// clang-format off
/* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org

   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.

   See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */

/* -------------------------------------------------------------------------------------
   Contributing authors: Mark Stevens (SNL), Aidan Thompson (SNL), Zheng Gong (ENS Lyon)
---------------------------------------------------------------------------------------- */

#include "fix_tgnh_drude.h"

#include "atom.h"
#include "comm.h"
#include "compute.h"
#include "domain.h"
#include "error.h"
#include "fix_deform.h"
#include "fix_drude.h"
#include "force.h"
#include "irregular.h"
#include "kspace.h"
#include "memory.h"
#include "modify.h"
#include "neighbor.h"
#include "respa.h"
#include "update.h"

#include <cstring>
#include <cmath>

using namespace LAMMPS_NS;
using namespace FixConst;

#define DELTAFLIP 0.1
#define TILTMAX 1.5

enum{NOBIAS,BIAS};
enum{NONE,XYZ,XY,YZ,XZ};
enum{ISO,ANISO,TRICLINIC};

/* ----------------------------------------------------------------------
   NVT,NPH,NPT integrators for improved Nose-Hoover equations of motion
 ---------------------------------------------------------------------- */

FixTGNHDrude::FixTGNHDrude(LAMMPS *lmp, int narg, char **arg) :
  Fix(lmp, narg, arg),
  rfix(nullptr), irregular(nullptr), id_temp(nullptr), id_press(nullptr),
  etamol(nullptr), etamol_dot(nullptr), etamol_dotdot(nullptr), etamol_mass(nullptr),
  etaint(nullptr), etaint_dot(nullptr), etaint_dotdot(nullptr), etaint_mass(nullptr),
  etadrude(nullptr), etadrude_dot(nullptr), etadrude_dotdot(nullptr), etadrude_mass(nullptr),
  etap(nullptr), etap_dot(nullptr), etap_dotdot(nullptr), etap_mass(nullptr)
{
  if (narg < 4) error->all(FLERR,"Illegal fix nvt/npt/nph command");

  restart_global = 1;
  dynamic_group_allow = 0;
  time_integrate = 1;
  scalar_flag = 1;
  vector_flag = 1;
  global_freq = 1;
  extscalar = 1;
  extvector = 0;
  ecouple_flag = 1;

  // default values

  pcouple = NONE;
  mtchain = mpchain = 3;
  nc_tchain = nc_pchain = 1;
  mtk_flag = 1;
  deviatoric_flag = 0;
  nreset_h0 = 0;
  flipflag = 1;

  tcomputeflag = 0;
  pcomputeflag = 0;
  id_temp = nullptr;
  id_press = nullptr;

  // turn on tilt factor scaling, whenever applicable

  dimension = domain->dimension;

  scaleyz = scalexz = scalexy = 0;
  if (domain->yperiodic && domain->xy != 0.0) scalexy = 1;
  if (domain->zperiodic && dimension == 3) {
    if (domain->yz != 0.0) scaleyz = 1;
    if (domain->xz != 0.0) scalexz = 1;
  }

  // set fixed-point to default = center of cell

  fixedpoint[0] = 0.5*(domain->boxlo[0]+domain->boxhi[0]);
  fixedpoint[1] = 0.5*(domain->boxlo[1]+domain->boxhi[1]);
  fixedpoint[2] = 0.5*(domain->boxlo[2]+domain->boxhi[2]);

  tstat_flag = 0;
  double t_period = 0.0, tdrude_period = 0.0;

  double p_period[6];
  for (int i = 0; i < 6; i++) {
    p_start[i] = p_stop[i] = p_period[i] = p_target[i] = 0.0;
    p_flag[i] = 0;
  }

  // process keywords

  int iarg = 3;

  while (iarg < narg) {
    if (strcmp(arg[iarg],"temp") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      tstat_flag = 1;
      t_start = utils::numeric(FLERR,arg[iarg+1],false,lmp);
      t_target = t_start;
      t_stop = utils::numeric(FLERR,arg[iarg+2],false,lmp);
      t_period = utils::numeric(FLERR,arg[iarg+3],false,lmp);
      if (t_start <= 0.0 || t_stop <= 0.0)
        error->all(FLERR,
                   "Target temperature for fix nvt/npt/nph cannot be 0.0");
      tdrude_target = utils::numeric(FLERR,arg[iarg+4],false,lmp);
      tdrude_period = utils::numeric(FLERR,arg[iarg+5],false,lmp);
      iarg += 6;

    } else if (strcmp(arg[iarg],"iso") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      pcouple = XYZ;
      p_start[0] = p_start[1] = p_start[2] = utils::numeric(FLERR,arg[iarg+1],false,lmp);
      p_stop[0] = p_stop[1] = p_stop[2] = utils::numeric(FLERR,arg[iarg+2],false,lmp);
      p_period[0] = p_period[1] = p_period[2] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
      p_flag[0] = p_flag[1] = p_flag[2] = 1;
      if (dimension == 2) {
        p_start[2] = p_stop[2] = p_period[2] = 0.0;
        p_flag[2] = 0;
      }
      iarg += 4;
    } else if (strcmp(arg[iarg],"aniso") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      pcouple = NONE;
      p_start[0] = p_start[1] = p_start[2] = utils::numeric(FLERR,arg[iarg+1],false,lmp);
      p_stop[0] = p_stop[1] = p_stop[2] = utils::numeric(FLERR,arg[iarg+2],false,lmp);
      p_period[0] = p_period[1] = p_period[2] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
      p_flag[0] = p_flag[1] = p_flag[2] = 1;
      if (dimension == 2) {
        p_start[2] = p_stop[2] = p_period[2] = 0.0;
        p_flag[2] = 0;
      }
      iarg += 4;
    } else if (strcmp(arg[iarg],"tri") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      pcouple = NONE;
      scalexy = scalexz = scaleyz = 0;
      p_start[0] = p_start[1] = p_start[2] = utils::numeric(FLERR,arg[iarg+1],false,lmp);
      p_stop[0] = p_stop[1] = p_stop[2] = utils::numeric(FLERR,arg[iarg+2],false,lmp);
      p_period[0] = p_period[1] = p_period[2] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
      p_flag[0] = p_flag[1] = p_flag[2] = 1;
      p_start[3] = p_start[4] = p_start[5] = 0.0;
      p_stop[3] = p_stop[4] = p_stop[5] = 0.0;
      p_period[3] = p_period[4] = p_period[5] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
      p_flag[3] = p_flag[4] = p_flag[5] = 1;
      if (dimension == 2) {
        p_start[2] = p_stop[2] = p_period[2] = 0.0;
        p_flag[2] = 0;
        p_start[3] = p_stop[3] = p_period[3] = 0.0;
        p_flag[3] = 0;
        p_start[4] = p_stop[4] = p_period[4] = 0.0;
        p_flag[4] = 0;
      }
      iarg += 4;
    } else if (strcmp(arg[iarg],"x") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      p_start[0] = utils::numeric(FLERR,arg[iarg+1],false,lmp);
      p_stop[0] = utils::numeric(FLERR,arg[iarg+2],false,lmp);
      p_period[0] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
      p_flag[0] = 1;
      deviatoric_flag = 1;
      iarg += 4;
    } else if (strcmp(arg[iarg],"y") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      p_start[1] = utils::numeric(FLERR,arg[iarg+1],false,lmp);
      p_stop[1] = utils::numeric(FLERR,arg[iarg+2],false,lmp);
      p_period[1] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
      p_flag[1] = 1;
      deviatoric_flag = 1;
      iarg += 4;
    } else if (strcmp(arg[iarg],"z") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      p_start[2] = utils::numeric(FLERR,arg[iarg+1],false,lmp);
      p_stop[2] = utils::numeric(FLERR,arg[iarg+2],false,lmp);
      p_period[2] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
      p_flag[2] = 1;
      deviatoric_flag = 1;
      iarg += 4;
      if (dimension == 2)
        error->all(FLERR,"Invalid fix nvt/npt/nph command for a 2d simulation");

    } else if (strcmp(arg[iarg],"yz") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      p_start[3] = utils::numeric(FLERR,arg[iarg+1],false,lmp);
      p_stop[3] = utils::numeric(FLERR,arg[iarg+2],false,lmp);
      p_period[3] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
      p_flag[3] = 1;
      deviatoric_flag = 1;
      scaleyz = 0;
      iarg += 4;
      if (dimension == 2)
        error->all(FLERR,"Invalid fix nvt/npt/nph command for a 2d simulation");
    } else if (strcmp(arg[iarg],"xz") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      p_start[4] = utils::numeric(FLERR,arg[iarg+1],false,lmp);
      p_stop[4] = utils::numeric(FLERR,arg[iarg+2],false,lmp);
      p_period[4] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
      p_flag[4] = 1;
      deviatoric_flag = 1;
      scalexz = 0;
      iarg += 4;
      if (dimension == 2)
        error->all(FLERR,"Invalid fix nvt/npt/nph command for a 2d simulation");
    } else if (strcmp(arg[iarg],"xy") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      p_start[5] = utils::numeric(FLERR,arg[iarg+1],false,lmp);
      p_stop[5] = utils::numeric(FLERR,arg[iarg+2],false,lmp);
      p_period[5] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
      p_flag[5] = 1;
      deviatoric_flag = 1;
      scalexy = 0;
      iarg += 4;

    } else if (strcmp(arg[iarg],"couple") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      if (strcmp(arg[iarg+1],"xyz") == 0) pcouple = XYZ;
      else if (strcmp(arg[iarg+1],"xy") == 0) pcouple = XY;
      else if (strcmp(arg[iarg+1],"yz") == 0) pcouple = YZ;
      else if (strcmp(arg[iarg+1],"xz") == 0) pcouple = XZ;
      else if (strcmp(arg[iarg+1],"none") == 0) pcouple = NONE;
      else error->all(FLERR,"Illegal fix nvt/npt/nph command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"tchain") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      mtchain = utils::inumeric(FLERR,arg[iarg+1],false,lmp);
      if (mtchain < 1) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"pchain") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      mpchain = utils::inumeric(FLERR,arg[iarg+1],false,lmp);
      if (mpchain < 0) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"mtk") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      mtk_flag = utils::logical(FLERR, arg[iarg + 1], false, lmp);
      iarg += 2;
    } else if (strcmp(arg[iarg],"tloop") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      nc_tchain = utils::inumeric(FLERR,arg[iarg+1],false,lmp);
      if (nc_tchain < 0) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"ploop") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      nc_pchain = utils::inumeric(FLERR,arg[iarg+1],false,lmp);
      if (nc_pchain < 0) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"nreset") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      nreset_h0 = utils::inumeric(FLERR,arg[iarg+1],false,lmp);
      if (nreset_h0 < 0) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"scalexy") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      scalexy = utils::logical(FLERR, arg[iarg + 1], false, lmp);
      iarg += 2;
    } else if (strcmp(arg[iarg],"scalexz") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      scalexz = utils::logical(FLERR, arg[iarg + 1], false, lmp);
      iarg += 2;
    } else if (strcmp(arg[iarg],"scaleyz") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      scaleyz = utils::logical(FLERR, arg[iarg + 1], false, lmp);
      iarg += 2;
    } else if (strcmp(arg[iarg],"flip") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      flipflag = utils::logical(FLERR, arg[iarg + 1], false, lmp);
      iarg += 2;
    } else if (strcmp(arg[iarg],"fixedpoint") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      fixedpoint[0] = utils::numeric(FLERR,arg[iarg+1],false,lmp);
      fixedpoint[1] = utils::numeric(FLERR,arg[iarg+2],false,lmp);
      fixedpoint[2] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
      iarg += 4;
    } else error->all(FLERR,"Illegal fix nvt/npt/nph command");
  }

