Question

Write a MatLab function J = Jcb(f, x) that computes the jacobian of the vector f of functions of x. Input f is the vector of functions [f1(x1, x2, x3...); f2(x1, x2, x3...); ...] and inout x is a vector of unkown x [x1; x2; x3;...]. Output J is the jacobian square matrix of vector f.

Answer 1

MATLAB Script:

close all
clear
clc

syms x1 x2 x3 x4
f1(x1,x2,x3,x4) = 1*x1 + 2*x2 + 3*x3 + 4*x4;
f2(x1,x2,x3,x4) = 2*x1 + 3*x2 + 4*x3 + 5*x4;
f3(x1,x2,x3,x4) = 3*x1 + 4*x2 + 5*x3 + 6*x4;
f = [f1; f2; f3]
x = [x1; x2; x3; x4]
J = Jcb(f, x)

function J = Jcb(f, x)
J = [];
for i = 1:length(x)
J = [J diff(f, x(i))];
end
end

Sample Output:

f(x1, x2, x3, x4) =
x1 + 2*x2 + 3*x3 + 4*x4
2*x1 + 3*x2 + 4*x3 + 5*x4
3*x1 + 4*x2 + 5*x3 + 6*x4
x =
x1
x2
x3
x4
J(x1, x2, x3, x4) =
[ 1, 2, 3, 4]
[ 2, 3, 4, 5]
[ 3, 4, 5, 6]