CODEWITHSUNDEEP
crfortranintegral
Joris Meys
Joris Meys

Reputation: 108563

calculating double integrals in R quickly

I'm looking for a solution for a double integral that is faster than 

integrate(function(y) { 
   sapply(y, function(y) {
     integrate(function(x) myfun(x,y), llim, ulim)$value
   })
 }, llim, ulim)

with eg

myfun <- function(x,y) cos(x+y)
llim <- -0.5
ulim <- 0.5

I found an old paper that referred to a FORTRAN program called quad2d, but I couldn't find anything else but some help pages for matlab for the rest. So I'm looking for a C or FORTRAN library that can do double integrals quick (i.e. without the sapply loop), and that can be called from R. All ideas are very much appreciated, as long as they're all GPL compatible.

If the solution involves calling other functions from the libraries that are already shipped with R, I'd love to hear from them as well.

Upvotes: 19

Views: 20993

Answers (2)

Jeffrey Sax
Jeffrey Sax

Reputation: 10323

The cubature package does 2D (and N-D) integration using an adaptive algorithm. It should outperform simpler approaches for most integrands.

Upvotes: 18

Richie Cotton
Richie Cotton

Reputation: 121077

The pracma package that Joshua pointed out contains a version of quad2d.

quad2d(myfun, llim, ulim, llim, ulim)

This gives the same answer, within numerical tolerance, as your loop, using the example function.

By default, with your example function, quad2d is slower than the loop. If you drop n down, you can make it faster, but I guess it depends upon how smooth your function is, and how much accuracy you are willing to sacrifice for speed.

Upvotes: 8

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