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.TH lufact G "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
luget - sparse lu factorization
.SH CALLING SEQUENCE
.nf
[P,L,U,Q]=luget(ptr)
.fi
.SH PARAMETERS
.TP
ptr
: pointer, output of \fVlufact\fR
.TP
P
: sparse permutation matrix
.TP
L
: sparse matrix, lower triangular if \fVptr\fR is obtained from a
non singular matrix
.TP
U
: square non singular upper triangular sparse matrix with ones along
the main diagonal
.TP
Q
: sparse permutation matrix
.SH DESCRIPTION
\fV[P,L,U,Q]=luget(ptr)\fR with \fVptr\fR obtained by
the command \fV[ptr,rk]=lufact(A)\fR with \fVA\fR a sparse matrix
returns four sparse matrices such that \fVP*L*U*Q=A\fR.
.LP
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).
.LP
If \fVA\fR is singular, the \fVL\fR matrix is column compressed (with
\fVrk\fR independent nonzero columns): the nonsingular sparse
matrix \fVQ'*inv(U)\fR column compresses \fVA\fR.
.SH EXAMPLE
.nf
a=rand(5,2)*rand(2,5);A=sparse(a);
[ptr,rk]=lufact(A);[P,L,U,Q]=luget(ptr);
full(L), P*L*U*Q-A
clean(P*L*U*Q-A)
ludel(ptr)
.fi
.SH SEE ALSO
sparse, lusolve, luget, clean
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