// clang-format off
/* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   Steve Plimpton, sjplimp@sandia.gov

   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:
------------------------------------------------------------------------- */

#include "fix_npt_cauchy.h"

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

#include <cmath>
#include <cstring>

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

FixNPTCauchy::FixNPTCauchy(LAMMPS *lmp, int narg, char **arg) :
  Fix(lmp, narg, arg),
  rfix(nullptr), id_dilate(nullptr), irregular(nullptr),
  id_temp(nullptr), id_press(nullptr),
  eta(nullptr), eta_dot(nullptr), eta_dotdot(nullptr),
  eta_mass(nullptr), etap(nullptr), etap_dot(nullptr), etap_dotdot(nullptr),
  etap_mass(nullptr), id_store(nullptr),init_store(nullptr)
{
  if (narg < 4) error->all(FLERR,"Illegal fix npt/cauchy command");

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

  // for CauchyStat

  alpha=0.001;
  initRUN = 0;
  restartPK = 0;
  restart_global = 1;
  restart_stored = 0;

  // default values

  pcouple = NONE;
  drag = 0.0;
  allremap = 1;
  mtchain = mpchain = 3;
  nc_tchain = nc_pchain = 1;
  mtk_flag = 1;
  deviatoric_flag = 0;
  nreset_h0 = 0;
  eta_mass_flag = 1;
  omega_mass_flag = 0;
  etap_mass_flag = 0;
  flipflag = 1;
  dipole_flag = 0;
  dlm_flag = 0;

  tcomputeflag = 0;
  pcomputeflag = 0;

  // 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]);

  // used by FixNVTSllod to preserve non-default value

  mtchain_default_flag = 1;

  tstat_flag = 0;
  double t_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 npt/cauchy 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 npt/cauchy cannot be 0.0");
      iarg += 4;

    } else if (strcmp(arg[iarg],"iso") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix npt/cauchy 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 npt/cauchy 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 npt/cauchy 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 npt/cauchy 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 npt/cauchy 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 npt/cauchy 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 npt/cauchy command for a 2d simulation");

    } else if (strcmp(arg[iarg],"yz") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix npt/cauchy 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 npt/cauchy command for a 2d simulation");
    } else if (strcmp(arg[iarg],"xz") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix npt/cauchy 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 npt/cauchy command for a 2d simulation");
    } else if (strcmp(arg[iarg],"xy") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix npt/cauchy 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 npt/cauchy 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 npt/cauchy command");
      iarg += 2;

    } else if (strcmp(arg[iarg],"drag") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix npt/cauchy command");
      drag = utils::numeric(FLERR,arg[iarg+1],false,lmp);
      if (drag < 0.0) error->all(FLERR,"Illegal fix npt/cauchy command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"dilate") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix npt/cauchy command");
      if (strcmp(arg[iarg+1],"all") == 0) allremap = 1;
      else {
        allremap = 0;
        delete [] id_dilate;
        id_dilate = utils::strdup(arg[iarg+1]);
        int idilate = group->find(id_dilate);
        if (idilate == -1)
          error->all(FLERR,"Fix npt/cauchy dilate group ID does not exist");
      }
      iarg += 2;

