Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: How to figure 'matrix coupling' out?
Replies: 3   Last Post: Apr 14, 2012 2:41 PM

 Messages: [ Previous | Next ]
 flying Posts: 10 Registered: 4/13/12
Re: How to figure 'matrix coupling' out?
Posted: Apr 14, 2012 3:15 AM

Actually,what you said is what i want to find.Just like you said 'how to reorder one arbitrary set of four points in the complex plane so as to best "correspond" to another arbitrary set of four'.So i can restore four eigenvalue pairs from the complex plane.

One method is like this:

[Mr lambdaAr] = eig(Ar); % Eigenvalues of Ar
Arc =inv(Mr)*Ac*Mr;
lambdaAc = eig(Ac); % eigenvalues of Ac
px = angle(diag(lambdaAr)); % location of scatterers in x-axis

[Y I] = sort(angle(diag(Arc)));
[Y1 I1] = sort(I);
[Y2 I2] = sort(angle(lambdaAc));
py = Y2(I1); % location of scatterers in y-axis
figure
plot(px,py,'*'); % plot eigenvalue pairs

but i find that sometimes it woks well, it can pair the correct eigenvalues,but sometimes it fails.

Sincerely frank

"Roger Stafford" wrote in message <jmb2rr\$19m\$1@newscl01ah.mathworks.com>...
> "flying" wrote in message <jmar84\$2ah\$1@newscl01ah.mathworks.com>...
> > Hi,everyone!I have a question for you.
> > I have two 4x4 complex matrices.
> >
> > Ar = 1.2485 + 0.1236i 0.0320 - 0.1570i 0.0245 + 0.0153i 0.0184 - 0.0097i
> > -0.0041 - 0.1868i 0.8390 + 0.5215i 0.1207 + 0.0593i -0.0008 + 0.1226i
> > -0.0604 - 0.0353i 0.0097 - 0.1781i 0.1500 + 0.9788i 0.0425 - 0.0036i
> > 0.0172 - 0.0026i -0.0864 + 0.0996i -0.0423 - 0.0094i 0.9084 + 0.3718i
> >
> > Ac = 0.8987 + 0.6650i 0.0302 - 0.0282i -0.0035 + 0.0219i -0.0146 - 0.0581i
> > 0.0328 - 0.0334i 0.7194 + 0.6143i 0.1217 + 0.1499i -0.0790 + 0.1035i
> > -0.0215 - 0.0325i 0.1310 - 0.2428i -0.4942 + 0.8434i -0.0291 + 0.0318i
> > 0.0256 - 0.0727i -0.1420 + 0.0203i 0.0053 + 0.0046i 0.6475 + 0.7799i
> >
> > I want to reorder their eigenvalues.First,i do eigenvalue decomposition of
> > matrix 'Ar'signing as 'lambdaAr'.It is a vector.
> >
> > lambdaAr = [1.2190 + 0.0767i 0.9510 + 0.3090i 0.8505 + 0.6179i 0.1253 + 0.9921i];
> > lambdaAc = [-0.5358 + 0.8443i 0.5878 + 0.8090i 0.8941 + 0.6496i 0.8254 + 0.5997i];
> >
> > My question is that i want to reorder matrix Ac's eigenvalues 'lambdaAc' corresponding to the order of 'lambdaAr'.
> > Maybe it is a question of 'matrix coupling'.
> > How can i do?Please do me a favor everybody.Thank you very much!

> - - - - - - - - -
> The two sets of eigenvalues of Ar and Ac are perfectly arbitrary, depending as they do on the complex contents of these matrices, so in effect you are asking how to reorder one arbitrary set of four points in the complex plane so as to best "correspond" to another arbitrary set of four.
>
> Can you describe what you would like to see in such a correspondence? I can think of criteria such as to minimize the sum of the Euclidean distances between corresponding pairs, or perhaps the sum of the squares of these distances. There must be many ways of finding a "best" correspondence among the 24 possibilities, but it is up to you to tell us what it is you want in this respect. We can't read your mind.
>
> Roger Stafford

Date Subject Author
4/13/12 flying
4/14/12 Roger Stafford
4/14/12 flying
4/14/12 Roger Stafford