Log-Euclidean Distance 2x2

Problem

Compute the log-Euclidean distance between two symmetric positive definite 2x2 matrices:

d(A, B) = ||log(A) - log(B)||_F

where log of a SPD matrix is computed from its eigendecomposition (orthonormal eigenvectors).

Hint

Log-Euclidean distances respect the manifold geometry of SPD matrices.

case 1

in: [[[2,0],[0,3]],[[2,0],[0,3]]]

expected: 0

case 2

in: [[[1,0],[0,1]],[[2,0],[0,4]]]

expected: 1.5499242141443583

case 3

in: [[[1,0],[0,1]],[[2.718281828459045,0],[0,2.718281828459045]]]

expected: 1.4142135623730951

case 4

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

expected: 0.7504758415354572

Starter codePython

def log_euclidean_distance_2x2(A, B):
    # Your code here
    pass

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