Newton Step 2D

Problem

Take a full Newton step for a two-dimensional problem.

Compute delta = -H^{-1} grad using the 2x2 inverse and return [x + delta, delta]. If det(H) is zero, return [x, [0.0, 0.0]] with x unchanged.

Hint

The 2x2 inverse swaps the diagonal, negates the off-diagonals, and divides by the determinant.

case 1

in: [[1,2],[1,1],[[2,0],[0,4]]]

expected: [[0.5,1.75],[-0.5,-0.25]]

case 2

in: [[0,0],[2,-2],[[3,1],[1,2]]]

expected: [[-1.2000000000000002,1.6],[-1.2000000000000002,1.6]]

case 3

in: [[1,1],[0,0],[[1,2],[2,4]]]

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

case 4

in: [[-1,0.5],[0.5,0.5],[[1,0],[0,1]]]

expected: [[-1.5,0],[-0.5,-0.5]]

Starter codePython

def newton_step_2d(x, grad, H):
    # Returns [x_new, delta]
    # Your code here
    pass

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