Jacobian Matrix

Problem

Compute the Jacobian matrix of the vector-valued function f(x1, x2) = [x1^2, x1*x2] at a given point using central differences (h = 1e-6).

J is a 2x2 matrix where J[j][i] = d f_j / d x_i.

Hint

Perturb each input dimension independently; record how each output component changes.

case 1

in: [[2,3]]

expected: [[4,0],[3,2]]

case 2

in: [[1,1]]

expected: [[2,0],[1,1]]

case 3

in: [[0,5]]

expected: [[0,0],[5,0]]

Starter codePython

def jacobian(point, h=1e-6):
    # f(x1, x2) = [x1**2, x1*x2]
    # Returns 2x2 Jacobian J[j][i] = d(f_j)/d(x_i)
    # Your code here
    pass

3 test cases · run your code against them in the editor