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

Jeff,

Here is something which is a little faster:

sum1 <- sum(outer(x, x, FUN="pmax"))
sum3 <- sum(outer(x, y, FUN="pmax"))

Best,
Ravi.

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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



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-----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'