  // error checks

  if (dimension == 2 && (p_flag[2] || p_flag[3] || p_flag[4]))
    error->all(FLERR,"Invalid fix nvt/npt/nph command for a 2d simulation");
  if (dimension == 2 && (pcouple == YZ || pcouple == XZ))
    error->all(FLERR,"Invalid fix nvt/npt/nph command for a 2d simulation");
  if (dimension == 2 && (scalexz == 1 || scaleyz == 1 ))
    error->all(FLERR,"Invalid fix nvt/npt/nph command for a 2d simulation");

  if (pcouple == XYZ && (p_flag[0] == 0 || p_flag[1] == 0))
    error->all(FLERR,"Invalid fix nvt/npt/nph command pressure settings");
  if (pcouple == XYZ && dimension == 3 && p_flag[2] == 0)
    error->all(FLERR,"Invalid fix nvt/npt/nph command pressure settings");
  if (pcouple == XY && (p_flag[0] == 0 || p_flag[1] == 0))
    error->all(FLERR,"Invalid fix nvt/npt/nph command pressure settings");
  if (pcouple == YZ && (p_flag[1] == 0 || p_flag[2] == 0))
    error->all(FLERR,"Invalid fix nvt/npt/nph command pressure settings");
  if (pcouple == XZ && (p_flag[0] == 0 || p_flag[2] == 0))
    error->all(FLERR,"Invalid fix nvt/npt/nph command pressure settings");

  // require periodicity in tensile dimension

  if (p_flag[0] && domain->xperiodic == 0)
    error->all(FLERR,"Cannot use fix nvt/npt/nph on a non-periodic dimension");
  if (p_flag[1] && domain->yperiodic == 0)
    error->all(FLERR,"Cannot use fix nvt/npt/nph on a non-periodic dimension");
  if (p_flag[2] && domain->zperiodic == 0)
    error->all(FLERR,"Cannot use fix nvt/npt/nph on a non-periodic dimension");

  // require periodicity in 2nd dim of off-diagonal tilt component

  if (p_flag[3] && domain->zperiodic == 0)
    error->all(FLERR,
               "Cannot use fix nvt/npt/nph on a 2nd non-periodic dimension");
  if (p_flag[4] && domain->zperiodic == 0)
    error->all(FLERR,
               "Cannot use fix nvt/npt/nph on a 2nd non-periodic dimension");
  if (p_flag[5] && domain->yperiodic == 0)
    error->all(FLERR,
               "Cannot use fix nvt/npt/nph on a 2nd non-periodic dimension");

  if (scaleyz == 1 && domain->zperiodic == 0)
    error->all(FLERR,"Cannot use fix nvt/npt/nph "
               "with yz scaling when z is non-periodic dimension");
  if (scalexz == 1 && domain->zperiodic == 0)
    error->all(FLERR,"Cannot use fix nvt/npt/nph "
               "with xz scaling when z is non-periodic dimension");
  if (scalexy == 1 && domain->yperiodic == 0)
    error->all(FLERR,"Cannot use fix nvt/npt/nph "
               "with xy scaling when y is non-periodic dimension");

  if (p_flag[3] && scaleyz == 1)
    error->all(FLERR,"Cannot use fix nvt/npt/nph with "
               "both yz dynamics and yz scaling");
  if (p_flag[4] && scalexz == 1)
    error->all(FLERR,"Cannot use fix nvt/npt/nph with "
               "both xz dynamics and xz scaling");
  if (p_flag[5] && scalexy == 1)
    error->all(FLERR,"Cannot use fix nvt/npt/nph with "
               "both xy dynamics and xy scaling");

  if (!domain->triclinic && (p_flag[3] || p_flag[4] || p_flag[5]))
    error->all(FLERR,"Can not specify Pxy/Pxz/Pyz in "
               "fix nvt/npt/nph with non-triclinic box");

  if (pcouple == XYZ && dimension == 3 &&
      (p_start[0] != p_start[1] || p_start[0] != p_start[2] ||
       p_stop[0] != p_stop[1] || p_stop[0] != p_stop[2] ||
       p_period[0] != p_period[1] || p_period[0] != p_period[2]))
    error->all(FLERR,"Invalid fix nvt/npt/nph pressure settings");
  if (pcouple == XYZ && dimension == 2 &&
      (p_start[0] != p_start[1] || p_stop[0] != p_stop[1] ||
       p_period[0] != p_period[1]))
    error->all(FLERR,"Invalid fix nvt/npt/nph pressure settings");
  if (pcouple == XY &&
      (p_start[0] != p_start[1] || p_stop[0] != p_stop[1] ||
       p_period[0] != p_period[1]))
    error->all(FLERR,"Invalid fix nvt/npt/nph pressure settings");
  if (pcouple == YZ &&
      (p_start[1] != p_start[2] || p_stop[1] != p_stop[2] ||
       p_period[1] != p_period[2]))
    error->all(FLERR,"Invalid fix nvt/npt/nph pressure settings");
  if (pcouple == XZ &&
      (p_start[0] != p_start[2] || p_stop[0] != p_stop[2] ||
       p_period[0] != p_period[2]))
    error->all(FLERR,"Invalid fix nvt/npt/nph pressure settings");

  if ((tstat_flag && t_period <= 0.0) ||
      (p_flag[0] && p_period[0] <= 0.0) ||
      (p_flag[1] && p_period[1] <= 0.0) ||
      (p_flag[2] && p_period[2] <= 0.0) ||
      (p_flag[3] && p_period[3] <= 0.0) ||
      (p_flag[4] && p_period[4] <= 0.0) ||
      (p_flag[5] && p_period[5] <= 0.0))
    error->all(FLERR,"Fix nvt/npt/nph damping parameters must be > 0.0");

  // set pstat_flag and box change and restart_pbc variables

  pre_exchange_flag = 0;
  pstat_flag = 0;
  pstyle = ISO;

  for (int i = 0; i < 6; i++)
    if (p_flag[i]) pstat_flag = 1;

  if (pstat_flag) {
    if (p_flag[0]) box_change |= BOX_CHANGE_X;
    if (p_flag[1]) box_change |= BOX_CHANGE_Y;
    if (p_flag[2]) box_change |= BOX_CHANGE_Z;
    if (p_flag[3]) box_change |= BOX_CHANGE_YZ;
    if (p_flag[4]) box_change |= BOX_CHANGE_XZ;
    if (p_flag[5]) box_change |= BOX_CHANGE_XY;
    no_change_box = 1;

    // pstyle = TRICLINIC if any off-diagonal term is controlled -> 6 dof
    // else pstyle = ISO if XYZ coupling or XY coupling in 2d -> 1 dof
    // else pstyle = ANISO -> 3 dof

    if (p_flag[3] || p_flag[4] || p_flag[5]) pstyle = TRICLINIC;
    else if (pcouple == XYZ || (dimension == 2 && pcouple == XY)) pstyle = ISO;
    else pstyle = ANISO;

    // pre_exchange only required if flips can occur due to shape changes

    if (flipflag && (p_flag[3] || p_flag[4] || p_flag[5]))
      pre_exchange_flag = pre_exchange_migrate = 1;
    if (flipflag && (domain->yz != 0.0 || domain->xz != 0.0 || domain->xy != 0.0))
      pre_exchange_flag = pre_exchange_migrate = 1;
  }

  // convert input periods to frequencies

  t_freq = tdrude_freq = 0.0;
  p_freq[0] = p_freq[1] = p_freq[2] = p_freq[3] = p_freq[4] = p_freq[5] = 0.0;

  if (tstat_flag) {
    t_freq = 1.0 / t_period;
    tdrude_freq = 1.0 / tdrude_period;
  }
  if (p_flag[0]) p_freq[0] = 1.0 / p_period[0];
  if (p_flag[1]) p_freq[1] = 1.0 / p_period[1];
  if (p_flag[2]) p_freq[2] = 1.0 / p_period[2];
  if (p_flag[3]) p_freq[3] = 1.0 / p_period[3];
  if (p_flag[4]) p_freq[4] = 1.0 / p_period[4];
  if (p_flag[5]) p_freq[5] = 1.0 / p_period[5];

  // Nose/Hoover temp and pressure init

  size_vector = 3;

  if (tstat_flag) {
    int ich;

    etaint = new double[mtchain];
    // add one extra dummy thermostat for eta_dot, set to zero
    etaint_dot = new double[mtchain+1];
    etaint_dot[mtchain] = 0.0;
    etaint_dotdot = new double[mtchain];
    for (ich = 0; ich < mtchain; ich++) {
      etaint[ich] = etaint_dot[ich] = etaint_dotdot[ich] = 0.0;
    }
    etaint_mass = new double[mtchain];

    etamol = new double[mtchain];
    // add one extra dummy thermostat for eta_dot, set to zero
    etamol_dot = new double[mtchain+1];
    etamol_dot[mtchain] = 0.0;
    etamol_dotdot = new double[mtchain];
    for (ich = 0; ich < mtchain; ich++) {
      etamol[ich] = etamol_dot[ich] = etamol_dotdot[ich] = 0.0;
    }
    etamol_mass = new double[mtchain];

    etadrude = new double[mtchain];
    // add one extra dummy thermostat for eta_dot, set to zero
    etadrude_dot = new double[mtchain+1];
    etadrude_dot[mtchain] = 0.0;
    etadrude_dotdot = new double[mtchain];
    for (ich = 0; ich < mtchain; ich++) {
      etadrude[ich] = etadrude_dot[ich] = etadrude_dotdot[ich] = 0.0;
    }
    etadrude_mass = new double[mtchain];
  }

  if (pstat_flag) {
    omega[0] = omega[1] = omega[2] = 0.0;
    omega_dot[0] = omega_dot[1] = omega_dot[2] = 0.0;
    omega_mass[0] = omega_mass[1] = omega_mass[2] = 0.0;
    omega[3] = omega[4] = omega[5] = 0.0;
    omega_dot[3] = omega_dot[4] = omega_dot[5] = 0.0;
    omega_mass[3] = omega_mass[4] = omega_mass[5] = 0.0;

    if (mpchain) {
      int ich;
      etap = new double[mpchain];

      // add one extra dummy thermostat, set to zero

      etap_dot = new double[mpchain+1];
      etap_dot[mpchain] = 0.0;
      etap_dotdot = new double[mpchain];
      for (ich = 0; ich < mpchain; ich++) {
        etap[ich] = etap_dot[ich] =
          etap_dotdot[ich] = 0.0;
      }
      etap_mass = new double[mpchain];
    }
  }

  nrigid = 0;
  rfix = nullptr;

  if (pre_exchange_flag) irregular = new Irregular(lmp);
  else irregular = nullptr;

