


"""simple docstring"""







from typing import Any

import numpy as np
def 					a__			(				SCREAMING_SNAKE_CASE    :    np.ndarray				):


  '''simple docstring'''







  return np.array_equal(SCREAMING_SNAKE_CASE				,      matrix.conjugate().T				)
def 					a__			(				SCREAMING_SNAKE_CASE    :    np.ndarray				,      SCREAMING_SNAKE_CASE    :    np.ndarray				):


  '''simple docstring'''







  lowerCAmelCase     :     Union[str, Any]								=							v.conjugate().T
  lowerCAmelCase     :     int								=							v_star.dot(SCREAMING_SNAKE_CASE				)
  assert isinstance(SCREAMING_SNAKE_CASE				,      np.ndarray				)
  return (v_star_dot.dot(SCREAMING_SNAKE_CASE				)) / (v_star.dot(SCREAMING_SNAKE_CASE				))
def 					a__			(				):


  '''simple docstring'''







  lowerCAmelCase     :     Dict								=							np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]				)
  lowerCAmelCase     :     Any								=							np.array([[1], [2], [3]]				)
  assert is_hermitian(SCREAMING_SNAKE_CASE				), f"""{a} is not hermitian."""
  print(rayleigh_quotient(SCREAMING_SNAKE_CASE				,      SCREAMING_SNAKE_CASE				)				)

  lowerCAmelCase     :     Dict								=							np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]				)
  assert is_hermitian(SCREAMING_SNAKE_CASE				), f"""{a} is not hermitian."""
  assert rayleigh_quotient(SCREAMING_SNAKE_CASE				,      SCREAMING_SNAKE_CASE				) == float(3				)


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     tests()









"""simple docstring"""







lowerCAmelCase__      				=   [
    '''Audio''',
    '''Array2D''',
    '''Array3D''',
    '''Array4D''',
    '''Array5D''',
    '''ClassLabel''',
    '''Features''',
    '''Sequence''',
    '''Value''',
    '''Image''',
    '''Translation''',
    '''TranslationVariableLanguages''',
]
from .audio import Audio
from .features import ArrayaD, ArrayaD, ArrayaD, ArrayaD, ClassLabel, Features, Sequence, Value
from .image import Image
from .translation import Translation, TranslationVariableLanguages





