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

[Hoffman, Gabriel]

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
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?


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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