Howto pass a function to a function in Python?

Question

I am a beginner/intermediate in Python. I have coded a 4th-order Runge-Kutta method (RK4) into Python. It is basically solving a pendulum, but that is not the point here.

I want to improve the RK4 method in the following way: I want to be able to pass the function f directly to the RK4 function, i.e. RK4(y_0, n, h) should become RK4(f,y_0,n,h). This would have the great advantage that I could use RK4 for other f functions that describe other systems, not just this one pendulum.

I have played around with just passing simple functions to RK4, but I am doing something wrong. How do I do this in Python?

import numpy as np

def RK4(y_0, n, h):
    #4th order Runge-Kutta solver, takes as input
    #initial value y_0, the number of steps n and stepsize h
    #returns solution vector y and time vector t
    #right now function f is defined below

    t = np.linspace(0,n*h,n,endpoint = False)   #create time vector t
    y = np.zeros((n,len(y_0))) #create solution vector y
    y[0] = y_0 #assign initial value to first position in y
    for i in range(0,n-1):
        #compute Runge-Kutta weights k_1 till k_4
        k_1 = f(t[i],y[i])
        k_2 = f(t[i] + 0.5*h, y[i] + 0.5*h*k_1)
        k_3 = f(t[i] + 0.5*h, y[i] + 0.5*h*k_2)
        k_4 = f(t[i] + 0.5*h, y[i] + h*k_3)
        #compute next y        
        y[i+1] = y[i] + h / 6. * (k_1 + 2.*k_2 + 2.*k_3 + k_4)
    return t,y

def f(t,vec):
    theta=vec[0]
    omega = vec[1]
    omegaDot = -np.sin(theta) - omega + np.cos(t)
    result = np.array([omega,omegaDot])    
    return result

test = np.array([0,0.5])
t,y = RK4(test,10,0.1)

Answer 1

You can pass a function to a function in Python just as you might expect:

def call_function(f):
    f()

def my_function():
    print "OK"

call_function(my_function)  # Prints OK

Maybe you should post your failing code?

Answer 2

Python functions are objects too. You can pass them around like any other object:

>>> def foo(): print 'Hello world!'
...
>>> foo
<function foo at 0x10c4685f0>
>>> foo()
Hello world!
>>> bar = foo
>>> bar()
Hello world!

Simply pass a function as an extra parameter to your RK4 function and use that as a local variable.

Answer 3

It's very simple. Change the definition of the RK4 function like so:

def RK4(f, y_0, n, h):

Here, I have added an extra argument, the function.

Then, when you call RK4, pass the function:

t, y = RK4(f, test, 10, 0.1)

And now, of course, you can substitute different functions without having to re-write the integration code.

Functions in Python are just another kind of object. You can pass them around just as you do more prosaic objects.