luget

Arguments

hand

handle, output of lufact

P

sparse permutation matrix

L

sparse matrix, lower triangular if hand is obtained from a non singular matrix

U

square non singular upper triangular sparse matrix with ones along the main diagonal

Q

sparse permutation matrix

Description

[P,L,U,Q]=luget(hand) with hand obtained by the command [hand,rk]=lufact(A) with A a sparse matrix returns four sparse matrices such that P*L*U*Q=A.

The A matrix needs not be full rank but must be square (since A is assumed sparse one may add zeros if necessary to squaring down A).

If A is singular, the L matrix is column compressed (with rk independent nonzero columns): the nonsingular sparse matrix Q'*inv(U) column compresses A.

Examples

a=rand(5,2)*rand(2,5);A=sparse(a);
[hand,rk]=lufact(A);[P,L,U,Q]=luget(hand);
full(L), P*L*U*Q-A
clean(P*L*U*Q-A)
ludel(hand)

See also

• sparse — sparse matrix definition
• lusolve — sparse linear system solver
• luget — extraction of sparse LU factors
• clean — cleans matrices (round to zero small entries)