    } else if (strcmp(arg[iarg],"tchain") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix npt/cauchy command");
      mtchain = utils::inumeric(FLERR,arg[iarg+1],false,lmp);
      // used by FixNVTSllod to preserve non-default value
      mtchain_default_flag = 0;
      if (mtchain < 1) error->all(FLERR,"Illegal fix npt/cauchy command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"pchain") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix npt/cauchy command");
      mpchain = utils::inumeric(FLERR,arg[iarg+1],false,lmp);
      if (mpchain < 0) error->all(FLERR,"Illegal fix npt/cauchy command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"mtk") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix npt/cauchy command");
      if (strcmp(arg[iarg+1],"yes") == 0) mtk_flag = 1;
      else if (strcmp(arg[iarg+1],"no") == 0) mtk_flag = 0;
      else error->all(FLERR,"Illegal fix npt/cauchy command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"tloop") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix npt/cauchy command");
      nc_tchain = utils::inumeric(FLERR,arg[iarg+1],false,lmp);
      if (nc_tchain < 0) error->all(FLERR,"Illegal fix npt/cauchy command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"ploop") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix npt/cauchy command");
      nc_pchain = utils::inumeric(FLERR,arg[iarg+1],false,lmp);
      if (nc_pchain < 0) error->all(FLERR,"Illegal fix npt/cauchy command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"nreset") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix npt/cauchy command");
      nreset_h0 = utils::inumeric(FLERR,arg[iarg+1],false,lmp);
      if (nreset_h0 < 0) error->all(FLERR,"Illegal fix npt/cauchy command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"scalexy") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix npt/cauchy command");
      if (strcmp(arg[iarg+1],"yes") == 0) scalexy = 1;
      else if (strcmp(arg[iarg+1],"no") == 0) scalexy = 0;
      else error->all(FLERR,"Illegal fix npt/cauchy command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"scalexz") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix npt/cauchy command");
      if (strcmp(arg[iarg+1],"yes") == 0) scalexz = 1;
      else if (strcmp(arg[iarg+1],"no") == 0) scalexz = 0;
      else error->all(FLERR,"Illegal fix npt/cauchy command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"scaleyz") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix npt/cauchy command");
      if (strcmp(arg[iarg+1],"yes") == 0) scaleyz = 1;
      else if (strcmp(arg[iarg+1],"no") == 0) scaleyz = 0;
      else error->all(FLERR,"Illegal fix npt/cauchy command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"flip") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix npt/cauchy command");
      if (strcmp(arg[iarg+1],"yes") == 0) flipflag = 1;
      else if (strcmp(arg[iarg+1],"no") == 0) flipflag = 0;
      else error->all(FLERR,"Illegal fix npt/cauchy command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"update") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix npt/cauchy command");
      if (strcmp(arg[iarg+1],"dipole") == 0) dipole_flag = 1;
      else if (strcmp(arg[iarg+1],"dipole/dlm") == 0) {
        dipole_flag = 1;
        dlm_flag = 1;
      } else error->all(FLERR,"Illegal fix npt/cauchy command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"alpha") == 0) {
      alpha = utils::numeric(FLERR,arg[iarg+1],false,lmp);
      iarg += 2;
    } else if (strcmp(arg[iarg],"continue") == 0) {
      if (strcmp(arg[iarg+1],"yes") != 0 && strcmp(arg[iarg+1],"no") != 0)
        error->all(FLERR,"Illegal cauchystat continue value.  "
                   "Must be 'yes' or 'no'");
      restartPK = !strcmp(arg[iarg+1],"yes");
      iarg += 2;
    } else if (strcmp(arg[iarg],"fixedpoint") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix npt/cauchy 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;

    // disc keyword is also parsed in fix/nh/sphere

    } else if (strcmp(arg[iarg],"disc") == 0) {
      iarg++;

    // keywords erate, strain, and ext are also parsed in fix/nh/uef

    } else if (strcmp(arg[iarg],"erate") == 0) {
      iarg += 3;
    } else if (strcmp(arg[iarg],"strain") == 0) {
      iarg += 3;
    } else if (strcmp(arg[iarg],"ext") == 0) {
      iarg += 2;

    } else error->all(FLERR,"Illegal fix npt/cauchy command");
  }

  // error checks

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

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

  // require periodicity in tensile dimension

  if (p_flag[0] && domain->xperiodic == 0)
    error->all(FLERR,"Cannot use fix npt/cauchy on a non-periodic dimension");
  if (p_flag[1] && domain->yperiodic == 0)
    error->all(FLERR,"Cannot use fix npt/cauchy on a non-periodic dimension");
  if (p_flag[2] && domain->zperiodic == 0)
    error->all(FLERR,"Cannot use fix npt/cauchy 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 npt/cauchy on a 2nd non-periodic dimension");
  if (p_flag[4] && domain->zperiodic == 0)
    error->all(FLERR,
               "Cannot use fix npt/cauchy on a 2nd non-periodic dimension");
  if (p_flag[5] && domain->yperiodic == 0)
    error->all(FLERR,
               "Cannot use fix npt/cauchy on a 2nd non-periodic dimension");

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

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

  if (dipole_flag) {
    if (!atom->sphere_flag)
      error->all(FLERR,"Using update dipole flag requires atom style sphere");
    if (!atom->mu_flag)
      error->all(FLERR,"Using update dipole flag requires atom attribute mu");
  }

  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 npt/cauchy 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;
    if (allremap == 0) restart_pbc = 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 = 1;
    if (flipflag && (domain->yz != 0.0 || domain->xz != 0.0 ||
                     domain->xy != 0.0))
      pre_exchange_flag = 1;
  }

  // convert input periods to frequencies

  t_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;
  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 = 0;

  if (tstat_flag) {
    int ich;
    eta = new double[mtchain];

    // add one extra dummy thermostat, set to zero

    eta_dot = new double[mtchain+1];
    eta_dot[mtchain] = 0.0;
    eta_dotdot = new double[mtchain];
    for (ich = 0; ich < mtchain; ich++) {
      eta[ich] = eta_dot[ich] = eta_dotdot[ich] = 0.0;
    }
    eta_mass = new double[mtchain];
    size_vector += 2*2*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 (pstyle == ISO) size_vector += 2*2*1;
    else if (pstyle == ANISO) size_vector += 2*2*3;
    else if (pstyle == TRICLINIC) size_vector += 2*2*6;

