[petsc-users] SLEPc error "The inner product is not well defined: indefinite matrix" when solving generalized EVP with positive semidefinite B

Vladislav Pimanov Vladislav.Pimanov at skoltech.ru
Thu Dec 9 17:57:33 CST 2021

Dear PETSc community!

Could you possibly help me with SLEPc generalized eigenproblem issue.

I am trying to solve Ax = \lambda Bx where A and B are positive semi-definite matrices, both have only constant vector in nullspace. To be precise, A is the Schur complement of the Stokes matrix and B is the Laplacian matrix (classical SIMPLE preconditioner).

I specified EPS_GHEP problem type and tried the Krylov-Schur and Lanczos methods. However, they resulted in error "The inner product is not well defined: indefinite matrix".

I used EPSSetDeflationSpace() to specify the constant nullspace following slepc manual, and the result were correct for problems Ax = \lambda x and Bx = \lambda x separately.

I also tried EPS_GHIEP problem type, but got strange results.

P.S full error message:

[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------

[0]PETSC ERROR: The inner product is not well defined: indefinite matrix

[0]PETSC ERROR: See https://www.mcs.anl.gov/petsc/documentation/faq.html for trouble shooting.

[0]PETSC ERROR: Petsc Release Version 3.13.4, Aug 01, 2020

[0]PETSC ERROR: ./scopes_slepc on a linux-gnu-real-32 named 608add14733f by hydra Thu Dec  9 23:38:43 2021

[0]PETSC ERROR: Configure options PETSC_ARCH=linux-gnu-real-32 --COPTFLAGS=-O3 -march=native -mtune=native --CXXOPTFLAGS=-O3 -march=native -mtune=native --FOPTFLAGS=-O3 -march=native -mtune=native --with-debugging=0 --with-fortran-bindings=0 --with-shared-libraries --download-hdf5 --download-blacs --download-hypre --download-metis --download-parmetis --download-mumps --download-ptscotch --download-scalapack --download-spai --download-suitesparse --with-scalar-type=real

[0]PETSC ERROR: #1 BV_SafeSqrt() line 128 in /usr/local/slepc/include/slepc/private/bvimpl.h

[0]PETSC ERROR: #2 BVNorm_Private() line 473 in /usr/local/slepc/src/sys/classes/bv/interface/bvglobal.c

[0]PETSC ERROR: #3 BVNormVec() line 586 in /usr/local/slepc/src/sys/classes/bv/interface/bvglobal.c

[0]PETSC ERROR: #4 BVOrthogonalizeMGS1() line 65 in /usr/local/slepc/src/sys/classes/bv/interface/bvorthog.c

[0]PETSC ERROR: #5 BVOrthogonalizeGS() line 188 in /usr/local/slepc/src/sys/classes/bv/interface/bvorthog.c

[0]PETSC ERROR: #6 BVOrthogonalizeColumn() line 348 in /usr/local/slepc/src/sys/classes/bv/interface/bvorthog.c

[0]PETSC ERROR: #7 BVInsertVecs() line 363 in /usr/local/slepc/src/sys/classes/bv/interface/bvfunc.c

[0]PETSC ERROR: #8 BVInsertConstraints() line 434 in /usr/local/slepc/src/sys/classes/bv/interface/bvfunc.c

[0]PETSC ERROR: #9 EPSSetUp() line 308 in /usr/local/slepc/src/eps/interface/epssetup.c

[0]PETSC ERROR: #10 EPSSolve() line 136 in /usr/local/slepc/src/eps/interface/epssolve.c

[0]PETSC ERROR: #11 computeCond() line 1634 in scopes_slepc.cpp

Thank you in advance!


Vladislav Pimanov

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