



'''simple docstring'''

import numpy as np







def 						__UpperCamelCase				(							_lowercase,				_lowercase,				_lowercase = 1E-1_2,				_lowercase = 100,				) ->			tuple[float, np.ndarray]:
	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					:       Optional[int]       =		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					:       Optional[Any]       =		False
	_lowercase					:       Any       =		0
	_lowercase					:       List[Any]       =		0
	_lowercase					:       List[Any]       =		1E1_2

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

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

		if error <= error_tol or iterations >= max_iterations:
			_lowercase					:       Optional[int]       =		True

		_lowercase					:       str       =		lambda_

	if is_complex:
		_lowercase					:       Any       =		np.real(lambda_					)

	return lambda_, vector







def 						__UpperCamelCase				(							) ->			None:
	_lowercase					:       Optional[int]       =		np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]					)
	_lowercase					:       Optional[int]       =		np.array([41, 4, 20]					)
	_lowercase					:       Any       =		real_input_matrix.astype(np.complexaaa					)
	_lowercase					:       str       =		np.triu(1j * complex_input_matrix,				1					)
	complex_input_matrix += imag_matrix
	complex_input_matrix += -1 * imag_matrix.T
	_lowercase					:       List[Any]       =		np.array([41, 4, 20]					).astype(np.complexaaa					)

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

		# Our implementation.
		_lowercase  ,    _lowercase					:       Union[str, Any]       =		power_iteration(_lowercase,				_lowercase					)

		# Numpy implementation.

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


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		test_power_iteration()





'''simple docstring'''

import argparse
from collections import defaultdict







def 						__UpperCamelCase				(							_lowercase,				_lowercase,				_lowercase,				_lowercase,				_lowercase					) ->			int:
	_lowercase					:       Optional[int]       =		f'''{file}_{class_name}_{test_name}'''
	done_test[_id] += 1

	with open(_lowercase,				'r'					) as f:
		_lowercase					:       Optional[int]       =		f.readlines()

	_lowercase					:       Dict       =		f'''class {class_name}('''
	_lowercase					:       List[Any]       =		f'''{4 * " "}def {test_name}('''
	_lowercase					:       List[str]       =		f'''{8 * " "}{correct_line.split()[0]}'''
	_lowercase					:       List[str]       =		f'''{16 * " "}{correct_line.split()[0]}'''
	_lowercase					:       Dict       =		False
	_lowercase					:       str       =		False
	_lowercase					:       List[Any]       =		False
	_lowercase					:       Union[str, Any]       =		False
	_lowercase					:       Any       =		0
	_lowercase					:       Tuple       =		0

	_lowercase					:       Optional[int]       =		[]
	for line in lines:
		if line.startswith(_lowercase					):
			_lowercase					:       int       =		True
		elif in_class and line.startswith(_lowercase					):
			_lowercase					:       List[Any]       =		True
		elif in_class and in_func and (line.startswith(_lowercase					) or line.startswith(_lowercase					)):
			_lowercase					:       str       =		len(line.split(correct_line.split()[0]					)[0]					)
			count += 1

			if count == done_test[_id]:
				_lowercase					:       List[Any]       =		True

		if in_class and in_func and in_line:
			if ")" not in line:
				continue
			else:
				_lowercase					:       Any       =		True

		if in_class and in_func and in_line and insert_line:
			new_lines.append(f'''{spaces * " "}{correct_line}'''					)
			_lowercase					:       Any       =		False
		else:
			new_lines.append(_lowercase					)

	with open(_lowercase,				'w'					) as f:
		for line in new_lines:
			f.write(_lowercase					)







def 						__UpperCamelCase				(							_lowercase,				_lowercase=None					) ->			Optional[Any]:
	if fail is not None:
		with open(_lowercase,				'r'					) as f:
			_lowercase					:       Any       =		{l.strip() for l in f.readlines()}
	else:
		_lowercase					:       str       =		None

	with open(_lowercase,				'r'					) as f:
		_lowercase					:       str       =		f.readlines()

	_lowercase					:       Union[str, Any]       =		defaultdict(_lowercase					)
	for line in correct_lines:
		_lowercase  ,    _lowercase  ,    _lowercase  ,    _lowercase					:       Union[str, Any]       =		line.split(';'					)
		if test_failures is None or "::".join([file, class_name, test_name]					) in test_failures:
			overwrite_file(_lowercase,				_lowercase,				_lowercase,				_lowercase,				_lowercase					)


if __name__ == "__main__":
		_A				:    str     						=argparse.ArgumentParser()
		parser.add_argument('''--correct_filename''', help='''filename of tests with expected result''')
		parser.add_argument('''--fail_filename''', help='''filename of test failures''', type=str, default=None)
		_A				:    Union[str, Any]     						=parser.parse_args()

		main(args.correct_filename, args.fail_filename)
