
from typing import List

from .keymap import KEYMAP, get_character




def 	UpperCamelCase__  (     SCREAMING_SNAKE_CASE_	:	str       )  ->     int:

						def decorator(SCREAMING_SNAKE_CASE_	:	str       ):
												_lowercase					       =					getattr(snake_case__		,   """handle_key"""		,   []       )
												handle += [key]
												setattr(snake_case__		,   """handle_key"""		,   snake_case__       )
												return func

						return decorator




def 	UpperCamelCase__  (     *SCREAMING_SNAKE_CASE_	:	Optional[Any]       )  ->     Optional[int]:

						def decorator(SCREAMING_SNAKE_CASE_	:	Dict       ):
												_lowercase					       =					getattr(snake_case__		,   """handle_key"""		,   []       )
												handle += keys
												setattr(snake_case__		,   """handle_key"""		,   snake_case__       )
												return func

						return decorator



class    a_ (			_SCREAMING_SNAKE_CASE    ):






			def __new__(      cls				,			__UpperCamelCase				,			__UpperCamelCase				,			__UpperCamelCase  ):
									_lowercase					       =					super().__new__(cls				,			lowerCAmelCase_				,			lowerCAmelCase_				,			lowerCAmelCase_  )
									if not hasattr(lowerCAmelCase_				,			"""key_handler"""  ):
															setattr(lowerCAmelCase_				,			"""key_handler"""				,			{}  )
									setattr(lowerCAmelCase_				,			"""handle_input"""				,			KeyHandler.handle_input  )

									for value in attrs.values():
															_lowercase					       =					getattr(lowerCAmelCase_				,			"""handle_key"""				,			[]  )
															for key in handled_keys:
																					_lowercase					       =					value
									return new_cls






			@staticmethod
			def    UpperCamelCase_				(      cls  ):
									_lowercase					       =					get_character()
									if char != KEYMAP["undefined"]:
															_lowercase					       =					ord(lowerCAmelCase_  )
									_lowercase					       =					cls.key_handler.get(lowerCAmelCase_  )
									if handler:
															_lowercase					       =					char
															return handler(cls  )
									else:
															return None







def 	UpperCamelCase__  (     cls	:	List[Any]       )  ->     int:
						return KeyHandler(cls.__name__		,   cls.__bases__		,   cls.__dict__.copy()       )







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






def       __UpperCamelCase						(		snake_case__ , snake_case__ , snake_case__ = 1E-12 , snake_case__ = 100 , ):
	assert np.shape(snake_case__       )[0] == np.shape(snake_case__       )[1]
	# Ensure proper dimensionality.
	assert np.shape(snake_case__       )[0] == np.shape(snake_case__       )[0]
	# Ensure inputs are either both complex or both real
	assert np.iscomplexobj(snake_case__       ) == np.iscomplexobj(snake_case__       )
	A_		:    Union[str, Any]						     = np.iscomplexobj(snake_case__       )
	if is_complex:
		# Ensure complex input_matrix is Hermitian
		assert np.array_equal(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_		:    List[str]						     = False
	A_		:    int						     = 0
	A_		:    List[Any]						     = 0
	A_		:    Tuple						     = 1E12

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

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

		if error <= error_tol or iterations >= max_iterations:
			A_		:    Optional[Any]						     = True

		A_		:    Union[str, Any]						     = lambda_

	if is_complex:
		A_		:    str						     = np.real(lambda_       )

	return lambda_, vector






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

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

		# Our implementation.
		A_     ,  A_		:    Dict						     = power_iteration(snake_case__ , snake_case__       )

		# Numpy implementation.

		# Get eigenvalues and eigenvectors using built-in numpy
		# eigh (eigh used for symmetric or hermetian matrices).
		A_     ,  A_		:    Optional[Any]						     = np.linalg.eigh(snake_case__       )
		# Last eigenvalue is the maximum one.
		A_		:    List[Any]						     = eigen_values[-1]
		# Last column in this matrix is eigenvector corresponding to largest eigenvalue.
		A_		:    Optional[Any]						     = 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(snake_case__       ) - np.abs(snake_case__       )       ) <= 1E-6


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							test_power_iteration()

