Hello PETSc developers,
I went through the ex23.c of ksp section attached herewith but I don't
understand the following part:
***********************************************
tol=1000.*PETSC_MACHINE_EPSILON
************************************************
and,
************************************************
ierr = VecAXPY(x,-1.0,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",
(double)norm,its);CHKERRQ(ierr);
}
************************************************
I don't understand what is "tol" here and "*PETSC_MACHINE_EPSILON"?
The if condition is also not clear to me.
Thanks.
Sincerely,
Huq
--
Fazlul Huq
Graduate Research Assistant
Department of Nuclear, Plasma & Radiological Engineering (NPRE)
University of Illinois at Urbana-Champaign (UIUC)
E-mail: huq2...@gmail.com
static char help[] = "Solves a tridiagonal linear system.\n\n";
/*T
Concepts: KSP^basic parallel example;
Processors: n
T*/
/*
Include "petscksp.h" so that we can use KSP solvers. Note that this file
automatically includes:
petscsys.h - base PETSc routines petscvec.h - vectors
petscmat.h - matrices
petscis.h - index sets petscksp.h - Krylov subspace methods
petscviewer.h - viewers petscpc.h - preconditioners
Note: The corresponding uniprocessor example is ex1.c
*/
#include <petscksp.h>
int main(int argc,char **args)
{
Vec x, b, u; /* approx solution, RHS, exact solution */
Mat A; /* linear system matrix */
KSP ksp; /* linear solver context */
PC pc; /* preconditioner context */
PetscReal norm,tol=1000.*PETSC_MACHINE_EPSILON; /* norm of solution error */
PetscErrorCode ierr;
PetscInt i,n = 10,col[3],its,rstart,rend,nlocal;
PetscScalar one = 1.0,value[3];
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrix and right-hand-side vector that define
the linear system, Ax = b.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create vectors. Note that we form 1 vector from scratch and
then duplicate as needed. For this simple case let PETSc decide how
many elements of the vector are stored on each processor. The second
argument to VecSetSizes() below causes PETSc to decide.
*/
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,PETSC_DECIDE,n);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);CHKERRQ(ierr);
/* Identify the starting and ending mesh points on each
processor for the interior part of the mesh. We let PETSc decide
above. */
ierr = VecGetOwnershipRange(x,&rstart,&rend);CHKERRQ(ierr);
ierr = VecGetLocalSize(x,&nlocal);CHKERRQ(ierr);
/*
Create matrix. When using MatCreate(), the matrix format can
be specified at runtime.
Performance tuning note: For problems of substantial size,
preallocation of matrix memory is crucial for attaining good
performance. See the matrix chapter of the users manual for details.
We pass in nlocal as the "local" size of the matrix to force it
to have the same parallel layout as the vector created above.
*/
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,nlocal,nlocal,n,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
/*
Assemble matrix.
The linear system is distributed across the processors by
chunks of contiguous rows, which correspond to contiguous
sections of the mesh on which the problem is discretized.
For matrix assembly, each processor contributes entries for
the part that it owns locally.
*/
if (!rstart) {
rstart = 1;
i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
if (rend == n) {
rend = n-1;
i = n-1; col[0] = n-2; col[1] = n-1; value[0] = -1.0; value[1] = 2.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
/* Set entries corresponding to the mesh interior */
value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
for (i=rstart; i<rend; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
/* Assemble the matrix */
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/*
Set exact solution; then compute right-hand-side vector.
*/
ierr = VecSet(u,one);CHKERRQ(ierr);
ierr = MatMult(A,u,b);CHKERRQ(ierr);
ierr = VecView(b,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the linear solver and set various options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create linear solver context
*/
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
/*
Set operators. Here the matrix that defines the linear system
also serves as the preconditioning matrix.
*/
ierr = KSPSetOperators(ksp,A,A);CHKERRQ(ierr);
/*
Set linear solver defaults for this problem (optional).
- By extracting the KSP and PC contexts from the KSP context,
we can then directly call any KSP and PC routines to set
various options.
- The following four statements are optional; all of these
parameters could alternatively be specified at runtime via
KSPSetFromOptions();
*/
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetType(pc,PCJACOBI);CHKERRQ(ierr);
ierr = KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);CHKERRQ(ierr);
/*
Set runtime options, e.g.,
-ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
These options will override those specified above as long as
KSPSetFromOptions() is called _after_ any other customization
routines.
*/
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the linear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Solve linear system
*/
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/*
View solver info; we could instead use the option -ksp_view to
print this info to the screen at the conclusion of KSPSolve().
*/
ierr = KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Check solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Check the error
*/
ierr = VecView(u,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecAXPY(x,-1.0,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);CHKERRQ(ierr);
}
/*
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
*/
ierr = VecDestroy(&x);CHKERRQ(ierr); ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr); ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
/*
Always call PetscFinalize() before exiting a program. This routine
- finalizes the PETSc libraries as well as MPI
- provides summary and diagnostic information if certain runtime
options are chosen (e.g., -log_view).
*/
ierr = PetscFinalize();
return ierr;
}
/*TEST
build:
requires: !complex !single
test:
args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
test:
suffix: 2
nsize: 3
args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
test:
suffix: 3
nsize: 2
args: -ksp_monitor_short -ksp_rtol 1e-6 -ksp_type pipefgmres
TEST*/
