You can verify there is a generalization of the inertia theorem thanks to Ikramov. Furthermore, recall the inertia theorem is about eigenvalues; for a Hermitian matrix, you can diagonalize it in a form that has real entries, and that preserves the eigenvalues.
Of course, being able to apply the theorem and actually applying the theorem/method are very different. Should be something that could be added to MUMPS. On Feb 22, 2018 8:39 PM, "Anthony Ruth" <[email protected]> wrote: > 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 >