    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];
      size_vector += 2*2*mpchain;
    }

    if (deviatoric_flag) size_vector += 1;
  }

  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;

  if (!tstat_flag)
    error->all(FLERR,"Temperature control must be used with fix npt/cauchy");
  if (!pstat_flag)
    error->all(FLERR,"Pressure control must be used with fix npt/cauchy");

  // create a new compute temp style
  // id = fix-ID + temp
  // compute group = all since pressure is always global (group all)
  // and thus its KE/temperature contribution should use group all

  id_temp = utils::strdup(std::string(id) + "_temp");
  modify->add_compute(fmt::format("{} all temp",id_temp));
  tcomputeflag = 1;

  // create a new compute pressure style
  // id = fix-ID + press, compute group = all
  // pass id_temp as 4th arg to pressure constructor

  id_press = utils::strdup(std::string(id) + "_press");
  modify->add_compute(fmt::format("{} all pressure {}",id_press, id_temp));
  pcomputeflag = 1;
}

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

void FixNPTCauchy::post_constructor()
{
  CauchyStat_init();
}

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

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

  delete [] id_dilate;
  delete [] rfix;

  delete [] id_store;
  delete irregular;

  // delete temperature and pressure if fix created them

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

  if (tstat_flag) {
    delete [] eta;
    delete [] eta_dot;
    delete [] eta_dotdot;
    delete [] eta_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 FixNPTCauchy::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 FixNPTCauchy::init()
{
  // recheck that dilate group has not been deleted

  if (allremap == 0) {
    int idilate = group->find(id_dilate);
    if (idilate == -1)
      error->all(FLERR,"Fix npt/cauchy dilate group ID does not exist");
    dilate_group_bit = group->bitmask[idilate];
  }

  // 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 = ((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/cauchy 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 npt/cauchy 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/cauchy 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]);
    }
    pdrag_factor = 1.0 - (update->dt * p_freq_max * drag / nc_pchain);
  }

  if (tstat_flag)
    tdrag_factor = 1.0 - (update->dt * t_freq * drag / nc_tchain);

  // 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 = ((Respa *) update->integrate)->nlevels;
    step_respa = ((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 FixNPTCauchy::setup(int /*vflag*/)
{
  // tdof needed by compute_temp_target()

  t_current = temperature->compute_scalar();
  tdof = temperature->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) {
    eta_mass[0] = tdof * boltz * t_target / (t_freq*t_freq);
    for (int ich = 1; ich < mtchain; ich++)
      eta_mass[ich] = boltz * t_target / (t_freq*t_freq);
    for (int ich = 1; ich < mtchain; ich++) {
      eta_dotdot[ich] = (eta_mass[ich-1]*eta_dot[ich-1]*eta_dot[ich-1] -
                         boltz * t_target) / eta_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 FixNPTCauchy::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 FixNPTCauchy::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;

  if (pstat_flag) {
    if (pstyle == ISO) pressure->compute_scalar();
    else 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 FixNPTCauchy::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 FixNPTCauchy::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 FixNPTCauchy::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 FixNPTCauchy::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 FixNPTCauchy::remap()
{
  int i;
  double oldlo,oldhi;
  double expfac;

  double **x = atom->x;
  int *mask = atom->mask;
  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

  if (allremap) domain->x2lamda(nlocal);
  else {
    for (i = 0; i < nlocal; i++)
      if (mask[i] & dilate_group_bit)
        domain->x2lamda(x[i],x[i]);
  }

  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/cauchy 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

  if (allremap) domain->lamda2x(nlocal);
  else {
    for (i = 0; i < nlocal; i++)
      if (mask[i] & dilate_group_bit)
        domain->lamda2x(x[i],x[i]);
  }

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

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

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

  return nsize;
}

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

int FixNPTCauchy::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++] = eta[ich];
    for (int ich = 0; ich < mtchain; ich++)
      list[n++] = eta_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 FixNPTCauchy::restart(char *buf)
{
  int n = 0;
  double *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++)
        eta[ich] = list[n++];
      for (int ich = 0; ich < mtchain; ich++)
        eta_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 FixNPTCauchy::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 FixNPTCauchy::compute_scalar()
{
  int i;
  double volume;
  double energy;
  double kt = boltz * t_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 += ke_target * eta[0] + 0.5*eta_mass[0]*eta_dot[0]*eta_dot[0];
    for (ich = 1; ich < mtchain; ich++)
      energy += kt * eta[ich] + 0.5*eta_mass[ich]*eta_dot[ich]*eta_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;
}

