static char help[] = "Example program demonstrating projection between particle and finite element spaces\n\n";

#include "petscdmplex.h"
#include "petscds.h"
#include "petscdmswarm.h"
#include "petscksp.h"

int main(int argc, char **argv) {
  DM            dm, sw;
  PetscFE       fe;
  KSP           ksp;
  PC            pc;
  Mat           M_p, PM_p = NULL;
  Vec           f, rho, rhs;
  PetscInt      dim, Nc = 1, timestep = 0, i, faces[3];
  PetscInt      Np = 10, p, field = 0, zero = 0, bs;
  PetscReal     time = 0.0, norm, energy_0, energy_1;
  PetscReal     lo[3], hi[3], h[3];
  PetscBool     removePoints = PETSC_TRUE;
  PetscReal    *wq, *coords;
  PetscDataType dtype;
  PetscBool     is_bjac;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, NULL, help));
  /* Create a mesh */
  PetscCall(DMCreate(PETSC_COMM_WORLD, &dm));
  PetscCall(DMSetType(dm, DMPLEX));
  PetscCall(DMSetFromOptions(dm));
  PetscCall(DMViewFromOptions(dm, NULL, "-dm_view"));

  PetscCall(DMGetDimension(dm, &dim));
  i = dim;
  PetscCall(PetscOptionsGetIntArray(NULL, NULL, "-dm_plex_box_faces", faces, &i, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-np", &Np, NULL));
  PetscCall(DMGetBoundingBox(dm, lo, hi));
  for (i = 0; i < dim; i++) {
    h[i] = (hi[i] - lo[i]) / faces[i];
    PetscCall(PetscPrintf(PETSC_COMM_SELF, " lo = %g hi = %g n = %" PetscInt_FMT " h = %g\n", (double)lo[i], (double)hi[i], faces[i], (double)h[i]));
  }

  PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, Nc, PETSC_FALSE, "", PETSC_DECIDE, &fe));
  PetscCall(PetscFESetFromOptions(fe));
  PetscCall(PetscObjectSetName((PetscObject)fe, "fe"));
  PetscCall(DMSetField(dm, field, NULL, (PetscObject)fe));
  PetscCall(DMCreateDS(dm));
  PetscCall(PetscFEDestroy(&fe));
  /* Create particle swarm */
  PetscCall(DMCreate(PETSC_COMM_SELF, &sw));
  PetscCall(DMSetType(sw, DMSWARM));
  PetscCall(DMSetDimension(sw, dim));
  PetscCall(DMSwarmSetType(sw, DMSWARM_PIC));
  PetscCall(DMSwarmSetCellDM(sw, dm));
  PetscCall(DMSwarmRegisterPetscDatatypeField(sw, "w_q", Nc, PETSC_SCALAR));
  PetscCall(DMSwarmFinalizeFieldRegister(sw));
  PetscCall(DMSwarmSetLocalSizes(sw, Np, zero));
  PetscCall(DMSetFromOptions(sw));
  PetscCall(DMSwarmGetField(sw, "w_q", &bs, &dtype, (void **)&wq));
  PetscCall(DMSwarmGetField(sw, "DMSwarmPIC_coor", &bs, &dtype, (void **)&coords));
  for (p = 0, energy_0 = 0; p < Np; p++) {
    coords[p * 2 + 0] = -PetscCosReal((PetscReal)(p + 1) / (PetscReal)(Np + 1) * PETSC_PI);
    coords[p * 2 + 1] = PetscSinReal((PetscReal)(p + 1) / (PetscReal)(Np + 1) * PETSC_PI);
    wq[p]             = 1.0;
    energy_0 += wq[p] * (PetscSqr(coords[p * 2 + 0]) + PetscSqr(coords[p * 2 + 1]));
  }
  PetscCall(DMSwarmRestoreField(sw, "DMSwarmPIC_coor", &bs, &dtype, (void **)&coords));
  PetscCall(DMSwarmRestoreField(sw, "w_q", &bs, &dtype, (void **)&wq));
  PetscCall(DMSwarmMigrate(sw, removePoints));
  PetscCall(PetscObjectSetName((PetscObject)sw, "Particle Grid"));
  PetscCall(DMViewFromOptions(sw, NULL, "-swarm_view"));

