Schur Complement Determinant

Problem

Compute the determinant of the 4x4 block matrix [[A, B], [C, D]] using the Schur complement with A as a 2x2 invertible block:

det = det(A) * det(D - C A^(-1) B)

Return None if det(A) is zero within 1e-12.

Hint

The Schur complement eliminates the top-left block and reduces the 4x4 determinant to a 2x2 one.

case 1

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

expected: 1

case 2

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

expected: 4

case 3

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

expected: 4

case 4

in: [[[1,2],[3,4]],[[1,0],[0,1]],[[1,1],[0,1]],[[0,0],[0,0]]]

expected: 1

case 5

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

expected: null

Starter codePython

def schur_complement_determinant(A, B, C, D):
    # Your code here
    pass

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