Large scale generalized eigenvalue problem involving dense symmetric positive-definite matrices

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N Madani SYED
N Madani SYED 2011-12-23
Hi all,
I need to solve a generalized eigenvalue problem [A][x]=[B][x][lambda]; where [A] and [B] are positive definite matrices and the resulting [x] should be normalised as [x'][B][x]=[I]; [I] = Identity matrix.
Uptil now, I was using the following commands to solve the problem on a 32-bit computer satisfactorily
L = chol(B);
CL = (inv(L))*A*(inv(L))';
make_mswindows
[v1,r1] = syev(CL,'qr');
eigvector = (inv(L))'*v1;
eigvalue = sqrt(r1);
Here, syev is a function from the MATLAB wrapper for LAPACK (available at <ftp://ftp.netlib.org/lapack/lapwrapmw/index.html>).
But now that I have switched over to a 64-bit workstation, I am getting NO COMPILER error. I reckon that I have to make changes in the mex-code files which I am not able to do.
Is there any other way to this problem? Can we solve the generalized eigenvalue problem by any other method, efficiently. It should be noted that the size of matrices A and B is quite big (200-800 and even more).
Regards, N. Madani SYED
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Walter Roberson
Walter Roberson 2011-12-23
When you say you are getting "NO COMPILER" error, do you mean that you are getting an error indicating that you have not set up a compiler, or do you mean that the code compiles without error message?

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Walter Roberson
Walter Roberson 2011-12-23
Perhaps the simple lapack wrapper would do, http://www.mathworks.com/matlabcentral/fileexchange/16777
This does require mex, which requires that you have installed appropriate compilers for your platform and MATLAB version, such as the ones listed at http://www.mathworks.com/support/compilers/R2011b/win64.html
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Walter Roberson
Walter Roberson 2011-12-25
Which compiler are you using for this? If you use
mex -setup
what did you select?
I would tend to associate that error with the WATCOM C compiler being very old, but that compiler would only be used for 32 bit MATLAB.

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Andrew Newell
Andrew Newell 2011-12-23
You could use eig in place of syev. Or, if you don't need the normalization, you could solve the generalized eigenvalue problem directly using
[eigvector,eigvalue] = eig(A,B)

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