





'''simple docstring'''


import numpy as np
def 							UpperCAmelCase_  (						__lowerCamelCase : np.ndarray     ,__lowerCamelCase : np.ndarray     ,__lowerCamelCase : float = 1e-12     ,__lowerCamelCase : int = 1_00     ,):
   assert np.shape(__lowerCamelCase			)[0] == np.shape(__lowerCamelCase			)[1]
   # Ensure proper dimensionality.
   assert np.shape(__lowerCamelCase			)[0] == np.shape(__lowerCamelCase			)[0]
   # Ensure inputs are either both complex or both real
   assert np.iscomplexobj(__lowerCamelCase			) == np.iscomplexobj(__lowerCamelCase			)
   lowercase_      :List[str]         =			np.iscomplexobj(__lowerCamelCase			)
   if is_complex:
      # Ensure complex input_matrix is Hermitian
      assert np.array_equal(__lowerCamelCase     ,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_      :Dict         =			False
   lowercase_      :Any         =			0
   lowercase_      :str         =			0
   lowercase_      :str         =			1e12

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

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

      if error <= error_tol or iterations >= max_iterations:
         lowercase_      :List[Any]         =			True

      lowercase_      :str         =			lambda_

   if is_complex:
      lowercase_      :str         =			np.real(lambda_			)

   return lambda_, vector
def 							UpperCAmelCase_  (						):
   lowercase_      :Tuple         =			np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]			)
   lowercase_      :int         =			np.array([41, 4, 20]			)
   lowercase_      :List[str]         =			real_input_matrix.astype(np.complexaaa			)
   lowercase_      :Union[str, Any]         =			np.triu(1J * complex_input_matrix     ,1			)
   complex_input_matrix += imag_matrix
   complex_input_matrix += -1 * imag_matrix.T
   lowercase_      :int         =			np.array([41, 4, 20]			).astype(np.complexaaa			)

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

      # Our implementation.
      lowercase_      ,							lowercase_      :Union[str, Any]         =			power_iteration(__lowerCamelCase     ,__lowerCamelCase			)

      # Numpy implementation.

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


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 test_power_iteration()









'''simple docstring'''


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowerCAmelCase :					Optional[int] 							={'''configuration_wavlm''': ['''WAVLM_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''WavLMConfig''']}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCAmelCase :					Optional[Any] 							=[
     '''WAVLM_PRETRAINED_MODEL_ARCHIVE_LIST''',
     '''WavLMForAudioFrameClassification''',
     '''WavLMForCTC''',
     '''WavLMForSequenceClassification''',
     '''WavLMForXVector''',
     '''WavLMModel''',
     '''WavLMPreTrainedModel''',
 ]

if TYPE_CHECKING:
 from .configuration_wavlm import WAVLM_PRETRAINED_CONFIG_ARCHIVE_MAP, WavLMConfig

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_wavlm import (
      WAVLM_PRETRAINED_MODEL_ARCHIVE_LIST,
      WavLMForAudioFrameClassification,
      WavLMForCTC,
      WavLMForSequenceClassification,
      WavLMForXVector,
      WavLMModel,
      WavLMPreTrainedModel,
  )

else:
 import sys

 lowerCAmelCase :					Union[str, Any] 							=_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)


