/* ----------------------------------------------------------------------
   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 author: Philipp Kloza (University of Cambridge)
                        pak37@cam.ac.uk
------------------------------------------------------------------------- */

#include "pair_mesocnt.h"

#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <string>

#include "atom.h"
#include "comm.h"
#include "force.h"
#include "neighbor.h"
#include "neigh_list.h"
#include "neigh_request.h"
#include "memory.h"
#include "error.h"
#include "update.h"
#include "utils.h"
#include "fmt/format.h"

#include "math_const.h"
#include "math_extra.h"

using namespace LAMMPS_NS;
using namespace MathConst;
using namespace MathExtra;

#define MAXLINE 1024
#define SELF_CUTOFF 20
#define SMALL 1.0e-6
#define SWITCH 1.0e-6
#define QUADRATURE 100

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

PairMesoCNT::PairMesoCNT(LAMMPS *lmp) : Pair(lmp)
{
  single_enable = 0;
  restartinfo = 0;
  respa_enable = 0;
  one_coeff = 1;
  manybody_flag = 1;
  no_virial_fdotr_compute = 0;
  writedata = 0;
  ghostneigh = 0;
}

/* ----------------------------------------------------------------------
   check if allocated, since class can be destructed when incomplete
------------------------------------------------------------------------- */

PairMesoCNT::~PairMesoCNT()
{
  if (allocated) {
    memory->destroy(cutsq);
    memory->destroy(setflag);

    memory->destroy(uinf_coeff);
    memory->destroy(gamma_coeff);
    memory->destroy(phi_coeff);
    memory->destroy(usemi_coeff);

    memory->destroy(reduced_neighlist);
    memory->destroy(reduced_nlist);
    memory->destroy(numchainlist);
    memory->destroy(nchainlist);
    memory->destroy(endlist);
    memory->destroy(chainlist);

    memory->destroy(w);
    memory->destroy(wnode);
    memory->destroy(dq_w);
    memory->destroy(q1_dq_w);
    memory->destroy(q2_dq_w);

    memory->destroy(param);

    memory->destroy(flocal);
    memory->destroy(fglobal);
    memory->destroy(basis);
  }
}

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

void PairMesoCNT::compute(int eflag, int vflag)
{
  int i,j,k,i1,i2,j1,j2;
  int endflag,endindex;
  int clen,numchain;
  int *end,*nchain;
  int **chain;
  double fend,lp,scale,sumw,sumw_inv;
  double evdwl,evdwl_chain;
  double *r1,*r2,*q1,*q2,*qe;
  double ftotal[3],ftorque[3],torque[3],delr1[3],delr2[3];
  double t1[3],t2[3];
  double dr1_sumw[3],dr2_sumw[3];
  double dr1_w[3],dr2_w[3],dq1_w[3],dq2_w[3];
  double fgrad_r1_p1[3],fgrad_r1_p2[3],fgrad_r2_p1[3],fgrad_r2_p2[3];
  double fgrad_q_p1[3],fgrad_q_p2[3];
  double q1_dr1_w[3][3],q1_dr2_w[3][3],q2_dr1_w[3][3],q2_dr2_w[3][3];
  double dr1_p1[3][3],dr1_p2[3][3],dr2_p1[3][3],dr2_p2[3][3];
  double dq_p1[3][3],dq_p2[3][3];
  double temp[3][3];

  evdwl = 0.0;
  ev_init(eflag,vflag);

  double **x = atom->x;
  double **f = atom->f;
  int **bondlist = neighbor->bondlist;
  int nbondlist = neighbor->nbondlist;

  // update bond neighbor list when necessary

  if (update->ntimestep == neighbor->lastcall) bond_neigh();

  // iterate over all bonds

  for (i = 0; i < nbondlist; i++) {
    i1 = bondlist[i][0];
    i2 = bondlist[i][1];

    r1 = x[i1];
    r2 = x[i2];

    numchain = numchainlist[i];
    end = endlist[i];
    nchain = nchainlist[i];
    chain = chainlist[i];

    // iterate over all neighbouring chains

    for (j = 0; j < numchain; j++) {
      clen = nchain[j];
      if (clen < 2) continue;

      // assign end position

      endflag = end[j];
      if (endflag == 1) {
        endindex = chain[j][0];
        qe = x[endindex];
      } else if (endflag == 2) {
        endindex = chain[j][clen-1];
        qe = x[endindex];
      }