  // initialize vol0,t0 to zero to signal uninitialized
  // values then assigned in init(), if necessary

  vol0 = t0 = 0.0;

  // find fix drude
  int ifix;
  for (ifix = 0; ifix < modify->nfix; ifix++)
    if (strcmp(modify->fix[ifix]->style,"drude") == 0) break;
  if (ifix == modify->nfix) error->all(FLERR, "fix tgnh/drude requires fix drude");
  fix_drude = dynamic_cast<FixDrude *>(modify->fix[ifix]);

  // make sure ghost atoms have velocity
  if (!comm->ghost_velocity)
    error->all(FLERR,"fix tgnh/drude requires ghost velocities. Use comm_modify vel yes");
}

/* ---------------------------------------------------------------------- */

FixTGNHDrude::~FixTGNHDrude()
{
  if (copymode) return;

  delete [] rfix;

  delete irregular;

  // delete temperature and pressure if fix created them

  if (tcomputeflag) modify->delete_compute(id_temp);
  delete [] id_temp;

  if (tstat_flag) {
    delete [] etaint;
    delete [] etaint_dot;
    delete [] etaint_dotdot;
    delete [] etaint_mass;
    delete [] etamol;
    delete [] etamol_dot;
    delete [] etamol_dotdot;
    delete [] etamol_mass;
    delete [] etadrude;
    delete [] etadrude_dot;
    delete [] etadrude_dotdot;
    delete [] etadrude_mass;
  }

  if (pstat_flag) {
    if (pcomputeflag) modify->delete_compute(id_press);
    delete [] id_press;
    if (mpchain) {
      delete [] etap;
      delete [] etap_dot;
      delete [] etap_dotdot;
      delete [] etap_mass;
    }
  }
}

/* ---------------------------------------------------------------------- */

int FixTGNHDrude::setmask()
{
  int mask = 0;
  mask |= INITIAL_INTEGRATE;
  mask |= FINAL_INTEGRATE;
  mask |= INITIAL_INTEGRATE_RESPA;
  mask |= PRE_FORCE_RESPA;
  mask |= FINAL_INTEGRATE_RESPA;
  if (pre_exchange_flag) mask |= PRE_EXCHANGE;
  return mask;
}

/* ---------------------------------------------------------------------- */

void FixTGNHDrude::init()
{
  // ensure no conflict with fix deform

  if (pstat_flag)
    for (int i = 0; i < modify->nfix; i++)
      if (strcmp(modify->fix[i]->style,"deform") == 0) {
        int *dimflag = (dynamic_cast<FixDeform *>(modify->fix[i]))->dimflag;
        if ((p_flag[0] && dimflag[0]) || (p_flag[1] && dimflag[1]) ||
            (p_flag[2] && dimflag[2]) || (p_flag[3] && dimflag[3]) ||
            (p_flag[4] && dimflag[4]) || (p_flag[5] && dimflag[5]))
          error->all(FLERR,"Cannot use fix npt and fix deform on "
                     "same component of stress tensor");
      }

  // set temperature and pressure ptrs

  int icompute = modify->find_compute(id_temp);
  if (icompute < 0)
    error->all(FLERR,"Temperature ID for fix nvt/npt does not exist");
  temperature = modify->compute[icompute];

  if (temperature->tempbias) which = BIAS;
  else which = NOBIAS;

  if (pstat_flag) {
    icompute = modify->find_compute(id_press);
    if (icompute < 0)
      error->all(FLERR,"Pressure ID for fix npt/nph does not exist");
    pressure = modify->compute[icompute];
  }

  // set timesteps and frequencies

  dtv = update->dt;
  dtf = 0.5 * update->dt * force->ftm2v;
  dthalf = 0.5 * update->dt;
  dt4 = 0.25 * update->dt;
  dt8 = 0.125 * update->dt;
  dto = dthalf;

  p_freq_max = 0.0;
  if (pstat_flag) {
    p_freq_max = MAX(p_freq[0],p_freq[1]);
    p_freq_max = MAX(p_freq_max,p_freq[2]);
    if (pstyle == TRICLINIC) {
      p_freq_max = MAX(p_freq_max,p_freq[3]);
      p_freq_max = MAX(p_freq_max,p_freq[4]);
      p_freq_max = MAX(p_freq_max,p_freq[5]);
    }
  }

  // tally the number of dimensions that are barostatted
  // set initial volume and reference cell, if not already done

  if (pstat_flag) {
    pdim = p_flag[0] + p_flag[1] + p_flag[2];
    if (vol0 == 0.0) {
      if (dimension == 3) vol0 = domain->xprd * domain->yprd * domain->zprd;
      else vol0 = domain->xprd * domain->yprd;
      h0_inv[0] = domain->h_inv[0];
      h0_inv[1] = domain->h_inv[1];
      h0_inv[2] = domain->h_inv[2];
      h0_inv[3] = domain->h_inv[3];
      h0_inv[4] = domain->h_inv[4];
      h0_inv[5] = domain->h_inv[5];
    }
  }

  boltz = force->boltz;
  nktv2p = force->nktv2p;

  if (force->kspace) kspace_flag = 1;
  else kspace_flag = 0;

  if (utils::strmatch(update->integrate_style,"^respa")) {
    nlevels_respa = (dynamic_cast<Respa *>(update->integrate))->nlevels;
    step_respa = (dynamic_cast<Respa *>(update->integrate))->step;
    dto = 0.5*step_respa[0];
  }

  // detect if any rigid fixes exist so rigid bodies move when box is remapped
  // rfix[] = indices to each fix rigid

  delete [] rfix;
  nrigid = 0;
  rfix = nullptr;

  for (int i = 0; i < modify->nfix; i++)
    if (modify->fix[i]->rigid_flag) nrigid++;
  if (nrigid) {
    rfix = new int[nrigid];
    nrigid = 0;
    for (int i = 0; i < modify->nfix; i++)
      if (modify->fix[i]->rigid_flag) rfix[nrigid++] = i;
  }
}

/* ----------------------------------------------------------------------
   compute T,P before integrator starts
------------------------------------------------------------------------- */

void FixTGNHDrude::setup_mol_mass_dof() {
  double *mass = atom->mass;
  int *mask = atom->mask;
  tagint *molecule = atom->molecule;
  int *type = atom->type;
  int *drudetype = fix_drude->drudetype;
  int n_drude, n_drude_tmp = 0;
  tagint id_mol = 0, n_mol_in_group = 0;

  for (int i = 0; i < atom->nlocal; i++) {
    // molecule id starts from 1. max(id_mol) equals to the number of molecules in the system
    id_mol = std::max(id_mol, molecule[i]);
    if (mask[i] & groupbit) {
      if (drudetype[type[i]] == DRUDE_TYPE)
        n_drude_tmp++;
    }
  }
  MPI_Allreduce(&n_drude_tmp, &n_drude, 1, MPI_LMP_TAGINT, MPI_SUM, world);
  MPI_Allreduce(&id_mol, &n_mol, 1, MPI_LMP_TAGINT, MPI_MAX, world);

  // use flag_mol to determine the number of molecules in the fix group
  int *flag_mol = new int[n_mol + 1];
  int *flag_mol_tmp = new int[n_mol + 1];
  memset(flag_mol_tmp, 0, sizeof(int) * (n_mol + 1));
  for (int i = 0; i < atom->nlocal; i++) {
    if (mask[i] & groupbit) {
      flag_mol_tmp[molecule[i]] = 1;
    }
  }
  MPI_Allreduce(flag_mol_tmp, flag_mol, n_mol + 1, MPI_INT, MPI_SUM, world);
  for (int i = 1; i < n_mol + 1; i++) {
    if (flag_mol[i])
      n_mol_in_group++;
  }
  delete[] flag_mol;
  delete[] flag_mol_tmp;

  // length of v_mol set to n_mol+1, so that the subscript start from 1, we can call v_mol[n_mol]
  memory->create(v_mol, n_mol + 1, 3, "fix_tgnh_drude::v_mol");
  memory->create(v_mol_tmp, n_mol + 1, 3, "fix_tgnh_drude::v_mol_tmp");
  memory->create(mass_mol, n_mol + 1, "fix_tgnh_drude::mass_mol");

  auto mass_tmp = new double[n_mol + 1];
  memset(mass_tmp, 0, sizeof(double) * (n_mol + 1));
  for (int i = 0; i < atom->nlocal; i++) {
    id_mol = molecule[i];
    mass_tmp[id_mol] += mass[type[i]];
  }
  MPI_Allreduce(mass_tmp, mass_mol, n_mol + 1, MPI_DOUBLE, MPI_SUM, world);
  delete[] mass_tmp;

  // DOFs
  t_current = temperature->compute_scalar();
  tdof = temperature->dof;
  // remove DOFs of COM translational motion based on the number of molecules in the group
  dof_mol = 3.0 * n_mol_in_group - 3.0 * n_mol_in_group / n_mol;
  dof_drude = 3.0 * n_drude;
  dof_int = tdof - dof_mol - dof_drude;

  if (comm->me == 0) {
    if (screen) {
      fprintf(screen, "TGNHC thermostat for Drude model\n");
      fprintf(screen, "  DOFs of molecules, atoms and dipoles: %.1f %.1f %.1f\n",
              dof_mol, dof_int, dof_drude);
    }
    if (logfile) {
      fprintf(logfile, "TGNHC thermostat for Drude model\n");
      fprintf(logfile, "  DOFs of molecules, atoms and dipoles: %.1f %.1f %.1f\n",
              dof_mol, dof_int, dof_drude);
    }
  }
  if (dof_mol <=0 || dof_int <=0 || dof_drude <=0)
    error->all(FLERR, "TGNHC thermostat requires DOFs of molecules, atoms and dipoles larger than 0");
}

void FixTGNHDrude::setup(int /*vflag*/)
{
  setup_mol_mass_dof();
  // t_target is needed by NVT and NPT in compute_scalar()
  // If no thermostat or using fix nphug,
  // t_target must be defined by other means.

  if (tstat_flag && strstr(style,"nphug") == nullptr) {
    compute_temp_target();
  } else if (pstat_flag) {

    // t0 = reference temperature for masses
    // cannot be done in init() b/c temperature cannot be called there
    // is b/c Modify::init() inits computes after fixes due to dof dependence
    // guesstimate a unit-dependent t0 if actual T = 0.0
    // if it was read in from a restart file, leave it be

    if (t0 == 0.0) {
      t0 = temperature->compute_scalar();
      if (t0 == 0.0) {
        if (strcmp(update->unit_style,"lj") == 0) t0 = 1.0;
        else t0 = 300.0;
      }
    }
    t_target = t0;
  }

  if (pstat_flag) compute_press_target();

  if (pstat_flag) {
    if (pstyle == ISO) pressure->compute_scalar();
    else pressure->compute_vector();
    couple();
    pressure->addstep(update->ntimestep+1);
  }