  /* Project particles to field */
  /* This gives M f = \int_\Omega \phi f, which looks like a rhs for a PDE */
  PetscCall(DMCreateMassMatrix(sw, dm, &M_p));
  PetscCall(DMCreateGlobalVector(dm, &rho));
  PetscCall(PetscObjectSetName((PetscObject)rho, "rho"));

  PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "w_q", &f));
  PetscCall(PetscObjectSetName((PetscObject)f, "weights"));
  PetscCall(MatMultTranspose(M_p, f, rho));

  /* Visualize mesh field */
  PetscCall(DMSetOutputSequenceNumber(dm, timestep, time));
  PetscCall(VecViewFromOptions(rho, NULL, "-rho_view"));

  /* Project field to particles */
  /*   This gives f_p = M_p^+ M f */
  PetscCall(DMCreateGlobalVector(dm, &rhs));
  PetscCall(VecCopy(rho, rhs)); /* Identity: M^1 M rho */

  PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
  PetscCall(KSPSetOptionsPrefix(ksp, "ftop_"));
  PetscCall(KSPSetFromOptions(ksp));
  PetscCall(KSPGetPC(ksp, &pc));
  PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCBJACOBI, &is_bjac));
  if (is_bjac) {
    PetscCall(DMSwarmCreateMassMatrixSquare(sw, dm, &PM_p));
    PetscCall(KSPSetOperators(ksp, M_p, PM_p));
  } else {
    PetscCall(KSPSetOperators(ksp, M_p, M_p));
  }
  PetscCall(KSPSolveTranspose(ksp, rhs, f));
  PetscCall(KSPDestroy(&ksp));
  PetscCall(VecDestroy(&rhs));

  /* Visualize particle field */
  PetscCall(DMSetOutputSequenceNumber(sw, timestep, time));
  PetscCall(VecViewFromOptions(f, NULL, "-weights_view"));
  PetscCall(VecNorm(f, NORM_1, &norm));
  PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "w_q", &f));

  /* compute energy */
  PetscCall(DMSwarmGetField(sw, "w_q", &bs, &dtype, (void **)&wq));
  PetscCall(DMSwarmGetField(sw, "DMSwarmPIC_coor", &bs, &dtype, (void **)&coords));
  for (p = 0, energy_1 = 0; p < Np; p++) { energy_1 += wq[p] * (PetscSqr(coords[p * 2 + 0]) + PetscSqr(coords[p * 2 + 1])); }
  PetscCall(DMSwarmRestoreField(sw, "DMSwarmPIC_coor", &bs, &dtype, (void **)&coords));
  PetscCall(DMSwarmRestoreField(sw, "w_q", &bs, &dtype, (void **)&wq));
  PetscCall(PetscPrintf(PETSC_COMM_SELF, "Total number = %20.12e. energy = %20.12e error = %20.12e\n", (double)norm, (double)energy_0, (double)((energy_1 - energy_0) / energy_0)));
  /* Cleanup */
  PetscCall(MatDestroy(&M_p));
  PetscCall(MatDestroy(&PM_p));
  PetscCall(VecDestroy(&rho));
  PetscCall(DMDestroy(&sw));
  PetscCall(DMDestroy(&dm));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

  build:
    requires: !complex

  test:
    suffix: 0
    requires: double triangle
    args: -dm_plex_simplex 0 -dm_plex_box_faces 4,2 -np 50 -dm_plex_box_lower -2.0,0.0 -dm_plex_box_upper 2.0,2.0 -petscspace_degree 2 -ftop_ksp_type lsqr -ftop_pc_type none -dm_view -swarm_view -ftop_ksp_rtol 1.e-14
    filter: grep -v DM_ | grep -v atomic

  test:
    suffix: bjacobi
    requires: double triangle
    args: -dm_plex_simplex 0 -dm_plex_box_faces 4,2 -np 50 -dm_plex_box_lower -2.0,0.0 -dm_plex_box_upper 2.0,2.0 -petscspace_degree 2 -dm_plex_hash_location -ftop_ksp_type lsqr -ftop_pc_type bjacobi -ftop_sub_pc_type lu -ftop_sub_pc_factor_shift_type nonzero -dm_view -swarm_view -ftop_ksp_rtol 1.e-14
    filter: grep -v DM_ | grep -v atomic

TEST*/