/* ----------------------------------------------------------------------
   return a single element of the following vectors, in this order:
      eta[tchain], eta_dot[tchain], omega[ndof], omega_dot[ndof]
      etap[pchain], etap_dot[pchain], PE_eta[tchain], KE_eta_dot[tchain]
      PE_omega[ndof], KE_omega_dot[ndof], PE_etap[pchain], KE_etap_dot[pchain]
      PE_strain[1]
  if no thermostat exists, related quantities are omitted from the list
  if no barostat exists, related quantities are omitted from the list
  ndof = 1,3,6 degrees of freedom for pstyle = ISO,ANISO,TRI
------------------------------------------------------------------------- */

double FixNPTCauchy::compute_vector(int n)
{
  int ilen;

  if (tstat_flag) {
    ilen = mtchain;
    if (n < ilen) return eta[n];
    n -= ilen;
    ilen = mtchain;
    if (n < ilen) return eta_dot[n];
    n -= ilen;
  }

  if (pstat_flag) {
    if (pstyle == ISO) {
      ilen = 1;
      if (n < ilen) return omega[n];
      n -= ilen;
    } else if (pstyle == ANISO) {
      ilen = 3;
      if (n < ilen) return omega[n];
      n -= ilen;
    } else {
      ilen = 6;
      if (n < ilen) return omega[n];
      n -= ilen;
    }

    if (pstyle == ISO) {
      ilen = 1;
      if (n < ilen) return omega_dot[n];
      n -= ilen;
    } else if (pstyle == ANISO) {
      ilen = 3;
      if (n < ilen) return omega_dot[n];
      n -= ilen;
    } else {
      ilen = 6;
      if (n < ilen) return omega_dot[n];
      n -= ilen;
    }

    if (mpchain) {
      ilen = mpchain;
      if (n < ilen) return etap[n];
      n -= ilen;
      ilen = mpchain;
      if (n < ilen) return etap_dot[n];
      n -= ilen;
    }
  }

  double volume;
  double kt = boltz * t_target;
  double lkt_press = kt;
  int ich;
  if (dimension == 3) volume = domain->xprd * domain->yprd * domain->zprd;
  else volume = domain->xprd * domain->yprd;

  if (tstat_flag) {
    ilen = mtchain;
    if (n < ilen) {
      ich = n;
      if (ich == 0)
        return ke_target * eta[0];
      else
        return kt * eta[ich];
    }
    n -= ilen;
    ilen = mtchain;
    if (n < ilen) {
      ich = n;
      if (ich == 0)
        return 0.5*eta_mass[0]*eta_dot[0]*eta_dot[0];
      else
        return 0.5*eta_mass[ich]*eta_dot[ich]*eta_dot[ich];
    }
    n -= ilen;
  }

  if (pstat_flag) {
    if (pstyle == ISO) {
      ilen = 1;
      if (n < ilen)
        return p_hydro*(volume-vol0) / nktv2p;
      n -= ilen;
    } else if (pstyle == ANISO) {
      ilen = 3;
      if (n < ilen) {
        if (p_flag[n])
          return p_hydro*(volume-vol0) / (pdim*nktv2p);
        else
          return 0.0;
      }
      n -= ilen;
    } else {
      ilen = 6;
      if (n < ilen) {
        if (n > 2) return 0.0;
        else if (p_flag[n])
          return p_hydro*(volume-vol0) / (pdim*nktv2p);
        else
          return 0.0;
      }
      n -= ilen;
    }

    if (pstyle == ISO) {
      ilen = 1;
      if (n < ilen)
        return pdim*0.5*omega_dot[n]*omega_dot[n]*omega_mass[n];
      n -= ilen;
    } else if (pstyle == ANISO) {
      ilen = 3;
      if (n < ilen) {
        if (p_flag[n])
          return 0.5*omega_dot[n]*omega_dot[n]*omega_mass[n];
        else return 0.0;
      }
      n -= ilen;
    } else {
      ilen = 6;
      if (n < ilen) {
        if (p_flag[n])
          return 0.5*omega_dot[n]*omega_dot[n]*omega_mass[n];
        else return 0.0;
      }
      n -= ilen;
    }

    if (mpchain) {
      ilen = mpchain;
      if (n < ilen) {
        ich = n;
        if (ich == 0) return lkt_press * etap[0];
        else return kt * etap[ich];
      }
      n -= ilen;
      ilen = mpchain;
      if (n < ilen) {
        ich = n;
        if (ich == 0)
          return 0.5*etap_mass[0]*etap_dot[0]*etap_dot[0];
        else
          return 0.5*etap_mass[ich]*etap_dot[ich]*etap_dot[ich];
      }
      n -= ilen;
    }

    if (deviatoric_flag) {
      ilen = 1;
      if (n < ilen)
        return compute_strain_energy();
      n -= ilen;
    }
  }

  return 0.0;
}

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

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

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

void FixNPTCauchy::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];

  if (pstat_flag)
    pdrag_factor = 1.0 - (update->dt * p_freq_max * drag / nc_pchain);

  if (tstat_flag)
    tdrag_factor = 1.0 - (update->dt * t_freq * drag / nc_tchain);
}

