R help - Oct 2006 - Generate a random bistochastic matrix

Please, I would like to generate a random bistochastic matrix, that is a squared
matrix of non-negative numbers  with  each row and each column sum to 1, for
example :

.2    .3    .5
.6    .3    .1 
.2     .4     .4

I don't know of to code this. Do you have any idea ?

Thanks

Florent Bresson




	

	
		
___________________________________________________________________________ 

Demandez ? ceux qui savent sur Yahoo! Questions/R?ponses

bistochastic.3x3 <- function() {
  B <- matrix(0, 3, 3)
  
  ## 2 df
  tmp.1 <- runif(3)
  B[1,] <- tmp.1/sum(tmp.1)
  
  ## 1 df
  tmp.2 <- runif(2)
  B[2:3, 1] <- (1-B[1,1]) * tmp.2/sum(tmp.2)
  
  ## 1 df
  B[2, 2] <- runif(1, max=min(1-B[1,2], 1-B[2,1]))
  
  ## Fill in the rest
  B[2,3] <- 1-sum(B[2, 1:2])
  B[3,2] <- 1-sum(B[1:2, 2])
  B[3,3] <- 1-sum(B[1:2, 3])
  
  B
}

B <- bistochastic.3x3()
apply(B, 1, sum)
apply(B, 2, sum)


To extend this to larger than 3x3 requires the same kind of
conditional generation of alternating rows and columns of the
matrix.  The hard part is the extension of the two-way conditioning
I illustrated in the B[2, 2] line.

Rich

you can try something like the following:

B <- 10
N <- 5
mats <- r2dtable(B, rep(1, N), rep(1, N))
out <- matrix(0, N, N)
for(i in 1:length(mats))
    out <- out + mats[[i]]
out <- out / B
out
colSums(out)
rowSums(out)



I hope it helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
     http://www.student.kuleuven.be/~m0390867/dimitris.htm


----- Original Message ----- 
From: "Florent Bresson" <f_bresson at yahoo.fr>
To: <r-help at stat.math.ethz.ch>
Sent: Monday, October 16, 2006 10:22 AM
Subject: [R] Generate a random bistochastic matrix


Please, I would like to generate a random bistochastic matrix, that is 
a squared matrix of non-negative numbers  with  each row and each 
column sum to 1, for example :

.2    .3    .5
.6    .3    .1
.2     .4     .4

I don't know of to code this. Do you have any idea ?

Thanks

Florent Bresson








___________________________________________________________________________



______________________________________________
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.


Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm