Performance difference between RcppArmadillo and Armadillo

Question

I'm trying to understand a difference in performance between a function written in RcppArmadillo and one written in a standalone C++ program using the Armadillo library. For example, consider the following simple function that computes the coefficients for a linear model using the traditional textbook formula.

// [[Rcpp::depends(RcppArmadillo)]]
#include <RcppArmadillo.h>

using namespace Rcpp;
using namespace arma;

// [[Rcpp::export]]
void simpleLm(NumericMatrix Xr, NumericMatrix yr) {
   int n = Xr.nrow(), k = Xr.ncol();
   mat X(Xr.begin(), n, k, false);
   colvec y(yr.begin(), yr.nrow(), false);

   colvec coef = inv(X.t()*X)*X.t()*y;
}

This takes about 6 seconds to run with a 1000000x100 matrix for X. Some timings in the code (not shown) indicated that all the time is spent on the coef calculation.

X <- matrix(rnorm(1000000*100), ncol=100)
y <- matrix(rep(1, 1000000))
system.time(simpleLm(X,y))

 user  system elapsed 
  6.028   0.009   6.040

Now consider a very similar function written in C++ that is then compiled with g++.

#include <iostream>
#include <armadillo>
#include <chrono>
#include <cstdlib>

using namespace std;
using namespace arma;

int main(int argc, char **argv) {
    int n = 1000000;
    mat X = randu<mat>(n,100);
    vec y = ones<vec>(n);

    chrono::steady_clock::time_point start = chrono::steady_clock::now();

    colvec coef = inv(X.t()*X)*X.t()*y;

    chrono::steady_clock::time_point end = chrono::steady_clock::now();

    chrono::duration<double, milli> diff = end - start;

    cout << diff.count() << endl;

    return 0;
}

Here the calculation of the coef variable only takes about 0.5 seconds, or only 1/12th the time as when done with RcppArmadillo.

I'm using Mac OS X 10.9.2 with R 3.1.0, Rcpp 0.11.1 and RcppArmadillo 0.4.200.0. I compiled the Rcpp example using the sourceCpp function. The standalone C++ example uses Armadillo 4.200.0, and I also installed the Fortran compiler for Mac using Homebrew (brew install gfortran).

Answer 1

Quick guess: your native program uses accelerated BLAS, you R build does not.

The actual "matrix math" is farmed out by Armadillo to the BLAS library. With RcppArmadillo, you get what R is built against. With a native program, maybe you use something else. It could be as simple as your program getting to use the Accelerate libraries whereas R doesn't -- I don't really know as I don't use OS X.

But to demonstrate, on my (i7, Linux) machine, times are near identical.

First, your program, unaltered:

edd@max:/tmp$ g++ -std=c++11 -O3 -o abiel abiel.cpp -larmadillo -llapack
edd@max:/tmp$ ./abiel 
2454
edd@max:/tmp$ 

Second, your program wrapped into something R can call (see below):

R> library(Rcpp)
R> sourceCpp("/tmp/abielviaR.cpp")
R> abielDemo()
2354.41
[1] TRUE
R> 

About the same.

The code of abielviaR.cpp follows.

#include <RcppArmadillo.h>
#include <chrono>

using namespace std;
using namespace arma;

// [[Rcpp::plugins(cpp11)]]
// [[Rcpp::depends(RcppArmadillo)]]
// [[Rcpp::export]]
bool abielDemo() {
    int n = 1000000;
    mat X = randu<mat>(n,100);
    vec y = ones<vec>(n);

    chrono::steady_clock::time_point start = chrono::steady_clock::now();
    colvec coef = inv(X.t()*X)*X.t()*y;
    chrono::steady_clock::time_point end = chrono::steady_clock::now();
    chrono::duration<double, milli> diff = end - start;
    Rcpp::Rcout << diff.count() << endl;

    return true;
}

PS You really should not compute OLS via (X'X)^(-1) X though.