# Setting size of DENSE set of equations.

## !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 which will
possibly sweep out some or all of the terms remaining in the dense section.
!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.
## 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.
## See Also

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