Setting size of DENSE set of equations.
Sparse versus Dense
ASReml partitions the terms in the linear model into two parts: a dense set
and a sparse set.
The partition is at the !r
point unless explicitly set with the !DENSE data line qualifier
or mv is included
before !r,
The special term mv is always included
in sparse. Thus random
and sparse terms are
estimated using sparse matrix methods which result in faster
processing.
The inverse coefficient matrix is fully formed for the terms in the
dense set. The inverse
coefficient matrix is only partially formed for terms in the sparse
set. Typically, the sparse set is large and sparse storage results in savings in memory
and computing. A consequence is that the variance matrix for estimates
is only available for equations in the dense portion and is
printed to the
.vrb
if
!VRB
is specified. (
!CINV
requests printing portion of the C inverse matrix to a
.cii
file.
!DENSE
ASReml normally solves the first set of fixed effect equations
in the linear model in the order the terms are defined using
dense equations. However, if there are more than 800 such equations,
the higher model terms are moved into the sparse section.
Typically these will be the higher order interactions.
The sparse equations are fitted before the dense equations so
putting an interaction in the sparse equations which sweep
aout any terms marginal to it that appear in the dense equations.
!DENSE n
sets the number of equations solved
densely up to a maximum of 5000. By default, sparse matrix methods are applied to the random
effects and any fixed effects listed after random
factors or whose equation numbers exceed 800.
Use !DENSE n to apply sparse methods to effects listed
before the !r (reducing the size of the DENSE block) or if you have
large fixed model terms and want them included in the ANOVA table. Individual model terms will not be
split so that only part is in the dense section.
n should be kept
small (<100) for faster
processing.
!GDENSE: Processing random terms as DENSE
Typically, all random terms and very large fixed terms
are included in the SPARSE equations.
However, if a random term G structure is actually dense and large as in a
genomic relationship matrix, there will be a computational penalty
from traeting it as SPARSE. The !GDENSE qualifier
includes the first random term in the DENSE equations if the term is
has a dense Ginverse matrix.
ASReml uses link list matrix methods for the sparse equations
and has always included random model terms in these sparse equations.
However, in the case of GRM matrices, they are typically quite large (several thousand) and dense, and is generally
more efficient to process them as such. ASReml 4 has a
!GDENSE qualifier (set just before the model line).
If !GDENSE is set and the first random term is a GRM term,
its equations will be processed as DENSE. In one example with 3226 rows
in the GRM matrix, this reduced the iteration time from 196 to 175 seconds.
See Also
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