static char help[] = "Bilinear elements on the unit square for the Laplacian. Input arguments are:\n\
  -m <size> : problem size\n\n";

#include <petscksp.h>

PetscErrorCode FormElementStiffness(PetscReal H, PetscScalar *Ke)
{
  Ke[0]  = H / 6.0;
  Ke[1]  = -.125 * H;
  Ke[2]  = H / 12.0;
  Ke[3]  = -.125 * H;
  Ke[4]  = -.125 * H;
  Ke[5]  = H / 6.0;
  Ke[6]  = -.125 * H;
  Ke[7]  = H / 12.0;
  Ke[8]  = H / 12.0;
  Ke[9]  = -.125 * H;
  Ke[10] = H / 6.0;
  Ke[11] = -.125 * H;
  Ke[12] = -.125 * H;
  Ke[13] = H / 12.0;
  Ke[14] = -.125 * H;
  Ke[15] = H / 6.0;
  return PETSC_SUCCESS;
}

PetscErrorCode FormElementRhs(PetscReal x, PetscReal y, PetscReal H, PetscScalar *r)
{
  r[0] = 0.;
  r[1] = 0.;
  r[2] = 0.;
  r[3] = 0.0;
  return PETSC_SUCCESS;
}

/* Note: this code is for testing purposes only. The assembly process is not scalable */
int main(int argc, char **args)
{
  Mat         C;
  PetscInt    i, m = 2, N, M, its, idx[4], count, *rows;
  PetscScalar val, Ke[16], r[4];
  PetscReal   x, y, h, norm;
  Vec         u, ustar, b;
  KSP         ksp;
  PetscMPIInt rank;
  PetscBool   usezerorows = PETSC_TRUE;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-usezerorows", &usezerorows, NULL));
  N = (m + 1) * (m + 1); /* dimension of matrix */
  M = m * m;             /* number of elements */
  h = 1.0 / m;           /* mesh width */

  /* create stiffness matrix */
  PetscCall(MatCreate(PETSC_COMM_WORLD, &C));
  PetscCall(MatSetSizes(C, PETSC_DECIDE, PETSC_DECIDE, N, N));
  PetscCall(MatSetFromOptions(C));
  PetscCall(MatMPIAIJSetPreallocation(C, 9, NULL, 9, NULL));
  PetscCall(MatSeqAIJSetPreallocation(C, 9, NULL));
#if defined(PETSC_HAVE_HYPRE)
  PetscCall(MatHYPRESetPreallocation(C, 9, NULL, 9, NULL));
#endif

  /* forms the element stiffness for the Laplacian */
  PetscCall(FormElementStiffness(h * h, Ke));

  /* assemble the matrix: only process 0 adds the values, not scalable */
  if (rank == 0) {
    for (i = 0; i < M; i++) {
      /* node numbers for the four corners of element */
      idx[0] = (m + 1) * (i / m) + (i % m);
      idx[1] = idx[0] + 1;
      idx[2] = idx[1] + m + 1;
      idx[3] = idx[2] - 1;
      if (i == M - 1 && !usezerorows) { /* If MatZeroRows not supported -> make it non-singular */
        for (PetscInt ii = 0; ii < 4; ii++) {
          Ke[2 * 4 + ii] = 0.0;
          Ke[ii * 4 + 2] = 0.0;
        }
        Ke[10] = 1.0;
      }
      PetscCall(MatSetValues(C, 4, idx, 4, idx, Ke, ADD_VALUES));
    }
  }
  PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

  /* create right hand side and solution */
  PetscCall(MatCreateVecs(C, &u, &b));
  PetscCall(VecDuplicate(u, &ustar));
  PetscCall(VecSet(u, 0.0));
  PetscCall(VecSet(b, 0.0));

  /* assemble the right hand side: only process 0 adds the values, not scalable */
  if (rank == 0) {
    for (i = 0; i < M; i++) {
      /* location of lower left corner of element */
      x = h * (i % m);
      y = h * (i / m);
      /* node numbers for the four corners of element */
      idx[0] = (m + 1) * (i / m) + (i % m);
      idx[1] = idx[0] + 1;
      idx[2] = idx[1] + m + 1;
      idx[3] = idx[2] - 1;
      PetscCall(FormElementRhs(x, y, h * h, r));
      PetscCall(VecSetValues(b, 4, idx, r, ADD_VALUES));
    }
  }
  PetscCall(VecAssemblyBegin(b));
  PetscCall(VecAssemblyEnd(b));

