[R] 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?

Here is my example:

library(Matrix)
library(inline)

# construct sparse matrix
#########################

# construct a matrix C that is N x X with S total entries
N = 10000
S = 1000000
i = sample(1:1000, S, replace=TRUE)
j = sample(1:1000, S, replace=TRUE)
idx = i >= j
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

Thanks,
- Gabriel




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[Jeff Newmiller]

I believe you have the wrong list. (Read the Posting Guide... you seem to have R under control.) Try Rcpp-devel.

FWIW You probably need to spend some time with a C++ profiler... any language can be unintentionally mis-used, and you first need to identify whether your calling code is inefficiently handling memory or invoking setup code repetitively before blaming BLAS. A reproducible example will probably help when you ask at Rcpp-devel.

Post by 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 X with S total entries
N = 10000
S = 1000000
i = sample(1:1000, S, replace=TRUE)
j = sample(1:1000, S, replace=TRUE)
idx = i >= j
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>

Post by Hoffman, Gabriel
(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 )))
# user system elapsed
# 0.341 0.014 0.355
system.time(replicate(10, CholSparse( C )))
# user system elapsed
# 1.639 0.046 1.687

Post by Hoffman, Gabriel
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
/Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
/Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
[1] stats graphics grDevices datasets utils methods base
[1] inline_0.3.15 Matrix_1.2-15
[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
Thanks,
- Gabriel
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