python_trans_of_julia_dual.py

# modified from the python code in
# https://pizzaseminar.speicherleck.de/automatic-differentiation/notes.pdf


class Dual(object):
    def __init__(self, x, a=0):
        self.x = x
        self.a = a

    def __add__(self, other):
        return Dual(self.x + other.x, self.a + other.a)

    def __mul__(self, other):
        return Dual(self.x * other.x,
                    other.x * self.a + self.x * other.a)

    def __truediv__(self, other):
        return Dual(self.x / other.x,
                    (other.x * self.a - self.x * other.a)/other.x**2)


def babylonia_raw(x, N=10):
    t = (1+x)/2
    for i in range(1, N):
        t = (t+x/t)/2
    return t


def babylonia(x, N=10):
    """python do not have enough type infor to auto convert the type as 
    julia, so have to convert manually"""
    t = (Dual(1)+x)/Dual(2)
    for i in range(1, N):
        t = (t+x/t)/Dual(2)
    return t


if __name__ == "__main__":
    x = babylonia(Dual(49, 1), 10).x
    a = babylonia(Dual(49, 1), 10).a
    print(x, a)