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luget — extraction of sparse LU factors
[P,L,U,Q]=luget(hand)
| 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 |
[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.
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)
| << lufact | lusolve >> |