subject:"\[petsc\-users\] Inertia of Hermitian Matrix"

Re: [petsc-users] Inertia of Hermitian Matrix

2018-03-08 Thread Adam Denchfield

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"  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,_row,_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
>

Re: [petsc-users] Inertia of Hermitian Matrix

2018-02-23 Thread Jose E. Roman

Unfortunately MUMPS does not return inertia with complex matrices, it seems 
that it is not implemented. See the note "Usage with Complex Scalars" in 
section 3.4.5 of SLEPc users manual.

You could use multi-communicators with as many partitions as MPI processes, so 
that each process performs a factorization sequentially with PETSc's Cholesky 
(which returns inertia for complex Hermitian matrices). But this is useful only 
for matrices that are not too large.

Jose


> El 23 feb 2018, a las 5:39, Anthony Ruth  escribió:
> 
> 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,_row,_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 
>

[petsc-users] Inertia of Hermitian Matrix

2018-02-22 Thread 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,_row,_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

Re: [petsc-users] Inertia of Hermitian Matrix

Re: [petsc-users] Inertia of Hermitian Matrix

[petsc-users] Inertia of Hermitian Matrix

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