Calculate curl of a vector field in Python and plot it with matplotlib

Question

I need to calculate the curl of a vector field and plot it with matplotlib. A simple example of what I am looking for could be put like that:

How can I calculate and

Answer 1

To calculate the curl of a vector function you can also use numdifftools for automatic numerical differentiation without a detour through symbolic differentiation. Numdifftools doesn't provide a curl() function, but it does compute the Jacobian matrix of a vector valued function of one or more variables, and this provides the derivatives of all components of a vector field with respect to all of the variables; this is all that's necessary for the calculation of the curl.

import import scipy as sp
import numdifftools as nd

def h(x):
    return sp.array([3*x[0]**2,4*x[1]*x[2]**3, 2*x[0]])

def curl(f,x):
    jac = nd.Jacobian(f)(x)
    return sp.array([jac[2,1]-jac[1,2],jac[0,2]-jac[2,0],jac[1,0]-jac[0,1]])

x = sp.array([1,2,3)]
curl(h,x)

This returns the value of the curl at x: array([-216., -2., 0.]) Plotting is as suggested above.