[R] Help with efficient double sum of max (X_i, Y_i) (X & Y vectors)

[Thomas Lumley]

On Thu, 1 Feb 2007, Ravi Varadhan wrote:

> Jeff,
>
> Here is something which is a little faster:
>
> sum1 <- sum(outer(x, x, FUN="pmax"))
> sum3 <- sum(outer(x, y, FUN="pmax"))

This is the sort of problem where profiling can be useful.  My experience 
with pmax() is that it is surprisingly slow, presumably because it handles 
recycling and NAs

In the example I profiled (an MCMC calculation) it was measurably faster 
to use
    function(x,y) {i<- x<y; x[i]<-y[i]; x}

 	-thomas

>
> Best,
> Ravi.
>
> ----------------------------------------------------------------------------
> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvaradhan at jhmi.edu
>
> Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
>
>
>
> ----------------------------------------------------------------------------
> --------
>
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Jeffrey Racine
> Sent: Thursday, February 01, 2007 1:18 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] Help with efficient double sum of max (X_i, Y_i) (X & Y
> vectors)
>
> Greetings.
>
> For R gurus this may be a no brainer, but I could not find pointers to
> efficient computation of this beast in past help files.
>
> Background - I wish to implement a Cramer-von Mises type test statistic
> which involves double sums of max(X_i,Y_j) where X and Y are vectors of
> differing length.
>
> I am currently using ifelse pointwise in a vector, but have a nagging
> suspicion that there is a more efficient way to do this. Basically, I
> require three sums:
>
> sum1: \sum_i\sum_j max(X_i,X_j)
> sum2: \sum_i\sum_j max(Y_i,Y_j)
> sum3: \sum_i\sum_j max(X_i,Y_j)
>
> Here is my current implementation - any pointers to more efficient
> computation greatly appreciated.
>
>  nx <- length(x)
>  ny <- length(y)
>
>  sum1 <- 0
>  sum3 <- 0
>
>  for(i in 1:nx) {
>    sum1 <- sum1 + sum(ifelse(x[i]>x,x[i],x))
>    sum3 <- sum3 + sum(ifelse(x[i]>y,x[i],y))
>  }
>
>  sum2 <- 0
>  sum4 <- sum3 # symmetric and identical
>
>  for(i in 1:ny) {
>    sum2 <- sum2 + sum(ifelse(y[i]>y,y[i],y))
>  }
>
> Thanks in advance for your help.
>
> -- Jeff
>
> -- 
> Professor J. S. Racine         Phone:  (905) 525 9140 x 23825
> Department of Economics        FAX:    (905) 521-8232
> McMaster University            e-mail: racinej at mcmaster.ca
> 1280 Main St. W.,Hamilton,     URL:
> http://www.economics.mcmaster.ca/racine/
> Ontario, Canada. L8S 4M4
>
> `The generation of random numbers is too important to be left to chance'
>
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> ______________________________________________
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
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>

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle