Smoothness Constant 2x2 Quadratic

Problem

For f(x) = 0.5 x^T A x with symmetric A = [[a, b], [b, d]], the smoothness constant is the larger eigenvalue (a + d + sqrt((a - d)^2 + 4 b^2)) / 2, which bounds the local curvature of the gradient.

Given the entries, return the constant.

Hint

The top eigenvalue of the Hessian controls the gradient Lipschitz bound.

Test cases

case 1

in: [2,0,4]

expected: 4

case 2

in: [1,1,1]

expected: 2

case 3

in: [0,2,0]

expected: 2

Starter codePython

def smoothness_constant_2x2_quadratic(a, b, d):
    # Your code here
    pass

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