/* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   http://lammps.sandia.gov, 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: Mark Stevens (SNL), Aidan Thompson (SNL)
------------------------------------------------------------------------- */

#include "string.h"
#include "stdlib.h"
#include "math.h"
#include "fix_nh.h"
#include "math_extra.h"
#include "atom.h"
#include "force.h"
#include "comm.h"
#include "irregular.h"
#include "modify.h"
#include "fix_deform.h"
#include "compute.h"
#include "kspace.h"
#include "update.h"
#include "respa.h"
#include "domain.h"
#include "memory.h"
#include "error.h"

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

FixNH::FixNH(LAMMPS *lmp, int narg, char **arg) : Fix(lmp, narg, arg)
{
  if (narg < 4) error->all(FLERR,"Illegal fix nvt/npt/nph command");

  restart_global = 1;
  time_integrate = 1;
  scalar_flag = 1;
  vector_flag = 1;
  global_freq = 1;
  extscalar = 1;
  extvector = 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;

  // 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 nvt/npt/nph command");
      tstat_flag = 1;
      t_start = atof(arg[iarg+1]);
      t_stop = atof(arg[iarg+2]);
      t_period = atof(arg[iarg+3]);
      if (t_start < 0.0 || t_stop <= 0.0)
	error->all(FLERR,"Target temperature for fix nvt/npt/nph cannot be 0.0");
      iarg += 4;

    } 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] = atof(arg[iarg+1]);
      p_stop[0] = p_stop[1] = p_stop[2] = atof(arg[iarg+2]);
      p_period[0] = p_period[1] = p_period[2] = atof(arg[iarg+3]);
      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] = atof(arg[iarg+1]);
      p_stop[0] = p_stop[1] = p_stop[2] = atof(arg[iarg+2]);
      p_period[0] = p_period[1] = p_period[2] = atof(arg[iarg+3]);
      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] = atof(arg[iarg+1]);
      p_stop[0] = p_stop[1] = p_stop[2] = atof(arg[iarg+2]);
      p_period[0] = p_period[1] = p_period[2] = atof(arg[iarg+3]);
      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] = atof(arg[iarg+3]);
      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] = atof(arg[iarg+1]);
      p_stop[0] = atof(arg[iarg+2]);
      p_period[0] = atof(arg[iarg+3]);
      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] = atof(arg[iarg+1]);
      p_stop[1] = atof(arg[iarg+2]);
      p_period[1] = atof(arg[iarg+3]);
      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] = atof(arg[iarg+1]);
      p_stop[2] = atof(arg[iarg+2]);
      p_period[2] = atof(arg[iarg+3]);
      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");
      scaleyz = 0;
      p_start[3] = atof(arg[iarg+1]);
      p_stop[3] = atof(arg[iarg+2]);
      p_period[3] = atof(arg[iarg+3]);
      p_flag[3] = 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],"xz") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      scalexz = 0;
      p_start[4] = atof(arg[iarg+1]);
      p_stop[4] = atof(arg[iarg+2]);
      p_period[4] = atof(arg[iarg+3]);
      p_flag[4] = 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],"xy") == 0) {
      scalexy = 0;
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      p_start[5] = atof(arg[iarg+1]);
      p_stop[5] = atof(arg[iarg+2]);
      p_period[5] = atof(arg[iarg+3]);
      p_flag[5] = 1;
      deviatoric_flag = 1;
      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],"drag") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      drag = atof(arg[iarg+1]);
      if (drag < 0.0) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"dilate") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      if (strcmp(arg[iarg+1],"all") == 0) allremap = 1;
      else if (strcmp(arg[iarg+1],"partial") == 0) allremap = 0;
      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 = atoi(arg[iarg+1]);
      // used by FixNVTSllod to preserve non-default value  
      mtchain_default_flag = 0;
      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 = atoi(arg[iarg+1]);
      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");
      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 nvt/npt/nph command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"tloop") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      nc_tchain = atoi(arg[iarg+1]);
      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 = atoi(arg[iarg+1]);
      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 = atoi(arg[iarg+1]);
      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");
      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 nvt/npt/nph command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"scalexz") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph 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 nvt/npt/nph command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"scaleyz") == 0) {
      if (iarg+2 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph 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 nvt/npt/nph command");
      iarg += 2;
    } else if (strcmp(arg[iarg],"fixedpoint") == 0) {
      if (iarg+4 > narg) error->all(FLERR,"Illegal fix nvt/npt/nph command");
      fixedpoint[0] = atof(arg[iarg+1]);
      fixedpoint[1] = atof(arg[iarg+2]);
      fixedpoint[2] = atof(arg[iarg+3]);
      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 dynamics when z is non-periodic dimension");
  if (scalexz == 1 && domain->zperiodic == 0)
    error->all(FLERR,"Cannot use fix nvt/npt/nph "
	       "with xz dynamics when z is non-periodic dimension");
  if (scalexy == 1 && domain->yperiodic == 0)
    error->all(FLERR,"Cannot use fix nvt/npt/nph "
	       "with xy dynamics 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

