[petsc-users] Inertia of Hermitian Matrix

[Anthony Ruth]

Hello,

I am trying to diagonalize a hermitian matrix using the Eigen Problem
Solver in SLEPc, I run into errors on calls to MatGetInertia() with complex
hermitian matrices that I did not see with real matrices. The complex and
real versions were done with separate PETSC_ARCH. I do not know if the
problem is with the set up of the matrix or more generally a problem
calculating the inertia for a complex matrix.
The matrix is created by:

ierr = MatSetType(A,MATAIJ);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
        ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&first_row,&last_row);CHKERRQ(ierr);
ierr = MatSetValues(A,m,idxm,n,idxn,data,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

For a hermitian matrix, all the eigenvalues are real, so I believe it is
possible to calculate an inertia by looking at the signs of the diagonal
entries. I believe if it was complex but not hermitian, the complex
eigenvalues calculating inertia would be difficult.  Is there some problem
with doing this through sparse iterative methods? Is there a certain place
the matrix needs to be specified as hermitian besides upon assembly?

Here is the error stack I see when running:


Mat Object: 1 MPI processes
  type: seqaij
row 0: (0, 0.)  (1, 1. + 1. i) (2, 0.)  (3, 0.)  (4, 0.)
row 1: (0, 1. - 1. i) (1, 0.)  (2, 1. + 1. i) (3, 0.)  (4, 0.)
row 2: (0, 0.)  (1, 1. - 1. i) (2, 0.)  (3, 1. + 1. i) (4, 0.)
row 3: (0, 0.)  (1, 0.)  (2, 1. - 1. i) (3, 0.)  (4, 1. + 1. i)
row 4: (0, 0.)  (1, 0.)  (2, 0.)  (3, 1. - 1. i) (4, 0.)
[0]PETSC ERROR: --------------------- Error Message
--------------------------------------------------------------
[0]PETSC ERROR: No support for this operation for this object type
[0]PETSC ERROR: Mat type mumps
[0]PETSC ERROR: See http://www.mcs.anl.gov/petsc/documentation/faq.html for
trouble shooting.
[0]PETSC ERROR: Petsc Release Version 3.8.2, Nov, 09, 2017
[0]PETSC ERROR: Configure options --download-metis --download-mumps
--download-parmetis --download-scalapack --with-scalar-type=complex
[0]PETSC ERROR: #1 MatGetInertia() line 8416 in
/home/anthony/DFTB+SIPs/petsc-3.8.2/src/mat/interface/matrix.c
[0]PETSC ERROR: #2 EPSSliceGetInertia() line 333 in
/home/anthony/DFTB+SIPs/slepc-3.8.1/src/eps/impls/krylov/krylovschur/ks-slice.c
[0]PETSC ERROR: #3 EPSSetUp_KrylovSchur_Slice() line 459 in
/home/anthony/DFTB+SIPs/slepc-3.8.1/src/eps/impls/krylov/krylovschur/ks-slice.c
[0]PETSC ERROR: #4 EPSSetUp_KrylovSchur() line 146 in
/home/anthony/DFTB+SIPs/slepc-3.8.1/src/eps/impls/krylov/krylovschur/krylovschur.c
[0]PETSC ERROR: #5 EPSSetUp() line 165 in
/home/anthony/DFTB+SIPs/slepc-3.8.1/src/eps/interface/epssetup.c
[0]PETSC ERROR: #6 EPSSliceGetEPS() line 298 in
/home/anthony/DFTB+SIPs/slepc-3.8.1/src/eps/impls/krylov/krylovschur/ks-slice.c
[0]PETSC ERROR: #7 EPSSetUp_KrylovSchur_Slice() line 408 in
/home/anthony/DFTB+SIPs/slepc-3.8.1/src/eps/impls/krylov/krylovschur/ks-slice.c
[0]PETSC ERROR: #8 EPSSetUp_KrylovSchur() line 146 in
/home/anthony/DFTB+SIPs/slepc-3.8.1/src/eps/impls/krylov/krylovschur/krylovschur.c
[0]PETSC ERROR: #9 EPSSetUp() line 165 in
/home/anthony/DFTB+SIPs/slepc-3.8.1/src/eps/interface/epssetup.c
[0]PETSC ERROR: #10 SIPSolve() line 195 in
/home/anthony/DFTB+SIPs/dftb-eig15/sips.c
[0]PETSC ERROR: --------------------- Error Message
--------------------------------------------------------------
[0]PETSC ERROR: Invalid argument
[0]PETSC ERROR: Wrong type of object: Parameter # 1
[0]PETSC ERROR: See http://www.mcs.anl.gov/petsc/documentation/faq.html for
trouble shooting.
[0]PETSC ERROR: Petsc Release Version 3.8.2, Nov, 09, 2017
[0]PETSC ERROR: Configure options --download-metis --download-mumps
--download-parmetis --download-scalapack --with-scalar-type=complex
[0]PETSC ERROR: #11 EPSGetConverged() line 257 in
/home/anthony/DFTB+SIPs/slepc-3.8.1/src/eps/interface/epssolve.c
[0]PETSC ERROR: #12 squareFromEPS() line 131 in
/home/anthony/DFTB+SIPs/dftb-eig15/sips_square.c



regards,
Anthony Ruth
Condensed Matter Theory
University of Notre Dame
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