



"""simple docstring"""
from typing import TYPE_CHECKING

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


__SCREAMING_SNAKE_CASE  :						Tuple    							=      {
    '''configuration_transfo_xl''': ['''TRANSFO_XL_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''TransfoXLConfig'''],
    '''tokenization_transfo_xl''': ['''TransfoXLCorpus''', '''TransfoXLTokenizer'''],
}

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			__SCREAMING_SNAKE_CASE  :						Union[str, Any]    							=      [
			    '''TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST''',
			    '''AdaptiveEmbedding''',
			    '''TransfoXLForSequenceClassification''',
			    '''TransfoXLLMHeadModel''',
			    '''TransfoXLModel''',
			    '''TransfoXLPreTrainedModel''',
			    '''load_tf_weights_in_transfo_xl''',
			]

try:
			if not is_tf_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			__SCREAMING_SNAKE_CASE  :						int    							=      [
			    '''TF_TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST''',
			    '''TFAdaptiveEmbedding''',
			    '''TFTransfoXLForSequenceClassification''',
			    '''TFTransfoXLLMHeadModel''',
			    '''TFTransfoXLMainLayer''',
			    '''TFTransfoXLModel''',
			    '''TFTransfoXLPreTrainedModel''',
			]


if TYPE_CHECKING:
			from .configuration_transfo_xl import TRANSFO_XL_PRETRAINED_CONFIG_ARCHIVE_MAP, TransfoXLConfig
			from .tokenization_transfo_xl import TransfoXLCorpus, TransfoXLTokenizer

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_transfo_xl import (
						    TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
						    AdaptiveEmbedding,
						    TransfoXLForSequenceClassification,
						    TransfoXLLMHeadModel,
						    TransfoXLModel,
						    TransfoXLPreTrainedModel,
						    load_tf_weights_in_transfo_xl,
						)

			try:
						if not is_tf_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_tf_transfo_xl import (
						    TF_TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
						    TFAdaptiveEmbedding,
						    TFTransfoXLForSequenceClassification,
						    TFTransfoXLLMHeadModel,
						    TFTransfoXLMainLayer,
						    TFTransfoXLModel,
						    TFTransfoXLPreTrainedModel,
						)

else:
			import sys

			__SCREAMING_SNAKE_CASE  :						List[str]    							=      _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)





"""simple docstring"""
import numpy as np



def        lowerCAmelCase_(   lowercase_     :							np.ndarray						,   lowercase_     :							np.ndarray						,   lowercase_     :							float = 1e-12						,   lowercase_     :							int = 1_00						,   )	->       tuple[float, np.ndarray]:
				assert np.shape(lowercase_							)[0] == np.shape(lowercase_							)[1]
				# Ensure proper dimensionality.
				assert np.shape(lowercase_							)[0] == np.shape(lowercase_							)[0]
				# Ensure inputs are either both complex or both real
				assert np.iscomplexobj(lowercase_							) == np.iscomplexobj(lowercase_							)
				_lowerCamelCase        =				np.iscomplexobj(lowercase_							)
				if is_complex:
								# Ensure complex input_matrix is Hermitian
								assert np.array_equal(lowercase_						,   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        =				False
				_lowerCamelCase        =				0
				_lowerCamelCase        =				0
				_lowerCamelCase        =				1e12

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

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

								if error <= error_tol or iterations >= max_iterations:
												_lowerCamelCase        =				True

								_lowerCamelCase        =				lambda_

				if is_complex:
								_lowerCamelCase        =				np.real(lambda_							)

				return lambda_, vector



def        lowerCAmelCase_(   )	->       None:
				_lowerCamelCase        =				np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]							)
				_lowerCamelCase        =				np.array([41, 4, 20]							)
				_lowerCamelCase        =				real_input_matrix.astype(np.complexaaa							)
				_lowerCamelCase        =				np.triu(1j * complex_input_matrix						,   1							)
				complex_input_matrix += imag_matrix
				complex_input_matrix += -1 * imag_matrix.T
				_lowerCamelCase        =				np.array([41, 4, 20]							).astype(np.complexaaa							)

				for problem_type in ["real", "complex"]:
								if problem_type == "real":
												_lowerCamelCase        =				real_input_matrix
												_lowerCamelCase        =				real_vector
								elif problem_type == "complex":
												_lowerCamelCase        =				complex_input_matrix
												_lowerCamelCase        =				complex_vector

								# Our implementation.
								_lowerCamelCase  ,     _lowerCamelCase        =				power_iteration(lowercase_						,   lowercase_							)

								# Numpy implementation.

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


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			test_power_iteration()
