


"""simple docstring"""







from typing import Any

import numpy as np
def _A						(						lowercase		):







    """simple docstring"""
    return np.array_equal(UpperCamelCase__       ,    matrix.conjugate().T		)
def _A						(						lowercase       ,    lowercase		):







    """simple docstring"""
    a 		=v.conjugate().T
    a 		=v_star.dot(UpperCamelCase__		)
    assert isinstance(UpperCamelCase__       ,    np.ndarray		)
    return (v_star_dot.dot(UpperCamelCase__		)) / (v_star.dot(UpperCamelCase__		))
def _A						(						):







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

    a 		=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']							)


