


import numpy as np






def 					lowerCamelCase_   (	_a     ,       _a     ,       _a = 1e-1_2     ,       _a = 100     ,       ):




		"""simple docstring"""






		assert np.shape(_a	)[0] == np.shape(_a	)[1]
		# Ensure proper dimensionality.
		assert np.shape(_a	)[0] == np.shape(_a	)[0]
		# Ensure inputs are either both complex or both real
		assert np.iscomplexobj(_a	) == np.iscomplexobj(_a	)
		lowerCAmelCase__       :      Optional[Any]   					= np.iscomplexobj(_a	)
		if is_complex:
				# Ensure complex input_matrix is Hermitian
				assert np.array_equal(_a     ,       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.

		lowerCAmelCase__       :      Union[str, Any]   					= False
		lowerCAmelCase__       :      str   					= 0
		lowerCAmelCase__       :      Optional[Any]   					= 0
		lowerCAmelCase__       :      Any   					= 1e1_2

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

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

				if error <= error_tol or iterations >= max_iterations:
						lowerCAmelCase__       :      List[str]   					= True

				lowerCAmelCase__       :      Union[str, Any]   					= lambda_

		if is_complex:
				lowerCAmelCase__       :      List[str]   					= np.real(lambda_	)

		return lambda_, vector






def 					lowerCamelCase_   (	):




		"""simple docstring"""






		lowerCAmelCase__       :      Optional[Any]   					= np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]	)
		lowerCAmelCase__       :      Dict   					= np.array([41, 4, 20]	)
		lowerCAmelCase__       :      List[str]   					= real_input_matrix.astype(np.complexaaa	)
		lowerCAmelCase__       :      List[Any]   					= np.triu(1J * complex_input_matrix     ,       1	)
		complex_input_matrix += imag_matrix
		complex_input_matrix += -1 * imag_matrix.T
		lowerCAmelCase__       :      List[str]   					= np.array([41, 4, 20]	).astype(np.complexaaa	)

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

				# Our implementation.
				lowerCAmelCase__					,     lowerCAmelCase__       :      Optional[Any]   					= power_iteration(_a     ,       _a	)

				# Numpy implementation.

				# Get eigenvalues and eigenvectors using built-in numpy
				# eigh (eigh used for symmetric or hermetian matrices).
				lowerCAmelCase__					,     lowerCAmelCase__       :      Optional[int]   					= np.linalg.eigh(_a	)
				# Last eigenvalue is the maximum one.
				lowerCAmelCase__       :      str   					= eigen_values[-1]
				# Last column in this matrix is eigenvector corresponding to largest eigenvalue.
				lowerCAmelCase__       :      Optional[int]   					= 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(_a	) - np.abs(_a	)	) <= 1e-6


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		test_power_iteration()








from ...utils import is_note_seq_available, is_transformers_available, is_torch_available
from ...utils import OptionalDependencyNotAvailable


try:
		if not (is_transformers_available() and is_torch_available()):
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		from ...utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
		from .notes_encoder import SpectrogramNotesEncoder
		from .continous_encoder import SpectrogramContEncoder
		from .pipeline_spectrogram_diffusion import (
		    SpectrogramContEncoder,
		    SpectrogramDiffusionPipeline,
		    TaFilmDecoder,
		)

try:
		if not (is_transformers_available() and is_torch_available() and is_note_seq_available()):
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		from ...utils.dummy_transformers_and_torch_and_note_seq_objects import *  # noqa F403
else:
		from .midi_utils import MidiProcessor




