


import numpy as np



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase = 1E-12  ,  __UpperCamelCase = 1_0_0  ,  ):
     assert np.shape(__UpperCamelCase )[0] == np.shape(__UpperCamelCase )[1]
     # Ensure proper dimensionality.
     assert np.shape(__UpperCamelCase )[0] == np.shape(__UpperCamelCase )[0]
     # Ensure inputs are either both complex or both real
     assert np.iscomplexobj(__UpperCamelCase ) == np.iscomplexobj(__UpperCamelCase )
     a_    :     Union[str, Any]										=    np.iscomplexobj(__UpperCamelCase )
     if is_complex:
          # Ensure complex input_matrix is Hermitian
          assert np.array_equal(__UpperCamelCase  ,  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.

     a_    :     Optional[Any]										=    False
     a_    :     Optional[Any]										=    0
     a_    :     Tuple										=    0
     a_    :     int										=    1E12

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

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

          if error <= error_tol or iterations >= max_iterations:
               a_    :     Optional[int]										=    True

          a_    :     List[str]										=    lambda_

     if is_complex:
          a_    :     Union[str, Any]										=    np.real(lambda_ )

     return lambda_, vector



def  _a			(						):
     a_    :     str										=    np.array([[4_1, 4, 2_0], [4, 2_6, 3_0], [2_0, 3_0, 5_0]] )
     a_    :     Union[str, Any]										=    np.array([4_1, 4, 2_0] )
     a_    :     List[str]										=    real_input_matrix.astype(np.complexaaa )
     a_    :     Optional[Any]										=    np.triu(1j * complex_input_matrix  ,  1 )
     complex_input_matrix += imag_matrix
     complex_input_matrix += -1 * imag_matrix.T
     a_    :     Dict										=    np.array([4_1, 4, 2_0] ).astype(np.complexaaa )

     for problem_type in ["real", "complex"]:
          if problem_type == "real":
               a_    :     str										=    real_input_matrix
               a_    :     int										=    real_vector
          elif problem_type == "complex":
               a_    :     List[Any]										=    complex_input_matrix
               a_    :     List[str]										=    complex_vector

          # Our implementation.
          a_			,			a_    :     Tuple										=    power_iteration(__UpperCamelCase  ,  __UpperCamelCase )

          # Numpy implementation.

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


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       test_power_iteration()







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__lowerCamelCase        =     {
    '''configuration_pegasus_x''': ['''PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''PegasusXConfig'''],
}

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       __lowerCamelCase        =     [
           '''PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST''',
           '''PegasusXForConditionalGeneration''',
           '''PegasusXModel''',
           '''PegasusXPreTrainedModel''',
       ]


if TYPE_CHECKING:
       from .configuration_pegasus_x import PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP, PegasusXConfig

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_pegasus_x import (
                  PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST,
                  PegasusXForConditionalGeneration,
                  PegasusXModel,
                  PegasusXPreTrainedModel,
              )


else:
       import sys

       __lowerCamelCase        =     _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)



