Re: [Rd] multiplying multidimensional arrays (was: Re: [R] Manipulation involving arrays)

From: RAVI VARADHAN <rvaradhan_at_jhmi.edu>
Date: Mon 17 Jul 2006 - 13:18:45 GMT

Dear Gabor,

Thank you very much for your solution. It speeded calculations by a factor of two.

Now to your recommendation about making this solution a basic operation. I completely agree with your suggestion. That is exactly what I would have hoped for. In fact, my first try was to do:

Tbar <- tarray %*% t(wt)

Since tarray is (3,3,mcsamp) and wt is (n,mcsamp), I figured that the result would be a (3,3,n) array that would sum over mcsamp, as in the case of 2-dim array multiplication. But obviously that didn't work as "non-conformable". Your simple trick of forcing the 3-dim array to a 2-dim matrix using matrix(tarray, 3*3) is quite clever.

Thanks again for your help.

Best,
Ravi.

> I am moving this to r-devel.
>
> The problem and solution below posted on r-help could have been
> a bit slicker if %*% worked with multidimensional arrays multiplying
> them so that if the first arg is a multidimensional array it is
> mulitpliedalong the last dimension (and first dimension for the
> second arg).
> Then one could have written:
>
> Tbar <- tarray %*% t(wt) / rep(wti, each = 9)
>
> which is a bit nicer than what had to be done, see below, given
> that %*% only
> works with matrices.
>
> I suggest that %*% be so extended to multidimensional arrays. Note
> that this is upwardly compatible and all existing cases would continue
> to work unchanged.
>
> On 7/16/06, Gabor Grothendieck <ggrothendieck@gmail.com> wrote:
> > The double loop is the same as:
> >
> > Tbar[] <- matrix(tarray, 9) %*% t(wt) / rep(wti, each = 9)
> >
> >
> > On 7/16/06, RAVI VARADHAN <rvaradhan@jhmi.edu> wrote:
> > > Hi,
> > >
> > > I have the following piece of code that is part of a larger
> function. This piece is the most time consuming part of the
> function, and I would like to make this a bit more efficient.
> Could anyone suggest a way to do this faster?
> > >
> > > In particular, I would like to replace the nested "for" loop
> with a faster construct. I tried things like "kronecker" and
> "outer" combined with apply, but couldn't get it to work.
> > >
> > >
> > > Here is a sample code:
> > >
> > > ##########################
> > > n <- 120
> > > sigerr <- 5
> > > covmat <- diag(c(8,6,3.5))
> > > mu <- c(105,12,10)
> > > mcsamp <- 10000
> > >
> > > Tbar <- array(0, dim=c(3,3,n))
> > >
> > > # theta is a mcsamp x 3 matrix
> > > theta <- mvrnorm(mcsamp, mu = mu, Sigma = covmat)
> > >
> > > wt <- matrix(runif(n*mcsamp),n,mcsamp)
> > > wti <- apply(wt,1,sum)
> > >
> > > tarray <-
> array(apply(theta,1,function(x)outer(x,x)),dim=c(3,3,mcsamp))> >
> > > for (i in 1:n) {
> > > for (k in 1:mcsamp) {
> > > Tbar[,,i] <- Tbar[,,i] + wt[i,k] * tarray[,,k]
> > > }
> > > Tbar[,,i] <- Tbar[,,i] / wti[i]
> > > }
> > >
> >
>



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https://stat.ethz.ch/mailman/listinfo/r-devel Received on Mon Jul 17 23:22:34 2006

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