





import numpy as np



def      __lowercase     (   _SCREAMING_SNAKE_CASE				,		_SCREAMING_SNAKE_CASE				,		_SCREAMING_SNAKE_CASE = 1E-12				,		_SCREAMING_SNAKE_CASE = 1_00				,		)				->     List[Any]:


      '''simple docstring'''


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

      SCREAMING_SNAKE_CASE	=		False
      SCREAMING_SNAKE_CASE	=		0
      SCREAMING_SNAKE_CASE	=		0
      SCREAMING_SNAKE_CASE	=		1E12

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

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

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

            SCREAMING_SNAKE_CASE	=		lambda_

      if is_complex:
            SCREAMING_SNAKE_CASE	=		np.real(lambda_			)

      return lambda_, vector



def      __lowercase     (   )				->     List[Any]:


      '''simple docstring'''


      SCREAMING_SNAKE_CASE	=		np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]			)
      SCREAMING_SNAKE_CASE	=		np.array([41, 4, 20]			)
      SCREAMING_SNAKE_CASE	=		real_input_matrix.astype(np.complexaaa			)
      SCREAMING_SNAKE_CASE	=		np.triu(1J * complex_input_matrix				,		1			)
      complex_input_matrix += imag_matrix
      complex_input_matrix += -1 * imag_matrix.T
      SCREAMING_SNAKE_CASE	=		np.array([41, 4, 20]			).astype(np.complexaaa			)

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

            # Our implementation.
            SCREAMING_SNAKE_CASE,      SCREAMING_SNAKE_CASE	=		power_iteration(snake_case__				,		snake_case__			)

            # Numpy implementation.

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


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      test_power_iteration()









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


SCREAMING_SNAKE_CASE_		     = logging.get_logger(__name__)

SCREAMING_SNAKE_CASE_		     = {
    """google/pegasus-large""": """https://huggingface.co/google/pegasus-large/resolve/main/config.json""",
    # See all PEGASUS models at https://huggingface.co/models?filter=pegasus
}

class 	UpperCamelCase__				(   lowerCAmelCase_     ):



     '''simple docstring'''

     __snake_case					:			str				=    "pegasus"
     __snake_case					:			List[Any]				=    ["past_key_values"]
     __snake_case					:			Any				=    {"num_attention_heads": "encoder_attention_heads", "hidden_size": "d_model"}






     def __init__(							self		:					Dict		,lowerCamelCase__		:					List[str]=50265		,lowerCamelCase__		:					int=1024		,lowerCamelCase__		:					Optional[Any]=12		,lowerCamelCase__		:					Tuple=4096		,lowerCamelCase__		:					Dict=16		,lowerCamelCase__		:					Optional[Any]=12		,lowerCamelCase__		:					str=4096		,lowerCamelCase__		:					Dict=16		,lowerCamelCase__		:					Tuple=0.0		,lowerCamelCase__		:					Dict=0.0		,lowerCamelCase__		:					str=True		,lowerCamelCase__		:					Any=True		,lowerCamelCase__		:					List[Any]="gelu"		,lowerCamelCase__		:					Tuple=1024		,lowerCamelCase__		:					Optional[int]=0.1		,lowerCamelCase__		:					Tuple=0.0		,lowerCamelCase__		:					Dict=0.0		,lowerCamelCase__		:					Optional[int]=0.02		,lowerCamelCase__		:					Optional[int]=0		,lowerCamelCase__		:					List[Any]=False		,lowerCamelCase__		:					Union[str, Any]=0		,lowerCamelCase__		:					Optional[int]=1		,lowerCamelCase__		:					Any=1		,**lowerCamelCase__		:					Dict		,)  ->	str:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE	=		vocab_size
           SCREAMING_SNAKE_CASE	=		max_position_embeddings
           SCREAMING_SNAKE_CASE	=		d_model
           SCREAMING_SNAKE_CASE	=		encoder_ffn_dim
           SCREAMING_SNAKE_CASE	=		encoder_layers
           SCREAMING_SNAKE_CASE	=		encoder_attention_heads
           SCREAMING_SNAKE_CASE	=		decoder_ffn_dim
           SCREAMING_SNAKE_CASE	=		decoder_layers
           SCREAMING_SNAKE_CASE	=		decoder_attention_heads
           SCREAMING_SNAKE_CASE	=		dropout
           SCREAMING_SNAKE_CASE	=		attention_dropout
           SCREAMING_SNAKE_CASE	=		activation_dropout
           SCREAMING_SNAKE_CASE	=		activation_function
           SCREAMING_SNAKE_CASE	=		init_std
           SCREAMING_SNAKE_CASE	=		encoder_layerdrop
           SCREAMING_SNAKE_CASE	=		decoder_layerdrop
           SCREAMING_SNAKE_CASE	=		use_cache
           SCREAMING_SNAKE_CASE	=		encoder_layers
           SCREAMING_SNAKE_CASE	=		scale_embedding  # scale factor will be sqrt(d_model) if True
           super().__init__(
               pad_token_id=lowerCamelCase__		,eos_token_id=lowerCamelCase__		,is_encoder_decoder=lowerCamelCase__		,decoder_start_token_id=lowerCamelCase__		,forced_eos_token_id=lowerCamelCase__		,**lowerCamelCase__		,)






     @property
     def        SCREAMING_SNAKE_CASE__						(							self		:					Tuple )  ->	int:




           '''simple docstring'''


           return self.encoder_attention_heads






     @property
     def        SCREAMING_SNAKE_CASE__						(							self		:					List[str] )  ->	int:




           '''simple docstring'''


           return self.d_model