  // masses and initial forces on thermostat variables

  if (tstat_flag) {
    etaint_mass[0] = ke2int_target / (t_freq * t_freq);
    etamol_mass[0] = ke2mol_target / (t_freq * t_freq);
    etadrude_mass[0] = ke2drude_target / (tdrude_freq * tdrude_freq);
    for (int ich = 1; ich < mtchain; ich++) {
      etaint_mass[ich] = boltz * t_target / (t_freq * t_freq);
      etamol_mass[ich] = boltz * t_target / (t_freq * t_freq);
      etadrude_mass[ich] = boltz * tdrude_target / (tdrude_freq * tdrude_freq);

      etaint_dotdot[ich] = (etaint_mass[ich - 1] * etaint_dot[ich - 1] * etaint_dot[ich - 1] -
                            boltz * t_target) / etaint_mass[ich];
      etamol_dotdot[ich] = (etamol_mass[ich - 1] * etamol_dot[ich - 1] * etamol_dot[ich - 1] -
                            boltz * t_target) / etamol_mass[ich];
      etadrude_dotdot[ich] = (etadrude_mass[ich - 1] * etadrude_dot[ich - 1] * etadrude_dot[ich - 1] -
                              boltz * tdrude_target) / etadrude_mass[ich];
    }
  }

  // masses and initial forces on barostat variables

  if (pstat_flag) {
    double kt = boltz * t_target;
    double nkt = (atom->natoms + 1) * kt;

    for (int i = 0; i < 3; i++)
      if (p_flag[i])
        omega_mass[i] = nkt/(p_freq[i]*p_freq[i]);

    if (pstyle == TRICLINIC) {
      for (int i = 3; i < 6; i++)
        if (p_flag[i]) omega_mass[i] = nkt/(p_freq[i]*p_freq[i]);
    }

  // masses and initial forces on barostat thermostat variables

    if (mpchain) {
      etap_mass[0] = boltz * t_target / (p_freq_max*p_freq_max);
      for (int ich = 1; ich < mpchain; ich++)
        etap_mass[ich] = boltz * t_target / (p_freq_max*p_freq_max);
      for (int ich = 1; ich < mpchain; ich++)
        etap_dotdot[ich] =
          (etap_mass[ich-1]*etap_dot[ich-1]*etap_dot[ich-1] -
           boltz * t_target) / etap_mass[ich];
    }
  }
}

/* ----------------------------------------------------------------------
   1st half of Verlet update
------------------------------------------------------------------------- */

void FixTGNHDrude::initial_integrate(int /*vflag*/)
{
  // update eta_press_dot

  if (pstat_flag && mpchain) nhc_press_integrate();

  // update eta_dot

  if (tstat_flag) {
    compute_temp_target();
    nhc_temp_integrate();
  }

  // need to recompute pressure to account for change in KE
  // t_current is up-to-date, but compute_temperature is not
  // compute appropriately coupled elements of mvv_current

  if (pstat_flag) {
    if (pstyle == ISO) {
      temperature->compute_scalar();
      pressure->compute_scalar();
    } else {
      temperature->compute_vector();
      pressure->compute_vector();
    }
    couple();
    pressure->addstep(update->ntimestep+1);
  }

  if (pstat_flag) {
    compute_press_target();
    nh_omega_dot();
    nh_v_press();
  }

  nve_v();

  // remap simulation box by 1/2 step

  if (pstat_flag) remap();

  nve_x();

  // remap simulation box by 1/2 step
  // redo KSpace coeffs since volume has changed

  if (pstat_flag) {
    remap();
    if (kspace_flag) force->kspace->setup();
  }
}

/* ----------------------------------------------------------------------
   2nd half of Verlet update
------------------------------------------------------------------------- */

void FixTGNHDrude::final_integrate()
{
  nve_v();

  // re-compute temp before nh_v_press()
  // only needed for temperature computes with BIAS on reneighboring steps:
  //   b/c some biases store per-atom values (e.g. temp/profile)
  //   per-atom values are invalid if reneigh/comm occurred
  //     since temp->compute() in initial_integrate()

  if (which == BIAS && neighbor->ago == 0)
    t_current = temperature->compute_scalar();

  if (pstat_flag) nh_v_press();

  // compute new T,P after velocities rescaled by nh_v_press()
  // compute appropriately coupled elements of mvv_current

  t_current = temperature->compute_scalar();
  tdof = temperature->dof;

  // need to recompute pressure to account for change in KE
  // t_current is up-to-date, but compute_temperature is not
  // compute appropriately coupled elements of mvv_current

  if (pstat_flag) {
    if (pstyle == ISO) pressure->compute_scalar();
    else {
      temperature->compute_vector();
      pressure->compute_vector();
    }
    couple();
    pressure->addstep(update->ntimestep+1);
  }

  if (pstat_flag) nh_omega_dot();

  // update eta_dot
  // update eta_press_dot

  if (tstat_flag) nhc_temp_integrate();
  if (pstat_flag && mpchain) nhc_press_integrate();
}

/* ---------------------------------------------------------------------- */

void FixTGNHDrude::initial_integrate_respa(int /*vflag*/, int ilevel, int /*iloop*/)
{
  // set timesteps by level

  dtv = step_respa[ilevel];
  dtf = 0.5 * step_respa[ilevel] * force->ftm2v;
  dthalf = 0.5 * step_respa[ilevel];

  // outermost level - update eta_dot and omega_dot, apply to v
  // all other levels - NVE update of v
  // x,v updates only performed for atoms in group

  if (ilevel == nlevels_respa-1) {

    // update eta_press_dot

    if (pstat_flag && mpchain) nhc_press_integrate();

    // update eta_dot

    if (tstat_flag) {
      compute_temp_target();
      nhc_temp_integrate();
    }

    // recompute pressure to account for change in KE
    // t_current is up-to-date, but compute_temperature is not
    // compute appropriately coupled elements of mvv_current

    if (pstat_flag) {
      if (pstyle == ISO) {
        temperature->compute_scalar();
        pressure->compute_scalar();
      } else {
        temperature->compute_vector();
        pressure->compute_vector();
      }
      couple();
      pressure->addstep(update->ntimestep+1);
    }

    if (pstat_flag) {
      compute_press_target();
      nh_omega_dot();
      nh_v_press();
    }

    nve_v();

  } else nve_v();

  // innermost level - also update x only for atoms in group
  // if barostat, perform 1/2 step remap before and after

  if (ilevel == 0) {
    if (pstat_flag) remap();
    nve_x();
    if (pstat_flag) remap();
  }
}

/* ---------------------------------------------------------------------- */

void FixTGNHDrude::pre_force_respa(int /*vflag*/, int ilevel, int /*iloop*/)
{
  // if barostat, redo KSpace coeffs at outermost level,
  // since volume has changed

  if (ilevel == nlevels_respa-1 && kspace_flag && pstat_flag)
    force->kspace->setup();
}

/* ---------------------------------------------------------------------- */

void FixTGNHDrude::final_integrate_respa(int ilevel, int /*iloop*/)
{
  // set timesteps by level

  dtf = 0.5 * step_respa[ilevel] * force->ftm2v;
  dthalf = 0.5 * step_respa[ilevel];

  // outermost level - update eta_dot and omega_dot, apply via final_integrate
  // all other levels - NVE update of v

  if (ilevel == nlevels_respa-1) final_integrate();
  else nve_v();
}

/* ---------------------------------------------------------------------- */

void FixTGNHDrude::couple()
{
  double *tensor = pressure->vector;

  if (pstyle == ISO)
    p_current[0] = p_current[1] = p_current[2] = pressure->scalar;
  else if (pcouple == XYZ) {
    double ave = 1.0/3.0 * (tensor[0] + tensor[1] + tensor[2]);
    p_current[0] = p_current[1] = p_current[2] = ave;
  } else if (pcouple == XY) {
    double ave = 0.5 * (tensor[0] + tensor[1]);
    p_current[0] = p_current[1] = ave;
    p_current[2] = tensor[2];
  } else if (pcouple == YZ) {
    double ave = 0.5 * (tensor[1] + tensor[2]);
    p_current[1] = p_current[2] = ave;
    p_current[0] = tensor[0];
  } else if (pcouple == XZ) {
    double ave = 0.5 * (tensor[0] + tensor[2]);
    p_current[0] = p_current[2] = ave;
    p_current[1] = tensor[1];
  } else {
    p_current[0] = tensor[0];
    p_current[1] = tensor[1];
    p_current[2] = tensor[2];
  }

  if (!std::isfinite(p_current[0]) || !std::isfinite(p_current[1]) || !std::isfinite(p_current[2]))
    error->all(FLERR,"Non-numeric pressure - simulation unstable");

  // switch order from xy-xz-yz to Voigt

  if (pstyle == TRICLINIC) {
    p_current[3] = tensor[5];
    p_current[4] = tensor[4];
    p_current[5] = tensor[3];

    if (!std::isfinite(p_current[3]) || !std::isfinite(p_current[4]) || !std::isfinite(p_current[5]))
      error->all(FLERR,"Non-numeric pressure - simulation unstable");
  }
}

/* ----------------------------------------------------------------------
   change box size
   remap all atoms or dilate group atoms depending on allremap flag
   if rigid bodies exist, scale rigid body centers-of-mass
------------------------------------------------------------------------- */

void FixTGNHDrude::remap()
{
  int i;
  double oldlo,oldhi;
  double expfac;

  int nlocal = atom->nlocal;
  double *h = domain->h;

  // omega is not used, except for book-keeping

  for (int i = 0; i < 6; i++) omega[i] += dto*omega_dot[i];

  // convert pertinent atoms and rigid bodies to lamda coords

  domain->x2lamda(nlocal);

  if (nrigid)
    for (i = 0; i < nrigid; i++)
      modify->fix[rfix[i]]->deform(0);

  // reset global and local box to new size/shape

  // this operation corresponds to applying the
  // translate and scale operations
  // corresponding to the solution of the following ODE:
  //
  // h_dot = omega_dot * h
  //
  // where h_dot, omega_dot and h are all upper-triangular
  // 3x3 tensors. In Voigt notation, the elements of the
  // RHS product tensor are:
  // h_dot = [0*0, 1*1, 2*2, 1*3+3*2, 0*4+5*3+4*2, 0*5+5*1]
  //
  // Ordering of operations preserves time symmetry.

  double dto2 = dto/2.0;
  double dto4 = dto/4.0;
  double dto8 = dto/8.0;

  // off-diagonal components, first half

  if (pstyle == TRICLINIC) {

    if (p_flag[4]) {
      expfac = exp(dto8*omega_dot[0]);
      h[4] *= expfac;
      h[4] += dto4*(omega_dot[5]*h[3]+omega_dot[4]*h[2]);
      h[4] *= expfac;
    }

    if (p_flag[3]) {
      expfac = exp(dto4*omega_dot[1]);
      h[3] *= expfac;
      h[3] += dto2*(omega_dot[3]*h[2]);
      h[3] *= expfac;
    }

    if (p_flag[5]) {
      expfac = exp(dto4*omega_dot[0]);
      h[5] *= expfac;
      h[5] += dto2*(omega_dot[5]*h[1]);
      h[5] *= expfac;
    }

    if (p_flag[4]) {
      expfac = exp(dto8*omega_dot[0]);
      h[4] *= expfac;
      h[4] += dto4*(omega_dot[5]*h[3]+omega_dot[4]*h[2]);
      h[4] *= expfac;
    }
  }

