Eigenvalues for singular matrices

[perholm]

Hi,
I am using IPP 5.2 and ippmEigenValuesVectorsSym_m_32f to calculate the eigenvectors of a symmetric matrix. In my case the matrix can sometimes be singular, and that's fine, but then the function returns ippStsSingularErr and no eigenvectors are calculated. I find this quite strange since e.g Matlab has no problem calculating eigenvectors for singular matrices.

Q1) Does anyone have any workaround for this?
Q2) Intel, do you plan on or maby already have, solved this in newer versions?

/Per

[Ying_H_Intel]

Quoting - perholm

Hi,
I am using IPP 5.2 and ippmEigenValuesVectorsSym_m_32f to calculate the eigenvectors of a symmetric matrix. In my case the matrix can sometimes be singular, and that's fine, but then the function returns ippStsSingularErr and no eigenvectors are calculated. I find this quite strange since e.g Matlab has no problem calculating eigenvectors for singular matrices.

Q1) Does anyone have any workaround for this?
Q2) Intel, do you plan on or maby already have, solved this in newer versions?

/Per

Hi Per,

IPP's ippmEigenValuesVectorsSym function uses QR algorithm for solving eigenvalue problem.
the algorithm are numerical unstable for badly conditioned matrix (det is close to 0). That's is why there are error condition (ippStsSingularErr)for the function. When Abs(det) < ( 2.2204460492503131e-016, the function willreturn "ippStsSingularErr". As i knew, we haven't planed to change the algorithm at least in recently version, IPP 6.x.

I guess, Matlab use different algorithm for calculating this.

For workaround, you may tryother function like ippsSVDSort, which is in ippsman.pdf and can do singular value decomposition.
or you maycheck IPP's sister library - math kernal library (MKL, http://software.intel.com/en-us/intel-mkl/, which provide much more functions for Eigenvalue Problem.

Regards,
Ying

[Michael_C_Intel4]

Actually, QR algorithm is quite stable, at least, it's known as most stable among other algorithms. You should try MKL, there's no problem for MKL to solve eigenproblem with the singular matrix.

You may look at the example of the MKL eigensolver usage at http://software.intel.com/sites/products/documentation/hpc/mkl/lapack/mkl_lapack_examples/ssyev_ex.c.htm.

Michael.