Performance Difference Between RcppArmadillo and Armadillo

Question

I am trying to understand the 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 calculates coefficients for a linear model using a 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;
}

It takes about 6 seconds to work with the matrix 1000000x100for X. Some code timings (not shown) show that all the time is spent on computing coef.

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 ++, which 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;
}

coef 0,5 1/12- , RcppArmadillo.

Mac OS X 10.9.2 R 3.1.0, Rcpp 0.11.1 RcppArmadillo 0.4.200.0. Rcpp, sourceCpp. ++ Armadillo 4.200.0, Fortran Mac Homebrew (brew install gfortran).

Answer 1

: BLAS, R build.

" " Armadillo BLAS. RcppArmadillo , R. , , - . , , , R - , OS X.

, (i7, Linux), .

-, :

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

-, , , R (. ):

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

.

abielviaR.cpp.

#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 OLS (X'X) ^ (- 1) X, .