  // scale diagonal components
  // scale tilt factors with cell, if set

  if (p_flag[0]) {
    oldlo = domain->boxlo[0];
    oldhi = domain->boxhi[0];
    expfac = exp(dto*omega_dot[0]);
    domain->boxlo[0] = (oldlo-fixedpoint[0])*expfac + fixedpoint[0];
    domain->boxhi[0] = (oldhi-fixedpoint[0])*expfac + fixedpoint[0];
  }

  if (p_flag[1]) {
    oldlo = domain->boxlo[1];
    oldhi = domain->boxhi[1];
    expfac = exp(dto*omega_dot[1]);
    domain->boxlo[1] = (oldlo-fixedpoint[1])*expfac + fixedpoint[1];
    domain->boxhi[1] = (oldhi-fixedpoint[1])*expfac + fixedpoint[1];
    if (scalexy) h[5] *= expfac;
  }

  if (p_flag[2]) {
    oldlo = domain->boxlo[2];
    oldhi = domain->boxhi[2];
    expfac = exp(dto*omega_dot[2]);
    domain->boxlo[2] = (oldlo-fixedpoint[2])*expfac + fixedpoint[2];
    domain->boxhi[2] = (oldhi-fixedpoint[2])*expfac + fixedpoint[2];
    if (scalexz) h[4] *= expfac;
    if (scaleyz) h[3] *= expfac;
  }

  // off-diagonal components, second half

  if (pstyle == TRICLINIC) {

    if (p_flag[4]) {
      expfac = exp(dto8*omega_dot[0]);
      h[4] *= expfac;
      h[4] += dto4*(omega_dot[5]*h[3]+omega_dot[4]*h[2]);
      h[4] *= expfac;
    }

    if (p_flag[3]) {
      expfac = exp(dto4*omega_dot[1]);
      h[3] *= expfac;
      h[3] += dto2*(omega_dot[3]*h[2]);
      h[3] *= expfac;
    }

    if (p_flag[5]) {
      expfac = exp(dto4*omega_dot[0]);
      h[5] *= expfac;
      h[5] += dto2*(omega_dot[5]*h[1]);
      h[5] *= expfac;
    }

    if (p_flag[4]) {
      expfac = exp(dto8*omega_dot[0]);
      h[4] *= expfac;
      h[4] += dto4*(omega_dot[5]*h[3]+omega_dot[4]*h[2]);
      h[4] *= expfac;
    }

  }

  domain->yz = h[3];
  domain->xz = h[4];
  domain->xy = h[5];

  // tilt factor to cell length ratio can not exceed TILTMAX in one step

  if (domain->yz < -TILTMAX*domain->yprd ||
      domain->yz > TILTMAX*domain->yprd ||
      domain->xz < -TILTMAX*domain->xprd ||
      domain->xz > TILTMAX*domain->xprd ||
      domain->xy < -TILTMAX*domain->xprd ||
      domain->xy > TILTMAX*domain->xprd)
    error->all(FLERR,"Fix npt/nph has tilted box too far in one step - "
               "periodic cell is too far from equilibrium state");

  domain->set_global_box();
  domain->set_local_box();

  // convert pertinent atoms and rigid bodies back to box coords

  domain->lamda2x(nlocal);

  if (nrigid)
    for (i = 0; i < nrigid; i++)
      modify->fix[rfix[i]]->deform(1);
}

/* ----------------------------------------------------------------------
   pack entire state of Fix into one write
------------------------------------------------------------------------- */

void FixTGNHDrude::write_restart(FILE *fp)
{
  int nsize = size_restart_global();

  double *list;
  memory->create(list,nsize,"nh:list");

  pack_restart_data(list);

  if (comm->me == 0) {
    int size = nsize * sizeof(double);
    fwrite(&size,sizeof(int),1,fp);
    fwrite(list,sizeof(double),nsize,fp);
  }

  memory->destroy(list);
}

/* ----------------------------------------------------------------------
    calculate the number of data to be packed
------------------------------------------------------------------------- */

int FixTGNHDrude::size_restart_global()
{
  int nsize = 2;
  if (tstat_flag) nsize += 1 + 6*mtchain;
  if (pstat_flag) {
    nsize += 16 + 2*mpchain;
    if (deviatoric_flag) nsize += 6;
  }

  return nsize;
}

/* ----------------------------------------------------------------------
   pack restart data
------------------------------------------------------------------------- */

int FixTGNHDrude::pack_restart_data(double *list)
{
  int n = 0;

  list[n++] = tstat_flag;
  if (tstat_flag) {
    list[n++] = mtchain;
    for (int ich = 0; ich < mtchain; ich++) {
      list[n++] = etamol[ich];
      list[n++] = etaint[ich];
      list[n++] = etadrude[ich];
    }
    for (int ich = 0; ich < mtchain; ich++) {
      list[n++] = etamol_dot[ich];
      list[n++] = etaint_dot[ich];
      list[n++] = etadrude_dot[ich];
    }
  }

  list[n++] = pstat_flag;
  if (pstat_flag) {
    list[n++] = omega[0];
    list[n++] = omega[1];
    list[n++] = omega[2];
    list[n++] = omega[3];
    list[n++] = omega[4];
    list[n++] = omega[5];
    list[n++] = omega_dot[0];
    list[n++] = omega_dot[1];
    list[n++] = omega_dot[2];
    list[n++] = omega_dot[3];
    list[n++] = omega_dot[4];
    list[n++] = omega_dot[5];
    list[n++] = vol0;
    list[n++] = t0;
    list[n++] = mpchain;
    if (mpchain) {
      for (int ich = 0; ich < mpchain; ich++)
        list[n++] = etap[ich];
      for (int ich = 0; ich < mpchain; ich++)
        list[n++] = etap_dot[ich];
    }

    list[n++] = deviatoric_flag;
    if (deviatoric_flag) {
      list[n++] = h0_inv[0];
      list[n++] = h0_inv[1];
      list[n++] = h0_inv[2];
      list[n++] = h0_inv[3];
      list[n++] = h0_inv[4];
      list[n++] = h0_inv[5];
    }
  }

  return n;
}

/* ----------------------------------------------------------------------
   use state info from restart file to restart the Fix
------------------------------------------------------------------------- */

void FixTGNHDrude::restart(char *buf)
{
  int n = 0;
  auto list = (double *) buf;
  int flag = static_cast<int> (list[n++]);
  if (flag) {
    int m = static_cast<int> (list[n++]);
    if (tstat_flag && m == mtchain) {
      for (int ich = 0; ich < mtchain; ich++) {
        etamol[ich] = list[n++];
        etaint[ich] = list[n++];
        etadrude[ich] = list[n++];
      }
      for (int ich = 0; ich < mtchain; ich++) {
        etamol_dot[ich] = list[n++];
        etaint_dot[ich] = list[n++];
        etadrude_dot[ich] = list[n++];
      }
    } else n += 2*m;
  }
  flag = static_cast<int> (list[n++]);
  if (flag) {
    omega[0] = list[n++];
    omega[1] = list[n++];
    omega[2] = list[n++];
    omega[3] = list[n++];
    omega[4] = list[n++];
    omega[5] = list[n++];
    omega_dot[0] = list[n++];
    omega_dot[1] = list[n++];
    omega_dot[2] = list[n++];
    omega_dot[3] = list[n++];
    omega_dot[4] = list[n++];
    omega_dot[5] = list[n++];
    vol0 = list[n++];
    t0 = list[n++];
    int m = static_cast<int> (list[n++]);
    if (pstat_flag && m == mpchain) {
      for (int ich = 0; ich < mpchain; ich++)
        etap[ich] = list[n++];
      for (int ich = 0; ich < mpchain; ich++)
        etap_dot[ich] = list[n++];
    } else n+=2*m;
    flag = static_cast<int> (list[n++]);
    if (flag) {
      h0_inv[0] = list[n++];
      h0_inv[1] = list[n++];
      h0_inv[2] = list[n++];
      h0_inv[3] = list[n++];
      h0_inv[4] = list[n++];
      h0_inv[5] = list[n++];
    }
  }
}

/* ---------------------------------------------------------------------- */

int FixTGNHDrude::modify_param(int narg, char **arg)
{
  if (strcmp(arg[0],"temp") == 0) {
    if (narg < 2) error->all(FLERR,"Illegal fix_modify command");
    if (tcomputeflag) {
      modify->delete_compute(id_temp);
      tcomputeflag = 0;
    }
    delete [] id_temp;
    id_temp = utils::strdup(arg[1]);

    int icompute = modify->find_compute(arg[1]);
    if (icompute < 0)
      error->all(FLERR,"Could not find fix_modify temperature ID");
    temperature = modify->compute[icompute];

    if (temperature->tempflag == 0)
      error->all(FLERR,
                 "Fix_modify temperature ID does not compute temperature");
    if (temperature->igroup != 0 && comm->me == 0)
      error->warning(FLERR,"Temperature for fix modify is not for group all");

    // reset id_temp of pressure to new temperature ID

    if (pstat_flag) {
      icompute = modify->find_compute(id_press);
      if (icompute < 0)
        error->all(FLERR,"Pressure ID for fix modify does not exist");
      modify->compute[icompute]->reset_extra_compute_fix(id_temp);
    }

    return 2;

  } else if (strcmp(arg[0],"press") == 0) {
    if (narg < 2) error->all(FLERR,"Illegal fix_modify command");
    if (!pstat_flag) error->all(FLERR,"Illegal fix_modify command");
    if (pcomputeflag) {
      modify->delete_compute(id_press);
      pcomputeflag = 0;
    }
    delete [] id_press;
    id_press = utils::strdup(arg[1]);

    int icompute = modify->find_compute(arg[1]);
    if (icompute < 0) error->all(FLERR,"Could not find fix_modify pressure ID");
    pressure = modify->compute[icompute];

    if (pressure->pressflag == 0)
      error->all(FLERR,"Fix_modify pressure ID does not compute pressure");
    return 2;
  }

  return 0;
}

/* ---------------------------------------------------------------------- */

double FixTGNHDrude::compute_scalar()
{
  int i;
  double volume;
  double energy;
  double kt = boltz * t_target;
  double kt_drude = boltz * tdrude_target;
  double lkt_press = 0.0;
  int ich;
  if (dimension == 3) volume = domain->xprd * domain->yprd * domain->zprd;
  else volume = domain->xprd * domain->yprd;

  energy = 0.0;