/* ----------------------------------------------------------------------
   extract thermostat properties
------------------------------------------------------------------------- */

void *FixNPTCauchy::extract(const char *str, int &dim)
{
  dim=0;
  if (tstat_flag && strcmp(str,"t_target") == 0) {
    return &t_target;
  } else if (tstat_flag && strcmp(str,"t_start") == 0) {
    return &t_start;
  } else if (tstat_flag && strcmp(str,"t_stop") == 0) {
    return &t_stop;
  } else if (tstat_flag && strcmp(str,"mtchain") == 0) {
    return &mtchain;
  } else if (pstat_flag && strcmp(str,"mpchain") == 0) {
    return &mtchain;
  }
  dim=1;
  if (tstat_flag && strcmp(str,"eta") == 0) {
    return &eta;
  } else if (pstat_flag && strcmp(str,"etap") == 0) {
    return &eta;
  } else if (pstat_flag && strcmp(str,"p_flag") == 0) {
    return &p_flag;
  } else if (pstat_flag && strcmp(str,"p_start") == 0) {
    return &p_start;
  } else if (pstat_flag && strcmp(str,"p_stop") == 0) {
    return &p_stop;
  } else if (pstat_flag && strcmp(str,"p_target") == 0) {
    return &p_target;
  }
  return nullptr;
}

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

void FixNPTCauchy::nhc_temp_integrate()
{
  int ich;
  double expfac;
  double kecurrent = tdof * boltz * t_current;

  // Update masses, to preserve initial freq, if flag set

  if (eta_mass_flag) {
    eta_mass[0] = tdof * boltz * t_target / (t_freq*t_freq);
    for (int ich = 1; ich < mtchain; ich++)
      eta_mass[ich] = boltz * t_target / (t_freq*t_freq);
  }

  if (eta_mass[0] > 0.0)
    eta_dotdot[0] = (kecurrent - ke_target)/eta_mass[0];
  else eta_dotdot[0] = 0.0;

  double ncfac = 1.0/nc_tchain;
  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] *= tdrag_factor;
      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] *= tdrag_factor;
    eta_dot[0] *= expfac;

    factor_eta = exp(-ncfac*dthalf*eta_dot[0]);
    nh_v_temp();

    // rescale temperature due to velocity scaling
    // should not be necessary to explicitly recompute the temperature

    t_current *= factor_eta*factor_eta;
    kecurrent = tdof * boltz * t_current;

    if (eta_mass[0] > 0.0)
      eta_dotdot[0] = (kecurrent - ke_target)/eta_mass[0];
    else eta_dotdot[0] = 0.0;

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

    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 * t_target)/eta_mass[ich];
      eta_dot[ich] += eta_dotdot[ich] * ncfac*dt4;
      eta_dot[ich] *= expfac;
    }
  }
}

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

void FixNPTCauchy::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 flag set

  if (omega_mass_flag) {
    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 (etap_mass_flag) {
    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];
    }
  }

  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++;
      }
  }

  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] *= pdrag_factor;
      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] *= pdrag_factor;
    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] - boltz*t_target) /
        etap_mass[ich];
      etap_dot[ich] += etap_dotdot[ich] * ncfac*dt4;
      etap_dot[ich] *= expfac;
    }
  }
}

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

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

  if (which == NOBIAS) {
    for (int i = 0; i < nlocal; i++) {
      if (mask[i] & groupbit) {
        v[i][0] *= factor_eta;
        v[i][1] *= factor_eta;
        v[i][2] *= factor_eta;
      }
    }
  } 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_eta;
        v[i][1] *= factor_eta;
        v[i][2] *= factor_eta;
        temperature->restore_bias(i,v[i]);
      }
    }
  }
}

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

void FixNPTCauchy::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 FixNPTCauchy::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 FixNPTCauchy::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 FixNPTCauchy::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);
  ke_target = tdof * boltz * t_target;
}

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

void FixNPTCauchy::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]);

  // CauchyStat: call CauchyStat to modify p_target[i] and p_hydro,
  // if CauchyStat enabled and pressure->vector computation has been initiated

  if (initRUN == 1) CauchyStat();
  if (initRUN == 0) {
    for (int i=0; i < 6; i++) {
      h_old[i]=domain->h[i];
    }
  }

  // when run is initialized tensor[] not available (pressure on cell wall)

  initRUN=1;

  // if deviatoric, recompute sigma each time p_target changes

  if (deviatoric_flag) compute_sigma();
}

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

void FixNPTCauchy::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;
      omega_dot[i] *= pdrag_factor;
    }

  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;
        omega_dot[i] *= pdrag_factor;
      }
    }
  }
}

