I wrote the following program in Python 2 to do Newton's method computations for my math problem set, and while it works perfectly, for reasons unbeknownst to me, when I initially load it in ipython with %run -i NewtonsMethodMultivariate.py, the Python 3 division is not imported. I know this because after I load my Python program, entering x**(3/4) gives "1". After manually importing the new division, then x**(3/4) remains x**(3/4), as expected. Why is this?
# coding: utf-8
from __future__ import division
from sympy import symbols, Matrix, zeros
x, y = symbols('x y')
X = Matrix([[x],[y]])
tol = 1e-3
def roots(h,a):
def F(s):
return h.subs({x: s[0,0], y: s[1,0]})
def D(s):
return h.jacobian(X).subs({x: s[0,0], y: s[1,0]})
if F(a) == zeros(2)[:,0]:
return a
else:
while (F(a)).norm() > tol:
a = a - ((D(a))**(-1))*F(a)
print a.evalf(10)
I would use Python 3 to avoid this issue, but my Linux distribution only ships SymPy for Python 2. Thanks to the help anyone can provide.
Also, in case anyone was wondering, I haven't yet generalized this script for nxn Jacobians, and only had to deal with 2x2 in my problem set. Additionally, I'm slicing the 2x2 zero matrix instead of using the command zeros(2,1) because SymPy 0.7.1, installed on my machine, complains that "zeros() takes exactly one argument", though the wiki suggests otherwise. Maybe this command is only for the git version.
