






import numpy as np



def       _SCREAMING_SNAKE_CASE    (			__lowercase :      np.ndarray      ,					__lowercase :      np.ndarray      ,					__lowercase :      float = 1E-12      ,					__lowercase :      int = 1_0_0      ,					)    ->   tuple[float, np.ndarray]:





    """simple docstring"""

    assert np.shape(__lowercase     )[0] == np.shape(__lowercase     )[1]
    # Ensure proper dimensionality.
    assert np.shape(__lowercase     )[0] == np.shape(__lowercase     )[0]
    # Ensure inputs are either both complex or both real
    assert np.iscomplexobj(__lowercase     ) == np.iscomplexobj(__lowercase     )
    __A       =						np.iscomplexobj(__lowercase     )
    if is_complex:
        # Ensure complex input_matrix is Hermitian
        assert np.array_equal(__lowercase      ,					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(__lowercase      ,					__lowercase     )
        # Normalize the resulting output vector.
        __A       =						w / np.linalg.norm(__lowercase     )
        # 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(__lowercase      ,					np.dot(__lowercase      ,					__lowercase     )     )

        # 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       _SCREAMING_SNAKE_CASE    (			)    ->   None:





    """simple docstring"""

    __A       =						np.array([[4_1, 4, 2_0], [4, 2_6, 3_0], [2_0, 3_0, 5_0]]     )
    __A       =						np.array([4_1, 4, 2_0]     )
    __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([4_1, 4, 2_0]     ).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(__lowercase      ,					__lowercase     )

        # Numpy implementation.

        # Get eigenvalues and eigenvectors using built-in numpy
        # eigh (eigh used for symmetric or hermetian matrices).
        __A     ,						__A       =						np.linalg.eigh(__lowercase     )
        # 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(__lowercase     ) - np.abs(__lowercase     )     ) <= 1E-6


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  test_power_iteration()












from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


__a   :							Optional[int]						= {"configuration_xlnet": ["XLNET_PRETRAINED_CONFIG_ARCHIVE_MAP", "XLNetConfig"]}

try:
  if not is_sentencepiece_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  __a   :							Tuple						= ["XLNetTokenizer"]

try:
  if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  __a   :							List[str]						= ["XLNetTokenizerFast"]

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  __a   :							Any						= [
      "XLNET_PRETRAINED_MODEL_ARCHIVE_LIST",
      "XLNetForMultipleChoice",
      "XLNetForQuestionAnswering",
      "XLNetForQuestionAnsweringSimple",
      "XLNetForSequenceClassification",
      "XLNetForTokenClassification",
      "XLNetLMHeadModel",
      "XLNetModel",
      "XLNetPreTrainedModel",
      "load_tf_weights_in_xlnet",
  ]

try:
  if not is_tf_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  __a   :							Dict						= [
      "TF_XLNET_PRETRAINED_MODEL_ARCHIVE_LIST",
      "TFXLNetForMultipleChoice",
      "TFXLNetForQuestionAnsweringSimple",
      "TFXLNetForSequenceClassification",
      "TFXLNetForTokenClassification",
      "TFXLNetLMHeadModel",
      "TFXLNetMainLayer",
      "TFXLNetModel",
      "TFXLNetPreTrainedModel",
  ]


if TYPE_CHECKING:
  from .configuration_xlnet import XLNET_PRETRAINED_CONFIG_ARCHIVE_MAP, XLNetConfig

  try:
    if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_xlnet import XLNetTokenizer

  try:
    if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_xlnet_fast import XLNetTokenizerFast

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_xlnet import (
        XLNET_PRETRAINED_MODEL_ARCHIVE_LIST,
        XLNetForMultipleChoice,
        XLNetForQuestionAnswering,
        XLNetForQuestionAnsweringSimple,
        XLNetForSequenceClassification,
        XLNetForTokenClassification,
        XLNetLMHeadModel,
        XLNetModel,
        XLNetPreTrainedModel,
        load_tf_weights_in_xlnet,
    )

  try:
    if not is_tf_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_tf_xlnet import (
        TF_XLNET_PRETRAINED_MODEL_ARCHIVE_LIST,
        TFXLNetForMultipleChoice,
        TFXLNetForQuestionAnsweringSimple,
        TFXLNetForSequenceClassification,
        TFXLNetForTokenClassification,
        TFXLNetLMHeadModel,
        TFXLNetMainLayer,
        TFXLNetModel,
        TFXLNetPreTrainedModel,
    )

else:
  import sys

  __a   :							str						= _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)




