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>

 20: int main(int argc,char **argv)
 21: {
 22:   KSP                solver;
 23:   PC                 prec;
 24:   Mat                A,M;
 25:   Vec                X,B,D;
 26:   MPI_Comm           comm;
 27:   PetscScalar        v;
 28:   KSPConvergedReason reason;
 29:   PetscInt           i,j,its;
 30:   PetscErrorCode     ierr;

 32:   PetscInitialize(&argc,&argv,0,help);if (ierr) return ierr;
 33:   comm = MPI_COMM_SELF;

 35:   /*
 36:    * Construct the Kershaw matrix
 37:    * and a suitable rhs / initial guess
 38:    */
 39:   MatCreateSeqAIJ(comm,4,4,4,0,&A);
 40:   VecCreateSeq(comm,4,&B);
 41:   VecDuplicate(B,&X);
 42:   for (i=0; i<4; i++) {
 43:     v    = 3;
 44:     MatSetValues(A,1,&i,1,&i,&v,INSERT_VALUES);
 45:     v    = 1;
 46:     VecSetValues(B,1,&i,&v,INSERT_VALUES);
 47:     VecSetValues(X,1,&i,&v,INSERT_VALUES);
 48:   }

 50:   i=0; v=0;
 51:   VecSetValues(X,1,&i,&v,INSERT_VALUES);

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

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

 67:   /*
 68:    * A Conjugate Gradient method
 69:    * with ILU(0) preconditioning
 70:    */
 71:   KSPCreate(comm,&solver);
 72:   KSPSetOperators(solver,A,A);

 74:   KSPSetType(solver,KSPCG);
 75:   KSPSetInitialGuessNonzero(solver,PETSC_TRUE);

 77:   /*
 78:    * ILU preconditioner;
 79:    * this will break down unless you add the Shift line,
 80:    * or use the -pc_factor_shift_positive_definite option */
 81:   KSPGetPC(solver,&prec);
 82:   PCSetType(prec,PCILU);
 83:   /* PCFactorSetShiftType(prec,MAT_SHIFT_POSITIVE_DEFINITE); */

 85:   KSPSetFromOptions(solver);
 86:   KSPSetUp(solver);

 88:   /*
 89:    * Now that the factorisation is done, show the pivots;
 90:    * note that the last one is negative. This in itself is not an error,
 91:    * but it will make the iterative method diverge.
 92:    */
 93:   PCFactorGetMatrix(prec,&M);
 94:   VecDuplicate(B,&D);
 95:   MatGetDiagonal(M,D);

 97:   /*
 98:    * Solve the system;
 99:    * without the shift this will diverge with
100:    * an indefinite preconditioner
101:    */
102:   KSPSolve(solver,B,X);
103:   KSPGetConvergedReason(solver,&reason);
104:   if (reason==KSP_DIVERGED_INDEFINITE_PC) {
105:     PetscPrintf(PETSC_COMM_WORLD,"\nDivergence because of indefinite preconditioner;\n");
106:     PetscPrintf(PETSC_COMM_WORLD,"Run the executable again but with '-pc_factor_shift_type POSITIVE_DEFINITE' option.\n");
107:   } else if (reason<0) {
108:     PetscPrintf(PETSC_COMM_WORLD,"\nOther kind of divergence: this should not happen.\n");
109:   } else {
110:     KSPGetIterationNumber(solver,&its);
111:   }

113:   VecDestroy(&X);
114:   VecDestroy(&B);
115:   VecDestroy(&D);
116:   MatDestroy(&A);
117:   KSPDestroy(&solver);
118:   PetscFinalize();
119:   return ierr;
120: }


123: /*TEST

125:    test:
126:       args: -pc_factor_shift_type positive_definite

128: TEST*/