luget

extraction of sparse LU factors

Calling Sequence

[P,L,U,Q]=luget(hand)

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)