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

  if (pstat_flag) {
    box_change = 1;
    if (p_flag[0] || p_flag[1] || p_flag[2]) box_change_size = 1;
    if (p_flag[3] || p_flag[4] || p_flag[5]) box_change_shape = 1;
    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;

  // reneighboring only forced if flips will occur due to shape changes

  if (p_flag[3] || p_flag[4] || p_flag[5]) force_reneighbor = 1;
  if (scaleyz || scalexz || scalexy) force_reneighbor = 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 = NULL;

  if (force_reneighbor) irregular = new Irregular(lmp);
  else irregular = NULL;

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

  vol0 = t0 = 0.0;
}
  
/* ---------------------------------------------------------------------- */
  
FixNH::~FixNH()
{
  delete [] rfix;

  delete irregular;

  // delete temperature and pressure if fix created them

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

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

int FixNH::setmask()
{
  int mask = 0;
  mask |= INITIAL_INTEGRATE;
  mask |= FINAL_INTEGRATE;
  mask |= THERMO_ENERGY;
  mask |= INITIAL_INTEGRATE_RESPA;
  mask |= FINAL_INTEGRATE_RESPA;
  if (force_reneighbor) mask |= PRE_EXCHANGE;
  return mask;
}

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

void FixNH::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 = ((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/nph/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]);
    }
    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 (strstr(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 = NULL;

  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 FixNH::setup(int vflag)
{
  // initialize some quantities that were not available earlier

  tdof = temperature->dof;

  // t_target is needed by NPH and NPT in compute_scalar()
  // If no thermostat or using fix nphug, 
  // t_target must be defined by other means.

  if (tstat_flag && strcmp(style,"nphug") != 0) {
    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();

  t_current = temperature->compute_scalar();
  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 * 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 FixNH::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 FixNH::final_integrate()
{
  nve_v();

  if (pstat_flag) nh_v_press();

  // compute new T,P
  // compute appropriately coupled elements of mvv_current

  t_current = temperature->compute_scalar();
  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 FixNH::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();
  }

  // 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 FixNH::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 FixNH::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];
  }
  
  // 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];
  }
}

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

void FixNH::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] & groupbit)
	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/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

  if (allremap) domain->lamda2x(nlocal);
  else {
    for (i = 0; i < nlocal; i++)
      if (mask[i] & groupbit)
	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 FixNH::write_restart(FILE *fp)
{
  int nsize = size_restart_global();

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

  int n = 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 FixNH::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 FixNH::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 FixNH::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 FixNH::modify_param(int narg, char **arg)
{
  if (strcmp(arg[0],"temp") == 0) {
    if (narg < 2) error->all(FLERR,"Illegal fix_modify command");
    if (tflag) {
      modify->delete_compute(id_temp);
      tflag = 0;
    }
    delete [] id_temp;
    int n = strlen(arg[1]) + 1;
    id_temp = new char[n];
    strcpy(id_temp,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 (pflag) {
      modify->delete_compute(id_press);
      pflag = 0;
    }
    delete [] id_press;
    int n = strlen(arg[1]) + 1;
    id_press = new char[n];
    strcpy(id_press,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 FixNH::compute_scalar()
{
  int i;
  double volume;
  double energy;
  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;

  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);

    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]; 
    }

    // 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 FixNH::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 FixNH::reset_target(double t_new)
{
  t_start = t_stop = t_new;
}

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

void FixNH::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 (strstr(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);
}

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

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

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

  if (omega_mass_flag) { 
    double nkt = atom->natoms * 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;
  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];

  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 FixNH::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 FixNH::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 FixNH::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 FixNH::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 FixNH::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 FixNH::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 FixNH::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 FixNH::compute_temp_target()
{
  double delta = update->ntimestep - update->beginstep;
  if (update->endstep > update->beginstep)
    delta /= update->endstep - update->beginstep;
  else delta = 0.0;
      
  t_target = t_start + delta * (t_stop-t_start);
  ke_target = tdof * boltz * t_target;
}

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

void FixNH::compute_press_target()
{
  double delta = update->ntimestep - update->beginstep;
  if (update->endstep > update->beginstep)
    delta /= update->endstep - update->beginstep;
  else delta = 0.0;
      
  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];
    }
  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 FixNH::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];
    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 0.5, set flip = 1 & compute new tilt_flip values
  do not flip in x or y if non-periodic
  when yz flips and xy is non-zero, xz must also change
  this is to keep the edge vectors of the flipped shape matrix
    an integer combination of the edge vectors of the unflipped shape matrix
  perform irregular on atoms in lamda coords to get atoms to new procs
------------------------------------------------------------------------- */

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

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

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

  int flip = 0;

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

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

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

    double **x = atom->x;
    int *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);
  }
}