[petsc-users] SLEPc: non-real singular vectors from SVD of real matrix
Jose E. Roman
jroman at dsic.upv.es
Thu Apr 29 06:00:03 CDT 2021
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 example 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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