Gauss-Newton Step 1D

Problem

Take one Gauss-Newton step fitting y = a * x to data.

Return a + sum(xi * (yi - a * xi)) / sum(xi ** 2). If every xi is 0, return a unchanged. This is the exact least-squares slope update for a linear model through the origin.

Hint

The Jacobian entries are the xi values themselves.

Test cases

case 1

in: [0,[1,2,3],[2,4,6]]

expected: 2

case 2

in: [1,[1,2],[3,5]]

expected: 2.6

case 3

in: [0.5,[1,1],[1,2]]

expected: 1.5

case 4

in: [2,[],[]]

expected: 2

Starter codePython

def gauss_newton_step(a, X, y):
    # Your code here
    pass

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