Compute the Jacobian matrix in Python

Question

import numpy as np


a = np.array([[1,2,3],
              [4,5,6],
              [7,8,9]])


b = np.array([[1,2,3]]).T

c = a.dot(b) #function

jacobian = a # as partial         


        

Answer 1

Here is a Python implementation of the mathematical Jacobian of a vector function f(x), which is assumed to return a 1-D numpy array.

import numpy as np

def J(f, x, dx=1e-8):
    n = len(x)
    func = f(x)
    jac = np.zeros((n, n))
    for j in range(n):  # through columns to allow for vector addition
        Dxj = (abs(x[j])*dx if x[j] != 0 else dx)
        x_plus = [(xi if k != j else xi + Dxj) for k, xi in enumerate(x)]
        jac[:, j] = (f(x_plus) - func)/Dxj
    return jac

It is recommended to make dx ~ 10^-8.