1: static char help[] = "Tests PC and KSP on a tridiagonal matrix.  Note that most\n\
  2: users should employ the KSP interface instead of using PC directly.\n\n";

  4: #include <petscksp.h>

  6: int main(int argc, char **args)
  7: {
  8:   Mat         mat;         /* matrix */
  9:   Vec         b, ustar, u; /* vectors (RHS, exact solution, approx solution) */
 10:   PC          pc;          /* PC context */
 11:   KSP         ksp;         /* KSP context */
 12:   PetscInt    n = 10, i, its, col[3];
 13:   PetscScalar value[3];
 14:   PCType      pcname;
 15:   KSPType     kspname;
 16:   PetscReal   norm, tol = 1000. * PETSC_MACHINE_EPSILON;

 18:   PetscFunctionBeginUser;
 19:   PetscCall(PetscInitialize(&argc, &args, NULL, help));
 20:   /* Create and initialize vectors */
 21:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, n, &b));
 22:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, n, &ustar));
 23:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, n, &u));
 24:   PetscCall(VecSet(ustar, 1.0));

 26:   /* Create and assemble matrix */
 27:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, n, n, 3, NULL, &mat));
 28:   value[0] = -1.0;
 29:   value[1] = 2.0;
 30:   value[2] = -1.0;
 31:   for (i = 1; i < n - 1; i++) {
 32:     col[0] = i - 1;
 33:     col[1] = i;
 34:     col[2] = i + 1;
 35:     PetscCall(MatSetValues(mat, 1, &i, 3, col, value, INSERT_VALUES));
 36:   }
 37:   i      = n - 1;
 38:   col[0] = n - 2;
 39:   col[1] = n - 1;
 40:   PetscCall(MatSetValues(mat, 1, &i, 2, col, value, INSERT_VALUES));
 41:   i        = 0;
 42:   col[0]   = 0;
 43:   col[1]   = 1;
 44:   value[0] = 2.0;
 45:   value[1] = -1.0;
 46:   PetscCall(MatSetValues(mat, 1, &i, 2, col, value, INSERT_VALUES));
 47:   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
 48:   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));

 50:   /* Compute right-hand-side vector */
 51:   PetscCall(MatMult(mat, ustar, b));

 53:   /* Create PC context and set up data structures */
 54:   PetscCall(PCCreate(PETSC_COMM_WORLD, &pc));
 55:   PetscCall(PCSetType(pc, PCNONE));
 56:   PetscCall(PCSetFromOptions(pc));
 57:   PetscCall(PCSetOperators(pc, mat, mat));
 58:   PetscCall(PCSetUp(pc));

 60:   /* Create KSP context and set up data structures */
 61:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
 62:   PetscCall(KSPSetType(ksp, KSPRICHARDSON));
 63:   PetscCall(KSPSetFromOptions(ksp));
 64:   PetscCall(PCSetOperators(pc, mat, mat));
 65:   PetscCall(KSPSetPC(ksp, pc));
 66:   PetscCall(KSPSetUp(ksp));

 68:   /* Solve the problem */
 69:   PetscCall(KSPGetType(ksp, &kspname));
 70:   PetscCall(PCGetType(pc, &pcname));
 71:   PetscCall(PetscPrintf(PETSC_COMM_SELF, "Running %s with %s preconditioning\n", kspname, pcname));
 72:   PetscCall(KSPSolve(ksp, b, u));
 73:   PetscCall(VecAXPY(u, -1.0, ustar));
 74:   PetscCall(VecNorm(u, NORM_2, &norm));
 75:   PetscCall(KSPGetIterationNumber(ksp, &its));
 76:   if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "2 norm of error %g Number of iterations %" PetscInt_FMT "\n", (double)norm, its));

 78:   /* Free data structures */
 79:   PetscCall(KSPDestroy(&ksp));
 80:   PetscCall(VecDestroy(&u));
 81:   PetscCall(VecDestroy(&ustar));
 82:   PetscCall(VecDestroy(&b));
 83:   PetscCall(MatDestroy(&mat));
 84:   PetscCall(PCDestroy(&pc));

 86:   PetscCall(PetscFinalize());
 87:   return 0;
 88: }

 90: /*TEST

 92:    test:
 93:       args: -ksp_type cg -ksp_monitor

 95: TEST*/