


'''simple docstring'''
from typing import Any

import numpy as np


def 			a      (			__a   )  ->	bool:



					'''simple docstring'''






					return np.array_equal(__a ,					matrix.conjugate().T   )


def 			a      (			__a ,					__a   )  ->	Any:



					'''simple docstring'''






					UpperCamelCase__   :Dict												= v.conjugate().T
					UpperCamelCase__   :Optional[Any]												= v_star.dot(__a   )
					assert isinstance(__a ,					np.ndarray   )
					return (v_star_dot.dot(__a   )) / (v_star.dot(__a   ))


def 			a      (			)  ->	None:



					'''simple docstring'''






					UpperCamelCase__   :Any												= np.array([[2, 2 + 1J, 4], [2 - 1J, 3, 1J], [4, -1J, 1]]   )
					UpperCamelCase__   :Tuple												= np.array([[1], [2], [3]]   )
					assert is_hermitian(__a   ), f'''{a} is not hermitian.'''
					print(rayleigh_quotient(__a ,					__a   )   )

					UpperCamelCase__   :Any												= np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]   )
					assert is_hermitian(__a   ), f'''{a} is not hermitian.'''
					assert rayleigh_quotient(__a ,					__a   ) == float(3   )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		tests()



'''simple docstring'''
__snake_case							      =     65521


def 			a      (			__a   )  ->	int:



					'''simple docstring'''






					UpperCamelCase__   :Tuple												= 1
					UpperCamelCase__   :Any												= 0
					for plain_chr in plain_text:
										UpperCamelCase__   :List[str]												= (a + ord(__a   )) % MOD_ADLER
										UpperCamelCase__   :Tuple												= (b + a) % MOD_ADLER
					return (b << 16) | a