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Re: docs for MINRES, only for positive definite?


On Feb 28, 2008, at 11:44 AM, Lisandro Dalcin wrote:

Indeed.

In my example, the diagonal matrix has positive and negative entries,
thus being symmetric indefinite. Using PCNONE(==identity), MINRES
success, but with PCJACOBI (despite the preconditioned operator being
the identity, thus SPD) MINRES fails.

The question is if preconditione MINRES could be implemented for the
case of a symmetric but indefinite PC. No time to look for the anwer


  Unlikely. One has to do the minimization in some norm, with minres it
is the norm defined by the preconditioner (or I if no preconditioner)).

   Barry


:-( .

On 2/28/08, Barry Smith <bsmith@xxxxxxxxxxx> wrote: 

  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





--
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