


"""simple docstring"""
from math import cos, sin






def 						lowercase				(	_snake_case		: float	)	->list[list[float]]:
	"""simple docstring"""





	__snake_case      :		Optional[Any]         =							float(_snake_case	)
	return [[scaling_factor * int(x == y	) for x in range(2	)] for y in range(2	)]






def 						lowercase				(	_snake_case		: float	)	->list[list[float]]:
	"""simple docstring"""





	__snake_case      ,				__snake_case      :		Union[str, Any]         =							cos(_snake_case	), sin(_snake_case	)
	return [[c, -s], [s, c]]






def 						lowercase				(	_snake_case		: float	)	->list[list[float]]:
	"""simple docstring"""





	__snake_case      ,				__snake_case      :		str         =							cos(_snake_case	), sin(_snake_case	)
	__snake_case      :		int         =							c * s
	return [[c * c, cs], [cs, s * s]]






def 						lowercase				(	_snake_case		: float	)	->list[list[float]]:
	"""simple docstring"""





	__snake_case      ,				__snake_case      :		Union[str, Any]         =							cos(_snake_case	), sin(_snake_case	)
	__snake_case      :		Optional[int]         =							c * s
	return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(F'    {scaling(5) = }')
print(F'  {rotation(45) = }')
print(F'{projection(45) = }')

print(F'{reflection(45) = }')








def      a__	(						UpperCAmelCase				:     list     )    ->		list:
  UpperCAmelCase			:				Tuple										=					len(UpperCAmelCase     )

  # Set the gap value to be decreased by a factor of 1.3
  # after each iteration
  UpperCAmelCase			:				Optional[Any]										=					1.3

  # Continue sorting until the gap is 1
  while gap > 1:
    # Decrease the gap value
    UpperCAmelCase			:				int										=					int(gap / shrink     )

    # Sort the elements using insertion sort
    for i in range(UpperCAmelCase							,					len(UpperCAmelCase     )     ):
      UpperCAmelCase			:				Union[str, Any]										=					collection[i]
      UpperCAmelCase			:				List[Any]										=					i
      while j >= gap and collection[j - gap] > temp:
        UpperCAmelCase			:				int										=					collection[j - gap]
        j -= gap
      UpperCAmelCase			:				List[Any]										=					temp

  return collection


if __name__ == "__main__":
     import doctest

     doctest.testmod()





