



"""simple docstring"""
import numpy as np





def  lowerCamelCase_						(UpperCamelCase__		:		np.ndarray     ,       UpperCamelCase__		:		np.ndarray     ,       UpperCamelCase__		:		float = 1E-1_2     ,       UpperCamelCase__		:		int = 100     ,       ):
    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__							)
    _UpperCAmelCase							:  Tuple											=    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.

    _UpperCAmelCase							:  Union[str, Any]											=    False
    _UpperCAmelCase							:  int											=    0
    _UpperCAmelCase							:  Dict											=    0
    _UpperCAmelCase							:  Optional[Any]											=    1E1_2

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

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

        if error <= error_tol or iterations >= max_iterations:
            _UpperCAmelCase							:  Tuple											=    True

        _UpperCAmelCase							:  Optional[int]											=    lambda_

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

    return lambda_, vector





def  lowerCamelCase_						():
    _UpperCAmelCase							:  int											=    np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]							)
    _UpperCAmelCase							:  List[str]											=    np.array([41, 4, 20]							)
    _UpperCAmelCase							:  int											=    real_input_matrix.astype(np.complexaaa							)
    _UpperCAmelCase							:  Optional[Any]											=    np.triu(1J * complex_input_matrix     ,       1							)
    complex_input_matrix += imag_matrix
    complex_input_matrix += -1 * imag_matrix.T
    _UpperCAmelCase							:  str											=    np.array([41, 4, 20]							).astype(np.complexaaa							)

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

        # Our implementation.
        _UpperCAmelCase							,				_UpperCAmelCase							:  str											=    power_iteration(UpperCamelCase__     ,       UpperCamelCase__							)

        # Numpy implementation.

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







"""simple docstring"""
from typing import TYPE_CHECKING

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


_lowerCAmelCase    :str     =					{
    'configuration_squeezebert': [
        'SQUEEZEBERT_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'SqueezeBertConfig',
        'SqueezeBertOnnxConfig',
    ],
    'tokenization_squeezebert': ['SqueezeBertTokenizer'],
}

try:
  if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _lowerCAmelCase    :Optional[int]     =					['SqueezeBertTokenizerFast']

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _lowerCAmelCase    :str     =					[
      'SQUEEZEBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
      'SqueezeBertForMaskedLM',
      'SqueezeBertForMultipleChoice',
      'SqueezeBertForQuestionAnswering',
      'SqueezeBertForSequenceClassification',
      'SqueezeBertForTokenClassification',
      'SqueezeBertModel',
      'SqueezeBertModule',
      'SqueezeBertPreTrainedModel',
  ]


if TYPE_CHECKING:
  from .configuration_squeezebert import (
      SQUEEZEBERT_PRETRAINED_CONFIG_ARCHIVE_MAP,
      SqueezeBertConfig,
      SqueezeBertOnnxConfig,
  )
  from .tokenization_squeezebert import SqueezeBertTokenizer

  try:
    if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_squeezebert_fast import SqueezeBertTokenizerFast

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_squeezebert import (
        SQUEEZEBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
        SqueezeBertForMaskedLM,
        SqueezeBertForMultipleChoice,
        SqueezeBertForQuestionAnswering,
        SqueezeBertForSequenceClassification,
        SqueezeBertForTokenClassification,
        SqueezeBertModel,
        SqueezeBertModule,
        SqueezeBertPreTrainedModel,
    )

else:
  import sys

  _lowerCAmelCase    :Optional[Any]     =					_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)


