PLU Reconstruct Check

Problem

Verify a PLU factorization: return True if P*A equals L*U entrywise within 1e-9.

P is a permutation matrix, L is unit lower triangular, U is upper triangular, and all matrices are square and the same size.

Hint

A valid factorization satisfies P*A = L*U exactly; any mismatch means the factors are wrong.

case 1

in: [[[1,0],[0,1]],[[1,0],[0.5,1]],[[2,1],[0,2.5]],[[2,1],[1,3]]]

expected: true

case 2

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

expected: true

case 3

in: [[[1,0],[0,1]],[[1,0],[0,1]],[[1,2],[3,4]],[[1,2],[3,5]]]

expected: false

case 4

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

expected: false

Starter codePython

def plu_reconstruct_check(P, L, U, A):
    # Your code here
    pass

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