import numpy as np






def 							__UpperCAmelCase     (							UpperCAmelCase,		UpperCAmelCase,		UpperCAmelCase = 1e-12,		UpperCAmelCase = 100,		)->							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							)
			lowercase       		=		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.

			lowercase       		=		False
			lowercase       		=		0
			lowercase       		=		0
			lowercase       		=		1e12

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

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

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

						lowercase       		=		lambda_

			if is_complex:
						lowercase       		=		np.real(lambda_							)

			return lambda_, vector






def 							__UpperCAmelCase     (							)->							None:



			"""simple docstring"""







			lowercase       		=		np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]							)
			lowercase       		=		np.array([41, 4, 20]							)
			lowercase       		=		real_input_matrix.astype(np.complexaaa							)
			lowercase       		=		np.triu(1j * complex_input_matrix,		1							)
			complex_input_matrix += imag_matrix
			complex_input_matrix += -1 * imag_matrix.T
			lowercase       		=		np.array([41, 4, 20]							).astype(np.complexaaa							)

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

						# Our implementation.
						lowercase		,lowercase       		=		power_iteration(__lowercase,		__lowercase							)

						# Numpy implementation.

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













import warnings

from ...utils import logging
from .image_processing_deit import DeiTImageProcessor


__a   :							Any						= logging.get_logger(__name__)


class    __lowercase   (						lowercase_	):







     '''simple docstring'''




     def __init__(					self							:      Union[str, Any]			,						*UpperCamelCase_							:      Tuple			,						**UpperCamelCase_							:      Tuple					):


         """simple docstring"""



         warnings.warn(
             """The class DeiTFeatureExtractor is deprecated and will be removed in version 5 of Transformers. Please"""
             """ use DeiTImageProcessor instead."""			,						UpperCamelCase_			,						)
         super().__init__(*UpperCamelCase_			,						**UpperCamelCase_					)




