R help - Feb 2007 - 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'

Well, a reproducible example would be nice =)

not tested:

x = rnorm(10)
y = rnorm(20)
mymax <- function(t1, t2) apply(cbind(t1, t2), 1, max)
sum(outer(x, y, mymax))

is this sth like what you need?

b

On Feb 1, 2007, at 1:18 PM, Jeffrey Racine wrote:
> 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'
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting- 
> guide.html
> and provide commented, minimal, self-contained, reproducible code.

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.

----------------------------------------------------------------------------
-------

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'

______________________________________________
R-help at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Jeff,

you can do
> sum1: \sum_i\sum_j max(X_i,X_j)
> sum2: \sum_i\sum_j max(Y_i,Y_j)
sum(x * (2 * rank(x) - 1))
> sum3: \sum_i\sum_j max(X_i,Y_j)
sum(outer(x, y, pmax))

Probably, the latter can be speeded up even more...
Z