forward_mode.py

import math

def type_checker(f):
	def inner(self, other):
		return f(self, other) if isinstance(other, Dual) else f(self, Dual(other, 0))
	return inner


class Dual:
	def __init__(self, u, du=1):
		self.u = u
		self.du = du

	def __str__(self):
		return f"({self.u}, {self.du})"

	def __pos__(self):
		return self

	def __neg__(self):
		return Dual(-self.u, -self.du)

	# @type_checker
	def __add__(self, other):
		return Dual(self.u+other.u, self.du+other.du)

	# @type_checker
	def __sub__(self, other): 
		return self+(-other)

	# @type_checker
	def __mul__(self, other):
		return Dual(self.u*other.u, self.u*other.du+self.du*other.u)

	# @type_checker
	def __truediv__(self, other):
		return Dual(self.u/other.u, (other.u*self.du - self.u*other.du)/(other.u**2))

	def __pow__(self, n):
		return Dual(self.u**n, n*self.u**(n-1)*self.du)

def dual_sin(self):
	if not isinstance(self, Dual):
		return math.sin(self)
	return Dual(math.sin(self.u), math.cos(self.u)*self.du)

def dual_cos(self):
	if not isinstance(self, Dual):
		return math.cos(self)
	return Dual(math.cos(self.u), math.sin(self.u)*self.du)