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

/* ----------------------------------------------------------------------
   initialize Cauchystat
------------------------------------------------------------------------- */

void FixNPTCauchy::CauchyStat_init()
{
  if (comm->me == 0) {
    std::string mesg = fmt::format("Using fix npt/cauchy with alpha={:.8f}\n",alpha);
    if (restartPK==1) {
      mesg += "   (this is a continuation run)\n";
    } else {
      mesg += "   (this is NOT a continuation run)\n";
    }
    utils::logmesg(lmp, mesg);
  }

  if (!id_store)
    id_store = utils::strdup(std::string(id) + "_FIX_NH_STORE");
  restart_stored = modify->find_fix(id_store);

  if (restartPK==1 && restart_stored < 0)
    error->all(FLERR,"Illegal npt/cauchy command.  Continuation run"
               " must follow a previously equilibrated npt/cauchy run");

  if (alpha<=0.0)
    error->all(FLERR,"Illegal fix npt/cauchy command: Alpha cannot be zero or negative.");

  if (restart_stored < 0) {
    modify->add_fix(std::string(id_store) + " all STORE global 1 6");
    restart_stored = modify->find_fix(id_store);
  }
  init_store = (FixStore *)modify->fix[restart_stored];

  initRUN = 0;
  initPK = 1;

#define H0(row,col) (H0[(row-1)][(col-1)])
#define invH0(row,col) (invH0[(row-1)][(col-1)])

  // initialize H0 to current box shape

  double *h = domain->h;
  double *h_inv = domain->h_inv;

  H0(1,1)=h[0];  H0(1,2)=h[5];  H0(1,3)=h[4];
  H0(2,1)=0.0;   H0(2,2)=h[1];  H0(2,3)=h[3];
  H0(3,1)=0.0;   H0(3,2)=0.0;   H0(3,3)=h[2];

  invH0(1,1)=h_inv[0];  invH0(1,2)=h_inv[5];  invH0(1,3)=h_inv[4];
  invH0(2,1)=0.0;       invH0(2,2)=h_inv[1];  invH0(2,3)=h_inv[3];
  invH0(3,1)=0.0;       invH0(3,2)=0.0;       invH0(3,3)=h_inv[2];

  CSvol0 = fabs(MathExtra::det3(H0));   //find reference volume

#undef H0
#undef invH0
}

/* ----------------------------------------------------------------------
   Cauchystat
------------------------------------------------------------------------- */

void FixNPTCauchy::CauchyStat()
{
  double* h = domain->h;           // shape matrix in Voigt notation
  double* h_rate = domain->h_rate; // rate of box size/shape change in Voigt notation
  double H[3][3];
  double Hdot[3][3];

#define H(row,col) (H[(row-1)][(col-1)])
#define Hdot(row,col) (Hdot[(row-1)][(col-1)])
#define F(row,col) (F[(row-1)][(col-1)])
#define Fi(row,col) (Fi[(row-1)][(col-1)])
#define Fdot(row,col) (Fdot[(row-1)][(col-1)])
#define invH0(row,col) (invH0[(row-1)][(col-1)])
#define cauchy(row,col) (cauchy[(row-1)][(col-1)])
#define setcauchy(row,col) (setcauchy[(row-1)][(col-1)])
#define setPK(row,col) (setPK[(row-1)][(col-1)])
#define sigmahat(row,col) (sigmahat[(row-1)][(col-1)])

  H(1,1)=h[0]; H(1,2)=0.0;  H(1,3)=0.0;
  H(2,1)=0.0;  H(2,2)=h[1];  H(2,3)=0.0;
  H(3,1)=0.0;  H(3,2)=0.0;   H(3,3)=h[2];

  for (int i=0;i<6;i++) {
    h_rate[i]=(h[i]-h_old[i])/update->dt;
    h_old[i]=h[i];
  }

  Hdot(1,1)=h_rate[0]; Hdot(1,2)=0.0;        Hdot(1,3)=0.0;
  Hdot(2,1)=0.0;       Hdot(2,2)=h_rate[1];  Hdot(2,3)=0.0;
  Hdot(3,1)=0.0;       Hdot(3,2)=0.0;        Hdot(3,3)=h_rate[2];

  if (domain->triclinic) {
    H(1,2)=h[5];  H(1,3)=h[4]; H(2,3)=h[3];
    Hdot(1,2)=h_rate[5];  Hdot(1,3)=h_rate[4]; Hdot(2,3)=h_rate[3];
  }

  double F[3][3]={{0.0,0.0,0.0},{0.0,0.0,0.0},{0.0,0.0,0.0}};
  double Fi[3][3]={{0.0,0.0,0.0},{0.0,0.0,0.0},{0.0,0.0,0.0}};
  double Fdot[3][3]={{0.0,0.0,0.0},{0.0,0.0,0.0},{0.0,0.0,0.0}};
  double J,vol;

