Commit 30b1861a authored by kadir's avatar kadir

smaples for krylov methods are added

parent 12534ca5
......@@ -12,3 +12,12 @@ In this Sparse Linear Algebra folder, there are sample codes for beginners, as w
- spgemm: Multiplication of two sparse matrices.
- mkl_shmem: Using MKL's routine mkl_dcsrmultcsr() on a multicore processor
- mkl_xphi: Using MKL's routine mkl_dcsrmultcsr() via offloading to a Xeon Phi coprocessor
- Krylov Subspace Methods
- Linear system solution in parallel
- 2D Laplacian (2D mesh)
- Repeatedly solving two linear systems
- Same preconditioner
- Two different matrices with the same nonzero pattern
- Solving multiple linear systems
- Same cofficient matrix
- Different right-hand-side vectors
# ==================================================================================================
# This file is part of the CodeVault project. The project is licensed under Apache Version 2.0.
# CodeVault is part of the EU-project PRACE-4IP (WP7.3.C).
#
# Author(s):
# Valeriu Codreanu <valeriu.codreanu@surfsara.nl>
#
# ==================================================================================================
cmake_minimum_required(VERSION 2.8.10 FATAL_ERROR)
list(APPEND CMAKE_MODULE_PATH "${CMAKE_CURRENT_SOURCE_DIR}/../../../../cmake/Modules")
set(CMAKE_VERBOSE_MAKEFILE ON)
## OGUZ: Edit accordingly
include(${CMAKE_CURRENT_SOURCE_DIR}/../../../cmake/common.cmake)
# ==================================================================================================
if ("${DWARF_PREFIX}" STREQUAL "")
set(DWARF_PREFIX 2_sparse)
endif()
## OGUZ: Add executables. There must be more convenient way :-)
set(NAME ${DWARF_PREFIX}_krylov_simple)
set(NAMEB ${DWARF_PREFIX}_krylov_twosys)
set(NAMEC ${DWARF_PREFIX}_krylov_multirhs)
# ==================================================================================================
# C++ compiler settings
find_package(Common)
find_package(PETSc REQUIRED)
find_package(MPI)
select_compiler_flags(cxx_flags
GNU "-march=native" # I suggest remove "-O3" as this is controlled by the CMAKE_BUILD_TYPE
CLANG "-march=native" # same here
Intel "-axavx2,avx")
set(CXX_FLAGS ${cxx_flags})
if("${CMAKE_CXX_COMPILER_ID}" STREQUAL "GNU")
set(CXX_FLAGS "${CXX_FLAGS} -Wall -Wno-comment")
if(APPLE)
set(CXX_FLAGS "${CXX_FLAGS} -Wa,-q")
endif()
endif()
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${CXX_FLAGS}")
# ==================================================================================================
# LUD with the MKL library
if (PETSc_FOUND AND MPI_FOUND)
message("Petsc dir: ${PETSC_DIR}")
message("Petsc arch: ${PETSC_ARCH}")
message("Petsc includes: ${PETSC_INCLUDES}")
message("Petsc libs: ${PETSC_LIBRARIES}")
include_directories(${PETSC_INCLUDES})
add_definitions (${PETSC_DEFINITIONS})
link_directories(${petsc_lib_dir})
add_executable(${NAME} ksp_solver_simple.c)
target_link_libraries(${NAME} ${PETSC_LIBRARIES})
install(TARGETS ${NAME} DESTINATION bin)
add_executable(${NAMEB} ksp_solver_two_sys.c)
target_link_libraries(${NAMEB} ${PETSC_LIBRARIES} mpi)
install(TARGETS ${NAMEB} DESTINATION bin)
add_executable(${NAMEC} ksp_solver_multi_rhs.c)
target_link_libraries(${NAMEC} ${PETSC_LIBRARIES} mpi)
install(TARGETS ${NAMEC} DESTINATION bin)
else ()
message("## Skipping '${NAME}': no PETSC support found")
install(CODE "MESSAGE(\"${NAME} can only be built with PETSC.\")")
endif()
unset(NAME)
# ==================================================================================================
=======
README
=======
The samples in this folder demonstrate the usage of PETSc (implicit parallelism)
- Basic structures (Mat, Vec, KSP, PC, etc.)
