1: static char help[] = "Test file for the PCFactorSetShiftType()\n";
  2: /*
  3:  * Test file for the PCFactorSetShiftType() routine or -pc_factor_shift_type POSITIVE_DEFINITE option.
  4:  * The test matrix is the example from Kershaw's paper [J.Comp.Phys 1978]
  5:  * of a positive definite matrix for which ILU(0) will give a negative pivot.
  6:  * This means that the CG method will break down; the Manteuffel shift
  7:  * [Math. Comp. 1980] repairs this.
  8:  *
  9:  * Run the executable twice:
 10:  * 1/ without options: the iterative method diverges because of an
 11:  *    indefinite preconditioner
 12:  * 2/ with -pc_factor_shift_type POSITIVE_DEFINITE option (or comment in the PCFactorSetShiftType() line below):
 13:  *    the method will now successfully converge.
 14:  *
 15:  * Contributed by Victor Eijkhout 2003.
 16:  */

 18: #include <petscksp.h>

 22: int main(int argc,char **argv)
 23: {
 24:   KSP                solver;
 25:   PC                 prec;
 26:   Mat                A,M;
 27:   Vec                X,B,D;
 28:   MPI_Comm           comm;
 29:   PetscScalar        v;
 30:   KSPConvergedReason reason;
 31:   PetscInt           i,j,its;
 32:   PetscErrorCode     ierr;

 34:   PetscInitialize(&argc,&argv,0,help);
 35:   comm = MPI_COMM_SELF;

 37:   /*
 38:    * Construct the Kershaw matrix
 39:    * and a suitable rhs / initial guess
 40:    */
 41:   MatCreateSeqAIJ(comm,4,4,4,0,&A);
 42:   VecCreateSeq(comm,4,&B);
 43:   VecDuplicate(B,&X);
 44:   for (i=0; i<4; i++) {
 45:     v    = 3;
 46:     MatSetValues(A,1,&i,1,&i,&v,INSERT_VALUES);
 47:     v    = 1;
 48:     VecSetValues(B,1,&i,&v,INSERT_VALUES);
 49:     VecSetValues(X,1,&i,&v,INSERT_VALUES);
 50:   }

 52:   i=0; v=0;
 53:   VecSetValues(X,1,&i,&v,INSERT_VALUES);

 55:   for (i=0; i<3; i++) {
 56:     v    = -2; j=i+1;
 57:     MatSetValues(A,1,&i,1,&j,&v,INSERT_VALUES);
 58:     MatSetValues(A,1,&j,1,&i,&v,INSERT_VALUES);
 59:   }
 60:   i=0; j=3; v=2;

 62:   MatSetValues(A,1,&i,1,&j,&v,INSERT_VALUES);
 63:   MatSetValues(A,1,&j,1,&i,&v,INSERT_VALUES);
 64:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 65:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 66:   VecAssemblyBegin(B);
 67:   VecAssemblyEnd(B);

 69:   /*
 70:    * A Conjugate Gradient method
 71:    * with ILU(0) preconditioning
 72:    */
 73:   KSPCreate(comm,&solver);
 74:   KSPSetOperators(solver,A,A);

 76:   KSPSetType(solver,KSPCG);
 77:   KSPSetInitialGuessNonzero(solver,PETSC_TRUE);

 79:   /*
 80:    * ILU preconditioner;
 81:    * this will break down unless you add the Shift line,
 82:    * or use the -pc_factor_shift_positive_definite option */
 83:   KSPGetPC(solver,&prec);
 84:   PCSetType(prec,PCILU);
 85:   /* PCFactorSetShiftType(prec,MAT_SHIFT_POSITIVE_DEFINITE); */

 87:   KSPSetFromOptions(solver);
 88:   KSPSetUp(solver);

 90:   /*
 91:    * Now that the factorisation is done, show the pivots;
 92:    * note that the last one is negative. This in itself is not an error,
 93:    * but it will make the iterative method diverge.
 94:    */
 95:   PCFactorGetMatrix(prec,&M);
 96:   VecDuplicate(B,&D);
 97:   MatGetDiagonal(M,D);

 99:   /*
100:    * Solve the system;
101:    * without the shift this will diverge with
102:    * an indefinite preconditioner
103:    */
104:   KSPSolve(solver,B,X);
105:   KSPGetConvergedReason(solver,&reason);
106:   if (reason==KSP_DIVERGED_INDEFINITE_PC) {
107:     PetscPrintf(PETSC_COMM_WORLD,"\nDivergence because of indefinite preconditioner;\n");
108:     PetscPrintf(PETSC_COMM_WORLD,"Run the executable again but with '-pc_factor_shift_type POSITIVE_DEFINITE' option.\n");
109:   } else if (reason<0) {
110:     PetscPrintf(PETSC_COMM_WORLD,"\nOther kind of divergence: this should not happen.\n");
111:   } else {
112:     KSPGetIterationNumber(solver,&its);
113:   }

115:   VecDestroy(&X);
116:   VecDestroy(&B);
117:   VecDestroy(&D);
118:   MatDestroy(&A);
119:   KSPDestroy(&solver);
120:   PetscFinalize();
121:   return 0;
122: }