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

[Peder Jørgensgaard Olesen]

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
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