- Profiling stages of the code
- Examples can make use of different preconditioners and solvers (provided via command line arguments)
- 1. Code sample name
ksp_solver_simple.c
ksp_solver_two_sys.c
ksp_colver_multi_rhs.c
- 2. Description of the code sample package
Samples for introduction to Krylov Subspace Methods by using PETSc:
- Linear system solution in parallel
- 2D Laplacian (2D mesh)
- Repeatedly solving two linear systems
- Same preconditioner
- Two different matrices with the same nonzero pattern
- Solving multiple linear systems
- Same cofficient matrix
- Different right-hand-side vectors
- 3. Release date
20 January 2016
- 4. Version history
1.0: initial version
- 5. Contributor (s) / Maintainer(s)
Cevdet Aykanat (aykanat@cs.bilkent.edu.tr)
Kadir Akbudak (kadir.cs@gmail.com)
Reha Oguz Selvitopi(reha@cs.bilkent.edu.tr)
- 6. Copyright / License of the code sample
- 7. Language(s)
C
- 8. Parallelisation Implementation(s)
MPI
- 9. Level of the code sample complexity
new starters
- 10. Instructions on how to compile the code
*Note that PETSc and MPI libraries must be available.*
$ rm -rf CMakeFiles CMakeCache.txt; cmake .;make
- 11. Instructions on how to run the code
$./run.sh
- 12. Sample input(s)
No input is required.
- 13. Sample output(s)
No file is produced. norm are printed to standard output.
/*
2-clause BSD license
Copyright (c) 1991-2014, UChicago Argonne, LLC and the PETSc Development Team
All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice, this
list of conditions and the following disclaimer in the documentation and/or
other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
static char help[] = "Solves a sequence of linear systems with different right-hand-side vectors.\n\
Input parameters include:\n\
-ntimes <ntimes> : number of linear systems to solve\n\
-view_exact_sol : write exact solution vector to stdout\n\
-m <mesh_x> : number of mesh points in x-direction\n\
-n <mesh_n> : number of mesh points in y-direction\n\n";
/*T
Concepts: KSP^repeatedly solving linear systems;
Concepts: KSP^Laplacian, 2d
Concepts: Laplacian, 2d
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
*/
#include <petscksp.h>
#undef __FUNCT__
#define __FUNCT__ "main"
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 */
PetscReal norm; /* norm of solution error */
PetscErrorCode ierr;
PetscInt ntimes,i,j,k,Ii,J,Istart,Iend;
PetscInt m = 8,n = 7,its;
PetscBool flg = PETSC_FALSE;
PetscScalar v,one = 1.0,neg_one = -1.0,rhs;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrix for use in solving a series of
linear systems of the form, A x_i = b_i, for i=1,2,...
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create parallel matrix, specifying only its global dimensions.
When using MatCreate(), the matrix format can be specified at
runtime. Also, the parallel partitioning of the matrix is
determined by PETSc at runtime.
*/
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
/*
Currently, all PETSc parallel matrix formats are partitioned by
contiguous chunks of rows across the processors. Determine which
rows of the matrix are locally owned.
*/
ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
/*
Set matrix elements for the 2-D, five-point stencil in parallel.
- Each processor needs to insert only elements that it owns
locally (but any non-local elements will be sent to the
appropriate processor during matrix assembly).
- Always specify global rows and columns of matrix entries.
*/
for (Ii=Istart; Ii<Iend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {J = Ii - n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (i<m-1) {J = Ii + n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (j>0) {J = Ii - 1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (j<n-1) {J = Ii + 1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
v = 4.0; ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);CHKERRQ(ierr);
}
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd()
Computations can be done while messages are in transition
by placing code between these two statements.
*/
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/*
Create parallel vectors.
- When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
we specify only the vector's global
dimension; the parallel partitioning is determined at runtime.
- When solving a linear system, the vectors and matrices MUST
be partitioned accordingly. PETSc automatically generates
appropriately partitioned matrices and vectors when MatCreate()
and VecCreate() are used with the same communicator.
- Note: We form 1 vector from scratch and then duplicate as needed.
*/
ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
ierr = VecSetSizes(u,PETSC_DECIDE,m*n);CHKERRQ(ierr);
ierr = VecSetFromOptions(u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecDuplicate(b,&x);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 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 several linear systems of the form A x_i = b_i
I.e., we retain the same matrix (A) for all systems, but
change the right-hand-side vector (b_i) at each step.
In this case, we simply call KSPSolve() multiple times. The
preconditioner setup operations (e.g., factorization for ILU)
be done during the first call to KSPSolve() only; such operations
will NOT be repeated for successive solves.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ntimes = 2;
ierr = PetscOptionsGetInt(NULL,"-ntimes",&ntimes,NULL);CHKERRQ(ierr);
for (k=1; k<ntimes+1; k++) {
/*
Set exact solution; then compute right-hand-side vector. We use
an exact solution of a vector with all elements equal to 1.0*k.
*/
rhs = one * (PetscReal)k;
ierr = VecSet(u,rhs);CHKERRQ(ierr);
ierr = MatMult(A,u,b);CHKERRQ(ierr);
/*
View the exact solution vector if desired
*/
ierr = PetscOptionsGetBool(NULL,"-view_exact_sol",&flg,NULL);CHKERRQ(ierr);
if (flg) {ierr = VecView(u,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/*
Check the error
*/
ierr = VecAXPY(x,neg_one,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
/*
Print convergence information. PetscPrintf() produces a single
print statement from all processes that share a communicator.
