Newton Decrement Value 2D

Problem

The Newton decrement squared is g^T H^{-1} g, a measure of proximity to the minimum; the decrement itself is half of it for the standard convention used here: 0.5 * g^T H^{-1} g.

Given the gradient and the inverse Hessian as nested rows, return the decrement value.

Hint

Compute H^{-1} g first, then take half the dot product with g.

Test cases

case 1

in: [[1,1],[[1,0],[0,1]]]

expected: 1

case 2

in: [[2,0],[[0.5,0],[0,0.5]]]

expected: 1

case 3

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

expected: 4.5

Starter codePython

def newton_decrement_value_2d(g, h_inv):
    # Your code here
    pass

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