[petsc-users] SLEPc: non-real singular vectors from SVD of real matrix

[Stefano Zampini]

Peder 

We have a fix for the hdf5 complex reader here if you want to give it a try https://gitlab.com/petsc/petsc/-/merge_requests/4044

Sorry it took so long and thank you for reporting the bug

> On Apr 29, 2021, at 2:55 PM, Peder Jørgensgaard Olesen via petsc-users <petsc-users at mcs.anl.gov> wrote:
> 
> Thank you for your advice, Jose.
> 
> I tried using a single column of the data matrix as a basis for left singular vector space, and a row for the right one - and lo and behold, all singular vectors become real.
> 
> Somehow it did not occur to me that I was I was looking at was simply a complex phase on U and V which would cancel upon computing UΣV*. In other words, rather than an incorrect result it was a slightly inconvenient representation of a correct result.
> 
> Best regards
> Peder
> Fra: Jose E. Roman <jroman at dsic.upv.es>
> Sendt: 29. april 2021 13:00:03
> Til: Peder Jørgensgaard Olesen
> Cc: petsc-users at mcs.anl.gov
> Emne: Re: [petsc-users] SLEPc: non-real singular vectors from SVD of real matrix
>  
> In complex scalars there is no way of knowing if the user-provided matrix is real or not. If there was an option of MatSetOption() we could use it.
> 
> If you set a real initial vector with SVDSetInitialSpaces(), then most probably the computed singular vectors will be real. But still rounding errors could introduce a nonzero imaginary part.
> 
> In any case, you could normalize the computed singular vectors, as is done for instance in FixSign() in this examplehttps://slepc.upv.es/documentation/current/src/nep/tutorials/ex20.c.html <https://slepc.upv.es/documentation/current/src/nep/tutorials/ex20.c.html>
> 
> Jose
> 
> 
> > El 29 abr 2021, a las 12:42, Peder Jørgensgaard Olesen via petsc-users <petsc-users at mcs.anl.gov> escribió:
> > 
> > Hello
> > 
> > I've noticed that doing a singular value decomposition of a real matrix appears to result in non-real singular vectors. This should not be the case - singular vectors of a real matrix must be real-valued.
> > 
> > In the example attached I read a matrix from a binary file (also attached), perform the SVD, and write singular vectors to an HDF5 file which I subsequently inspect using h5dump, revealing  non-zero imaginary parts of vector elements as highlighted below:
> > [pjool at svol mwes]$ h5dump -d U0_sample_svd -c "5,2" sample_svecs.h5 
> > HDF5 "sample_svecs.h5" {
> > DATASET "U0_sample_svd" {
> >    DATATYPE  H5T_IEEE_F64LE
> >    DATASPACE  SIMPLE { ( 882, 2 ) / ( 882, 2 ) }
> >    SUBSET {
> >       START ( 0, 0 );
> >       STRIDE ( 1, 1 );
> >       COUNT ( 5, 2 );
> >       BLOCK ( 1, 1 );
> >       DATA {
> >       (0,0): 0.0226108, 0.0299595,
> >       (1,0): 0.035414, 0.0469237,
> >       (2,0): 0.0276317, 0.0366122,
> >       (3,0): 0.0145344, 0.0192581,
> >       (4,0): 0.0110376, 0.0146249
> >       }
> >    }
> >    ATTRIBUTE "complex" {
> >       DATATYPE  H5T_STD_I32LE
> >       DATASPACE  SCALAR
> >       DATA {
> >       (0): 1
> >       }
> >    }
> > }
> > }
> > I also extract the imaginary part of the input matrix and print its norm to ensure that the matrix is indeed real.
> > 
> > I'm running v3.14, but I don't believe that alone should cause the issue, since it what I'm trying to do appears like a rather common and basic task.
> > 
> > What might be the reason behind this behavior, and what can be done to resolve it?
> > 
> > 
> > Med venlig hilsen / Best Regards
> > 
> > Peder Jørgensgaard Olesen
> > PhD Student, Turbulence Research Lab
> > Dept. of Mechanical Engineering
> > Technical University of Denmark
> > Niels Koppels Allé
> > Bygning 403, Rum 105
> > DK-2800 Kgs. Lyngby
> > <read_bin.c><sample_data>

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