





import numpy as np





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE = 1e-12							,     _SCREAMING_SNAKE_CASE = 100							,     )							-> tuple[float, np.ndarray]:




    """simple docstring"""




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

        # 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 				__lowerCAmelCase(       )							-> None:




    """simple docstring"""




    _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(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)

        # Numpy implementation.

        # Get eigenvalues and eigenvectors using built-in numpy
        # eigh (eigh used for symmetric or hermetian matrices).
        _A,			_A     =							np.linalg.eigh(_SCREAMING_SNAKE_CASE				)
        # 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(_SCREAMING_SNAKE_CASE				) - np.abs(_SCREAMING_SNAKE_CASE				)				) <= 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,
    is_vision_available,
)


lowerCamelCase		       =      {
    """configuration_blip""": [
        """BLIP_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """BlipConfig""",
        """BlipTextConfig""",
        """BlipVisionConfig""",
    ],
    """processing_blip""": ["""BlipProcessor"""],
}

try:
						if not is_vision_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCamelCase		       =      ["""BlipImageProcessor"""]


try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCamelCase		       =      [
						    """BLIP_PRETRAINED_MODEL_ARCHIVE_LIST""",
						    """BlipModel""",
						    """BlipPreTrainedModel""",
						    """BlipForConditionalGeneration""",
						    """BlipForQuestionAnswering""",
						    """BlipVisionModel""",
						    """BlipTextModel""",
						    """BlipForImageTextRetrieval""",
						]

try:
						if not is_tf_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCamelCase		       =      [
						    """TF_BLIP_PRETRAINED_MODEL_ARCHIVE_LIST""",
						    """TFBlipModel""",
						    """TFBlipPreTrainedModel""",
						    """TFBlipForConditionalGeneration""",
						    """TFBlipForQuestionAnswering""",
						    """TFBlipVisionModel""",
						    """TFBlipTextModel""",
						    """TFBlipForImageTextRetrieval""",
						]

if TYPE_CHECKING:
						from .configuration_blip import BLIP_PRETRAINED_CONFIG_ARCHIVE_MAP, BlipConfig, BlipTextConfig, BlipVisionConfig
						from .processing_blip import BlipProcessor

						try:
												if not is_vision_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .image_processing_blip import BlipImageProcessor

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_blip import (
												    BLIP_PRETRAINED_MODEL_ARCHIVE_LIST,
												    BlipForConditionalGeneration,
												    BlipForImageTextRetrieval,
												    BlipForQuestionAnswering,
												    BlipModel,
												    BlipPreTrainedModel,
												    BlipTextModel,
												    BlipVisionModel,
												)

						try:
												if not is_tf_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_tf_blip import (
												    TF_BLIP_PRETRAINED_MODEL_ARCHIVE_LIST,
												    TFBlipForConditionalGeneration,
												    TFBlipForImageTextRetrieval,
												    TFBlipForQuestionAnswering,
												    TFBlipModel,
												    TFBlipPreTrainedModel,
												    TFBlipTextModel,
												    TFBlipVisionModel,
												)

else:
						import sys

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


