[Rcpp-devel] [R] fast rowCumsums wanted for calculating the cdf

Hi,

You might look at Reduce(). ?It seems faster. ?I converted the matrix
to a list in an incredibly sloppy way (which you should not emulate)
because I cannot think of ?the simple way.

probs <- t(matrix(rep(1:10000000), nrow=10)) # matrix with row-wise probabilites
F <- matrix(0, nrow=nrow(probs), ncol=ncol(probs));
F[,1] <- probs[,1,drop=TRUE];
add <- function(x) {Reduce(`+`, x, accumulate = TRUE)}


system.time(F.slow <- t(apply(probs, 1, cumsum)))

? user ?system elapsed
?36.758 ? 0.416 ?42.464

system.time(for (cc in 2:ncol(F)) {

+ ?F[,cc] <- F[,cc-1,drop=TRUE] + probs[,cc,drop=TRUE];
+ })
? user ?system elapsed
?0.980 ? 0.196 ? 1.328

system.time(add(list(probs[,1], probs[,2], probs[,3], probs[,4], probs[,5], probs[,6], probs[,7], probs[,8], probs[,9], probs[,10])))

? user ?system elapsed
?0.420 ? 0.072 ? 0.539

.539 seconds for 10 vectors each with 1 million elements does not seem
bad. ?For 30000 each, on my system it took .014 seconds, which for
200,000 iterations, I estimated as:

(200000*.014)/60/60

[1] 0.7777778

(and this is on a stone age system with a single core processor and
only 756MB of RAM)

It should not be difficult to get the list back to a matrix.

Cheers,

Josh



On Thu, Oct 14, 2010 at 11:51 PM, Gregor <mailinglist at gmx.at> wrote:

Dear all,

Maybe the "easiest" solution: Is there anything that speaks against generalizing
cumsum from base to cope with matrices (as is done in matlab)? E.g.:

"cumsum(Matrix, 1)"
equivalent to
"apply(Matrix, 1, cumsum)"

The main advantage could be optimized code if the Matrix is extreme nonsquare
(e.g. 100,000x10), but the summation is done over the short side (in this case 10).
apply would practically yield a loop over 100,000 elements, and vectorization w.r.t.
the long side (loop over 10 elements) provides considerable efficiency gains.

Many regards,
Gregor




On Tue, 12 Oct 2010 10:24:53 +0200
Gregor <mailinglist at gmx.at> wrote:

Dear all,

I am struggling with a (currently) cost-intensive problem: calculating the
(non-normalized) cumulative distribution function, given the (non-normalized)
probabilities. something like:

probs <- t(matrix(rep(1:100),nrow=10)) # matrix with row-wise probabilites
F <- t(apply(probs, 1, cumsum)) #SLOOOW!

One (already faster, but for sure not ideal) solution - thanks to Henrik Bengtsson:

F <- matrix(0, nrow=nrow(probs), ncol=ncol(probs));
F[,1] <- probs[,1,drop=TRUE];
for (cc in 2:ncol(F)) {
? F[,cc] <- F[,cc-1,drop=TRUE] + probs[,cc,drop=TRUE];
}

In my case, probs is a (30,000 x 10) matrix, and i need to iterate this step around
200,000 times, so speed is crucial. I currently can make sure to have no NAs, but
in order to extend matrixStats, this could be a nontrivial issue.

Any ideas for speeding up this - probably routine - task?

Thanks in advance,
Gregor

--
Joshua Wiley
Ph.D. Student, Health Psychology
University of California, Los Angeles
http://www.joshuawiley.com/