      // compute substitute straight (semi-)infinite CNT

      zero3(p1);
      zero3(p2);
      zero3(dr1_sumw);
      zero3(dr2_sumw);
      zeromat3(q1_dr1_w);
      zeromat3(q2_dr1_w);
      zeromat3(q1_dr2_w);
      zeromat3(q2_dr2_w);
      for (k = 0; k < clen; k++) {
        wnode[k] = 0.0;
        zero3(dq_w[k]);
        zeromat3(q1_dq_w[k]);
        zeromat3(q2_dq_w[k]);
      }
      sumw = 0.0;

      for (k = 0; k < clen-1; k++) {
        j1 = chain[j][k];
        j2 = chain[j][k+1];
        j1 &= NEIGHMASK;
        j2 &= NEIGHMASK;
        q1 = x[j1];
        q2 = x[j2];

        weight(r1,r2,q1,q2,w[k],dr1_w,dr2_w,dq1_w,dq2_w);

        if (w[k] == 0.0) {
          if (endflag == 1 && k == 0) endflag = 0;
          else if (endflag == 2 && k == clen-2) endflag = 0;
          continue;
        }

        sumw += w[k];
        wnode[k] += w[k];
        wnode[k+1] += w[k];

        scaleadd3(w[k],q1,p1,p1);
        scaleadd3(w[k],q2,p2,p2);

        // weight gradient terms

        add3(dr1_w,dr1_sumw,dr1_sumw);
        add3(dr2_w,dr2_sumw,dr2_sumw);

        outer3(q1,dr1_w,temp);
        plus3(temp,q1_dr1_w,q1_dr1_w);
        outer3(q2,dr1_w,temp);
        plus3(temp,q2_dr1_w,q2_dr1_w);
        outer3(q1,dr2_w,temp);
        plus3(temp,q1_dr2_w,q1_dr2_w);
        outer3(q2,dr2_w,temp);
        plus3(temp,q2_dr2_w,q2_dr2_w);

        add3(dq1_w,dq_w[k],dq_w[k]);
        add3(dq2_w,dq_w[k+1],dq_w[k+1]);

        outer3(q1,dq1_w,temp);
        plus3(temp,q1_dq_w[k],q1_dq_w[k]);
        outer3(q1,dq2_w,temp);
        plus3(temp,q1_dq_w[k+1],q1_dq_w[k+1]);
        outer3(q2,dq1_w,temp);
        plus3(temp,q2_dq_w[k],q2_dq_w[k]);
        outer3(q2,dq2_w,temp);
        plus3(temp,q2_dq_w[k+1],q2_dq_w[k+1]);
      }

      if (sumw == 0.0) continue;

      sumw_inv = 1.0 / sumw;
      scale3(sumw_inv,p1);
      scale3(sumw_inv,p2);

      // compute geometry and forces

      // infinite CNT case

      if (endflag == 0) {
        geometry(r1,r2,p1,p2,NULL,p,m,param,basis);
        if (param[0] > cutoff) continue;
        finf(param,evdwl,flocal);

        // semi-infinite CNT case with end at start of chain

      } else if (endflag == 1) {
        geometry(r1,r2,p1,p2,qe,p,m,param,basis);
        if (param[0] > cutoff) continue;
        fsemi(param,evdwl,fend,flocal);

        // semi-infinite CNT case with end at end of chain

      } else {
        geometry(r1,r2,p2,p1,qe,p,m,param,basis);
        if (param[0] > cutoff) continue;
        fsemi(param,evdwl,fend,flocal);
      }

      evdwl *= 0.5;

      // transform to global coordinate system

      matvec(basis[0],basis[1],basis[2],flocal[0],fglobal[0]);
      matvec(basis[0],basis[1],basis[2],flocal[1],fglobal[1]);

      // forces acting on approximate chain

      add3(fglobal[0],fglobal[1],ftotal);
      if (endflag) scaleadd3(fend,m,ftotal,ftotal);
      scale3(-0.5,ftotal);

      sub3(r1,p,delr1);
      sub3(r2,p,delr2);
      cross3(delr1,fglobal[0],t1);
      cross3(delr2,fglobal[1],t2);
      add3(t1,t2,torque);

      cross3(torque,m,ftorque);
      lp = param[5] - param[4];
      scale3(1.0/lp,ftorque);

      if (endflag == 2) {
        add3(ftotal,ftorque,fglobal[3]);
        sub3(ftotal,ftorque,fglobal[2]);
      } else {
        add3(ftotal,ftorque,fglobal[2]);
        sub3(ftotal,ftorque,fglobal[3]);
      }

      scale3(0.5,fglobal[0]);
      scale3(0.5,fglobal[1]);
      scale3(0.5,fglobal[2]);
      scale3(0.5,fglobal[3]);

      // weight gradient terms acting on current segment

      outer3(p1,dr1_sumw,temp);
      minus3(q1_dr1_w,temp,dr1_p1);
      outer3(p2,dr1_sumw,temp);
      minus3(q2_dr1_w,temp,dr1_p2);
      outer3(p1,dr2_sumw,temp);
      minus3(q1_dr2_w,temp,dr2_p1);
      outer3(p2,dr2_sumw,temp);
      minus3(q2_dr2_w,temp,dr2_p2);

      transpose_matvec(dr1_p1,fglobal[2],fgrad_r1_p1);
      transpose_matvec(dr1_p2,fglobal[3],fgrad_r1_p2);
      transpose_matvec(dr2_p1,fglobal[2],fgrad_r2_p1);
      transpose_matvec(dr2_p2,fglobal[3],fgrad_r2_p2);