  // thermostat chain energy is equivalent to Eq. (2) in
  // Martyna, Tuckerman, Tobias, Klein, Mol Phys, 87, 1117
  // Sum(0.5*p_eta_k^2/Q_k,k=1,M) + L*k*T*eta_1 + Sum(k*T*eta_k,k=2,M),
  // where L = tdof
  //       M = mtchain
  //       p_eta_k = Q_k*eta_dot[k-1]
  //       Q_1 = L*k*T/t_freq^2
  //       Q_k = k*T/t_freq^2, k > 1

  if (tstat_flag) {
    energy += ke2mol_target * etamol[0] + 0.5 * etamol_mass[0] * etamol_dot[0] * etamol_dot[0];
    energy += ke2int_target * etaint[0] + 0.5 * etaint_mass[0] * etaint_dot[0] * etaint_dot[0];
    energy += ke2drude_target * etadrude[0] + 0.5 * etadrude_mass[0] * etadrude_dot[0] * etadrude_dot[0];
    for (ich = 1; ich < mtchain; ich++) {
      energy += kt * etamol[ich] + 0.5*etamol_mass[ich]*etamol_dot[ich]*etamol_dot[ich];
      energy += kt * etaint[ich] + 0.5*etaint_mass[ich]*etaint_dot[ich]*etaint_dot[ich];
      energy += kt_drude * etadrude[ich] + 0.5*etadrude_mass[ich]*etadrude_dot[ich]*etadrude_dot[ich];
    }
  }

  // barostat energy is equivalent to Eq. (8) in
  // Martyna, Tuckerman, Tobias, Klein, Mol Phys, 87, 1117
  // Sum(0.5*p_omega^2/W + P*V),
  // where N = natoms
  //       p_omega = W*omega_dot
  //       W = N*k*T/p_freq^2
  //       sum is over barostatted dimensions

  if (pstat_flag) {
    for (i = 0; i < 3; i++) {
      if (p_flag[i]) {
        energy += 0.5*omega_dot[i]*omega_dot[i]*omega_mass[i] +
          p_hydro*(volume-vol0) / (pdim*nktv2p);
        lkt_press += kt;
      }
    }

    if (pstyle == TRICLINIC) {
      for (i = 3; i < 6; i++) {
        if (p_flag[i]) {
          energy += 0.5*omega_dot[i]*omega_dot[i]*omega_mass[i];
          lkt_press += kt;
        }
      }
    }

    // extra contributions from thermostat chain for barostat

    if (mpchain) {
      energy += lkt_press * etap[0] + 0.5*etap_mass[0]*etap_dot[0]*etap_dot[0];
      for (ich = 1; ich < mpchain; ich++)
        energy += kt * etap[ich] +
          0.5*etap_mass[ich]*etap_dot[ich]*etap_dot[ich];
    }

    // extra contribution from strain energy

    if (deviatoric_flag) energy += compute_strain_energy();
  }

  return energy;
}

/* ---------------------------------------------------------------------- */

double FixTGNHDrude::compute_vector(int n)
{
  if (!temp_computed_end_of_step)
    compute_temp_mol_int_drude(true);
  switch (n) {
    case 0:
      return t_mol;
    case 1:
      return t_int;
    case 2:
      return t_drude;
    default:
      return 0.0;
  }
}

/* ---------------------------------------------------------------------- */

void FixTGNHDrude::reset_target(double t_new)
{
  t_target = t_start = t_stop = t_new;
}

/* ---------------------------------------------------------------------- */

void FixTGNHDrude::reset_dt()
{
  dtv = update->dt;
  dtf = 0.5 * update->dt * force->ftm2v;
  dthalf = 0.5 * update->dt;
  dt4 = 0.25 * update->dt;
  dt8 = 0.125 * update->dt;
  dto = dthalf;

  // If using respa, then remap is performed in innermost level

  if (utils::strmatch(update->integrate_style,"^respa"))
    dto = 0.5*step_respa[0];
}

void FixTGNHDrude::compute_temp_mol_int_drude(bool end_of_step) {
  double **v = atom->v;
  double *mass = atom->mass;
  tagint *molecule = atom->molecule;
  int *type = atom->type;
  int *mask = atom->mask;
  int *drudetype = fix_drude->drudetype;
  tagint *drudeid = fix_drude->drudeid;
  int imol, ci, di;
  double mass_com, mass_reduced, mass_core, mass_drude;
  double vint, vcom, vrel;
  // use array instead of two numbers to save MPI_Allreduce()
  double ke2_int_drude_tmp[2] = {0.0, 0.0};
  double ke2_int_drude[2];

  memset(*v_mol_tmp, 0, sizeof(double) * (n_mol + 1) * 3); // the length of v_mol is n_mol+1

  /**
   * If there are velocity bias, need to remove them before calculate kinetic energies
   */
  for (int i = 0; i < atom->nlocal; i++) {
    if (mask[i] & groupbit) {
      if (which == BIAS)
        temperature->remove_bias(i, v[i]);

      imol = molecule[i];
      for (int k = 0; k < 3; k++)
        v_mol_tmp[imol][k] += v[i][k] * mass[type[i]];

      if (which == BIAS)
        temperature->restore_bias(i, v[i]);
    }
  }
  MPI_Allreduce(*v_mol_tmp, *v_mol, (n_mol + 1) * 3, MPI_DOUBLE, MPI_SUM, world);

  ke2mol = 0;
  for (int i = 1; i < n_mol + 1; i++) {
    for (int k = 0; k < 3; k++) {
      v_mol[i][k] /= mass_mol[i];
      ke2mol += mass_mol[i] * (v_mol[i][k] * v_mol[i][k]);
    }
  }
  ke2mol *= force->mvv2e;
  t_mol = ke2mol / dof_mol / boltz;

  /**
   * Have to call remove_bias at the innermost loop, because drude atom may be a ghost
   */
  for (int i = 0; i < atom->nlocal; i++) {
    if (mask[i] & groupbit) {
      imol = molecule[i];
      if (drudetype[type[i]] == NOPOL_TYPE) {
        if (which == BIAS)
          temperature->remove_bias(i, v[i]);
        for (int k = 0; k < 3; k++) {
          vint = v[i][k] - v_mol[imol][k];
          ke2_int_drude_tmp[0] += mass[type[i]] * vint * vint;
        }
        if (which == BIAS)
          temperature->restore_bias(i, v[i]);
      } else if (drudetype[type[i]] == CORE_TYPE) {
        /**
         * have to use closet_image()
         * even though all images have the same velocity and it's sort of read-only
         * but the bias velocity may depends on it's position like in compute vis/pp
         */
        ci = i;
        di = domain->closest_image(i, atom->map(drudeid[i]));
        if (which == BIAS) {
          temperature->remove_bias(ci, v[ci]);
          temperature->remove_bias(di, v[di]);
        }
        mass_core = mass[type[ci]];
        mass_drude = mass[type[di]];
        mass_com = mass_core + mass_drude;
        mass_reduced = mass_core * mass_drude / mass_com;
        for (int k = 0; k < 3; k++) {
          vcom = (mass_core * v[ci][k] + mass_drude * v[di][k]) / mass_com;
          vint = vcom - v_mol[imol][k];
          ke2_int_drude_tmp[0] += mass_com * vint * vint;
          vrel = v[di][k] - v[ci][k];
          ke2_int_drude_tmp[1] += mass_reduced * vrel * vrel;
        }
        if (which == BIAS) {
          temperature->restore_bias(ci, v[ci]);
          temperature->restore_bias(di, v[di]);
        }
      }
    }
  }
  MPI_Allreduce(ke2_int_drude_tmp, ke2_int_drude, 2, MPI_DOUBLE, MPI_SUM, world);
  ke2int = ke2_int_drude[0] * force->mvv2e;
  ke2drude = ke2_int_drude[1] * force->mvv2e;
  t_int = ke2int / dof_int / boltz;
  t_drude = ke2drude / dof_drude / boltz;

  temp_computed_end_of_step = end_of_step;
}

/* ----------------------------------------------------------------------
   perform half-step update of chain thermostat variables
------------------------------------------------------------------------- */

void FixTGNHDrude::nhc_temp_integrate()
{
  compute_temp_mol_int_drude(false);

  // update masses of thermostat in case target temperature changes
  etamol_mass[0] = ke2mol_target / (t_freq*t_freq);
  etaint_mass[0] = ke2int_target / (t_freq*t_freq);
  for (int ich = 1; ich < mtchain; ich++) {
    etamol_mass[ich] = boltz * t_target / (t_freq*t_freq);
    etaint_mass[ich] = boltz * t_target / (t_freq*t_freq);
  }

  // thermostat for molecular COM
  factor_eta_mol = propagate(etamol, etamol_dot, etamol_dotdot, etamol_mass,
                             ke2mol, ke2mol_target, t_target);
  factor_eta_int = propagate(etaint, etaint_dot, etaint_dotdot, etaint_mass,
                             ke2int, ke2int_target, t_target);
  factor_eta_drude = propagate(etadrude, etadrude_dot, etadrude_dotdot, etadrude_mass,
                               ke2drude, ke2drude_target, tdrude_target);

  nh_v_temp();
}

double FixTGNHDrude::propagate(double *eta, double *eta_dot, double *eta_dotdot, const double *eta_mass,
                               const double &ke2, const double &ke2_target, const double &tt) const {
  int ich;
  double expfac;
  double ncfac = 1.0 / nc_tchain;
  double factor_eta = 1.0;

  eta_dotdot[0] = (ke2 - ke2_target) / eta_mass[0];
  for (int iloop = 0; iloop < nc_tchain; iloop++) {
    for (ich = mtchain - 1; ich > 0; ich--) {
      expfac = exp(-ncfac * dt8 * eta_dot[ich + 1]);
      eta_dot[ich] *= expfac;
      eta_dot[ich] += eta_dotdot[ich] * ncfac * dt4;
      eta_dot[ich] *= expfac;
    }
    expfac = exp(-ncfac * dt8 * eta_dot[1]);
    eta_dot[0] *= expfac;
    eta_dot[0] += eta_dotdot[0] * ncfac * dt4;
    eta_dot[0] *= expfac;
    factor_eta *= exp(-ncfac * dthalf * eta_dot[0]);

    for (ich = 0; ich < mtchain; ich++)
      eta[ich] += ncfac * dthalf * eta_dot[ich];

    eta_dotdot[0] = (ke2 * factor_eta * factor_eta - ke2_target) / eta_mass[0];
    eta_dot[0] *= expfac;
    eta_dot[0] += eta_dotdot[0] * ncfac * dt4;
    eta_dot[0] *= expfac;
    for (ich = 1; ich < mtchain; ich++) {
      expfac = exp(-ncfac * dt8 * eta_dot[ich + 1]);
      eta_dot[ich] *= expfac;
      eta_dotdot[ich] = (eta_mass[ich - 1] * eta_dot[ich - 1] * eta_dot[ich - 1]
                         - boltz * tt) / eta_mass[ich];
      eta_dot[ich] += eta_dotdot[ich] * ncfac * dt4;
      eta_dot[ich] *= expfac;
    }
  }
  return factor_eta;
}

/* ----------------------------------------------------------------------
   perform half-step update of chain thermostat variables for barostat
   scale barostat velocities
------------------------------------------------------------------------- */

void FixTGNHDrude::nhc_press_integrate()
{
  int ich,i,pdof;
  double expfac,factor_etap,kecurrent;
  double kt = boltz * t_target;
  double lkt_press;

