Actual source code: ex24.c
petsc-3.12.4 2020-02-04
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      2: static char help[] = "Tests CG, MINRES and SYMMLQ on symmetric matrices with SBAIJ format. The preconditioner ICC only works on sequential SBAIJ format. \n\n";

      4:  #include <petscksp.h>

      7: int main(int argc,char **args)
      8: {
      9:   Mat            C;
     10:   PetscScalar    v,none = -1.0;
     11:   PetscInt       i,j,Ii,J,Istart,Iend,N,m = 4,n = 4,its,k;
     13:   PetscMPIInt    size,rank;
     14:   PetscReal      err_norm,res_norm;
     15:   Vec            x,b,u,u_tmp;
     16:   PC             pc;
     17:   KSP            ksp;

     19:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
     20:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
     21:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     22:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     23:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     24:   N    = m*n;

     26:   /* Generate matrix */
     27:   MatCreate(PETSC_COMM_WORLD,&C);
     28:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);
     29:   MatSetFromOptions(C);
     30:   MatSetUp(C);
     31:   MatGetOwnershipRange(C,&Istart,&Iend);
     32:   for (Ii=Istart; Ii<Iend; Ii++) {
     33:     v = -1.0; i = Ii/n; j = Ii - i*n;
     34:     if (i>0)   {J = Ii - n; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
     35:     if (i<m-1) {J = Ii + n; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
     36:     if (j>0)   {J = Ii - 1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
     37:     if (j<n-1) {J = Ii + 1; MatSetValues(C,1,&Ii,1,&J,&v,ADD_VALUES);}
     38:     v = 4.0; MatSetValues(C,1,&Ii,1,&Ii,&v,ADD_VALUES);
     39:   }
     40:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
     41:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

     43:   /* a shift can make C indefinite. Preconditioners LU, ILU (for BAIJ format) and ICC may fail */
     44:   /* MatShift(C,alpha); */
     45:   /* MatView(C,PETSC_VIEWER_STDOUT_WORLD); */

     47:   /* Setup and solve for system */
     48:   /* Create vectors.  */
     49:   VecCreate(PETSC_COMM_WORLD,&x);
     50:   VecSetSizes(x,PETSC_DECIDE,N);
     51:   VecSetFromOptions(x);
     52:   VecDuplicate(x,&b);
     53:   VecDuplicate(x,&u);
     54:   VecDuplicate(x,&u_tmp);
     55:   /* Set exact solution u; then compute right-hand-side vector b. */
     56:   VecSet(u,1.0);
     57:   MatMult(C,u,b);

     59:   for (k=0; k<3; k++) {
     60:     if (k == 0) {                              /* CG  */
     61:       KSPCreate(PETSC_COMM_WORLD,&ksp);
     62:       KSPSetOperators(ksp,C,C);
     63:       PetscPrintf(PETSC_COMM_WORLD,"\n CG: \n");
     64:       KSPSetType(ksp,KSPCG);
     65:     } else if (k == 1) {                       /* MINRES */
     66:       KSPCreate(PETSC_COMM_WORLD,&ksp);
     67:       KSPSetOperators(ksp,C,C);
     68:       PetscPrintf(PETSC_COMM_WORLD,"\n MINRES: \n");
     69:       KSPSetType(ksp,KSPMINRES);
     70:     } else {                                 /* SYMMLQ */
     71:       KSPCreate(PETSC_COMM_WORLD,&ksp);
     72:       KSPSetOperators(ksp,C,C);
     73:       PetscPrintf(PETSC_COMM_WORLD,"\n SYMMLQ: \n");
     74:       KSPSetType(ksp,KSPSYMMLQ);
     75:     }
     76:     KSPGetPC(ksp,&pc);
     77:     /* PCSetType(pc,PCICC); */
     78:     PCSetType(pc,PCJACOBI);
     79:     KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

     81:     /*
     82:     Set runtime options, e.g.,
     83:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
     84:     These options will override those specified above as long as
     85:     KSPSetFromOptions() is called _after_ any other customization
     86:     routines.
     87:     */
     88:     KSPSetFromOptions(ksp);

     90:     /* Solve linear system; */
     91:     KSPSetUp(ksp);
     92:     KSPSolve(ksp,b,x);

     94:     KSPGetIterationNumber(ksp,&its);
     95:     /* Check error */
     96:     VecCopy(u,u_tmp);
     97:     VecAXPY(u_tmp,none,x);
     98:     VecNorm(u_tmp,NORM_2,&err_norm);
     99:     MatMult(C,x,u_tmp);
    100:     VecAXPY(u_tmp,none,b);
    101:     VecNorm(u_tmp,NORM_2,&res_norm);

    103:     PetscPrintf(PETSC_COMM_WORLD,"Number of iterations = %3D\n",its);
    104:     PetscPrintf(PETSC_COMM_WORLD,"Residual norm %g;",(double)res_norm);
    105:     PetscPrintf(PETSC_COMM_WORLD,"  Error norm %g.\n",(double)err_norm);
    106:     KSPDestroy(&ksp);
    107:   }

    109:   /*
    110:        Free work space.  All PETSc objects should be destroyed when they
    111:        are no longer needed.
    112:   */
    113:   VecDestroy(&b);
    114:   VecDestroy(&u);
    115:   VecDestroy(&x);
    116:   VecDestroy(&u_tmp);
    117:   MatDestroy(&C);

    119:   PetscFinalize();
    120:   return ierr;
    121: }

    124: /*TEST

    126:     test:
    127:       args: -pc_type icc -mat_type seqsbaij -mat_ignore_lower_triangular

    129:     test:
    130:       suffix: 2
    131:       args: -pc_type icc -pc_factor_levels 2  -mat_type seqsbaij -mat_ignore_lower_triangular

    133:     test:
    134:       suffix: 3
    135:       nsize: 2
    136:       args: -pc_type bjacobi -sub_pc_type icc  -mat_type mpisbaij -mat_ignore_lower_triangular -ksp_max_it 8

    138:     test:
    139:       suffix: 4
    140:       nsize: 2
    141:       args: -pc_type bjacobi -sub_pc_type icc -sub_pc_factor_levels 1 -mat_type mpisbaij -mat_ignore_lower_triangular

    143: TEST*/