






import numpy as np
def 						_a    (      a :np.ndarray	,							a :np.ndarray	,							a :float = 1e-12	,							a :int = 100	,							)							->			tuple[float, np.ndarray]:
 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 )
 a		  =      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.

 a		  =      False
 a		  =      0
 a		  =      0
 a		  =      1e12

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

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

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

  a		  =      lambda_

 if is_complex:
  a		  =      np.real(lambda_ )

 return lambda_, vector
def 						_a    (      )							->			None:
 a		  =      np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]] )
 a		  =      np.array([41, 4, 20] )
 a		  =      real_input_matrix.astype(np.complexaaa )
 a		  =      np.triu(1j * complex_input_matrix	,							1 )
 complex_input_matrix += imag_matrix
 complex_input_matrix += -1 * imag_matrix.T
 a		  =      np.array([41, 4, 20] ).astype(np.complexaaa )

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

  # Our implementation.
  a  ,     a		  =      power_iteration(a	,							a )

  # Numpy implementation.

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










from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


UpperCAmelCase__				   =		{
    "configuration_groupvit": [
        "GROUPVIT_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "GroupViTConfig",
        "GroupViTOnnxConfig",
        "GroupViTTextConfig",
        "GroupViTVisionConfig",
    ],
}

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     UpperCAmelCase__				   =		[
         "GROUPVIT_PRETRAINED_MODEL_ARCHIVE_LIST",
         "GroupViTModel",
         "GroupViTPreTrainedModel",
         "GroupViTTextModel",
         "GroupViTVisionModel",
     ]

try:
     if not is_tf_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     UpperCAmelCase__				   =		[
         "TF_GROUPVIT_PRETRAINED_MODEL_ARCHIVE_LIST",
         "TFGroupViTModel",
         "TFGroupViTPreTrainedModel",
         "TFGroupViTTextModel",
         "TFGroupViTVisionModel",
     ]

if TYPE_CHECKING:
     from .configuration_groupvit import (
         GROUPVIT_PRETRAINED_CONFIG_ARCHIVE_MAP,
         GroupViTConfig,
         GroupViTOnnxConfig,
         GroupViTTextConfig,
         GroupViTVisionConfig,
     )

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_groupvit import (
              GROUPVIT_PRETRAINED_MODEL_ARCHIVE_LIST,
              GroupViTModel,
              GroupViTPreTrainedModel,
              GroupViTTextModel,
              GroupViTVisionModel,
          )

     try:
          if not is_tf_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_tf_groupvit import (
              TF_GROUPVIT_PRETRAINED_MODEL_ARCHIVE_LIST,
              TFGroupViTModel,
              TFGroupViTPreTrainedModel,
              TFGroupViTTextModel,
              TFGroupViTVisionModel,
          )

else:
     import sys

     UpperCAmelCase__				   =		_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)


