




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

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    snake_case_	:      List[str]            =  float(_lowerCamelCase    )
    return [[scaling_factor * int(x == y    ) for x in range(2    )] for y in range(2    )]

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    snake_case_     ,	snake_case_	:      Tuple            =  cos(_lowerCamelCase    ), sin(_lowerCamelCase    )
    return [[c, -s], [s, c]]

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    snake_case_     ,	snake_case_	:      Dict            =  cos(_lowerCamelCase    ), sin(_lowerCamelCase    )
    snake_case_	:      str            =  c * s
    return [[c * c, cs], [cs, s * s]]

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    snake_case_     ,	snake_case_	:      Dict            =  cos(_lowerCamelCase    ), sin(_lowerCamelCase    )
    snake_case_	:      Dict            =  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) = }""")






'''simple docstring'''
def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    snake_case_	:      Optional[int]            =  len(__SCREAMING_SNAKE_CASE    )

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

    # Continue sorting until the gap is 1
    while gap > 1:
        # Decrease the gap value
        snake_case_	:      Optional[Any]            =  int(gap / shrink    )

        # Sort the elements using insertion sort
        for i in range(__SCREAMING_SNAKE_CASE,						len(__SCREAMING_SNAKE_CASE    )    ):
            snake_case_	:      Any            =  collection[i]
            snake_case_	:      int            =  i
            while j >= gap and collection[j - gap] > temp:
                snake_case_	:      Dict            =  collection[j - gap]
                j -= gap
            snake_case_	:      Optional[int]            =  temp

    return collection


if __name__ == "__main__":
  import doctest

  doctest.testmod()




