Speeding things up

[dmbates]

There are a couple of things I have noticed when doing some timings that could be rewritten to speed things up a bit.

When fitting a linear mixed model the bulk of the time is spent in calls to updateL! defined in src/linearmixedmodel.jl. For a model with crossed vector-valued random effects some timings show quite a bit of the time being spent in the lmulΛ!.method defined around line 192 of src/remat.jl (line positions are those in the explicitloops branch). I think this occurs in the mulitplication on the left by Λ₂' of the (2,2) block of L. The point is that this block has a block diagonal structure at the time of the multiplication even though it is stored as a dense matrix. It will become a dense lower-triangular matrix after the next stage of the Cholesky factorization because crossed random-effects terms create fill-in in the (2,2) block.

Probably the best way around this is to combine the copyto! operation with the left- and right Λ multiplications, for the diagonal blocks at least. If A₂,₂ is uniform block diagonal then Λ₂'A₂,₂Λ₂ will also be uniform block diagonal and those update operations can be done much faster by exploiting this structure.

Another place where I think things can be speeded up is in the rmul! and rdiv! operations that were converted to explicit loops in the explicitloops branch. In all of these operations there is a small triangular matrix operating in-place on a block of columns in a dense matrix. This is a natural application for multi-threading. I tried the naive approach of wrapping the outer loop with Threads.@threads but that just managed to make things much, much slower - I suspect because I don't understand how @threads works.

If anyone wants to attack either of these please assign yourself. I do plan to get at these but I am not sure when.

[dmbates]

Hmm! It seems I may already have done the first one. The diagonal block is handled by a call to a scaleinflate! method so it must be the lmulΛ! multiplication of the (1,2) block that is taking up time.

[dmbates]

Another possible enhancement is to define the λ matrix in the ReMat struct to be Union{Diagonal,LowerTriangular}. Using a Diagonal λ when appropriate may make the lmulΛ! and rmulΛ! methods cleaner and faster. It may be worthwhile incorporating the type of λ in the type of the ReMat so that methods can dispatch on it.

[dmbates]

Done.