> I am using a sum of squared differences in the objective function of an
> optimization problem I am doing and I have managed to speed it up using
> the outer function versus the nested for loops, but my suspicion is
> that the calculation could be done even quicker. Please see the code
> below for a simple example. If anyone can point out a faster way I
> would appreciate it greatly.
First, look at ?system.time ; it's intended for finding out how much compute
time a command takes. You're also calculating elapsed time which is dependent
on (among other things) other processes running so maybe not the most reliable
thing for benchmarking.
Second, outer() is fast because it avoids loops and uses the fastest vector
routines R can (essentially, replicating the vector and then relying on simple
subtraction of vectors). In principle calling outer() loses a little time in
internal checks on what object types and function you've provided etc.; in
practice that doesn't add up to much. You can check by using just the core code
from outer with an added multiplication instead of the dimensioning statement:
ssqdif <- function(X, Y=X) {
#From 'outer' without modification
Y <- rep(Y, rep.int(length(X), length(Y)))
X <- rep(X, times = ceiling(length(Y)/length(X)))
#For this case:
sum((X-Y)^2) #SLIGHTLY quicker than d<-X-Y; sum(d*d)
}
system.time(ssqdif(X))
#Comparing outer() method:
system.time({gg <- outer(X, X, FUN="-"); sum(gg*gg)})
There's little practical difference; both hover from 0.00 to 0.03 s system
time. I could barely tell the difference even averaged over 100 runs; I was
getting an average around 0.007 (system time) and 2.5s user time for both
methods.
Conclusion: hard to beat outer() for this purpose in R
S Ellison
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