




"""simple docstring"""






from typing import Any

import numpy as np





def 							UpperCAmelCase		(		snake_case			:					np.ndarray    ):
					return np.array_equal(snake_case      ,       matrix.conjugate().T    )





def 							UpperCAmelCase		(		snake_case			:					np.ndarray      ,       snake_case			:					np.ndarray    ):
					_lowerCAmelCase:Optional[int]									=  v.conjugate().T
					_lowerCAmelCase:Union[str, Any]									=  v_star.dot(snake_case    )
					assert isinstance(snake_case      ,       np.ndarray    )
					return (v_star_dot.dot(snake_case    )) / (v_star.dot(snake_case    ))





def 							UpperCAmelCase		(		):
					_lowerCAmelCase:Optional[Any]									=  np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]    )
					_lowerCAmelCase:Optional[Any]									=  np.array([[1], [2], [3]]    )
					assert is_hermitian(snake_case    ), F'{a} is not hermitian.'
					print(rayleigh_quotient(snake_case      ,       snake_case    )    )

					_lowerCAmelCase:Tuple									=  np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]    )
					assert is_hermitian(snake_case    ), F'{a} is not hermitian.'
					assert rayleigh_quotient(snake_case      ,       snake_case    ) == float(3    )


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							tests()












"""simple docstring"""






from ...configuration_utils import PretrainedConfig




class   a__			(       UpperCamelCase_  ):
						snake_case__             = '''bert-generation'''





						def __init__(							self      :	Dict     ,a__      :	str=5_0358     ,a__      :	List[str]=1024     ,a__      :	int=24     ,a__      :	Optional[Any]=16     ,a__      :	List[str]=4096     ,a__      :	Optional[int]="gelu"     ,a__      :	str=0.1     ,a__      :	Union[str, Any]=0.1     ,a__      :	int=512     ,a__      :	Dict=0.02     ,a__      :	List[Any]=1E-12     ,a__      :	List[Any]=0     ,a__      :	int=2     ,a__      :	str=1     ,a__      :	Dict="absolute"     ,a__      :	int=True     ,**a__      :	List[str]     ,)						->       List[Any]:




											"""simple docstring"""







											super().__init__(pad_token_id=a__     ,bos_token_id=a__     ,eos_token_id=a__     ,**a__)

											_lowerCAmelCase:Optional[Any]									=  vocab_size
											_lowerCAmelCase:Union[str, Any]									=  hidden_size
											_lowerCAmelCase:Any									=  num_hidden_layers
											_lowerCAmelCase:int									=  num_attention_heads
											_lowerCAmelCase:int									=  hidden_act
											_lowerCAmelCase:List[Any]									=  intermediate_size
											_lowerCAmelCase:Optional[Any]									=  hidden_dropout_prob
											_lowerCAmelCase:int									=  attention_probs_dropout_prob
											_lowerCAmelCase:Optional[int]									=  max_position_embeddings
											_lowerCAmelCase:Dict									=  initializer_range
											_lowerCAmelCase:Union[str, Any]									=  layer_norm_eps
											_lowerCAmelCase:int									=  position_embedding_type
											_lowerCAmelCase:Tuple									=  use_cache






