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lufact(G) Scilab Function lufact(G)
NAME
lufact - sparse lu factorization
CALLING SEQUENCE
[hand,rk]=lufact(A,prec)
PARAMETERS
A : square sparse matrix
hand : handle to sparse lu factors
rk : integer (rank of A)
prec : a vector of size two prec=[eps,reps] giving the absolute and rela-
tive thresolds.
DESCRIPTION
[hand,rk]=lufact(A) performs the lu factorization of sparse matrix A. hand
(no display) is used by lusolve (for solving linear system) and luget (for
retrieving the factors). hand should be cleared by the command:
ludel(hand);
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).
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 %eps.
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.
EXAMPLE
a=rand(5,5);b=rand(5,1);A=sparse(a);
[h,rk]=lufact(A);
x=lusolve(h,b);a*x-b
ludel(h)
SEE ALSO
sparse, lusolve, luget
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