MediumCalculusca-190

Loss-Landscape Curvature

Problem

The curvature of the quadratic loss f(w) = 0.5 * w^T A w along the unit direction u is the Rayleigh quotient u^T A u / (u^T u).

For A = [[a, b], [b, c]] and direction (d1, d2), return (a*d1^2 + 2*b*d1*d2 + c*d2^2) / (d1^2 + d2^2).

Hint

The Rayleigh quotient lies between the smallest and largest Hessian eigenvalues.

case 1

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

expected: 2

case 2

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

expected: 2.5

case 3

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

expected: -1

case 4

in: [3,0,3,3,4]

expected: 3

Starter codePython

def landscape_curvature(a, b, c, d1, d2):
    # Your code here
    pass

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