






import numpy as np





def        _snake_case   (_snake_case				:       np.ndarray      ,    _snake_case				:       np.ndarray      ,    _snake_case				:       float = 1E-12      ,    _snake_case				:       int = 100      ,    )					->	tuple[float, np.ndarray]:
   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)
   _lowercase              =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.

   _lowercase              =False
   _lowercase              =0
   _lowercase              =0
   _lowercase              =1E12

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

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

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

      _lowercase              =lambda_

   if is_complex:
      _lowercase              =np.real(lambda_)

   return lambda_, vector





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

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

      # Our implementation.
      _lowercase       ,       _lowercase              =power_iteration(_snake_case      ,    _snake_case)

      # Numpy implementation.

      # Get eigenvalues and eigenvectors using built-in numpy
      # eigh (eigh used for symmetric or hermetian matrices).
      _lowercase       ,       _lowercase              =np.linalg.eigh(_snake_case)
      # Last eigenvalue is the maximum one.
      _lowercase              =eigen_values[-1]
      # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
      _lowercase              =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   =  {
    "uw-madison/mra-base-512-4": "https://huggingface.co/uw-madison/mra-base-512-4/resolve/main/config.json",
}






class 					SCREAMING_SNAKE_CASE_  (       _a ):
       """simple docstring"""


       __lowerCAmelCase    :		str					='''mra'''





       def __init__(				self	:Any,      snake_case	:List[str]=5_0265,      snake_case	:List[Any]=768,      snake_case	:Optional[Any]=12,      snake_case	:Optional[Any]=12,      snake_case	:str=3072,      snake_case	:Tuple="gelu",      snake_case	:Optional[int]=0.1,      snake_case	:int=0.1,      snake_case	:Any=512,      snake_case	:Union[str, Any]=1,      snake_case	:Union[str, Any]=0.0_2,      snake_case	:List[Any]=1e-5,      snake_case	:Optional[int]="absolute",      snake_case	:Optional[int]=4,      snake_case	:str="full",      snake_case	:Optional[int]=0,      snake_case	:List[Any]=0,      snake_case	:int=1,      snake_case	:List[Any]=0,      snake_case	:Dict=2,      **snake_case	:Dict,      ):



          """simple docstring"""

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

          _lowercase              =vocab_size
          _lowercase              =max_position_embeddings
          _lowercase              =hidden_size
          _lowercase              =num_hidden_layers
          _lowercase              =num_attention_heads
          _lowercase              =intermediate_size
          _lowercase              =hidden_act
          _lowercase              =hidden_dropout_prob
          _lowercase              =attention_probs_dropout_prob
          _lowercase              =initializer_range
          _lowercase              =type_vocab_size
          _lowercase              =layer_norm_eps
          _lowercase              =position_embedding_type
          _lowercase              =block_per_row
          _lowercase              =approx_mode
          _lowercase              =initial_prior_first_n_blocks
          _lowercase              =initial_prior_diagonal_n_blocks


