




from typing import Any

import numpy as np







def 			lowerCamelCase_		(       UpperCamelCase__				:      np.ndarray      )     ->       bool:





				"""simple docstring"""


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







def 			lowerCamelCase_		(       UpperCamelCase__				:      np.ndarray ,     UpperCamelCase__				:      np.ndarray      )     ->       Any:





				"""simple docstring"""


				__lowerCamelCase		       =    v.conjugate().T
				__lowerCamelCase		       =    v_star.dot(UpperCamelCase__      )
				assert isinstance(UpperCamelCase__ ,     np.ndarray      )
				return (v_star_dot.dot(UpperCamelCase__      )) / (v_star.dot(UpperCamelCase__      ))







def 			lowerCamelCase_		(       )     ->       None:





				"""simple docstring"""


				__lowerCamelCase		       =    np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]      )
				__lowerCamelCase		       =    np.array([[1], [2], [3]]      )
				assert is_hermitian(UpperCamelCase__      ), F"""{a} is not hermitian."""
				print(rayleigh_quotient(UpperCamelCase__ ,     UpperCamelCase__      )      )

				__lowerCamelCase		       =    np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]      )
				assert is_hermitian(UpperCamelCase__      ), F"""{a} is not hermitian."""
				assert rayleigh_quotient(UpperCamelCase__ ,     UpperCamelCase__      ) == float(3      )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					tests()








from ..utils import DummyObject, requires_backends







class     __lowerCAmelCase (       metaclass=__magic_name__ ):

			"""simple docstring"""







			snake_case_   		=       ['''onnx''']


			def __init__(      self			,						*lowerCamelCase__			,						**lowerCamelCase__							)    ->      Optional[Any]:



							'''simple docstring'''
							requires_backends(self			,						['onnx']							)


			@classmethod
			def       lowercase_    (      cls			,						*lowerCamelCase__			,						**lowerCamelCase__							)    ->      Dict:



							'''simple docstring'''
							requires_backends(cls			,						['onnx']							)






			@classmethod
			def       lowercase_    (      cls			,						*lowerCamelCase__			,						**lowerCamelCase__							)    ->      List[str]:



							'''simple docstring'''
							requires_backends(cls			,						['onnx']							)


