'''simple docstring'''

from typing import TYPE_CHECKING

from ...utils import _LazyModule


UpperCamelCase__  :						List[str]					=      {'tokenization_byt5': ['ByT5Tokenizer']}


if TYPE_CHECKING:
  from .tokenization_byta import ByTaTokenizer
else:
  import sys

  UpperCamelCase__  :						List[str]					=      _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)





'''simple docstring'''

import numpy as np







def __UpperCamelCase( _A       :					np.ndarray	,      _A       :					np.ndarray	,      _A       :					float = 1e-12	,      _A       :					int = 1_00	,      ):
   '''simple docstring'''
   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     )
   UpperCAmelCase__				:					int 					=	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.

   UpperCAmelCase__				:					Any 					=	False
   UpperCAmelCase__				:					str 					=	0
   UpperCAmelCase__				:					Optional[int] 					=	0
   UpperCAmelCase__				:					Optional[int] 					=	1e12

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

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

      if error <= error_tol or iterations >= max_iterations:
         UpperCAmelCase__				:					Optional[Any] 					=	True

      UpperCAmelCase__				:					Optional[int] 					=	lambda_

   if is_complex:
      UpperCAmelCase__				:					Tuple 					=	np.real(lambda_     )

   return lambda_, vector







def __UpperCamelCase( ):
   '''simple docstring'''
   UpperCAmelCase__				:					Optional[int] 					=	np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]     )
   UpperCAmelCase__				:					int 					=	np.array([41, 4, 20]     )
   UpperCAmelCase__				:					str 					=	real_input_matrix.astype(np.complexaaa     )
   UpperCAmelCase__				:					Union[str, Any] 					=	np.triu(1J * complex_input_matrix	,      1     )
   complex_input_matrix += imag_matrix
   complex_input_matrix += -1 * imag_matrix.T
   UpperCAmelCase__				:					Tuple 					=	np.array([41, 4, 20]     ).astype(np.complexaaa     )

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

      # Our implementation.
      UpperCAmelCase__					,   UpperCAmelCase__				:					str 					=	power_iteration(_A	,      _A     )

      # Numpy implementation.

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




