Strong Convexity Modulus

Problem

Compute the strong convexity modulus of a 2x2 Hessian, which is its smallest eigenvalue.

For the symmetric matrix A = [[a, b], [b, d]] return mid - sqrt(((a - d) / 2) ** 2 + b ** 2) with mid = (a + d) / 2. The result can be negative when A is not positive semidefinite.

Hint

mid minus the eigenvalue spread gives the smaller eigenvalue.

Test cases

case 1

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

expected: 1

case 2

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

expected: 2.381966011250105

case 3

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

expected: -1

case 4

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

expected: 3

Starter codePython

def strong_convexity_modulus(A):
    # Your code here
    pass

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