Actual source code: ex1.c


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

  4: /*
  5:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
  6:   automatically includes:
  7:      petscsys.h    - base PETSc routines   petscvec.h - vectors
  8:      petscmat.h    - matrices              petscpc.h  - preconditioners
  9:      petscis.h     - index sets
 10:      petscviewer.h - viewers

 12:   Note:  The corresponding parallel example is ex23.c
 13: */
 14: #include <petscksp.h>

 16: int main(int argc,char **args)
 17: {
 18:   Vec            x, b, u;      /* approx solution, RHS, exact solution */
 19:   Mat            A;            /* linear system matrix */
 20:   KSP            ksp;          /* linear solver context */
 21:   PC             pc;           /* preconditioner context */
 22:   PetscReal      norm;         /* norm of solution error */
 23:   PetscInt       i,n = 10,col[3],its;
 24:   PetscMPIInt    size;
 25:   PetscScalar    value[3];

 27:   PetscInitialize(&argc,&args,(char*)0,help);
 28:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 30:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);

 32:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 33:          Compute the matrix and right-hand-side vector that define
 34:          the linear system, Ax = b.
 35:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 37:   /*
 38:      Create vectors.  Note that we form 1 vector from scratch and
 39:      then duplicate as needed.
 40:   */
 41:   VecCreate(PETSC_COMM_WORLD,&x);
 42:   PetscObjectSetName((PetscObject) x, "Solution");
 43:   VecSetSizes(x,PETSC_DECIDE,n);
 44:   VecSetFromOptions(x);
 45:   VecDuplicate(x,&b);
 46:   VecDuplicate(x,&u);

 48:   /*
 49:      Create matrix.  When using MatCreate(), the matrix format can
 50:      be specified at runtime.

 52:      Performance tuning note:  For problems of substantial size,
 53:      preallocation of matrix memory is crucial for attaining good
 54:      performance. See the matrix chapter of the users manual for details.
 55:   */
 56:   MatCreate(PETSC_COMM_WORLD,&A);
 57:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
 58:   MatSetFromOptions(A);
 59:   MatSetUp(A);

 61:   /*
 62:      Assemble matrix
 63:   */
 64:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
 65:   for (i=1; i<n-1; i++) {
 66:     col[0] = i-1; col[1] = i; col[2] = i+1;
 67:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 68:   }
 69:   i    = n - 1; col[0] = n - 2; col[1] = n - 1;
 70:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 71:   i    = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
 72:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 73:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 74:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 76:   /*
 77:      Set exact solution; then compute right-hand-side vector.
 78:   */
 79:   VecSet(u,1.0);
 80:   MatMult(A,u,b);

 82:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 83:                 Create the linear solver and set various options
 84:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 85:   KSPCreate(PETSC_COMM_WORLD,&ksp);

 87:   /*
 88:      Set operators. Here the matrix that defines the linear system
 89:      also serves as the matrix that defines the preconditioner.
 90:   */
 91:   KSPSetOperators(ksp,A,A);

 93:   /*
 94:      Set linear solver defaults for this problem (optional).
 95:      - By extracting the KSP and PC contexts from the KSP context,
 96:        we can then directly call any KSP and PC routines to set
 97:        various options.
 98:      - The following four statements are optional; all of these
 99:        parameters could alternatively be specified at runtime via
100:        KSPSetFromOptions();
101:   */
102:   KSPGetPC(ksp,&pc);
103:   PCSetType(pc,PCJACOBI);
104:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

106:   /*
107:     Set runtime options, e.g.,
108:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
109:     These options will override those specified above as long as
110:     KSPSetFromOptions() is called _after_ any other customization
111:     routines.
112:   */
113:   KSPSetFromOptions(ksp);

115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116:                       Solve the linear system
117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
118:   KSPSolve(ksp,b,x);

120:   /*
121:      View solver info; we could instead use the option -ksp_view to
122:      print this info to the screen at the conclusion of KSPSolve().
123:   */
124:   KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);

126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127:                       Check the solution and clean up
128:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
129:   VecAXPY(x,-1.0,u);
130:   VecNorm(x,NORM_2,&norm);
131:   KSPGetIterationNumber(ksp,&its);
132:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);

134:   /*
135:      Free work space.  All PETSc objects should be destroyed when they
136:      are no longer needed.
137:   */
138:   VecDestroy(&x)); PetscCall(VecDestroy(&u);
139:   VecDestroy(&b)); PetscCall(MatDestroy(&A);
140:   KSPDestroy(&ksp);

142:   /*
143:      Always call PetscFinalize() before exiting a program.  This routine
144:        - finalizes the PETSc libraries as well as MPI
145:        - provides summary and diagnostic information if certain runtime
146:          options are chosen (e.g., -log_view).
147:   */
148:   PetscFinalize();
149:   return 0;
150: }

152: /*TEST

154:    test:
155:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

157:    test:
158:       suffix: 2
159:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

161:    test:
162:       suffix: 2_aijcusparse
163:       requires: cuda
164:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda

166:    test:
167:       suffix: 3
168:       args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

170:    test:
171:       suffix: 3_aijcusparse
172:       requires: cuda
173:       args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda

175:    test:
176:       suffix: aijcusparse
177:       requires: cuda
178:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda
179:       output_file: output/ex1_1_aijcusparse.out

181: TEST*/