  MathExtra::times3(H,invH0,F);
  MathExtra::times3(Hdot,invH0,Fdot);
  MathExtra::invert3(F,Fi);
  J = MathExtra::det3(F);
  vol=CSvol0*J;

  double deltat;
  deltat = update->dt; //increment of time step

  // Current pressure on the cell boundaries:
  //tensor:  0    1    2    3    4    5
  //         x    y    z    xy   xz   yz

  double *tensor = pressure->vector;

  double cauchy[3][3];
  cauchy(1,1)=-tensor[0]; cauchy(1,2)=0.0;        cauchy(1,3)=0.0;
  cauchy(2,1)=0.0;        cauchy(2,2)=-tensor[1]; cauchy(2,3)=0.0;
  cauchy(3,1)=0.0;        cauchy(3,2)=0.0;        cauchy(3,3)=-tensor[2];

  if (domain->triclinic) {
    cauchy(1,2)=-tensor[3]; cauchy(1,3)=-tensor[4];
    cauchy(2,1)=-tensor[3]; cauchy(2,3)=-tensor[5];
    cauchy(3,1)=-tensor[4]; cauchy(3,2)=-tensor[5];
  }

  // target pressure on the cell boundaries:
  // p_target:          0          1          2          3          4          5
  //                   x          y          z         yz         xz         xy

  double setcauchy[3][3];
  setcauchy(1,1)=-p_target[0]; setcauchy(1,2)=0.0;          setcauchy(1,3)=0.0;
  setcauchy(2,1)=0.0;          setcauchy(2,2)=-p_target[1]; setcauchy(2,3)=0.0;
  setcauchy(3,1)=0.0;          setcauchy(3,2)=0.0;          setcauchy(3,3)=-p_target[2];

  if (domain->triclinic) {
    setcauchy(1,2)=-p_target[5]; setcauchy(1,3)=-p_target[4];
    setcauchy(2,1)=-p_target[5]; setcauchy(2,3)=-p_target[3];
    setcauchy(3,1)=-p_target[4]; setcauchy(3,2)=-p_target[3];
  }

  //initialize:
  if (initPK==1) {
    if (restartPK==1) {
      double *setPKinit = init_store->astore[0];
      setPK(1,1)=setPKinit[0]; setPK(1,2)=setPKinit[1]; setPK(1,3)=setPKinit[2];
      setPK(2,1)=setPKinit[1]; setPK(2,2)=setPKinit[3]; setPK(2,3)=setPKinit[4];
      setPK(3,1)=setPKinit[2]; setPK(3,2)=setPKinit[4]; setPK(3,3)=setPKinit[5];
    }else {
      setPK(1,1)=cauchy(1,1); setPK(1,2)=cauchy(1,2); setPK(1,3)=cauchy(1,3);
      setPK(2,1)=cauchy(2,1); setPK(2,2)=cauchy(2,2); setPK(2,3)=cauchy(2,3);
      setPK(3,1)=cauchy(3,1); setPK(3,2)=cauchy(3,2); setPK(3,3)=cauchy(3,3);
    }
    initPK=0;
  }

  CauchyStat_Step(Fi,Fdot,cauchy,setcauchy,setPK,vol,CSvol0,deltat,alpha);

  // use currentPK as new target:
  // p_target:         0          1          2          3          4          5
  //                   x          y          z         yz         xz         xy

  p_target[0]=-setPK(1,1);
  p_target[1]=-setPK(2,2);
  p_target[2]=-setPK(3,3);
  if (pstyle == TRICLINIC) {
    p_target[3]=-setPK(2,3);
    p_target[4]=-setPK(1,3);
    p_target[5]=-setPK(1,2);
  }

  p_hydro = 0.0;
  for (int i = 0; i < 3; i++)
    if (p_flag[i]) {
      p_hydro += p_target[i];
    }
  p_hydro /= pdim;

  // save information for Cauchystat restart
  double *setPKinit = init_store->astore[0];
  setPKinit[0] = setcauchy(1,1);
  setPKinit[1] = setcauchy(1,2);
  setPKinit[2] = setcauchy(1,3);
  setPKinit[3] = setcauchy(2,2);
  setPKinit[4] = setcauchy(2,3);
  setPKinit[5] = setcauchy(3,3);

#undef H
#undef Hdot
#undef F
#undef Fi
#undef Fdot
#undef invH0
#undef cauchy
#undef setcauchy
#undef setPK
#undef sigmahat

}

/* ----------------------------------------------------------------------
   CauchyStat_Step

   Inputs:
   Fi(3,3)          :  inverse of the deformation gradient
   Fdot(3,3)        :  time derivative of the deformation gradient (velocity)
   cauchy(3,3)      :  current cauchy stress tensor
   setcauchy(3,3)   :  target cauchy stress tensor
   alpha            :  parameter =0.01
   setPK(3,3)       :  current PK stress tensor, at initialization (time=0) setPK=cauchy
   volume           :  current volume of the periodic box
   volume0          :  initial volume of the periodic box
   deltat           :  simulation step increment
   alpha            :  parameter

   Outputs:
   setPK(3,3)       :  PK stress tensor at the next time step
   ------------------------------------------------------------------------- */

void FixNPTCauchy::CauchyStat_Step(double (&Fi)[3][3], double (&Fdot)[3][3],
                            double (&cauchy)[3][3], double (&setcauchy)[3][3],
                            double (&setPK)[3][3], double volume,
                            double volume0, double deltat, double alpha)
{

