[petsc-users] Pseudoinverse of a large matrix

[Modhurita Mitra]

I am trying to express the radiation pattern of an antenna in terms of
spherical harmonic basis functions. I have radiation pattern data at
N=324360 points. Therefore, my matrix is spherical harmonic basis functions
evaluated till order sqrt(N) (which makes up at total of N elements),
evaluated at N data points. So this is a linear least squares problem, and
I have been trying to solve it by finding its pseudoinverse which uses SVD.
The elements of the matrix are complex, and the matrix is non-sparse. I
have solved it in MATLAB using a subsample of the data, but MATLAB runs out
of memory while calculating the SVD at input matrix size 2500 X 2500. I
need to solve this problem using the entire data.

I was thinking of using SLEPc because I found a ready-to-use code which
computes the SVD of a complex-valued matrix (
http://www.grycap.upv.es/slepc/documentation/current/src/svd/examples/tutorials/ex14.c.html).
I don't know how to use either PETSc or SLEPc (or Elemental) yet, so I
am trying to figure out where to start and what I should learn.

Thanks,
Modhurita


On Mon, Dec 19, 2011 at 12:31 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Mon, Dec 19, 2011 at 12:21 PM, Modhurita Mitra <modhurita at gmail.com>wrote:
>
>> Hi,
>>
>> I have to compute the pseudoinverse of a 324360 X 324360 matrix. Can
>> PETSc compute the SVD of this matrix without parallelization? If
>> parallelization is needed, do I need to use SLEPc?
>>
>
> With enough memory, yes. However, I am not sure you want to wait. I am not
> sure how SLEPc would help here.
> From the very very little detail you have given, you would need parallel
> linear algebra, like Elemental. However,
> I would start out from a more fundamental viewpoint. Such as replacing
> "compute the psuedoinverse" with
> "solve a least-squares problem" if that is indeed the case.
>
>    Matt
>
>
>>
>> Thanks,
>> Modhurita
>>
>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
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