Question

I’m new to Python. I am writing a script that will numerically integrate a set of ordinary differential equations using a Runge-Kutta method. Since the Runge-Kutta method is a useful mathematical algorithm, I’ve put it in its own .py file, rk4.py.

def rk4(x,dt):
    k1=diff(x)*dt
    k2=diff(x+k1/2)*dt
    k3=diff(x+k2/2)*dt
    k4=diff(x+k3)*dt
    return x+(k1+2*k2+2*k3+k4)/6

The method needs to know the set of equations that the user is working with in order to perform the algorithm, so it calls a function diff(x) that will find give rk4 the derivatives it needs to work. Since the equations will change by use, I want diff() to be defined in the script that will run the particular problem. In this case the problem is the orbit of mercury, so I wrote mercury.py. (This isn’t how it will look in the end, but I’ve simplified it for the sake of figuring out what I’m doing.)

from rk4 import rk4
import numpy as np

def diff(x):
    return x

def mercury(u0,phi0,dphi):
    x=np.array([u0,phi0])
    dt=2
    x=rk4(x,dt)
    return x

mercury(1,1,2)

When I run mercury.py, I get an error:

  File "PATH/mercury.py", line 10, in mercury
    x=rk4(x,dt)
  File "PATH/rk4.py", line 2, in rk4
    k1=diff(x)*dt
NameError: global name 'diff' is not defined

I take it since diff() is not a global function, when rk4 runs it knows nothing about diff. Obviously rk4 is a small piece of code and I could just shove it into whatever script I’m using at the time, but I think a Runge-Kutta integrator is a fundamental mathematical tool, just like the array defined in NumPy, and so it makes sense to make it a function that is called rather one that is defined in every script that uses it (which may be many). But I also can’t go telling rk4.py to import a particular diff from a particular .py file, because that ruins the generality of rk4 that I want in the first place.

Is there a way to define diff globally within a script like mercury.py so that when rk4 is called, it will know about diff?

Answer 1

Accept the function as an argument:

def rk4(diff,  # accept an argument of the function to call
        x, dt)
    k1=diff(x)*dt
    k2=diff(x+k1/2)*dt
    k3=diff(x+k2/2)*dt
    k4=diff(x+k3)*dt
    return x+(k1+2*k2+2*k3+k4)/6

Then, when you call rk4, simply pass in the function to be executed:

from rk4 import rk4
import numpy as np

def diff(x):
    return x

def mercury(u0,phi0,dphi):
    x=np.array([u0,phi0])
    dt=2
    x=rk4(diff,  # here we send the function to rk4
          x, dt)
    return x
mercury(1,1,2)

It might be a good idea for mercury to accept diff as an argument too, rather than getting it from the closure (the surrounding code). You then have to pass it in as usual – your call to mercury in the last line would read mercury(diff, 1, 1, 2).

Functions are ‘first-class citizens’ in Python (as is nearly everything, including classes and modules), in the sense that they can be used as arguments, be held in lists, be assigned to names in namespaces, etc etc.