[R] Re : Re : Generate a random bistochastic matrix
Yes, you're right. In fact, it's just an adaptation of a matlab command and the author advises using N^4 replications that's why it's the default in the function. The bistochastic matrix is not my subject of interest, but I need it to perform some random tranformation of a vector of incomes. Florent Bresson - Message d'origine De : Richard M. Heiberger [EMAIL PROTECTED] À : Florent Bresson [EMAIL PROTECTED]; r-help@stat.math.ethz.ch Envoyé le : Lundi, 16 Octobre 2006, 16h23mn 39s Objet : Re: Re : [R] Generate a random bistochastic matrix I am sorry, I can't figure out what your function is doing. Why do you have N^4 in the argument? A matrix should have N rows and N columns, that is, it should have length N^2. The function returns a vector, not a matrix. There is no example of its use. I am guessing that your function somewhere uses a bistochastic matrix as an intermediate calculation. I recommend isolating the bistochastic matrix function from the larger function that you have constructed. PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@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.
[R] Re : Re : Generate a random bistochastic matrix
Thanks, it's perfect for my needs.
- Message d'origine
De : Martin Maechler [EMAIL PROTECTED]
À : Florent Bresson [EMAIL PROTECTED]
Cc : Richard M. Heiberger [EMAIL PROTECTED]; r-help@stat.math.ethz.ch
Envoyé le : Lundi, 16 Octobre 2006, 16h29mn 47s
Objet : Re: [R] Re : Generate a random bistochastic matrix
A simpler approach --- as in similar problems ---
is to use an iterative solution which works quite fast for any 'n'.
Interestingly, the number of necessary iterations seems to
*decrease* for increasing 'n' :
bistochMat - function(n, tol = 1e-7, maxit = 1000)
{
## Purpose: Random bistochastic *square* matrix (M_{ij}):
##M_{ij} = 0; sum_i M_{ij} = sum_j M_{ij} = 1 (for all i, j)
## --
## Arguments: n: (n * n) matrix dimension;
## --
## Author: Martin Maechler, Date: 16 Oct 2006, 14:47
stopifnot(maxit = 1, tol = 0)
M - matrix(runif(n*n), n,n)
for(i in 1:maxit) {
M - M / outer((rM - rowSums(M)), (cM - colSums(M))) * sum(rM) / n
if(all(abs(c(rM,cM) - 1) tol))
break
}
## cat(needed, i, iterations\n)
## or rather
attr(M, iter) - i
M
}
attr(M - bistochMat(70), iter)
## typically:
## [1] 8
attr(M - bistochMat(10), iter)
## - 13, 16, 15, 17, ...
set.seed(101) ; attr(M - bistochMat(10), iter) ## 15
set.seed(101) ; attr(M - bistochMat(10, tol = 1e-15), iter)## 32
Initially, I tried to solve the general [ n x m ] case.
It seems that needs a slightly smarter bias correction
instead of just 'sum(M) / n'.
If someone figures that out, please post your solution!
Regards,
Martin Maechler, ETH Zurich
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
[R] Re : Re : Generate a random bistochastic matrix
Yes, I would like every generated matrix to be drawn from a uniform distribution. Martin Maechler's solution was interesting but when I compute the product of the obtained matrix with any N-vector Y, the resulting vector is most of the time quite close to a vector like mean(Y)*rep(1,N). Florent Bresson - Message d'origine De : Rolf Turner [EMAIL PROTECTED] À : [EMAIL PROTECTED] Cc : r-help@stat.math.ethz.ch Envoyé le : Lundi, 16 Octobre 2006, 17h50mn 24s Objet : Re: [R] Re : Generate a random bistochastic matrix I don't think this idea has been suggested yet: (1) Form all n! n x n permutation matrices, say M_1, ..., M_K, K = n!. (2) Generate K independent uniform variates x_1, ..., x_k. (3) Renormalize these to sum to 1, x - x/sum(x) (4) Form the convex combination M = x_1*M_1 + ... + x_K*M_K M is a ``random'' doubly stochastic matrix. The point is that the set of all doubly stochastic matrices is a convex set in n^2-dimensional space, and the extreme points are the permutation matrices. I.e. the set of all doubly stochastic matrices is the convex hull of the the permuation matrices. The resulting M will *not* be uniformly distributed on this convex hull. If you want a uniform distribution something more is required. It might be possible to effect uniformity of the distribution, but my guess is that it would be a hard problem. cheers, Rolf Turner [EMAIL PROTECTED] __ R-help@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.
