/*
  Laplacian in 3D. Use for testing BAIJ matrix.
  Modeled by the partial differential equation

   - Laplacian u = 1,0 < x,y,z < 1,

   with boundary conditions
   u = 1 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1.
*/

static char help[] = "Solves 3D Laplacian using wirebasket based multigrid.\n\n";

#include <petscdm.h>
#include <petscdmda.h>
#include <petscksp.h>

extern PetscErrorCode ComputeMatrix(DM, Mat);
extern PetscErrorCode ComputeRHS(DM, Vec);

int main(int argc, char **argv)
{
  KSP       ksp;
  PC        pc;
  Vec       x, b;
  DM        da;
  Mat       A, Atrans;
  PetscInt  dof = 1, M = 8;
  PetscBool flg, trans = PETSC_FALSE, sbaij = PETSC_FALSE;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, NULL, help));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-dof", &dof, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-M", &M, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-trans", &trans, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-sbaij", &sbaij, NULL));

  PetscCall(DMDACreate(PETSC_COMM_WORLD, &da));
  PetscCall(DMSetDimension(da, 3));
  PetscCall(DMDASetBoundaryType(da, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE));
  PetscCall(DMDASetStencilType(da, DMDA_STENCIL_STAR));
  PetscCall(DMDASetSizes(da, M, M, M));
  PetscCall(DMDASetNumProcs(da, PETSC_DECIDE, PETSC_DECIDE, PETSC_DECIDE));
  PetscCall(DMDASetDof(da, dof));
  PetscCall(DMDASetStencilWidth(da, 1));
  PetscCall(DMDASetOwnershipRanges(da, NULL, NULL, NULL));
  PetscCall(DMSetFromOptions(da));
  PetscCall(DMSetUp(da));

  PetscCall(DMCreateGlobalVector(da, &x));
  PetscCall(DMCreateGlobalVector(da, &b));
  PetscCall(ComputeRHS(da, b));
  PetscCall(DMSetMatType(da, MATBAIJ));
  if (sbaij) PetscCall(DMSetMatType(da, MATSBAIJ));
  PetscCall(DMCreateMatrix(da, &A));
  PetscCall(ComputeMatrix(da, A));

  /* A is non-symmetric. Make A = 0.5*(A + Atrans) symmetric for testing icc and cholesky */
  PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &Atrans));
  PetscCall(MatAXPY(A, 1.0, Atrans, DIFFERENT_NONZERO_PATTERN));
  PetscCall(MatScale(A, 0.5));
  PetscCall(MatDestroy(&Atrans));

  /* Test sbaij matrix */
  flg = PETSC_FALSE;
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_sbaij1", &flg, NULL));
  if (flg) {
    Mat       sA;
    PetscBool issymm;
    PetscCall(MatIsTranspose(A, A, 0.0, &issymm));
    if (issymm) {
      PetscCall(MatSetOption(A, MAT_SYMMETRIC, PETSC_TRUE));
    } else PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Warning: A is non-symmetric\n"));
    PetscCall(MatConvert(A, MATSBAIJ, MAT_INITIAL_MATRIX, &sA));
    PetscCall(MatDestroy(&A));
    A = sA;
  }

  PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
  PetscCall(KSPSetFromOptions(ksp));
  PetscCall(KSPSetOperators(ksp, A, A));
  PetscCall(KSPGetPC(ksp, &pc));
  PetscCall(PCSetDM(pc, (DM)da));

  if (trans) {
    PetscCall(KSPSolveTranspose(ksp, b, x));
  } else {
    PetscCall(KSPSolve(ksp, b, x));
  }

  /* check final residual */
  flg = PETSC_FALSE;
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-check_final_residual", &flg, NULL));
  if (flg) {
    Vec       b1;
    PetscReal norm;
    PetscCall(KSPGetSolution(ksp, &x));
    PetscCall(VecDuplicate(b, &b1));
    PetscCall(MatMult(A, x, b1));
    PetscCall(VecAXPY(b1, -1.0, b));
    PetscCall(VecNorm(b1, NORM_2, &norm));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Final residual %g\n", (double)norm));
    PetscCall(VecDestroy(&b1));
  }

  PetscCall(KSPDestroy(&ksp));
  PetscCall(VecDestroy(&x));
  PetscCall(VecDestroy(&b));
  PetscCall(MatDestroy(&A));
  PetscCall(DMDestroy(&da));
  PetscCall(PetscFinalize());
  return 0;
}

PetscErrorCode ComputeRHS(DM da, Vec b)
{
  PetscInt    mx, my, mz;
  PetscScalar h;

