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From: <HIDDEN>
Newsgroups: comp.soft-sys.matlab
Subject: Re: finding permutation matrices using eig()
Date: Wed, 20 Apr 2011 03:50:04 +0000 (UTC)
Organization: UCSD
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Xref: news.mathworks.com comp.soft-sys.matlab:722831

I have found Roger's code very useful for my application.  Thanks!
I'll just post a thing I had to fix.  Sometimes the permutation matrix has
values near 0.5 before thresholding as the comparisons done with min() come
out nearly a tie for me.   In the following code, I take all the close comparisons
are try flipping them...

SA = sort(VA); % Sort eigenvectors of A
SB = sort(VB); % Sort eigenvectors of B
MB = -flipud(SB); % Get sorted negatives of B eigenvectors
[t,ix] = min([sum(abs(SA-SB),1);sum(abs(SA-MB),1)],[],1); % Compare
[u,jx] = max([sum(abs(SA-SB),1);sum(abs(SA-MB),1)],[],1); % Compare
x=2*(ix==1)-1;
nVB = VB.*repmat(x,n,1); % Reverse signs accordingly
P = nVB*VA'; % Generate presumed permutation matrix
P = +(P>1-1e-12); % Turn all elements into 1's and 0's
uncert=find(u<1e-10);
if ~isempty(uncert) && (abs(det(P))~=1),
e=[1;-1]; xm=x;
for i=2:length(uncert),
e=[ones(length(e),1) e; -1*ones(length(e),1) e];
end
for i=2:length(e), % already tried first one above
xm(uncert)=x(uncert).*e(i,:);
nVB = VB.*repmat(xm,n,1); % Reverse signs accordingly
P = nVB*VA'; % Generate presumed permutation matrix
P = +(P>1-1e-12); % Turn all elements into 1's and 0's
if abs(det(P))==1,
break;
end
end
end
```