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

#include <petscksp.h>

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

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &args, NULL, help));
  /* Create and initialize vectors */
  PetscCall(VecCreateSeq(PETSC_COMM_SELF, n, &b));
  PetscCall(VecCreateSeq(PETSC_COMM_SELF, n, &ustar));
  PetscCall(VecCreateSeq(PETSC_COMM_SELF, n, &u));
  PetscCall(VecSet(ustar, 1.0));
  PetscCall(VecSet(u, 0.0));

  /* Create and assemble matrix */
  PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, n, n, 3, NULL, &mat));
  value[0] = -1.0;
  value[1] = 2.0;
  value[2] = -1.0;
  for (i = 1; i < n - 1; i++) {
    col[0] = i - 1;
    col[1] = i;
    col[2] = i + 1;
    PetscCall(MatSetValues(mat, 1, &i, 3, col, value, INSERT_VALUES));
  }
  i      = n - 1;
  col[0] = n - 2;
  col[1] = n - 1;
  PetscCall(MatSetValues(mat, 1, &i, 2, col, value, INSERT_VALUES));
  i        = 0;
  col[0]   = 0;
  col[1]   = 1;
  value[0] = 2.0;
  value[1] = -1.0;
  PetscCall(MatSetValues(mat, 1, &i, 2, col, value, INSERT_VALUES));
  PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));

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

  /* Create PC context and set up data structures */
  PetscCall(PCCreate(PETSC_COMM_WORLD, &pc));
  PetscCall(PCSetType(pc, PCNONE));
  PetscCall(PCSetFromOptions(pc));
  PetscCall(PCSetOperators(pc, mat, mat));
  PetscCall(PCSetUp(pc));

  /* Create KSP context and set up data structures */
  PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
  PetscCall(KSPSetType(ksp, KSPRICHARDSON));
  PetscCall(KSPSetFromOptions(ksp));
  PetscCall(PCSetOperators(pc, mat, mat));
  PetscCall(KSPSetPC(ksp, pc));
  PetscCall(KSPSetUp(ksp));

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

  /* Free data structures */
  PetscCall(KSPDestroy(&ksp));
  PetscCall(VecDestroy(&u));
  PetscCall(VecDestroy(&ustar));
  PetscCall(VecDestroy(&b));
  PetscCall(MatDestroy(&mat));
  PetscCall(PCDestroy(&pc));

  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   test:
      args: -ksp_type cg -ksp_monitor_short

TEST*/