



'''simple docstring'''

import numpy as np







def 						__UpperCamelCase				(							_lowercase,				_lowercase,				_lowercase = 1E-1_2,				_lowercase = 100,				) ->			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					)
	_lowercase					:       Optional[int]       =		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.

	_lowercase					:       Optional[Any]       =		False
	_lowercase					:       Any       =		0
	_lowercase					:       List[Any]       =		0
	_lowercase					:       List[Any]       =		1E1_2

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

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

		if error <= error_tol or iterations >= max_iterations:
			_lowercase					:       Optional[int]       =		True

		_lowercase					:       str       =		lambda_

	if is_complex:
		_lowercase					:       Any       =		np.real(lambda_					)

	return lambda_, vector







def 						__UpperCamelCase				(							) ->			None:
	_lowercase					:       Optional[int]       =		np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]					)
	_lowercase					:       Optional[int]       =		np.array([41, 4, 20]					)
	_lowercase					:       Any       =		real_input_matrix.astype(np.complexaaa					)
	_lowercase					:       str       =		np.triu(1j * complex_input_matrix,				1					)
	complex_input_matrix += imag_matrix
	complex_input_matrix += -1 * imag_matrix.T
	_lowercase					:       List[Any]       =		np.array([41, 4, 20]					).astype(np.complexaaa					)

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

		# Our implementation.
		_lowercase					:       Union[str, Any]       =		power_iteration(_lowercase,				_lowercase					)

		# Numpy implementation.

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


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		test_power_iteration()








'''simple docstring'''

from ...configuration_utils import PretrainedConfig
from ...utils import logging


_A				:    Optional[Any]     						=logging.get_logger(__name__)

_A				:    Optional[int]     						={
    '''microsoft/markuplm-base''': '''https://huggingface.co/microsoft/markuplm-base/resolve/main/config.json''',
    '''microsoft/markuplm-large''': '''https://huggingface.co/microsoft/markuplm-large/resolve/main/config.json''',
}



class 		lowerCamelCase__      (						A     ):




					'''simple docstring'''



					A_						    =						"""markuplm"""




					def __init__(  self				:	int     ,  UpperCamelCase_				:	Optional[Any]=3_0522     ,  UpperCamelCase_				:	Optional[Any]=768     ,  UpperCamelCase_				:	Tuple=12     ,  UpperCamelCase_				:	Union[str, Any]=12     ,  UpperCamelCase_				:	Tuple=3072     ,  UpperCamelCase_				:	Union[str, Any]="gelu"     ,  UpperCamelCase_				:	List[Any]=0.1     ,  UpperCamelCase_				:	List[Any]=0.1     ,  UpperCamelCase_				:	Dict=512     ,  UpperCamelCase_				:	Optional[int]=2     ,  UpperCamelCase_				:	Any=0.02     ,  UpperCamelCase_				:	Optional[Any]=1E-12     ,  UpperCamelCase_				:	List[str]=0     ,  UpperCamelCase_				:	Optional[int]=0     ,  UpperCamelCase_				:	Tuple=2     ,  UpperCamelCase_				:	str=256     ,  UpperCamelCase_				:	Optional[Any]=1024     ,  UpperCamelCase_				:	Union[str, Any]=216     ,  UpperCamelCase_				:	int=1001     ,  UpperCamelCase_				:	int=32     ,  UpperCamelCase_				:	int=50     ,  UpperCamelCase_				:	str="absolute"     ,  UpperCamelCase_				:	Union[str, Any]=True     ,  UpperCamelCase_				:	Optional[int]=None     ,  **UpperCamelCase_				:	Any     ,  )  ->       Optional[int]:



						'''simple docstring'''





						super().__init__(
						    pad_token_id=UpperCamelCase_     ,  bos_token_id=UpperCamelCase_     ,  eos_token_id=UpperCamelCase_     ,  **UpperCamelCase_     ,  )
						_lowercase					:       List[Any]       =		vocab_size
						_lowercase					:       Union[str, Any]       =		hidden_size
						_lowercase					:       Dict       =		num_hidden_layers
						_lowercase					:       Optional[Any]       =		num_attention_heads
						_lowercase					:       Dict       =		hidden_act
						_lowercase					:       Optional[Any]       =		intermediate_size
						_lowercase					:       Optional[int]       =		hidden_dropout_prob
						_lowercase					:       Union[str, Any]       =		attention_probs_dropout_prob
						_lowercase					:       Any       =		max_position_embeddings
						_lowercase					:       List[Any]       =		type_vocab_size
						_lowercase					:       Union[str, Any]       =		initializer_range
						_lowercase					:       Optional[int]       =		layer_norm_eps
						_lowercase					:       Optional[Any]       =		position_embedding_type
						_lowercase					:       str       =		use_cache
						_lowercase					:       str       =		classifier_dropout
						# additional properties
						_lowercase					:       int       =		max_depth
						_lowercase					:       Dict       =		max_xpath_tag_unit_embeddings
						_lowercase					:       str       =		max_xpath_subs_unit_embeddings
						_lowercase					:       List[str]       =		tag_pad_id
						_lowercase					:       Optional[int]       =		subs_pad_id
						_lowercase					:       Any       =		xpath_unit_hidden_size