  /* modify matrix and rhs for Dirichlet boundary conditions */
  if (rank == 0) {
    PetscCall(PetscMalloc1(4 * m + 1, &rows));
    for (i = 0; i < m + 1; i++) {
      rows[i]             = i;               /* bottom */
      rows[3 * m - 1 + i] = m * (m + 1) + i; /* top */
    }
    count = m + 1; /* left side */
    for (i = m + 1; i < m * (m + 1); i += m + 1) rows[count++] = i;

    count = 2 * m; /* right side */
    for (i = 2 * m + 1; i < m * (m + 1); i += m + 1) rows[count++] = i;

    for (i = 0; i < 4 * m; i++) {
      val = h * (rows[i] / (m + 1));
      PetscCall(VecSetValues(u, 1, &rows[i], &val, INSERT_VALUES));
      PetscCall(VecSetValues(b, 1, &rows[i], &val, INSERT_VALUES));
    }
    if (usezerorows) PetscCall(MatZeroRows(C, 4 * m, rows, 1.0, 0, 0));
    PetscCall(PetscFree(rows));
  } else {
    if (usezerorows) PetscCall(MatZeroRows(C, 0, NULL, 1.0, 0, 0));
  }
  PetscCall(VecAssemblyBegin(u));
  PetscCall(VecAssemblyEnd(u));
  PetscCall(VecAssemblyBegin(b));
  PetscCall(VecAssemblyEnd(b));

  if (!usezerorows) {
    PetscCall(VecSet(ustar, 1.0));
    PetscCall(MatMult(C, ustar, b));
  }

  /* solve linear system */
  PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
  PetscCall(KSPSetOperators(ksp, C, C));
  PetscCall(KSPSetFromOptions(ksp));
  PetscCall(KSPSetInitialGuessNonzero(ksp, PETSC_TRUE));
  PetscCall(KSPSolve(ksp, b, u));

  /* check error */
  if (usezerorows) {
    if (rank == 0) {
      for (i = 0; i < N; i++) {
        val = h * (i / (m + 1));
        PetscCall(VecSetValues(ustar, 1, &i, &val, INSERT_VALUES));
      }
    }
    PetscCall(VecAssemblyBegin(ustar));
    PetscCall(VecAssemblyEnd(ustar));
  }

  PetscCall(VecAXPY(u, -1.0, ustar));
  PetscCall(VecNorm(u, NORM_2, &norm));
  PetscCall(KSPGetIterationNumber(ksp, &its));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g Iterations %" PetscInt_FMT "\n", (double)(norm * h), its));

  PetscCall(KSPDestroy(&ksp));
  PetscCall(VecDestroy(&ustar));
  PetscCall(VecDestroy(&u));
  PetscCall(VecDestroy(&b));
  PetscCall(MatDestroy(&C));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

    test:
      args: -ksp_monitor_short -m 5 -pc_type jacobi -ksp_gmres_cgs_refinement_type refine_always

    test:
      suffix: 3
      args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -m 5 -ksp_gmres_cgs_refinement_type refine_always

    test:
      suffix: 5
      args: -pc_type eisenstat -ksp_monitor_short -m 5  -ksp_gmres_cgs_refinement_type refine_always

    test:
      requires: hypre defined(PETSC_HAVE_HYPRE_DEVICE)
      suffix: hypre_device_none
      output_file: output/ex4_hypre_none.out
      nsize: {{1 2}}
      args: -usezerorows 0 -mat_type hypre -pc_type none -m 5

    test:
      requires: hypre defined(PETSC_HAVE_HYPRE_DEVICE)
      suffix: hypre_device_amg
      nsize: {{1 2}}
      args: -usezerorows 0 -mat_type hypre -pc_type hypre -m 25 -ksp_type cg -ksp_norm_type natural

    test:
      requires: hypre defined(PETSC_HAVE_HYPRE_DEVICE)
      suffix: dev
      nsize: 2
      args: -m 25 -mat_type hypre -pc_type hypre -pc_hypre_type boomeramg -pc_hypre_boomeramg_coarsen_type PMIS

TEST*/
