Re: docs for MINRES, only for positive definite?

[Barry Smith <bsmith@xxxxxxxxxxx>]

  symmetry has nothing to do with it. Yes the matrix and  
preconditioner must be
symmetric. The point is that the preconditioner has to also be  
positive definite.
Because B is used in the algorithm to define a norm.

   Barry

On Feb 28, 2008, at 11:28 AM, Matthew Knepley wrote:

> On Thu, Feb 28, 2008 at 11:25 AM, Lisandro Dalcin  
> <dalcinl@xxxxxxxxx> wrote:
> > Good point, the current code seems to require that...
>
> Its not the code, its the algorithm. It requires symmetry.
>
>  Matt
>
> >  ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /*     z  <- B*r       */
> >  ierr = VecDot(R,Z,&dp);CHKERRQ(ierr);
> >  /*...*/
> >  if (dp < 0.0) {
> >    ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
> >    PetscFunctionReturn(0);
> >  }
> >
> > Indeed, the following (simple minded, diagonal matrix) test fails  
> > with
> > -pc_type jacobi, but success with -pc_type none
> >
> > import sys, petsc4py
> > petsc4py.init(sys.argv)
> > from petsc4py import PETSc
> > import numpy as N
> > A = PETSc.Mat().createAIJ([10,10])
> > for i in range(0,5):
> >    A[i,i] = -(i + 1)
> > for i in range(5,10):
> >    A[i,i] = +(i + 1)
> > A.assemble()
> > A.view()
> > x, b= A.getVecs()
> > b.set(1)
> > ksp = PETSc.KSP().create()
> > ksp.type = 'minres'
> > ksp.setOperators(A)
> > ksp.setFromOptions()
> > ksp.solve(b,x)
> >
> >
> >
> >
> > On 2/28/08, Barry Smith <bsmith@xxxxxxxxxxx> wrote:
> > >    But does it require a positive definite preconditioner?
> >
> >
> > >    Barry
> > >
> > >
> > > On Feb 28, 2008, at 9:32 AM, Matthew Knepley wrote:
> > >
> > > > Docs are wrong.
> > > >
> > > > Matt
> > > >
> > > > 2008/2/28 Lisandro Dalcin <dalcinl@xxxxxxxxx>:
> > > > > I've noticed that the docs for MINRES say that the operator and  
> > > > > the
> > > > > preconditioner must be POSITIVE DEFINITE. But I understand  
> > > > > MINRES is
> > > > > tailored for the symmetric/hermitian-indefinite case.
> > > > >
> > > > > Are the docs wrong? Or the actual code is a (very peculiar) MINRES
> > > > > variant?
> > > > >
> > > > >
> > > > > --
> > > > > Lisandro Dalcín
> > > > > ---------------
> > > > > Centro Internacional de Métodos Computacionales en Ingeniería  
> > > > > (CIMEC)
> > > > > Instituto de Desarrollo Tecnológico para la Industria Química  
> > > > > (INTEC)
> > > > > Consejo Nacional de Investigaciones Científicas y Técnicas  
> > > > > (CONICET)
> > > > > PTLC - Güemes 3450, (3000) Santa Fe, Argentina
> > > > > Tel/Fax: +54-(0)342-451.1594
> > > >
> > > >
> > > >
> > > > --
> > > > What most experimenters take for granted before they begin their
> > > > experiments is infinitely more interesting than any results to  
> > > > which
> > > > their experiments lead.
> > > > -- Norbert Wiener
> >
> >
> > --
> > Lisandro Dalcín
> > ---------------
> > Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC)
> > Instituto de Desarrollo Tecnológico para la Industria Química (INTEC)
> > Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
> > PTLC - Güemes 3450, (3000) Santa Fe, Argentina
> > Tel/Fax: +54-(0)342-451.1594
>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which
> their experiments lead.
> -- Norbert Wiener