Setting size of DENSE set of equations.


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 and is printed to the .vrb if !VRB is specified. ( !CINV request printing portion of the C inverse matrix to a .cii file.

See Also

Return to start