fast large matrix multiplication in R
There are many ways to approach this depending upon your code, effort, and hardware.
- Use the 'best' function for the job
The simplest is to use crossprod which is the same as t(a)%*% b (Note - this will only be a small increase in speed)
crossprod(a,b)
- Use Rcpp (and likely RcppEigen/RcppArmadillo).
C++ will likely greater increase the speed of your code. Using linear algebra libraries will likely also help this further (hence Eigen and Armadillo). This however assumes you are willing to write some C++.
- Use a better backend
After this point you are looking at BLAS backends such as OpenBLAS, Atlas, etc. Hooking these up to R varies depending upon your OS. It is quite easy if you are using a Debian system like Ubuntu. You can find a demo here. These can sometimes be leveraged further by libraries such as Armadillo and Eigen.
- GPU Computing
If you have a GPU (e.g. AMD, NVIDIA, etc.) you can leverage the many cores within to greatly speed up your computations. There are a few that could be useful including gpuR, gputools, and gmatrix
EDIT - to address @jenesaiquoi comment on benefit of Rcpp
test.cpp
// [[Rcpp::depends(RcppArmadillo, RcppEigen)]]
#include <RcppArmadillo.h>
#include <RcppEigen.h>
// [[Rcpp::export]]
SEXP armaMatMult(arma::mat A, arma::mat B){
arma::mat C = A * B;
return Rcpp::wrap(C);
}
// [[Rcpp::export]]
SEXP eigenMatMult(Eigen::MatrixXd A, Eigen::MatrixXd B){
Eigen::MatrixXd C = A * B;
return Rcpp::wrap(C);
}
// [[Rcpp::export]]
SEXP eigenMapMatMult(const Eigen::Map<Eigen::MatrixXd> A, Eigen::Map<Eigen::MatrixXd> B){
Eigen::MatrixXd C = A * B;
return Rcpp::wrap(C);
}
test.R
library(Rcpp)
A <- matrix(rnorm(10000), 100, 100)
B <- matrix(rnorm(10000), 100, 100)
library(microbenchmark)
sourceCpp("test.cpp")
microbenchmark(A%*%B, armaMatMult(A, B), eigenMatMult(A, B), eigenMapMatMult(A, B))
Unit: microseconds
expr min lq mean median uq max neval
A %*% B 885.846 892.1035 933.7457 901.1010 938.9255 1411.647 100
armaMatMult(A, B) 846.688 857.6320 915.0717 866.2265 893.7790 1421.557 100
eigenMatMult(A, B) 205.978 208.1295 233.1882 217.0310 229.4730 369.369 100
eigenMapMatMult(A, B) 192.366 194.9835 207.1035 197.5405 205.2550 366.945 100
To add to cdeterman's answer: You can use eigen's build in parallelization for dense matrix products. In order to do so, you need to compile with open mp activated.
// [[Rcpp::depends(RcppArmadillo, RcppEigen)]]
// [[Rcpp::plugins(openmp)]]
#include <omp.h>
#include <RcppArmadillo.h>
#include <RcppEigen.h>
// [[Rcpp::export]]
SEXP armaMatMult(arma::mat A, arma::mat B){
arma::mat C = A * B;
return Rcpp::wrap(C);
}
// [[Rcpp::export]]
SEXP eigenMatMult(Eigen::MatrixXd A,
Eigen::MatrixXd B,
int n_cores){
Eigen::setNbThreads(n_cores);
//qDebug() << Eigen::nbThreads( );
Eigen::MatrixXd C = A * B;
return Rcpp::wrap(C);
}
// [[Rcpp::export]]
SEXP eigenMapMatMult2(const Eigen::Map<Eigen::MatrixXd> A,
Eigen::Map<Eigen::MatrixXd> B,
int n_cores){
Eigen::setNbThreads(n_cores);
Eigen::MatrixXd C = A * B;
return Rcpp::wrap(C);
}
Here are some benchmarks:
Note that if N = k = 100, parallelization does not necessarily improve performance.
If the matrix dimensions get larger, parallelization starts to have an impact (N = k = 1000):
library(microbenchmark)
# Benchmark 1: N = k = 100
N <- 100
k <- 100
A <- matrix(rnorm(N*k), N, k)
B <- matrix(rnorm(N*k), k, N)
microbenchmark(A%*%B,
armaMatMult2(A, B),
eigenMatMult2(A, B, n_cores = 1),
eigenMatMult2(A, B, n_cores = 2),
eigenMatMult2(A, B, n_cores = 4),
eigenMapMatMult2(A, B, n_cores = 1),
eigenMapMatMult2(A, B, n_cores = 2),
eigenMapMatMult2(A, B, n_cores = 4),
times = 100
# Unit: microseconds
# expr min lq mean median uq max neval
# A %*% B 535.6 540.75 552.594 551.25 554.50 650.2 100
# armaMatMult2(A, B) 542.0 549.10 560.975 556.35 560.25 738.1 100
# eigenMatMult2(A, B, n_cores = 1) 147.1 152.65 159.165 159.65 162.90 180.5 100
# eigenMatMult2(A, B, n_cores = 2) 97.1 109.90 124.496 119.60 127.50 391.8 100
# eigenMatMult2(A, B, n_cores = 4) 71.7 88.15 155.220 115.55 216.95 507.3 100
# eigenMapMatMult2(A, B, n_cores = 1) 139.1 150.10 154.889 154.20 158.35 244.3 100
# eigenMapMatMult2(A, B, n_cores = 2) 93.4 105.70 116.808 113.55 120.40 323.7 100
# eigenMapMatMult2(A, B, n_cores = 4) 66.8 82.60 161.516 196.25 210.40 598.9 100
)
# Benchmark 2: N = k = 1000
N <- 1000
k <- 1000
A <- matrix(rnorm(N*k), N, k)
B <- matrix(rnorm(N*k), k, N)
microbenchmark(A%*%B,
armaMatMult2(A, B),
eigenMatMult2(A, B, n_cores = 1),
eigenMatMult2(A, B, n_cores = 2),
eigenMatMult2(A, B, n_cores = 4),
eigenMapMatMult2(A, B, n_cores = 1),
eigenMapMatMult2(A, B, n_cores = 2),
eigenMapMatMult2(A, B, n_cores = 4),
times = 100
)
Unit: milliseconds
expr min lq mean median uq
A %*% B 597.1293 605.56840 814.52389 665.86650 1025.5896
armaMatMult2(A, B) 603.3894 620.25675 830.98947 693.22355 1078.4853
eigenMatMult2(A, B, n_cores = 1) 131.4696 135.22475 186.69826 193.37870 219.8727
eigenMatMult2(A, B, n_cores = 2) 67.8948 71.71355 114.52759 74.17380 173.3060
eigenMatMult2(A, B, n_cores = 4) 41.8564 48.87075 79.55535 72.00705 106.8572
eigenMapMatMult2(A, B, n_cores = 1) 125.3890 129.26125 175.09933 177.23655 213.0536
eigenMapMatMult2(A, B, n_cores = 2) 62.2866 65.78785 115.74248 79.92470 167.0217
eigenMapMatMult2(A, B, n_cores = 4) 35.2977 40.42480 68.21669 63.13655 97.2571
max neval
1217.6475 100
1446.5127 100
419.2043 100
217.9513 100
139.9629 100
298.2859 100
230.6307 100
118.2553 100