I was using this Rcpp code to do a quickselect on a vector of values, i.e. obtain the kth largest element from a vector in O(n) time (I saved this as qselect.cpp):
// [[Rcpp::depends(RcppArmadillo)]]
#include <RcppArmadillo.h>
using namespace arma;
// [[Rcpp::export]]
double qSelect(arma::vec& x, const int k) {
// ARGUMENTS
// x: vector to find k-th largest element in
// k: desired k-th largest element
// safety copy since nth_element modifies in place
arma::vec y(x.memptr(), x.n_elem);
// partially sort y in O(n) time
std::nth_element(y.begin(), y.begin() + k - 1, y.end());
// the k-th largest value
const double kthValue = y(k-1);
return kthValue;
}
I was using this as a fast way to calculate a desired percentile. E.g.
n = 50000
set.seed(1)
x = rnorm(n=n, mean=100, sd=20)
tau = 0.01 # desired percentile
k = tau*n+1 # here we will get the 6th largest element
library(Rcpp)
Rcpp::sourceCpp('qselect.cpp')
library(microbenchmark)
microbenchmark(qSelect(x,k)) # 53.32917, 548 µs
microbenchmark(sort(x, partial=k)[k]) # 53.32917, 694 µs = pure R solution
[This may look like it's already fast but I need to do this millions of time in my application]
Now I would like to modify this Rcpp function so that it would do a multithreaded quickselect on all columns or all rows of an R matrix, and return the result as a vector. As I am a bit of a novice in Rcpp I would like some advice though on which framework would likely be fastest for this & would be easiest to code (it would have to work easily cross-platform & I would need good control over the nr of threads to use). Using OpenMP, RcppParallel or RcppThread? Or even better - if someone could perhaps demonstrate a fast and elegant way to do this?
Following the advice below I tried multithreading with OpenMP and this seems to give decent speedups using 8 threads on my laptop. I modified my qselect.cpp file to:
// [[Rcpp::depends(RcppArmadillo)]]
#define RCPP_ARMADILLO_RETURN_COLVEC_AS_VECTOR
#include <RcppArmadillo.h>
using namespace arma;
// [[Rcpp::export]]
double qSelect(arma::vec& x, const int k) {
// ARGUMENTS
// x: vector to find k-th largest element in
// k: k-th statistic to look up
// safety copy since nth_element modifies in place
arma::vec y(x.memptr(), x.n_elem);
// partially sorts y
std::nth_element(y.begin(), y.begin() + k - 1, y.end());
// the k-th largest value
const double kthValue = y(k-1);
return kthValue;
}
// [[Rcpp::export]]
arma::vec qSelectMbycol(arma::mat& M, const int k) {
// ARGUMENTS
// M: matrix for which we want to find the k-th largest elements of each column
// k: k-th statistic to look up
arma::mat Y(M.memptr(), M.n_rows, M.n_cols);
// we apply over columns
int c = M.n_cols;
arma::vec out(c);
int i;
for (i = 0; i < c; i++) {
arma::vec y = Y.col(i);
std::nth_element(y.begin(), y.begin() + k - 1, y.end());
out[i] = y(k-1); // the k-th largest value of each column
}
return out;
}
#include <omp.h>
// [[Rcpp::plugins(openmp)]]
// [[Rcpp::export]]
arma::vec qSelectMbycolOpenMP(arma::mat& M, const int k, int nthreads) {
// ARGUMENTS
// M: matrix for which we want to find the k-th largest elements of each column
// k: k-th statistic to look up
// nthreads: nr of threads to use
arma::mat Y(M.memptr(), M.n_rows, M.n_cols);
// we apply over columns
int c = M.n_cols;
arma::vec out(c);
int i;
omp_set_num_threads(nthreads);
#pragma omp parallel for shared(out) schedule(dynamic,1)
for (i = 0; i < c; i++) {
arma::vec y = Y.col(i);
std::nth_element(y.begin(), y.begin() + k - 1, y.end());
out(i) = y(k-1); // the k-th largest value of each column
}
return out;
}
Benchmarks:
n = 50000
set.seed(1)
x = rnorm(n=n, mean=100, sd=20)
M = matrix(rnorm(n=n*10, mean=100, sd=20), ncol=10)
tau = 0.01 # desired percentile
k = tau*n+1 # we will get the 6th smallest element
library(Rcpp)
Rcpp::sourceCpp('qselect.cpp')
library(microbenchmark
microbenchmark(apply(M, 2, function (col) sort(col, partial=k)[k]),
apply(M, 2, function (col) qSelect(col,k)),
qSelectMbycol(M,k),
qSelectMbycolOpenMP(M,k,nthreads=8))[,1:4]
Unit: milliseconds
expr min lq mean median uq max neval cld
apply(M, 2, function(col) sort(col, partial = k)[k]) 8.937091 9.301237 11.802960 11.828665 12.718612 43.316107 100 b
apply(M, 2, function(col) qSelect(col, k)) 6.757771 6.970743 11.047100 7.956696 9.994035 133.944735 100 b
qSelectMbycol(M, k) 5.370893 5.526772 5.753861 5.641812 5.826985 7.124698 100 a
qSelectMbycolOpenMP(M, k, nthreads = 8) 2.695924 2.810108 3.005665 2.899701 3.061996 6.796260 100 a
I was surprised by the ca 2 fold gain in speed of doing the apply in Rcpp without even using multithreading (qSelectMbycol function) and there was a further 2 fold speed increase with OpenMP multithreading (qSelectMbycolOpenMP).
Any advice on possible code optimization welcome though...
For small n (n<1000) the OpenMP version is not faster, maybe because the individuals jobs are just too small then. E.g. for n=500:
Unit: microseconds
expr min lq mean median uq max neval cld
apply(M, 2, function(col) sort(col, partial = k)[k]) 310.477 324.8025 357.47145 337.8465 361.5810 1782.885 100 c
apply(M, 2, function(col) qSelect(col, k)) 103.921 114.8255 141.59221 119.3155 131.9315 1990.298 100 b
qSelectMbycol(M, k) 24.377 32.2885 44.13873 35.2825 39.3440 900.210 100 a
qSelectMbycolOpenMP(M, k, nthreads = 8) 76.123 92.1600 130.42627 99.8575 112.4730 1303.059 100 b