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lufact Scilab Group Scilab Function lufact
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
relative 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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