*/
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g System %D: iterations %D\n",(double)norm,k,its);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
*/
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr); ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr); ierr = MatDestroy(&A);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_summary).
*/
ierr = PetscFinalize();
return 0;
}
/*
2-clause BSD license
Copyright (c) 1991-2014, UChicago Argonne, LLC and the PETSc Development Team
All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice, this
list of conditions and the following disclaimer in the documentation and/or
other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
static char help[] = "Solves a linear system in parallel with KSP.\n\
Input parameters include:\n\
-random_exact_sol : use a random exact solution vector\n\
-view_exact_sol : write exact solution vector to stdout\n\
-m <mesh_x> : number of mesh points in x-direction\n\
-n <mesh_n> : number of mesh points in y-direction\n\n";
/*T
Concepts: KSP^basic parallel example;
Concepts: KSP^Laplacian, 2d
Concepts: Laplacian, 2d
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
*/
#include <petscksp.h>
#undef __FUNCT__
#define __FUNCT__ "main"
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 */
PetscRandom rctx; /* random number generator context */
PetscReal norm; /* norm of solution error */
PetscInt i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
PetscErrorCode ierr;
PetscBool flg = PETSC_FALSE;
PetscScalar v;
#if defined(PETSC_USE_LOG)
PetscLogStage stage;
#endif
PetscInitialize(&argc,&args,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrix and right-hand-side vector that define
the linear system, Ax = b.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create parallel matrix, specifying only its global dimensions.
When using MatCreate(), the matrix format can be specified at
runtime. Also, the parallel partitioning of the matrix is
determined by PETSc 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.
*/
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);CHKERRQ(ierr);
ierr = MatSeqAIJSetPreallocation(A,5,NULL);CHKERRQ(ierr);
/*
Currently, all PETSc parallel matrix formats are partitioned by
contiguous chunks of rows across the processors. Determine which
rows of the matrix are locally owned.
*/
ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
/*
Set matrix elements for the 2-D, five-point stencil in parallel.
- Each processor needs to insert only elements that it owns
locally (but any non-local elements will be sent to the
appropriate processor during matrix assembly).
- Always specify global rows and columns of matrix entries.
Note: this uses the less common natural ordering that orders first
all the unknowns for x = h then for x = 2h etc; Hence you see J = Ii +- n
instead of J = I +- m as you might expect. The more standard ordering
would first do all variables for y = h, then y = 2h etc.
*/
ierr = PetscLogStageRegister("Assembly", &stage);CHKERRQ(ierr);
ierr = PetscLogStagePush(stage);CHKERRQ(ierr);
for (Ii=Istart; Ii<Iend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {J = Ii - n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (i<m-1) {J = Ii + n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {J = Ii - 1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {J = Ii + 1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
v = 4.0; ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd()
Computations can be done while messages are in transition
by placing code between these two statements.
*/
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
/* A is symmetric. Set symmetric flag to enable ICC/Cholesky preconditioner */
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
/*
Create parallel vectors.
- We form 1 vector from scratch and then duplicate as needed.
- When using VecCreate(), VecSetSizes and VecSetFromOptions()
in this example, we specify only the
vector's global dimension; the parallel partitioning is determined
at runtime.
- When solving a linear system, the vectors and matrices MUST
be partitioned accordingly. PETSc automatically generates
appropriately partitioned matrices and vectors when MatCreate()
and VecCreate() are used with the same communicator.
- The user can alternatively specify the local vector and matrix
dimensions when more sophisticated partitioning is needed
(replacing the PETSC_DECIDE argument in the VecSetSizes() statement
below).
*/
ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
ierr = VecSetSizes(u,PETSC_DECIDE,m*n);CHKERRQ(ierr);
ierr = VecSetFromOptions(u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecDuplicate(b,&x);CHKERRQ(ierr);
/*
Set exact solution; then compute right-hand-side vector.
By default we use an exact solution of a vector with all
elements of 1.0; Alternatively, using the runtime option
-random_sol forms a solution vector with random components.
*/
ierr = PetscOptionsGetBool(NULL,"-random_exact_sol",&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecSetRandom(u,rctx);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
} else {
ierr = VecSet(u,1.0);CHKERRQ(ierr);
}
ierr = MatMult(A,u,b);CHKERRQ(ierr);
/*
View the exact solution vector if desired
*/
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-view_exact_sol",&flg,NULL);CHKERRQ(ierr);
if (flg) {ierr = VecView(u,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 two statements are optional; all of these
parameters could alternatively be specified at runtime via
KSPSetFromOptions(). All of these defaults can be
overridden at runtime, as indicated below.
*/
ierr = KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,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
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Check solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Check the error
*/
ierr = VecAXPY(x,-1.0,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
/*
Print convergence information. PetscPrintf() produces a single