



"""simple docstring"""




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



def 				_lowerCAmelCase      (_lowerCAmelCase				,		_lowerCAmelCase):
					UpperCamelCase_					,      UpperCamelCase_											=				np.shape(_lowerCAmelCase)

					UpperCamelCase_											=				np.zeros((rows, 1)				,		dtype=_lowerCAmelCase)
					for row in reversed(range(_lowerCAmelCase)):
										UpperCamelCase_											=				0
										for col in range(row + 1				,		_lowerCAmelCase):
															total += coefficients[row, col] * x[col]

										UpperCamelCase_											=				(vector[row] - total) / coefficients[row, row]

					return x



def 				_lowerCAmelCase      (_lowerCAmelCase				,		_lowerCAmelCase):
					UpperCamelCase_					,      UpperCamelCase_											=				np.shape(_lowerCAmelCase)
					if rows != columns:
										return np.array(()				,		dtype=_lowerCAmelCase)

					# augmented matrix
					UpperCamelCase_											=				np.concatenate((coefficients, vector)				,		axis=1)
					UpperCamelCase_											=				augmented_mat.astype("float64")

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

					UpperCamelCase_											=				retroactive_resolution(
					    augmented_mat[:, 0:columns]				,		augmented_mat[:, columns : columns + 1])

					return x


if __name__ == "__main__":
	import doctest

	doctest.testmod()





from ...utils import is_transformers_available
from .pipeline_latent_diffusion_superresolution import LDMSuperResolutionPipeline


if is_transformers_available():
	from .pipeline_latent_diffusion import LDMBertModel, LDMTextToImagePipeline
