Function for Generating bistochastic matrix ?

2013 3 17
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Bistochastic matrix P is matrix where the sum each column or each row is 1, and aslo for n>=0 P^n is also bistochastic,
Another definition : a stochastic matrix P is bistochastic if P' is also stochastic . the question is :
Is there any predefined or sophisticated function to generate such matrices ?
I already tried a method using "magic" function :
>>H=magic(10); % say we want a Bistoch of dimension n
>>N=sum(H(1,:)); % to get the Unique SUM
>>P=H/N;
Cordially

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Matt J
Matt J 2013-3-17
Is there any predefined or sophisticated function to generate such functions ?
Generate them from what?
Youssef Khmou
Youssef Khmou 2013-3-17
like generating random numbers with "rand" function, given the dimensions
Cedric
Cedric 2013-3-17
The "magic" solution seems to be quite efficient already; did you ask because you need to be able to generate random bistochastic matrices?
Youssef Khmou
Youssef Khmou 2013-3-17
hi Cedric, the truth is that solution respects the definition of Bistochastic matrix but the repartition of the data is quite regular, a well built function can generate such quantity with randomness quality and why not having some parameters related to well known PDFs , to see the regularity try:
H=magic(100); % say we want a Bistoch of dimension n
N=sum(H(1,:)); % to get the Unique SUM
P=H/N;
imagesc(P);
Cedric
Cedric 2013-3-17
Hi Youssef, I asked precisely because of the regularity. I have no clean solution, but if I had to find some solution quickly, I would certainly go for yours, using two successive RANDPERM to permute rows and columns. It would not be optimal, but ok for a temporary approach I guess.
Youssef Khmou
Youssef Khmou 2013-3-17
alright, using Random permutation is good point , thanks

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Matt J
Matt J 2013-3-17
编辑：Matt J 2013-3-17

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Here's one idea. It uses interpMatrix ( Available Here ) to create circulant matrices, but any other method of making them would do.
function P=bistoch(N)
%Randomly generates an NxN bistochastic matrix, P
for ii=1:2
x=rand(N,1);
x=x/sum(x);
P=full(interpMatrix(x,1,length(x),1,'circ'));
A{ii}=P(randperm(N),randperm(N));
end
w=rand;
P=w*A{1}+A{2}*(1-w);

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Youssef Khmou
Youssef Khmou 2013-3-17
编辑：Youssef Khmou 2013-3-17
hi Mtt J,
Thanks for the answer, your function has a quality of generating randomness,
Just a small detail : The function interpMatrix.m seems to have an error :
??? Error: File: interpMatrix.m Line: 136 Column: 15
Expression or statement is incorrect--possibly unbalanced (, {, or [.
So in the line 136 :
case 'max'
[~,origin]=max(kernel);
i made an alteration :
case 'max'
[origin]=max(kernel);
And its functionning well,
Thanks .
Matt J
Matt J 2013-3-17
编辑：Matt J 2013-3-17
Hi Youssef,
No, that is not the fix you want. You're obviously using a (very!) old MATLAB version which doesn't support tilde arguments. Substitute this instead,
[discard,origin]=max(kernel);
Youssef Khmou
Youssef Khmou 2013-3-17
alright, that is good advice, thanks :

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