  //macros to go from c to fortran style for arrays:
#define F(row,col) (F[(row-1)][(col-1)])
#define Fi(row,col) (Fi[(row-1)][(col-1)])
#define Fdot(row,col) (Fdot[(row-1)][(col-1)])
#define cauchy(row,col) (cauchy[(row-1)][(col-1)])
#define setcauchy(row,col) (setcauchy[(row-1)][(col-1)])
#define setPK(row,col) (setPK[(row-1)][(col-1)])
#define uv(row,col) (uv[(row-1)][(col-1)])
#define deltastress(row) (deltastress[(row-1)])
#define fdotvec(row) (fdotvec[(row-1)])
#define dsdf(row,col) (dsdf[(row-1)][(col-1)])
#define dsds(row,col) (dsds[(row-1)][(col-1)])
#define deltaF(row) (deltaF[(row-1)])
#define deltaPK(row) (deltaPK[(row-1)])

  //initialize local variables:
  int i,j,m,n;

  double deltastress[6],fdotvec[6];
  double dsdf[6][6];
  double dsds[6][6];
  double jac;
  double deltaF[6];
  double deltaPK[6];

  // zero arrays
  for (i = 0; i < 6; ++i) {
    deltaF[i] = deltaPK[i] = deltastress[i] = fdotvec[i] = 0.0;
    for (j = 0; j < 6; ++j)
      dsdf[i][j] = dsds[i][j] = 0.0;
  }

  int uv[6][2];
  uv(1,1)=1; uv(1,2)=1;
  uv(2,1)=2; uv(2,2)=2;
  uv(3,1)=3; uv(3,2)=3;
  uv(4,1)=2; uv(4,2)=3;
  uv(5,1)=1; uv(5,2)=3;
  uv(6,1)=1; uv(6,2)=2;

  for (int ii = 1;ii <= 6;ii++) {
    i=uv(ii,1);
    j=uv(ii,2);
    deltastress(ii)=setcauchy(i,j)-cauchy(i,j);
    if (ii>3) deltastress(ii)=deltastress(ii)*2.0;
    fdotvec(ii)=Fdot(i,j)*deltat;
  }

  for (int ii = 1;ii <= 6;ii++) {
    i=uv(ii,1);
    j=uv(ii,2);
    for (int jj = 1;jj <= 6;jj++) {
      m=uv(jj,1);
      n=uv(jj,2);
      dsds(ii,jj) = Fi(i,m)*Fi(j,n) + Fi(i,n)*Fi(j,m) + Fi(j,m)*Fi(i,n) + Fi(j,n)*Fi(i,m);
      for (int l = 1;l <= 3;l++) {
        for (int k = 1;k <= 3;k++) {
          dsdf(ii,jj) = dsdf(ii,jj) + cauchy(k,l)*
            ( Fi(i,k)*Fi(j,l)*Fi(n,m) - Fi(i,m)*Fi(j,l)*Fi(n,k) - Fi(i,k)*Fi(j,m)*Fi(n,l) );
        }
      }
    }
  }

  jac=volume/volume0;
  for (int ii = 1;ii <= 6;ii++) {
    for (int jj = 1;jj <= 6;jj++) {
      dsds(ii,jj)=dsds(ii,jj)*jac/4.0;
      dsdf(ii,jj)=dsdf(ii,jj)*jac;
    }
  }

  for (int ii = 1;ii <= 6;ii++) {
    for (int jj = 1;jj <= 6;jj++) {
      deltaF(ii)=deltaF(ii)+dsdf(ii,jj)*fdotvec(jj);
    }
  }

  for (int ii = 1;ii <= 6;ii++) {
    for (int jj = 1;jj <= 6;jj++) {
      deltaPK(ii)=deltaPK(ii)+alpha*dsds(ii,jj)*deltastress(jj);
    }
    deltaPK(ii)=deltaPK(ii)+alpha*deltaF(ii);
  }

  setPK(1,1)=setPK(1,1)+deltaPK(1);
  setPK(2,2)=setPK(2,2)+deltaPK(2);
  setPK(3,3)=setPK(3,3)+deltaPK(3);
  setPK(2,3)=setPK(2,3)+deltaPK(4);
  setPK(3,2)=setPK(3,2)+deltaPK(4);
  setPK(1,3)=setPK(1,3)+deltaPK(5);
  setPK(3,1)=setPK(3,1)+deltaPK(5);
  setPK(1,2)=setPK(1,2)+deltaPK(6);
  setPK(2,1)=setPK(2,1)+deltaPK(6);

#undef F
#undef Fi
#undef Fdot
#undef cauchy
#undef setcauchy
#undef setPK
#undef uv
#undef deltastress
#undef fdotvec
#undef dsdf
#undef dsds
#undef deltaF
#undef deltaPK

}
