[Rcpp-devel] Speed of RCppEigen Cholesky decomposition on sparse matrix

[Dirk Eddelbuettel]

Gabriel,

On 26 November 2018 at 17:23, Hoffman, Gabriel wrote:
| I am developing a statistical model and I have a prototype working in R
| code.  I make extensive use of sparse matrices, so the R code is pretty
| fast, but hoped that using RCppEigen to evaluate the log-likelihood

(lowercase c generally: Rcpp, RcppEigen, ...)

| function could avoid a lot of memory copying and be substantially
| faster.  However, in a simple  example I am seeing that RCppEigen is
| 3-5x slower than standard R code for cholesky decomposition of a sparse
| matrix.  This is the case on R 3.5.1 using RcppEigen_0.3.3.4.0 on both
| OS X and CentOS 6.9.
| 
| Since this simple operation is so much slower it doesn't seem like
| using RCppEigen is worth it in this case.  Is this an issue with BLAS,
| some libraries or compiler options, or is R code really the fastest
| option?

Well Eigen (famously) does not use BLAS (for dense matrices) so that
comparison is off.  But then again sparse matrices never use BLAS anyway.

Eigen had sparse matrix code earlier which is why Doug originally connected
it to R via Rcpp and RcppEigen. We now also have sparse matrix code in
RcppArmadillo (thanks chiefly to Binxiang during his Google Summer of Code)
so you could compare those two.  And then there is of course the Matrix
package which had all of this first first so you could consider that (from C
/ C++ as well). That may be fastest, but the most work to get "wired up". Or
maybe not.

But in essence: "what you see is what you get". There should be no layer in
either of these packages slowing access down, and ultimately the sparse
matrix libraries are often called. I think there may be some run-time
checks.  RcppArmadillo has a vignette on this too...

I actually don't use sparse matrices all that much so maybe others will pipe
in.

Dirk

| library(Matrix)
| library(inline)
| 
| # construct sparse matrix
| #########################
| 
| # construct a matrix C that is N x N with S total entries
| # set C = crossprod(X)
| N = 100000
| S = 1000000
| i = sample(1:1000, S, replace=TRUE)
| j = sample(1:1000, S, replace=TRUE)
| values = runif(S, 0, .3)
| X = sparseMatrix(i=i, j=j, x = values, symmetric=FALSE )
| 
| C = as(crossprod(X), "dgCMatrix")
| 
| # check sparsity fraction
| S / N^2
| 
| # define RCppEigen code
| CholeskyCppSparse<-'
| using Rcpp::as;
| using Eigen::Map;
| using Eigen::SparseMatrix;
| using Eigen::MappedSparseMatrix;
| using Eigen::SimplicialLLT;
| 
| // get data into RcppEigen
| const MappedSparseMatrix<double> Sigma(as<MappedSparseMatrix<double> >(Sigma_in));
| 
| // compute Cholesky
| typedef SimplicialLLT<SparseMatrix<double> > SpChol;
| const SpChol Ch(Sigma);
| '
| 
| CholSparse <- cxxfunction(signature(Sigma_in = "dgCMatrix"), CholeskyCppSparse, plugin = "RcppEigen")
| 
| # compare times
| system.time(replicate(10, chol( C )))
| # output:
| #   user  system elapsed
| #  0.341   0.014   0.355
| 
| system.time(replicate(10, CholSparse( C )))
| # output:
| #   user  system elapsed
| # 1.639   0.046   1.687
| 
| sessionInfo()
| R version 3.5.1 (2018-07-02)
| Platform: x86_64-apple-darwin15.6.0 (64-bit)
| Running under: macOS  10.14
| 
| Matrix products: default
| BLAS:
| /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
| LAPACK:
| /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib
| 
| locale:
| [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
| 
| attached base packages:
| [1] stats     graphics  grDevices datasets  utils     methods   base
| 
| other attached packages:
| [1] inline_0.3.15 Matrix_1.2-15
| 
| loaded via a namespace (and not attached):
| [1] compiler_3.5.1      RcppEigen_0.3.3.4.0 Rcpp_1.0.0
| [4] grid_3.5.1          lattice_0.20-38
| 
| Changing the size of the matrix and the number of entries does not
| change the relative times much
| 
| Thanks,
| - Gabriel
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-- 
http://dirk.eddelbuettel.com | @eddelbuettel | edd at debian.org