




"""simple docstring"""


from typing import Any

import numpy as np


def 					UpperCAmelCase__       (snake_case__							:					np.ndarray    ):
  """simple docstring"""

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


def 					UpperCAmelCase__       (snake_case__							:					np.ndarray		,   snake_case__							:					np.ndarray    ):
  """simple docstring"""

  _snake_case							:		Optional[int]								=  v.conjugate().T
  _snake_case							:		List[Any]								=  v_star.dot(snake_case__    )
  assert isinstance(snake_case__		,   np.ndarray    )
  return (v_star_dot.dot(snake_case__    )) / (v_star.dot(snake_case__    ))


def 					UpperCAmelCase__       ():
  """simple docstring"""

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

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


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     tests()









"""simple docstring"""




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available


lowerCamelCase_     :						int						=					{}


try:
   if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   lowerCamelCase_     :						Tuple						=					['MLukeTokenizer']

if TYPE_CHECKING:
   try:
      if not is_sentencepiece_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_mluke import MLukeTokenizer


else:
   import sys

   lowerCamelCase_     :						List[str]						=					_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)