  // Update masses, to preserve initial freq, if t_target changed
  double nkt = (atom->natoms + 1) * kt;
  for (int i = 0; i < 3; i++)
    if (p_flag[i])
      omega_mass[i] = nkt / (p_freq[i] * p_freq[i]);
  if (pstyle == TRICLINIC) {
    for (int i = 3; i < 6; i++)
      if (p_flag[i]) omega_mass[i] = nkt / (p_freq[i] * p_freq[i]);
  }
  if (mpchain) {
    etap_mass[0] = kt / (p_freq_max * p_freq_max);
    for (int ich = 1; ich < mpchain; ich++)
      etap_mass[ich] = kt / (p_freq_max * p_freq_max);
    for (int ich = 1; ich < mpchain; ich++)
      etap_dotdot[ich] = (etap_mass[ich - 1] * etap_dot[ich - 1] * etap_dot[ich - 1]
                          - kt) / etap_mass[ich];
  }

  kecurrent = 0.0;
  pdof = 0;
  for (i = 0; i < 3; i++)
    if (p_flag[i]) {
      kecurrent += omega_mass[i]*omega_dot[i]*omega_dot[i];
      pdof++;
    }

  if (pstyle == TRICLINIC) {
    for (i = 3; i < 6; i++)
      if (p_flag[i]) {
        kecurrent += omega_mass[i]*omega_dot[i]*omega_dot[i];
        pdof++;
      }
  }

  if (pstyle == ISO) lkt_press = kt;
  else lkt_press = pdof * kt;
  etap_dotdot[0] = (kecurrent - lkt_press)/etap_mass[0];

  double ncfac = 1.0/nc_pchain;
  for (int iloop = 0; iloop < nc_pchain; iloop++) {

    for (ich = mpchain-1; ich > 0; ich--) {
      expfac = exp(-ncfac*dt8*etap_dot[ich+1]);
      etap_dot[ich] *= expfac;
      etap_dot[ich] += etap_dotdot[ich] * ncfac*dt4;
      etap_dot[ich] *= expfac;
    }

    expfac = exp(-ncfac*dt8*etap_dot[1]);
    etap_dot[0] *= expfac;
    etap_dot[0] += etap_dotdot[0] * ncfac*dt4;
    etap_dot[0] *= expfac;

    for (ich = 0; ich < mpchain; ich++)
      etap[ich] += ncfac*dthalf*etap_dot[ich];

    factor_etap = exp(-ncfac*dthalf*etap_dot[0]);
    for (i = 0; i < 3; i++)
      if (p_flag[i]) omega_dot[i] *= factor_etap;

    if (pstyle == TRICLINIC) {
      for (i = 3; i < 6; i++)
        if (p_flag[i]) omega_dot[i] *= factor_etap;
    }

    kecurrent = 0.0;
    for (i = 0; i < 3; i++)
      if (p_flag[i]) kecurrent += omega_mass[i]*omega_dot[i]*omega_dot[i];

    if (pstyle == TRICLINIC) {
      for (i = 3; i < 6; i++)
        if (p_flag[i]) kecurrent += omega_mass[i]*omega_dot[i]*omega_dot[i];
    }

    etap_dotdot[0] = (kecurrent - lkt_press)/etap_mass[0];

    etap_dot[0] *= expfac;
    etap_dot[0] += etap_dotdot[0] * ncfac*dt4;
    etap_dot[0] *= expfac;

    for (ich = 1; ich < mpchain; ich++) {
      expfac = exp(-ncfac*dt8*etap_dot[ich+1]);
      etap_dot[ich] *= expfac;
      etap_dotdot[ich] =
        (etap_mass[ich-1]*etap_dot[ich-1]*etap_dot[ich-1] - kt) / etap_mass[ich];
      etap_dot[ich] += etap_dotdot[ich] * ncfac*dt4;
      etap_dot[ich] *= expfac;
    }
  }
}

/* ----------------------------------------------------------------------
   perform half-step barostat scaling of velocities
-----------------------------------------------------------------------*/

void FixTGNHDrude::nh_v_press()
{
  double factor[3];
  double **v = atom->v;
  int *mask = atom->mask;
  int nlocal = atom->nlocal;
  if (igroup == atom->firstgroup) nlocal = atom->nfirst;

  factor[0] = exp(-dt4*(omega_dot[0]+mtk_term2));
  factor[1] = exp(-dt4*(omega_dot[1]+mtk_term2));
  factor[2] = exp(-dt4*(omega_dot[2]+mtk_term2));

  if (which == NOBIAS) {
    for (int i = 0; i < nlocal; i++) {
      if (mask[i] & groupbit) {
        v[i][0] *= factor[0];
        v[i][1] *= factor[1];
        v[i][2] *= factor[2];
        if (pstyle == TRICLINIC) {
          v[i][0] += -dthalf*(v[i][1]*omega_dot[5] + v[i][2]*omega_dot[4]);
          v[i][1] += -dthalf*v[i][2]*omega_dot[3];
        }
        v[i][0] *= factor[0];
        v[i][1] *= factor[1];
        v[i][2] *= factor[2];
      }
    }
  } else if (which == BIAS) {
    for (int i = 0; i < nlocal; i++) {
      if (mask[i] & groupbit) {
        temperature->remove_bias(i,v[i]);
        v[i][0] *= factor[0];
        v[i][1] *= factor[1];
        v[i][2] *= factor[2];
        if (pstyle == TRICLINIC) {
          v[i][0] += -dthalf*(v[i][1]*omega_dot[5] + v[i][2]*omega_dot[4]);
          v[i][1] += -dthalf*v[i][2]*omega_dot[3];
        }
        v[i][0] *= factor[0];
        v[i][1] *= factor[1];
        v[i][2] *= factor[2];
        temperature->restore_bias(i,v[i]);
      }
    }
  }
}

/* ----------------------------------------------------------------------
   perform half-step update of velocities
-----------------------------------------------------------------------*/

void FixTGNHDrude::nve_v()
{
  double dtfm;
  double **v = atom->v;
  double **f = atom->f;
  double *rmass = atom->rmass;
  double *mass = atom->mass;
  int *type = atom->type;
  int *mask = atom->mask;
  int nlocal = atom->nlocal;
  if (igroup == atom->firstgroup) nlocal = atom->nfirst;

  if (rmass) {
    for (int i = 0; i < nlocal; i++) {
      if (mask[i] & groupbit) {
        dtfm = dtf / rmass[i];
        v[i][0] += dtfm*f[i][0];
        v[i][1] += dtfm*f[i][1];
        v[i][2] += dtfm*f[i][2];
      }
    }
  } else {
    for (int i = 0; i < nlocal; i++) {
      if (mask[i] & groupbit) {
        dtfm = dtf / mass[type[i]];
        v[i][0] += dtfm*f[i][0];
        v[i][1] += dtfm*f[i][1];
        v[i][2] += dtfm*f[i][2];
      }
    }
  }
}

/* ----------------------------------------------------------------------
   perform full-step update of positions
-----------------------------------------------------------------------*/

void FixTGNHDrude::nve_x()
{
  double **x = atom->x;
  double **v = atom->v;
  int *mask = atom->mask;
  int nlocal = atom->nlocal;
  if (igroup == atom->firstgroup) nlocal = atom->nfirst;

  // x update by full step only for atoms in group

  for (int i = 0; i < nlocal; i++) {
    if (mask[i] & groupbit) {
      x[i][0] += dtv * v[i][0];
      x[i][1] += dtv * v[i][1];
      x[i][2] += dtv * v[i][2];
    }
  }
}

/* ----------------------------------------------------------------------
   perform half-step thermostat scaling of velocities
-----------------------------------------------------------------------*/

void FixTGNHDrude::nh_v_temp()
{
  double **v = atom->v;
  double *mass = atom->mass;
  int *mask = atom->mask;
  int *type = atom->type;
  tagint *molecule = atom->molecule;
  int *drudetype = fix_drude->drudetype;
  tagint *drudeid = fix_drude->drudeid;

  int imol, i, j, ci, di, itype;
  double mass_com, mass_core, mass_drude;
  double vint, vcom, vrel;

  /**
   * If there are velocity bias, need to remove them before scale velocity
   * Have to call remove_bias at the innermost loop, because drude atom may be a ghost
   */
  for (i = 0; i < atom->nlocal; i++) {
    if (mask[i] & groupbit) {
      imol = molecule[i];
      itype = drudetype[type[i]];
      if (itype == NOPOL_TYPE) {
        if (which == BIAS)
          temperature->remove_bias(i, v[i]);
        for (int k = 0; k < 3; k++) {
          vint = v[i][k] - v_mol[imol][k];
          vint *= factor_eta_int;
          v[i][k] = v_mol[imol][k] * factor_eta_mol + vint;
        }
        if (which == BIAS)
          temperature->restore_bias(i, v[i]);
      } else {
        // have to use closest_image() because we are manipulating the velocity
        j = domain->closest_image(i, atom->map(drudeid[i]));
        if (itype == DRUDE_TYPE && j < atom->nlocal) continue;
        if (itype == CORE_TYPE) {
          ci = i;
          di = j;
        } else {
          ci = j;
          di = i;
        }
        if (which == BIAS) {
          temperature->remove_bias(ci, v[ci]);
          temperature->remove_bias(di, v[di]);
        }
        mass_core = mass[type[ci]];
        mass_drude = mass[type[di]];
        mass_com = mass_core + mass_drude;
        for (int k = 0; k < 3; k++) {
          vcom = (mass_core * v[ci][k] + mass_drude * v[di][k]) / mass_com;
          vint = vcom - v_mol[imol][k];
          vrel = v[di][k] - v[ci][k];
          vint *= factor_eta_int;
          vrel *= factor_eta_drude;
          v[ci][k] = v_mol[imol][k] * factor_eta_mol + vint - vrel * mass_drude / mass_com;
          v[di][k] = v_mol[imol][k] * factor_eta_mol + vint + vrel * mass_core / mass_com;
        }
        if (which == BIAS) {
          temperature->restore_bias(ci, v[ci]);
          temperature->restore_bias(di, v[di]);
        }
      }
    }
  }
}

/* ----------------------------------------------------------------------
   compute sigma tensor
   needed whenever p_target or h0_inv changes
-----------------------------------------------------------------------*/

void FixTGNHDrude::compute_sigma()
{
  // if nreset_h0 > 0, reset vol0 and h0_inv
  // every nreset_h0 timesteps

  if (nreset_h0 > 0) {
    int delta = update->ntimestep - update->beginstep;
    if (delta % nreset_h0 == 0) {
      if (dimension == 3) vol0 = domain->xprd * domain->yprd * domain->zprd;
      else vol0 = domain->xprd * domain->yprd;
      h0_inv[0] = domain->h_inv[0];
      h0_inv[1] = domain->h_inv[1];
      h0_inv[2] = domain->h_inv[2];
      h0_inv[3] = domain->h_inv[3];
      h0_inv[4] = domain->h_inv[4];
      h0_inv[5] = domain->h_inv[5];
    }
  }