  PetscFunctionBeginUser;
  PetscCall(DMDAGetInfo(da, 0, &mx, &my, &mz, 0, 0, 0, 0, 0, 0, 0, 0, 0));
  h = 1.0 / ((mx - 1) * (my - 1) * (mz - 1));
  PetscCall(VecSet(b, h));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode ComputeMatrix(DM da, Mat B)
{
  PetscInt     i, j, k, mx, my, mz, xm, ym, zm, xs, ys, zs, dof, k1, k2, k3;
  PetscScalar *v, *v_neighbor, Hx, Hy, Hz, HxHydHz, HyHzdHx, HxHzdHy;
  MatStencil   row, col;

  PetscFunctionBeginUser;
  PetscCall(DMDAGetInfo(da, 0, &mx, &my, &mz, 0, 0, 0, &dof, 0, 0, 0, 0, 0));
  /* For simplicity, this example only works on mx=my=mz */
  PetscCheck(mx == my && mx == mz, PETSC_COMM_SELF, PETSC_ERR_SUP, "This example only works with mx %" PetscInt_FMT " = my %" PetscInt_FMT " = mz %" PetscInt_FMT, mx, my, mz);

  Hx      = 1.0 / (PetscReal)(mx - 1);
  Hy      = 1.0 / (PetscReal)(my - 1);
  Hz      = 1.0 / (PetscReal)(mz - 1);
  HxHydHz = Hx * Hy / Hz;
  HxHzdHy = Hx * Hz / Hy;
  HyHzdHx = Hy * Hz / Hx;

  PetscCall(PetscMalloc1(2 * dof * dof + 1, &v));
  v_neighbor = v + dof * dof;
  PetscCall(PetscArrayzero(v, 2 * dof * dof + 1));
  k3 = 0;
  for (k1 = 0; k1 < dof; k1++) {
    for (k2 = 0; k2 < dof; k2++) {
      if (k1 == k2) {
        v[k3]          = 2.0 * (HxHydHz + HxHzdHy + HyHzdHx);
        v_neighbor[k3] = -HxHydHz;
      } else {
        v[k3]          = k1 / (dof * dof);
        v_neighbor[k3] = k2 / (dof * dof);
      }
      k3++;
    }
  }
  PetscCall(DMDAGetCorners(da, &xs, &ys, &zs, &xm, &ym, &zm));

  for (k = zs; k < zs + zm; k++) {
    for (j = ys; j < ys + ym; j++) {
      for (i = xs; i < xs + xm; i++) {
        row.i = i;
        row.j = j;
        row.k = k;
        if (i == 0 || j == 0 || k == 0 || i == mx - 1 || j == my - 1 || k == mz - 1) { /* boundary points */
          PetscCall(MatSetValuesBlockedStencil(B, 1, &row, 1, &row, v, INSERT_VALUES));
        } else { /* interior points */
          /* center */
          col.i = i;
          col.j = j;
          col.k = k;
          PetscCall(MatSetValuesBlockedStencil(B, 1, &row, 1, &col, v, INSERT_VALUES));

          /* x neighbors */
          col.i = i - 1;
          col.j = j;
          col.k = k;
          PetscCall(MatSetValuesBlockedStencil(B, 1, &row, 1, &col, v_neighbor, INSERT_VALUES));
          col.i = i + 1;
          col.j = j;
          col.k = k;
          PetscCall(MatSetValuesBlockedStencil(B, 1, &row, 1, &col, v_neighbor, INSERT_VALUES));

          /* y neighbors */
          col.i = i;
          col.j = j - 1;
          col.k = k;
          PetscCall(MatSetValuesBlockedStencil(B, 1, &row, 1, &col, v_neighbor, INSERT_VALUES));
          col.i = i;
          col.j = j + 1;
          col.k = k;
          PetscCall(MatSetValuesBlockedStencil(B, 1, &row, 1, &col, v_neighbor, INSERT_VALUES));

          /* z neighbors */
          col.i = i;
          col.j = j;
          col.k = k - 1;
          PetscCall(MatSetValuesBlockedStencil(B, 1, &row, 1, &col, v_neighbor, INSERT_VALUES));
          col.i = i;
          col.j = j;
          col.k = k + 1;
          PetscCall(MatSetValuesBlockedStencil(B, 1, &row, 1, &col, v_neighbor, INSERT_VALUES));
        }
      }
    }
  }
  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  PetscCall(PetscFree(v));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*TEST

   test:
      args: -ksp_monitor_short -sbaij -ksp_monitor_short -pc_type cholesky -ksp_view

TEST*/
