L-BFGS Memory Scaling

Problem

Compute the L-BFGS initial Hessian scaling from the newest correction pair.

Return (s dot y) / (y dot y), the gamma that multiplies the identity before the two-loop recursion. If y is the zero vector, return 1.0.

Hint

This scalar keeps the scaled identity consistent with the local curvature.

case 1

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

expected: 0.5

case 2

in: [[1,1],[1,-1]]

expected: 0

case 3

in: [[0.5],[0]]

expected: 1

case 4

in: [[-1,2],[0.5,1.5]]

expected: 1

Starter codePython

def lbfgs_memory_scaling(s, y):
    # Your code here
    pass

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