Dual-Number Jacobian

Problem

Forward-mode automatic differentiation evaluates a function on dual numbers (value, derivative).

For f(x, y) = [x*y + x, x^2 - y], seed x first and then y to assemble the Jacobian [[df1/dx, df1/dy], [df2/dx, df2/dy]]. Return the numeric matrix, which equals [[y + 1, x], [2x, -1]].

Hint

Each forward sweep computes one Jacobian column for the cost of one function evaluation.

Test cases

case 1

in: [1,2]

expected: [[3,1],[2,-1]]

case 2

in: [0,0]

expected: [[1,0],[0,-1]]

case 3

in: [2,-1]

expected: [[0,2],[4,-1]]

case 4

in: [-1,3]

expected: [[4,-1],[-2,-1]]

Starter codePython

def dual_jacobian(x, y):
    # Return the 2x2 Jacobian
    # Your code here
    pass

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