[Rcpp-devel] Find number of elements less than some number: Elegant/fastsolution needed

On Thu, Apr 14, 2011 at 7:02 PM,
<rcpp-devel-request at r-forge.wu-wien.ac.at> wrote:

I was able to write a very short C++ function using the Rcpp package
that provided about a 1000-fold increase in speed relative to the best
I could do in R. ?I don't have the script on this computer so I will
post it tomorrow when I am back on the computer at the office.

Apologies for cross-posting to the Rcpp-devel list but I am doing so
because this might make a good example of the usefulness of Rcpp and
inline.

And RcppArmadillo, as the case may be.

This is a cool little problem. ?In the examples given, I'd caution
people against comparing apples and durian. ?The sort(x) is a cost
that should be considered *within* each implementation. I used
Armadillo to sort (src, f4), and get another 100% worth of speedup
that I can't reproducing using R's sort (src1, f1-f3). ?If i modify
SEXP in-place (and this always confuses me, so I tend to avoid it),
I'm seeing an additional ~5-10% speed gain (src2, f5) -- the advantage
of this last seems to be primarily in memory-constrained applications.

On to the code!

src = '
NumericVector xx_(clone(x)), yy_(clone(y));
int nxx = xx_.size();
int nyy = yy_.size();
arma::vec xx(xx_), yy(yy_);
yy = sort(yy);
xx = sort(xx);
//
//
int j = 0; //gt index for yy
for (int i=0; i < nxx; i++) {
? ?while ((j < nyy) && ( xx(i) > yy(j) ) ) {
? ? ? ?j++;
? ?}
? ?xx_(i) = j;
? }
return (xx_);
'

src1 = '
NumericVector xx_(clone(x)), yy_(clone(y));
// assumes x & y are already sorted
arma::vec xx(xx_), yy(yy_);
int nxx = xx.n_elem;
int nyy = yy.n_elem;
int j = 0; //gt index for yy
for (int i=0; i < nxx; i++) {
? ?while ((j < nyy) && ( xx(i) > yy(j) ) ) {
? ? ? ?j++;
? ?}
? ?xx_(i) = j;
?}
return (xx_);
'

src2 = '
NumericVector xx_(x), yy_(y); ?//kinda scary
int nxx = xx_.size();
int nyy = yy_.size();
arma::vec xx(xx_.begin(), nxx, false), yy(yy_.begin(), nyy, false);
//really kinda scary
yy = sort(yy);
xx = sort(xx);
//
//
int j = 0; //gt index for yy
for (int i=0; i < nxx; i++) {
? ?while ((j < nyy) && ( xx(i) > yy(j) ) ) {
? ? ? ?j++;
? ?}
? ?xx_(i) = j;
}
return (xx_);
'

require(inline)
require(RcppArmadillo)
f1 <- function(x, y) { sort(length(y) - findInterval(-x, rev(-sort(y))));}
f2 <- function(x, y) {x = sort(x); length(y) - findInterval(-x, rev(-sort(y)))}
f3.a <- cxxfunction(signature(x="numeric", y="numeric"), src1,
plugin='RcppArmadillo')
f3 <- function(x,y) {
? ? ? ?x <- sort(x)
? ? ? ?y <- sort(y)
? ? ? ?return(f3.a(x,y))
}
f4 <- cxxfunction(signature(x="numeric", y="numeric"), src,
plugin='RcppArmadillo')
## ?danger -- violates R semantics
f5 <- cxxfunction(signature(x="numeric", y="numeric"), src2,
plugin='RcppArmadillo')


## this is a really ugly test. ygwypf, i suppose :)

for (i in 1:5) {
?x1 <- x <- rnorm(5e6)
?y1 <- y <- rnorm(5e6)
?print( cbind(
? ?r1=system.time(r1 <- f1(x,y)),
? ?r2=system.time(r2 <- f2(x,y)), r3=system.time(r3 <- f3(x1,y1)),
? ?r4 = system.time(r4 <- f4(x,y)), r5 = system.time(r5 <- f5(x,y))
?))
}
print(all.equal(r1, r2))
print(all.equal(r1, r3))
print(all.equal(r1, r4))
print(all.equal(r1, r5))