Matrix multiplication in Rcpp - c++

Question

First of all, I am a novice user so forget my general ignorance. I am looking for a faster alternative to the %*% operator in R. Even though older posts suggest the use of RcppArmadillo, I have tried for 2 hours to make RcppArmadillo work without success. I always run into lexical issues that yield 'unexpected ...' errors. I have found the following function in Rcpp which I do can make work:
library(Rcpp)
func <- '
NumericMatrix mmult( NumericMatrix m , NumericMatrix v, bool byrow=true )
{
if( ! m.nrow() == v.nrow() ) stop("Non-conformable arrays") ;
if( ! m.ncol() == v.ncol() ) stop("Non-conformable arrays") ;
NumericMatrix out(m) ;
for (int i = 0; i < m.nrow(); i++)
{
for (int j = 0; j < m.ncol(); j++)
{
out(i,j)=m(i,j) * v(i,j) ;
}
}
return out ;
}
'
This function, however, performs element-wise multiplication and does not behave as %*%. Is there an easy way to modify the above code to achieve the intended result?
EDIT:
I have come up with a function using RcppEigen that seems to beat %*%:
etest <- cxxfunction(signature(tm="NumericMatrix",
tm2="NumericMatrix"),
plugin="RcppEigen",
body="
NumericMatrix tm22(tm2);
NumericMatrix tmm(tm);
const Eigen::Map<Eigen::MatrixXd> ttm(as<Eigen::Map<Eigen::MatrixXd> >(tmm));
const Eigen::Map<Eigen::MatrixXd> ttm2(as<Eigen::Map<Eigen::MatrixXd> >(tm22));
Eigen::MatrixXd prod = ttm*ttm2;
return(wrap(prod));
")
set.seed(123)
M1 <- matrix(sample(1e3),ncol=50)
M2 <- matrix(sample(1e3),nrow=50)
identical(etest(M1,M2), M1 %*% M2)
[1] TRUE
res <- microbenchmark(
+ etest(M1,M2),
+ M1 %*% M2,
+ times=10000L)
res
Unit: microseconds
expr min lq mean median uq max neval
etest(M1, M2) 5.709 6.61 7.414607 6.611 7.211 49.879 10000
M1 %*% M2 11.718 12.32 13.505272 12.621 13.221 58.592 10000

Answer 1

There are good reasons to rely on existing libraries / packages for standard tasks. The routines in the libraries are
optimized
thoroughly tested
a good means to keep the code compact, human-readable, and easy to maintain.
Therefore I think that using RcppArmadillo or RcppEigen should be preferable here. However, to answer your question, below is a possible Rcpp code to perform a matrix multiplication:
library(Rcpp)
cppFunction('NumericMatrix mmult(const NumericMatrix& m1, const NumericMatrix& m2){
if (m1.ncol() != m2.nrow()) stop ("Incompatible matrix dimensions");
NumericMatrix out(m1.nrow(),m2.ncol());
NumericVector rm1, cm2;
for (size_t i = 0; i < m1.nrow(); ++i) {
rm1 = m1(i,_);
for (size_t j = 0; j < m2.ncol(); ++j) {
cm2 = m2(_,j);
out(i,j) = std::inner_product(rm1.begin(), rm1.end(), cm2.begin(), 0.);
}
}
return out;
}')
Let's test it:
A <- matrix(c(1:6),ncol=2)
B <- matrix(c(0:7),nrow=2)
mmult(A,B)
# [,1] [,2] [,3] [,4]
#[1,] 4 14 24 34
#[2,] 5 19 33 47
#[3,] 6 24 42 60
identical(mmult(A,B), A %*% B)
#[1] TRUE
Hope this helps.
As benchmark tests show, the above Rcpp code is slower than R's built-in %*% operator. I assume that, while my Rcpp code can certainly be improved, it will be hard to beat the optimized code behind %*% in terms of performance:
library(microbenchmark)
set.seed(123)
M1 <- matrix(rnorm(1e4),ncol=100)
M2 <- matrix(rnorm(1e4),nrow=100)
identical(M1 %*% M2, mmult(M1,M2))
#[1] TRUE
res <- microbenchmark(
mmult(M1,M2),
M1 %*% M2,
times=1000L)
#> res
#Unit: microseconds
# expr min lq mean median uq max neval cld
# mmult(M1, M2) 1466.855 1484.8535 1584.9509 1494.0655 1517.5105 2699.643 1000 b
# M1 %*% M2 602.053 617.9685 687.6863 621.4335 633.7675 2774.954 1000 a

Answer 2

I would encourage to try to work out your issues with RcppArmadillo. Using it is as simple as this example also created by calling RcppArmadillo.package.skeleton():
// another simple example: outer product of a vector,
// returning a matrix
//
// [[Rcpp::export]]
arma::mat rcpparma_outerproduct(const arma::colvec & x) {
arma::mat m = x * x.t();
return m;
}
// and the inner product returns a scalar
//
// [[Rcpp::export]]
double rcpparma_innerproduct(const arma::colvec & x) {
double v = arma::as_scalar(x.t() * x);
return v;
}
There is actually more code in the example but this should give you an idea.

Answer 3

The following approach can also be used :
NumericMatrix mmult(NumericMatrix m, NumericMatrix v)
{
Environment base("package:base");
Function mat_Mult = base["%*%"];
return(mat_Mult(m, v));
}
With this approach, we use the operator %*% of R.