Evaluating a function at a point in SymPy

Question

I'm trying to code various optimisation methods, as a way of revising. I want to be able to use SymPy to evaluate a function with an arbitrary number of variables at a given point, where the co-ordinates of the point are stored in an array.

For example, I'd like to evaluate f(x,y) = 3*x**2 - 2*x*y + y**2 + 4*x + 3*y at the point b = [1,2] . But I'd really like a general way of doing it, that can handle a function with any number of variables and an appropriate length array as the point to be evaluated as, so sympy.evalf(f, subs = {foo}) isn't really very useful.

Answer 1

You are working with SymPy expression trees, not functions. On any expression you can do:

>>> vars = sorted(expression.free_symbols)
>>> evaluated = expression.subs(*zip(vars, your_values))

Answer 2

I would also expect this to be easier to do, but here's a good workaround:

If you know the symbol names ( 'x' , 'y' , eg), you can create a dict on the fly using zip :

fvars = sympy.symbols('x, y') #these probably already exist, use: fvars = [x,y]

b = [1,2]
sympy.evalf(f, subs = dict(zip(fvars,b)))

Answer 3

lambdify is a good option to generate a Python-callable function, and you can then use numpy arrays. As an example, assuming you have your function f and the symbols x and y :

f2 = lambdify((x, y), f)
import numpy as np
xn = np.arage(0, 2, 0.1)
yn = 3
print(f2(xn, yn))