docs for MINRES, only for positive definite?
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 Dalc?n --- Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC) Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC) Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET) PTLC - G?emes 3450, (3000) Santa Fe, Argentina Tel/Fax: +54-(0)342-451.1594
docs for MINRES, only for positive definite?
Docs are wrong. Matt 2008/2/28 Lisandro Dalcin dalcinl at gmail.com: 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 Dalc?n --- Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC) Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC) Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET) PTLC - G?emes 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
docs for MINRES, only for positive definite?
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 at gmail.com: 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 Dalc?n --- Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC) Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC) Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET) PTLC - G?emes 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
docs for MINRES, only for positive definite?
On Thu, Feb 28, 2008 at 10:56 AM, Barry Smith bsmith at mcs.anl.gov wrote: But does it require a positive definite preconditioner? You mean so I can play the trick with M^1/2 A M^1/2 to maintain symmetry? I think you may be right. Matt Barry On Feb 28, 2008, at 9:32 AM, Matthew Knepley wrote: Docs are wrong. Matt 2008/2/28 Lisandro Dalcin dalcinl at gmail.com: 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 Dalc?n --- Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC) Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC) Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET) PTLC - G?emes 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 -- 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
docs for MINRES, only for positive definite?
Good point, the current code seems to require that...
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 at mcs.anl.gov 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 at gmail.com:
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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET)
PTLC - G?emes 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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET)
PTLC - G?emes 3450, (3000) Santa Fe, Argentina
Tel/Fax: +54-(0)342-451.1594
docs for MINRES, only for positive definite?
On Thu, Feb 28, 2008 at 11:25 AM, Lisandro Dalcin dalcinl at gmail.com 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 at mcs.anl.gov 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 at gmail.com:
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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET)
PTLC - G?emes 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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET)
PTLC - G?emes 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
docs for MINRES, only for positive definite?
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 at gmail.com 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 at mcs.anl.gov 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 at gmail.com:
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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a
(CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica
(INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas
(CONICET)
PTLC - G?emes 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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET)
PTLC - G?emes 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
docs for MINRES, only for positive definite?
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
:-( .
On 2/28/08, Barry Smith bsmith at mcs.anl.gov 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 at gmail.com 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 at mcs.anl.gov 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 at gmail.com:
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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a
(CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica
(INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas
(CONICET)
PTLC - G?emes 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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET)
PTLC - G?emes 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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET)
PTLC - G?emes 3450, (3000) Santa Fe, Argentina
Tel/Fax: +54-(0)342-451.1594
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 at mcs.anl.gov 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 at gmail.com 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 at mcs.anl.gov 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 at gmail.com:
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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a
(CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica
(INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas
(CONICET)
PTLC - G?emes 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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a
(CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica
(INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas
(CONICET)
PTLC - G?emes 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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET)
PTLC - G?emes 3450, (3000) Santa Fe, Argentina
Tel/Fax: +54-(0)342-451.1594
docs for MINRES, only for positive definite?
On Thu, Feb 28, 2008 at 11:35 AM, Barry Smith bsmith at mcs.anl.gov 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.
I disagree. Here is a weaker condition:
1) A is symmetric indefinite and so is B
2) BA is also symmetric
Since A and B are full rank, so is BA. Thus BA is symmetric indefinite
and MINRES will work.
My comment was that if B is SPD, then BA is equivalent to B^1/2 A
B^1/2 and thus symmetric.
Matt
Barry
On Feb 28, 2008, at 11:28 AM, Matthew Knepley wrote:
On Thu, Feb 28, 2008 at 11:25 AM, Lisandro Dalcin
dalcinl at gmail.com 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 at mcs.anl.gov 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 at gmail.com:
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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a
(CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica
(INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas
(CONICET)
PTLC - G?emes 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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a (CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica (INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas (CONICET)
PTLC - G?emes 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
--
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
docs for MINRES, only for positive definite?
On Feb 28, 2008, at 11:44 AM, Matthew Knepley wrote:
On Thu, Feb 28, 2008 at 11:35 AM, Barry Smith bsmith at mcs.anl.gov
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.
I disagree. Here is a weaker condition:
1) A is symmetric indefinite and so is B
2) BA is also symmetric
Since A and B are full rank, so is BA. Thus BA is symmetric indefinite
and MINRES will work.
But that is a different algorithm. That is running minres on the
operator
BA with the preconditioner I which is very different than running
minres on A with the preconditioner B.
My comment was that if B is SPD, then BA is equivalent to B^1/2 A
B^1/2 and thus symmetric.
Matt
Barry
On Feb 28, 2008, at 11:28 AM, Matthew Knepley wrote:
On Thu, Feb 28, 2008 at 11:25 AM, Lisandro Dalcin
dalcinl at gmail.com 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 at mcs.anl.gov 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 at gmail.com:
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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a
(CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica
(INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas
(CONICET)
PTLC - G?emes 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 Dalc?n
---
Centro Internacional de M?todos Computacionales en Ingenier?a
(CIMEC)
Instituto de Desarrollo Tecnol?gico para la Industria Qu?mica
(INTEC)
Consejo Nacional de Investigaciones Cient?ficas y T?cnicas
(CONICET)
PTLC - G?emes 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
--
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
