Calculating the gradient in Python

This post is from an earlier year, meaning the information here is likely outdated. You should look for a newer post from the current year to get the newest exercises and notes.

The NumPy package in Python serves us with a huge selection of useful functions for working with all kinds of numerical problems. One such function is gradient(V), that takes in a mgrid based matrix V and returns three mgrid matrices for each component of the gradient.

For instance, if you have the electric potential as a function of x, y and z, you can use NumPy’s gradient function to find the electric field through the relation \mathbf E = - \nabla V. An example of this is shown below:

from numpy import *
from enthought.mayavi.mlab import *

x,y,z = mgrid[-100:101:25., -100:101:25., -100:101:25.]

V = 2*x**2 + 3*y**2 - 4*z # just a random function for the potential

Ex,Ey,Ez = gradient(V)
Ex = - Ex
Ey = - Ey
Ez = - Ez

quiver3d(x,y,z,Ex,Ey,Ez) # plot the electric field just for fun

Note that this potential is random and not necessarily something you would find in a real electromagnetic problem. The resulting electric field is shown below:

The field generated from using NumPy's gradient function on our random potential.


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