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

In python 3, you can try sympy package：

import sympy as sym

def Jacobian(v_str, f_list):
    vars = sym.symbols(v_str)
    f = sym.sympify(f_list)
    J = sym.zeros(len(f),len(vars))
    for i, fi in enumerate(f):
        for j, s in enumerate(vars):
            J[i,j] = sym.diff(fi, s)
    return J

Jacobian('u1 u2', ['2*u1 + 3*u2','2*u1 - 3*u2'])

which gives out:

Matrix([[2,  3],[2, -3]])