Actual source code: ex1.c


  2: static char help[] = "Solves a tridiagonal linear system with KSP.\n\n";

  4: /*T
  5:    Concepts: KSP^solving a system of linear equations
  6:    Processors: 1
  7: T*/

  9: /*
 10:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 11:   automatically includes:
 12:      petscsys.h    - base PETSc routines   petscvec.h - vectors
 13:      petscmat.h    - matrices              petscpc.h  - preconditioners
 14:      petscis.h     - index sets
 15:      petscviewer.h - viewers

 17:   Note:  The corresponding parallel example is ex23.c
 18: */
 19: #include <petscksp.h>

 21: int main(int argc,char **args)
 22: {
 23:   Vec            x, b, u;      /* approx solution, RHS, exact solution */
 24:   Mat            A;            /* linear system matrix */
 25:   KSP            ksp;          /* linear solver context */
 26:   PC             pc;           /* preconditioner context */
 27:   PetscReal      norm;         /* norm of solution error */
 29:   PetscInt       i,n = 10,col[3],its;
 30:   PetscMPIInt    size;
 31:   PetscScalar    value[3];

 33:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 34:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 35:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");
 36:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);

 38:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 39:          Compute the matrix and right-hand-side vector that define
 40:          the linear system, Ax = b.
 41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 43:   /*
 44:      Create vectors.  Note that we form 1 vector from scratch and
 45:      then duplicate as needed.
 46:   */
 47:   VecCreate(PETSC_COMM_WORLD,&x);
 48:   PetscObjectSetName((PetscObject) x, "Solution");
 49:   VecSetSizes(x,PETSC_DECIDE,n);
 50:   VecSetFromOptions(x);
 51:   VecDuplicate(x,&b);
 52:   VecDuplicate(x,&u);

 54:   /*
 55:      Create matrix.  When using MatCreate(), the matrix format can
 56:      be specified at runtime.

 58:      Performance tuning note:  For problems of substantial size,
 59:      preallocation of matrix memory is crucial for attaining good
 60:      performance. See the matrix chapter of the users manual for details.
 61:   */
 62:   MatCreate(PETSC_COMM_WORLD,&A);
 63:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
 64:   MatSetFromOptions(A);
 65:   MatSetUp(A);

 67:   /*
 68:      Assemble matrix
 69:   */
 70:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
 71:   for (i=1; i<n-1; i++) {
 72:     col[0] = i-1; col[1] = i; col[2] = i+1;
 73:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 74:   }
 75:   i    = n - 1; col[0] = n - 2; col[1] = n - 1;
 76:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 77:   i    = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
 78:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 79:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 80:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 82:   /*
 83:      Set exact solution; then compute right-hand-side vector.
 84:   */
 85:   VecSet(u,1.0);
 86:   MatMult(A,u,b);

 88:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 89:                 Create the linear solver and set various options
 90:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 91:   KSPCreate(PETSC_COMM_WORLD,&ksp);

 93:   /*
 94:      Set operators. Here the matrix that defines the linear system
 95:      also serves as the matrix that defines the preconditioner.
 96:   */
 97:   KSPSetOperators(ksp,A,A);

 99:   /*
100:      Set linear solver defaults for this problem (optional).
101:      - By extracting the KSP and PC contexts from the KSP context,
102:        we can then directly call any KSP and PC routines to set
103:        various options.
104:      - The following four statements are optional; all of these
105:        parameters could alternatively be specified at runtime via
106:        KSPSetFromOptions();
107:   */
108:   KSPGetPC(ksp,&pc);
109:   PCSetType(pc,PCJACOBI);
110:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

112:   /*
113:     Set runtime options, e.g.,
114:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
115:     These options will override those specified above as long as
116:     KSPSetFromOptions() is called _after_ any other customization
117:     routines.
118:   */
119:   KSPSetFromOptions(ksp);

121:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
122:                       Solve the linear system
123:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
124:   KSPSolve(ksp,b,x);

126:   /*
127:      View solver info; we could instead use the option -ksp_view to
128:      print this info to the screen at the conclusion of KSPSolve().
129:   */
130:   KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);

132:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133:                       Check the solution and clean up
134:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
135:   VecAXPY(x,-1.0,u);
136:   VecNorm(x,NORM_2,&norm);
137:   KSPGetIterationNumber(ksp,&its);
138:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);

140:   /*
141:      Free work space.  All PETSc objects should be destroyed when they
142:      are no longer needed.
143:   */
144:   VecDestroy(&x); VecDestroy(&u);
145:   VecDestroy(&b); MatDestroy(&A);
146:   KSPDestroy(&ksp);

148:   /*
149:      Always call PetscFinalize() before exiting a program.  This routine
150:        - finalizes the PETSc libraries as well as MPI
151:        - provides summary and diagnostic information if certain runtime
152:          options are chosen (e.g., -log_view).
153:   */
154:   PetscFinalize();
155:   return ierr;
156: }

158: /*TEST

160:    test:
161:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

163:    test:
164:       suffix: 2
165:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

167:    test:
168:       suffix: 2_aijcusparse
169:       requires: cuda
170:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda

172:    test:
173:       suffix: 3
174:       args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

176:    test:
177:       suffix: 3_aijcusparse
178:       requires: cuda
179:       args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda

181:    test:
182:       suffix: aijcusparse
183:       requires: cuda
184:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda
185:       output_file: output/ex1_1_aijcusparse.out

187: TEST*/