



'''simple docstring'''

import numpy as np






def       __lowercase  (_SCREAMING_SNAKE_CASE      :np.ndarray    ,	_SCREAMING_SNAKE_CASE      :np.ndarray    ,	_SCREAMING_SNAKE_CASE      :float = 1E-1_2    ,	_SCREAMING_SNAKE_CASE      :int = 1_00    ,	):
				assert np.shape(_SCREAMING_SNAKE_CASE       )[0] == np.shape(_SCREAMING_SNAKE_CASE       )[1]
				# Ensure proper dimensionality.
				assert np.shape(_SCREAMING_SNAKE_CASE       )[0] == np.shape(_SCREAMING_SNAKE_CASE       )[0]
				# Ensure inputs are either both complex or both real
				assert np.iscomplexobj(_SCREAMING_SNAKE_CASE       ) == np.iscomplexobj(_SCREAMING_SNAKE_CASE       )
				SCREAMING_SNAKE_CASE  :						Dict      					= np.iscomplexobj(_SCREAMING_SNAKE_CASE       )
				if is_complex:
								# Ensure complex input_matrix is Hermitian
								assert np.array_equal(_SCREAMING_SNAKE_CASE    ,	input_matrix.conj().T       )

				# Set convergence to False. Will define convergence when we exceed max_iterations
				# or when we have small changes from one iteration to next.

				SCREAMING_SNAKE_CASE  :						Union[str, Any]      					= False
				SCREAMING_SNAKE_CASE  :						int      					= 0
				SCREAMING_SNAKE_CASE  :						Union[str, Any]      					= 0
				SCREAMING_SNAKE_CASE  :						Union[str, Any]      					= 1E1_2

				while not convergence:
								# Multiple matrix by the vector.
								SCREAMING_SNAKE_CASE  :						Dict      					= np.dot(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE       )
								# Normalize the resulting output vector.
								SCREAMING_SNAKE_CASE  :						str      					= w / np.linalg.norm(_SCREAMING_SNAKE_CASE       )
								# Find rayleigh quotient
								# (faster than usual b/c we know vector is normalized already)
								SCREAMING_SNAKE_CASE  :						List[Any]      					= vector.conj().T if is_complex else vector.T
								SCREAMING_SNAKE_CASE  :						Any      					= np.dot(_SCREAMING_SNAKE_CASE    ,	np.dot(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE       )       )

								# Check convergence.
								SCREAMING_SNAKE_CASE  :						Dict      					= np.abs(lambda_ - lambda_previous       ) / lambda_
								iterations += 1

								if error <= error_tol or iterations >= max_iterations:
												SCREAMING_SNAKE_CASE  :						Union[str, Any]      					= True

								SCREAMING_SNAKE_CASE  :						str      					= lambda_

				if is_complex:
								SCREAMING_SNAKE_CASE  :						str      					= np.real(lambda_       )

				return lambda_, vector






def       __lowercase  ():
				SCREAMING_SNAKE_CASE  :						Any      					= np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]       )
				SCREAMING_SNAKE_CASE  :						Tuple      					= np.array([41, 4, 20]       )
				SCREAMING_SNAKE_CASE  :						Optional[Any]      					= real_input_matrix.astype(np.complexaaa       )
				SCREAMING_SNAKE_CASE  :						Union[str, Any]      					= np.triu(1j * complex_input_matrix    ,	1       )
				complex_input_matrix += imag_matrix
				complex_input_matrix += -1 * imag_matrix.T
				SCREAMING_SNAKE_CASE  :						str      					= np.array([41, 4, 20]       ).astype(np.complexaaa       )

				for problem_type in ["real", "complex"]:
								if problem_type == "real":
												SCREAMING_SNAKE_CASE  :						str      					= real_input_matrix
												SCREAMING_SNAKE_CASE  :						Union[str, Any]      					= real_vector
								elif problem_type == "complex":
												SCREAMING_SNAKE_CASE  :						Dict      					= complex_input_matrix
												SCREAMING_SNAKE_CASE  :						Union[str, Any]      					= complex_vector

								# Our implementation.
								SCREAMING_SNAKE_CASE					,					SCREAMING_SNAKE_CASE  :						Optional[int]      					= power_iteration(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE       )

								# Numpy implementation.

								# Get eigenvalues and eigenvectors using built-in numpy
								# eigh (eigh used for symmetric or hermetian matrices).
								SCREAMING_SNAKE_CASE					,					SCREAMING_SNAKE_CASE  :						Dict      					= np.linalg.eigh(_SCREAMING_SNAKE_CASE       )
								# Last eigenvalue is the maximum one.
								SCREAMING_SNAKE_CASE  :						Optional[Any]      					= eigen_values[-1]
								# Last column in this matrix is eigenvector corresponding to largest eigenvalue.
								SCREAMING_SNAKE_CASE  :						List[str]      					= eigen_vectors[:, -1]

								# Check our implementation and numpy gives close answers.
								assert np.abs(eigen_value - eigen_value_max       ) <= 1E-6
								# Take absolute values element wise of each eigenvector.
								# as they are only unique to a minus sign.
								assert np.linalg.norm(np.abs(_SCREAMING_SNAKE_CASE       ) - np.abs(_SCREAMING_SNAKE_CASE       )       ) <= 1E-6


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	test_power_iteration()









'''simple docstring'''

from ...utils import is_torch_available, is_transformers_available


if is_transformers_available() and is_torch_available():
	from .pipeline_vq_diffusion import LearnedClassifierFreeSamplingEmbeddings, VQDiffusionPipeline




