R: Can I use some sort of matrix multiplication with exponentials?

Question

I have data matrix (X) of the dimensions 5000x250 plus an extra parameter Y (Dim: 5000x1). The following loop gives me the desired results, but it takes forever to compute.

for (i in 1:ncol(X))
  for (j in 1:nrow(X))
   {
   X[j,i]=Y[j,1]^X[j,i]
   }

Is there any way to optimize this? If I didn't require the exponential, I'd use matrix multiplication. Thanks!

Doesn't `X^Y` work? If not, try `X^as.numeric(Y)`, vector recycling should ensure you get what you want. — James, Nov 19 '13 at 11:15
@James: I'm not sure what you're suggesting. X[] has to be the exponent. — aciM, Nov 19 '13 at 11:20
@aciM Oops, misread the Q. In that case you need to rbind your Y's together. I'll post an answer — James, Nov 19 '13 at 11:24
that would be great. As it is it would probably run for hours. — aciM, Nov 19 '13 at 11:27
@aciM "never say 'probably' " :-). Try using `microbenchmark` to see how your loop performs compared with Hong Ooi's solution. — Carl Witthoft, Nov 19 '13 at 12:24
@CarlWitthoft fair enough, but it is not even close. Actually it's a bit shocking how slow the loop is. — aciM, Nov 19 '13 at 12:32
Good work! Never taking anything for granted is the sign of solid science (or something like that) — Carl Witthoft, Nov 19 '13 at 12:35

score 3 · Accepted Answer · answered Nov 19 '13 at 11:33

3

Turn your column vector y into a matrix and use elementwise ^.

matrix(y, nrow=nrow(X), ncol=ncol(X)) ^ X

or

rep(y, times=ncol(X)) ^ X

answered Nov 19 '13 at 11:33

Hong Ooi

56,353
13
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score 1 · Answer 2 · answered Nov 19 '13 at 11:27

You can use the vectorised ^ if you construct a matrix of y's of the correct size:

x <- matrix(1:9,3)
y <- matrix(1:3,ncol=1)

do.call(cbind,replicate(ncol(x),list(y)))^x
     [,1] [,2]  [,3]
[1,]    1    1     1
[2,]    4   32   256
[3,]   27  729 19683

R: Can I use some sort of matrix multiplication with exponentials?

2 Answers2