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.TH lufact G "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
lufact - sparse lu factorization
.SH CALLING SEQUENCE
.nf
[hand,rk]=lufact(A,prec)
.fi
.SH PARAMETERS
.TP
A
: square sparse matrix
.TP
hand
: handle to sparse lu factors
.TP
rk
: integer (rank of A)
.TP
prec
: a vector of size two \fVprec=[eps,reps]\fR giving the absolute and relative
thresolds.
.SH DESCRIPTION
\fV[hand,rk]=lufact(A)\fR performs the lu factorization of sparse matrix \fVA\fR.
\fVhand\fR (no display) is used by \fVlusolve\fR (for solving linear
system) and \fVluget\fR (for retrieving the factors).
\fVhand\fR should be cleared by the command: \fVludel(hand)\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).
.TP
eps :
The absolute magnitude an element must have to be considered
as a pivot candidate, except as a last resort. This number
should be set significantly smaller than the smallest diagonal
element that is is expected to be placed in the matrix. the default
value is \fV%eps\fR.
.TP
reps :
This number determines what the pivot relative threshold will
be. It should be between zero and one. If it is one then the
pivoting method becomes complete pivoting, which is very slow
and tends to fill up the matrix. If it is set close to zero
the pivoting method becomes strict Markowitz with no
threshold. The pivot threshold is used to eliminate pivot
candidates that would cause excessive element growth if they
were used. Element growth is the cause of roundoff error.
Element growth occurs even in well-conditioned matrices.
Setting the reps large will reduce element growth and
roundoff error, but setting it too large will cause execution
time to be excessive and will result in a large number of
fill-ins. If this occurs, accuracy can actually be degraded
because of the large number of operations required on the
matrix due to the large number of fill-ins. A good value seems
to be 0.001 which is the default value. The default is chosen by giving a value larger
than one or less than or equal to zero. This value should be
increased and the matrix resolved if growth is found to be
excessive. Changing the pivot threshold does not improve
performance on matrices where growth is low, as is often the
case with ill-conditioned matrices.
reps was choosen for use with nearly diagonally
dominant matrices such as node- and modified-node admittance
matrices. For these matrices it is usually best to use
diagonal pivoting. For matrices without a strong diagonal, it
is usually best to use a larger threshold, such as 0.01 or 0.1.
.SH EXAMPLE
.nf
a=rand(5,5);b=rand(5,1);A=sparse(a);
[h,rk]=lufact(A);
x=lusolve(h,b);a*x-b
ludel(h)
.fi
.SH SEE ALSO
sparse, lusolve, luget
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