

UpperCAmelCase__ :     str				    =    """Tobias Carryer"""

from time import time







class        a__       :







  """simple docstring"""




  def __init__(			self    : str				,				UpperCAmelCase__    : int				,				UpperCAmelCase__    : Any				,				UpperCAmelCase__    : List[Any]				,				UpperCAmelCase__    : int=int(time()		)		)					->Any:  # noqa: B008
        """simple docstring"""







        SCREAMING_SNAKE_CASE :      Optional[int]       =   multiplier
        SCREAMING_SNAKE_CASE :      Optional[Any]       =   increment
        SCREAMING_SNAKE_CASE :      Any       =   modulo
        SCREAMING_SNAKE_CASE :      List[str]       =   seed




  def  _lowercase      (			self    : Optional[Any]		)					->Optional[int]:
        """simple docstring"""







        SCREAMING_SNAKE_CASE :      str       =   (self.multiplier * self.seed + self.increment) % self.modulo
        return self.seed


if __name__ == "__main__":
  # Show the LCG in action.
  UpperCAmelCase__ :     List[Any]				    =    LinearCongruentialGenerator(1_664_525, 1_013_904_223, 2 << 31)
  while True:
    print(lcg.next_number())







from typing import Any

import numpy as np






def 					__lowercase      (     _A			)     ->						bool:
      return np.array_equal(_A						,    matrix.conjugate().T			)






def 					__lowercase      (     _A						,    _A			)     ->						Any:
      SCREAMING_SNAKE_CASE :      Optional[int]       =   v.conjugate().T
      SCREAMING_SNAKE_CASE :      List[Any]       =   v_star.dot(_A			)
      assert isinstance(_A						,    np.ndarray			)
      return (v_star_dot.dot(_A			)) / (v_star.dot(_A			))






def 					__lowercase      (     )     ->						None:
      SCREAMING_SNAKE_CASE :      Any       =   np.array([[2, 2 + 1J, 4], [2 - 1J, 3, 1J], [4, -1J, 1]]			)
      SCREAMING_SNAKE_CASE :      Optional[int]       =   np.array([[1], [2], [3]]			)
      assert is_hermitian(_A			), F"{a} is not hermitian."
      print(rayleigh_quotient(_A						,    _A			)			)

      SCREAMING_SNAKE_CASE :      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()




