Smoothness Constant

Problem

Estimate the smoothness constant from sampled Hessians.

For each symmetric 2x2 matrix compute the largest absolute eigenvalue as abs(mid) + sqrt(((a - d) / 2) ** 2 + b ** 2) and return the maximum over the list. An empty list returns 0.0.

Hint

The smoothness constant is the largest absolute Hessian eigenvalue.

Test cases

case 1

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

expected: 4.618033988749895

case 2

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

expected: 1

case 3

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

expected: 3

case 4

in: [[]]

expected: 0

Starter codePython

def smoothness_constant(hessians):
    # Your code here
    pass

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