  // generate upper-triangular half of
  // sigma = vol0*h0inv*(p_target-p_hydro)*h0inv^t
  // units of sigma are are PV/L^2 e.g. atm.A
  //
  // [ 0 5 4 ]   [ 0 5 4 ] [ 0 5 4 ] [ 0 - - ]
  // [ 5 1 3 ] = [ - 1 3 ] [ 5 1 3 ] [ 5 1 - ]
  // [ 4 3 2 ]   [ - - 2 ] [ 4 3 2 ] [ 4 3 2 ]

  sigma[0] =
    vol0*(h0_inv[0]*((p_target[0]-p_hydro)*h0_inv[0] +
                     p_target[5]*h0_inv[5]+p_target[4]*h0_inv[4]) +
          h0_inv[5]*(p_target[5]*h0_inv[0] +
                     (p_target[1]-p_hydro)*h0_inv[5]+p_target[3]*h0_inv[4]) +
          h0_inv[4]*(p_target[4]*h0_inv[0]+p_target[3]*h0_inv[5] +
                     (p_target[2]-p_hydro)*h0_inv[4]));
  sigma[1] =
    vol0*(h0_inv[1]*((p_target[1]-p_hydro)*h0_inv[1] +
                     p_target[3]*h0_inv[3]) +
          h0_inv[3]*(p_target[3]*h0_inv[1] +
                     (p_target[2]-p_hydro)*h0_inv[3]));
  sigma[2] =
    vol0*(h0_inv[2]*((p_target[2]-p_hydro)*h0_inv[2]));
  sigma[3] =
    vol0*(h0_inv[1]*(p_target[3]*h0_inv[2]) +
          h0_inv[3]*((p_target[2]-p_hydro)*h0_inv[2]));
  sigma[4] =
    vol0*(h0_inv[0]*(p_target[4]*h0_inv[2]) +
          h0_inv[5]*(p_target[3]*h0_inv[2]) +
          h0_inv[4]*((p_target[2]-p_hydro)*h0_inv[2]));
  sigma[5] =
    vol0*(h0_inv[0]*(p_target[5]*h0_inv[1]+p_target[4]*h0_inv[3]) +
          h0_inv[5]*((p_target[1]-p_hydro)*h0_inv[1]+p_target[3]*h0_inv[3]) +
          h0_inv[4]*(p_target[3]*h0_inv[1]+(p_target[2]-p_hydro)*h0_inv[3]));
}

/* ----------------------------------------------------------------------
   compute strain energy
-----------------------------------------------------------------------*/

double FixTGNHDrude::compute_strain_energy()
{
  // compute strain energy = 0.5*Tr(sigma*h*h^t) in energy units

  double* h = domain->h;
  double d0,d1,d2;

  d0 =
    sigma[0]*(h[0]*h[0]+h[5]*h[5]+h[4]*h[4]) +
    sigma[5]*(          h[1]*h[5]+h[3]*h[4]) +
    sigma[4]*(                    h[2]*h[4]);
  d1 =
    sigma[5]*(          h[5]*h[1]+h[4]*h[3]) +
    sigma[1]*(          h[1]*h[1]+h[3]*h[3]) +
    sigma[3]*(                    h[2]*h[3]);
  d2 =
    sigma[4]*(                    h[4]*h[2]) +
    sigma[3]*(                    h[3]*h[2]) +
    sigma[2]*(                    h[2]*h[2]);

  double energy = 0.5*(d0+d1+d2)/nktv2p;
  return energy;
}

/* ----------------------------------------------------------------------
   compute deviatoric barostat force = h*sigma*h^t
-----------------------------------------------------------------------*/

void FixTGNHDrude::compute_deviatoric()
{
  // generate upper-triangular part of h*sigma*h^t
  // units of fdev are are PV, e.g. atm*A^3
  // [ 0 5 4 ]   [ 0 5 4 ] [ 0 5 4 ] [ 0 - - ]
  // [ 5 1 3 ] = [ - 1 3 ] [ 5 1 3 ] [ 5 1 - ]
  // [ 4 3 2 ]   [ - - 2 ] [ 4 3 2 ] [ 4 3 2 ]

  double* h = domain->h;

  fdev[0] =
    h[0]*(sigma[0]*h[0]+sigma[5]*h[5]+sigma[4]*h[4]) +
    h[5]*(sigma[5]*h[0]+sigma[1]*h[5]+sigma[3]*h[4]) +
    h[4]*(sigma[4]*h[0]+sigma[3]*h[5]+sigma[2]*h[4]);
  fdev[1] =
    h[1]*(              sigma[1]*h[1]+sigma[3]*h[3]) +
    h[3]*(              sigma[3]*h[1]+sigma[2]*h[3]);
  fdev[2] =
    h[2]*(                            sigma[2]*h[2]);
  fdev[3] =
    h[1]*(                            sigma[3]*h[2]) +
    h[3]*(                            sigma[2]*h[2]);
  fdev[4] =
    h[0]*(                            sigma[4]*h[2]) +
    h[5]*(                            sigma[3]*h[2]) +
    h[4]*(                            sigma[2]*h[2]);
  fdev[5] =
    h[0]*(              sigma[5]*h[1]+sigma[4]*h[3]) +
    h[5]*(              sigma[1]*h[1]+sigma[3]*h[3]) +
    h[4]*(              sigma[3]*h[1]+sigma[2]*h[3]);
}

/* ----------------------------------------------------------------------
   compute target temperature and kinetic energy
-----------------------------------------------------------------------*/

void FixTGNHDrude::compute_temp_target()
{
  double delta = update->ntimestep - update->beginstep;
  if (delta != 0.0) delta /= update->endstep - update->beginstep;

  t_target = t_start + delta * (t_stop-t_start);
  ke2mol_target = dof_mol * boltz * t_target;
  ke2int_target = dof_int * boltz * t_target;
  ke2drude_target = dof_drude * boltz * tdrude_target;
}

/* ----------------------------------------------------------------------
   compute hydrostatic target pressure
-----------------------------------------------------------------------*/

void FixTGNHDrude::compute_press_target()
{
  double delta = update->ntimestep - update->beginstep;
  if (delta != 0.0) delta /= update->endstep - update->beginstep;

  p_hydro = 0.0;
  for (int i = 0; i < 3; i++)
    if (p_flag[i]) {
      p_target[i] = p_start[i] + delta * (p_stop[i]-p_start[i]);
      p_hydro += p_target[i];
    }
  if (pdim > 0) p_hydro /= pdim;

  if (pstyle == TRICLINIC)
    for (int i = 3; i < 6; i++)
      p_target[i] = p_start[i] + delta * (p_stop[i]-p_start[i]);

  // if deviatoric, recompute sigma each time p_target changes

  if (deviatoric_flag) compute_sigma();
}

/* ----------------------------------------------------------------------
   update omega_dot, omega
-----------------------------------------------------------------------*/

void FixTGNHDrude::nh_omega_dot()
{
  double f_omega,volume;

  if (dimension == 3) volume = domain->xprd*domain->yprd*domain->zprd;
  else volume = domain->xprd*domain->yprd;

  if (deviatoric_flag) compute_deviatoric();

  mtk_term1 = 0.0;
  if (mtk_flag) {
    if (pstyle == ISO) {
      mtk_term1 = tdof * boltz * t_current;
      mtk_term1 /= pdim * atom->natoms;
    } else {
      double *mvv_current = temperature->vector;
      for (int i = 0; i < 3; i++)
        if (p_flag[i])
          mtk_term1 += mvv_current[i];
      mtk_term1 /= pdim * atom->natoms;
    }
  }

  for (int i = 0; i < 3; i++)
    if (p_flag[i]) {
      f_omega = (p_current[i]-p_hydro)*volume /
        (omega_mass[i] * nktv2p) + mtk_term1 / omega_mass[i];
      if (deviatoric_flag) f_omega -= fdev[i]/(omega_mass[i] * nktv2p);
      omega_dot[i] += f_omega*dthalf;
    }

  mtk_term2 = 0.0;
  if (mtk_flag) {
    for (int i = 0; i < 3; i++)
      if (p_flag[i])
        mtk_term2 += omega_dot[i];
    if (pdim > 0) mtk_term2 /= pdim * atom->natoms;
  }

  if (pstyle == TRICLINIC) {
    for (int i = 3; i < 6; i++) {
      if (p_flag[i]) {
        f_omega = p_current[i]*volume/(omega_mass[i] * nktv2p);
        if (deviatoric_flag)
          f_omega -= fdev[i]/(omega_mass[i] * nktv2p);
        omega_dot[i] += f_omega*dthalf;
      }
    }
  }
}

/* ----------------------------------------------------------------------
  if any tilt ratios exceed limits, set flip = 1 and compute new tilt values
  do not flip in x or y if non-periodic (can tilt but not flip)
    this is b/c the box length would be changed (dramatically) by flip
  if yz tilt exceeded, adjust C vector by one B vector
  if xz tilt exceeded, adjust C vector by one A vector
  if xy tilt exceeded, adjust B vector by one A vector
  check yz first since it may change xz, then xz check comes after
  if any flip occurs, create new box in domain
  image_flip() adjusts image flags due to box shape change induced by flip
  remap() puts atoms outside the new box back into the new box
  perform irregular on atoms in lamda coords to migrate atoms to new procs
  important that image_flip comes before remap, since remap may change
    image flags to new values, making eqs in doc of Domain:image_flip incorrect
------------------------------------------------------------------------- */

void FixTGNHDrude::pre_exchange()
{
  double xprd = domain->xprd;
  double yprd = domain->yprd;

  // flip is only triggered when tilt exceeds 0.5 by DELTAFLIP
  // this avoids immediate re-flipping due to tilt oscillations

  double xtiltmax = (0.5+DELTAFLIP)*xprd;
  double ytiltmax = (0.5+DELTAFLIP)*yprd;

  int flipxy,flipxz,flipyz;
  flipxy = flipxz = flipyz = 0;

  if (domain->yperiodic) {
    if (domain->yz < -ytiltmax) {
      domain->yz += yprd;
      domain->xz += domain->xy;
      flipyz = 1;
    } else if (domain->yz >= ytiltmax) {
      domain->yz -= yprd;
      domain->xz -= domain->xy;
      flipyz = -1;
    }
  }

  if (domain->xperiodic) {
    if (domain->xz < -xtiltmax) {
      domain->xz += xprd;
      flipxz = 1;
    } else if (domain->xz >= xtiltmax) {
      domain->xz -= xprd;
      flipxz = -1;
    }
    if (domain->xy < -xtiltmax) {
      domain->xy += xprd;
      flipxy = 1;
    } else if (domain->xy >= xtiltmax) {
      domain->xy -= xprd;
      flipxy = -1;
    }
  }

  int flip = 0;
  if (flipxy || flipxz || flipyz) flip = 1;

  if (flip) {
    domain->set_global_box();
    domain->set_local_box();

    domain->image_flip(flipxy,flipxz,flipyz);

    double **x = atom->x;
    imageint *image = atom->image;
    int nlocal = atom->nlocal;
    for (int i = 0; i < nlocal; i++) domain->remap(x[i],image[i]);

    domain->x2lamda(atom->nlocal);
    irregular->migrate_atoms();
    domain->lamda2x(atom->nlocal);
  }
}

/* ----------------------------------------------------------------------
   memory usage of Irregular
------------------------------------------------------------------------- */

double FixTGNHDrude::memory_usage()
{
  double bytes = 0.0;
  if (irregular) bytes += irregular->memory_usage();
  return bytes;
}
