




import numpy as np




def 		lowerCAmelCase_   (	lowerCamelCase	,     lowerCamelCase	,     lowerCamelCase = 1E-12	,     lowerCamelCase = 100	,     ):
				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_   )
				__magic_name__	:	str								=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.

				__magic_name__	:	List[Any]								=False
				__magic_name__	:	Any								=0
				__magic_name__	:	Any								=0
				__magic_name__	:	Dict								=1E12

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

								# Check convergence.
								__magic_name__	:	List[str]								=np.abs(lambda_ - lambda_previous   ) / lambda_
								iterations += 1

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

								__magic_name__	:	List[str]								=lambda_

				if is_complex:
								__magic_name__	:	List[Any]								=np.real(lambda_   )

				return lambda_, vector




def 		lowerCAmelCase_   (	):
				__magic_name__	:	Tuple								=np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]   )
				__magic_name__	:	Optional[int]								=np.array([41, 4, 20]   )
				__magic_name__	:	str								=real_input_matrix.astype(np.complexaaa   )
				__magic_name__	:	int								=np.triu(1J * complex_input_matrix	,     1   )
				complex_input_matrix += imag_matrix
				complex_input_matrix += -1 * imag_matrix.T
				__magic_name__	:	Tuple								=np.array([41, 4, 20]   ).astype(np.complexaaa   )

				for problem_type in ["real", "complex"]:
								if problem_type == "real":
												__magic_name__	:	int								=real_input_matrix
												__magic_name__	:	Any								=real_vector
								elif problem_type == "complex":
												__magic_name__	:	Any								=complex_input_matrix
												__magic_name__	:	Tuple								=complex_vector

								# Our implementation.
								__magic_name__				, __magic_name__	:	str								=power_iteration(A_	,     A_   )

								# Numpy implementation.

								# Get eigenvalues and eigenvectors using built-in numpy
								# eigh (eigh used for symmetric or hermetian matrices).
								__magic_name__				, __magic_name__	:	int								=np.linalg.eigh(A_   )
								# Last eigenvalue is the maximum one.
								__magic_name__	:	Union[str, Any]								=eigen_values[-1]
								# Last column in this matrix is eigenvector corresponding to largest eigenvalue.
								__magic_name__	:	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 ... import PretrainedConfig


UpperCAmelCase_		:				List[str]									=     {
    "sijunhe/nezha-cn-base": "https://huggingface.co/sijunhe/nezha-cn-base/resolve/main/config.json",
}




class 		__A      (			UpperCamelCase__			):
						UpperCamelCase     						=					NEZHA_PRETRAINED_CONFIG_ARCHIVE_MAP
						UpperCamelCase     						=					"""nezha"""

						def __init__(		self   :List[Any]    , __snake_case   :Optional[int]=2_11_28    , __snake_case   :Dict=7_68    , __snake_case   :str=12    , __snake_case   :List[Any]=12    , __snake_case   :Optional[int]=30_72    , __snake_case   :Any="gelu"    , __snake_case   :List[str]=0.1    , __snake_case   :Optional[int]=0.1    , __snake_case   :Dict=5_12    , __snake_case   :Optional[int]=64    , __snake_case   :Any=2    , __snake_case   :List[Any]=0.02    , __snake_case   :List[str]=1E-12    , __snake_case   :Any=0.1    , __snake_case   :str=0    , __snake_case   :int=2    , __snake_case   :str=3    , __snake_case   :Any=True    , **__snake_case   :Any    , ):
										'''simple docstring'''

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

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




