
from tempfile import TemporaryDirectory
from unittest.mock import Mock, patch

import diffusers.utils.hub_utils





class 						lowercase       (  unittest.TestCase					):
					@patch('''diffusers.utils.hub_utils.get_full_repo_name'''    )
					def lowercase_			(		self ,	SCREAMING_SNAKE_CASE__    ):
								"""simple docstring"""







								lowerCAmelCase__ :    str				      =			'''full_repo_name'''
								with TemporaryDirectory() as tmpdir:
											# Dummy args values
											lowerCAmelCase__ :    Optional[int]				      =			Mock()
											lowerCAmelCase__ :    Optional[int]				      =			tmpdir
											lowerCAmelCase__ :    Optional[Any]				      =			0
											lowerCAmelCase__ :    Optional[int]				      =			'''hub_token'''
											lowerCAmelCase__ :    Tuple				      =			'''dataset_name'''
											lowerCAmelCase__ :    int				      =			0.01
											lowerCAmelCase__ :    Optional[int]				      =			100000
											lowerCAmelCase__ :    Any				      =			10000
											lowerCAmelCase__ :    Union[str, Any]				      =			0.01
											lowerCAmelCase__ :    int				      =			0.02
											lowerCAmelCase__ :    Union[str, Any]				      =			0.03
											lowerCAmelCase__ :    str				      =			0.0_005
											lowerCAmelCase__ :    Dict				      =			0.000_001
											lowerCAmelCase__ :    Tuple				      =			1
											lowerCAmelCase__ :    Optional[int]				      =			10
											lowerCAmelCase__ :    int				      =			0.001
											lowerCAmelCase__ :    Union[str, Any]				      =			0.1
											lowerCAmelCase__ :    Tuple				      =			0.2
											lowerCAmelCase__ :    Optional[int]				      =			True

											# Model card mush be rendered and saved
											diffusers.utils.hub_utils.create_model_card(SCREAMING_SNAKE_CASE__ ,	model_name='''model_name'''    )
											self.assertTrue((Path(SCREAMING_SNAKE_CASE__    ) / '''README.md''').is_file()    )