      // add forces to nodes in current segment

      add3(fglobal[0],f[i1],f[i1]);
      add3(fglobal[1],f[i2],f[i2]);

      scaleadd3(sumw_inv,fgrad_r1_p1,f[i1],f[i1]);
      scaleadd3(sumw_inv,fgrad_r1_p2,f[i1],f[i1]);
      scaleadd3(sumw_inv,fgrad_r2_p1,f[i2],f[i2]);
      scaleadd3(sumw_inv,fgrad_r2_p2,f[i2],f[i2]);

      // add forces in approximate chain

      for (k = 0; k < clen-1; k++) {
        if (w[k] == 0.0) continue;
        j1 = chain[j][k];
        j2 = chain[j][k+1];
        j1 &= NEIGHMASK;
        j2 &= NEIGHMASK;
        scale = w[k] * sumw_inv;
        scaleadd3(scale,fglobal[2],f[j1],f[j1]);
        scaleadd3(scale,fglobal[3],f[j2],f[j2]);
      }

      // weight gradient terms acting on approximate chain
      // iterate over nodes instead of segments

      for (k = 0; k < clen; k++) {
        if (wnode[k] == 0.0) continue;
        j1 = chain[j][k];
        j1 &= NEIGHMASK;

        outer3(p1,dq_w[k],temp);
        minus3(q1_dq_w[k],temp,dq_p1);
        outer3(p2,dq_w[k],temp);
        minus3(q2_dq_w[k],temp,dq_p2);

        transpose_matvec(dq_p1,fglobal[2],fgrad_q_p1);
        transpose_matvec(dq_p2,fglobal[3],fgrad_q_p2);

        scaleadd3(sumw_inv,fgrad_q_p1,f[j1],f[j1]);
        scaleadd3(sumw_inv,fgrad_q_p2,f[j1],f[j1]);
      }

      // force on node at CNT end

      if (endflag) scaleadd3(0.5*fend,m,f[endindex],f[endindex]);

      // compute energy

      if (eflag_either) {
        if (eflag_global) eng_vdwl += evdwl;
        if (eflag_atom) {
          eatom[i1] += 0.25 * evdwl;
          eatom[i2] += 0.25 * evdwl;
          for (k = 0; k < clen-1; k++) {
            if (w[k] == 0.0) continue;
            j1 = chain[j][k];
            j2 = chain[j][k+1];
            j1 &= NEIGHMASK;
            j2 &= NEIGHMASK;
            evdwl_chain = 0.5 * w[k] * sumw_inv * evdwl;
            eatom[j1] += evdwl_chain;
            eatom[j2] += evdwl_chain;
          }
        }
      }
    }
  }

  if (vflag_fdotr) virial_fdotr_compute();
}

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

void PairMesoCNT::allocate()
{
  allocated = 1;
  int ntypes = atom->ntypes;
  nlocal_size = 512;
  reduced_neigh_size = 64;

  memory->create(cutsq,ntypes+1,ntypes+1,"pair:cutsq");
  memory->create(setflag,ntypes+1,ntypes+1,"pair:setflag");
  for (int i = 1; i <= ntypes; i++)
    for (int j = i; j <= ntypes; j++)
      setflag[i][j] = 0;

  memory->create(uinf_coeff,uinf_points,4,"pair:uinf_coeff");
  memory->create(gamma_coeff,gamma_points,4,"pair:gamma_coeff");
  memory->create(phi_coeff,phi_points,phi_points,4,4,"pair:phi_coeff");
  memory->create(usemi_coeff,usemi_points,usemi_points,4,4,"pair:usemi_coeff");

  memory->create(reduced_nlist,nlocal_size,"pair:reduced_nlist");
  memory->create(numchainlist,nlocal_size,"pair:numchainlist");

  memory->create(reduced_neighlist,
                nlocal_size,reduced_neigh_size,"pair:reduced_neighlist");
  memory->create(nchainlist,nlocal_size,reduced_neigh_size,"pair:nchainlist");
  memory->create(endlist,nlocal_size,reduced_neigh_size,"pair:endlist");
  memory->create(chainlist,nlocal_size,
                reduced_neigh_size,reduced_neigh_size,"pair:chainlist");

  memory->create(w,reduced_neigh_size,"pair:w");
  memory->create(wnode,reduced_neigh_size,"pair:wnode");
  memory->create(dq_w,reduced_neigh_size,3,"pair:dq_w");
  memory->create(q1_dq_w,reduced_neigh_size,3,3,"pair:q1_dq_w");
  memory->create(q2_dq_w,reduced_neigh_size,3,3,"pair:q2_dq_w");

  memory->create(param,7,"pair:param");

  memory->create(flocal,2,3,"pair:flocal");
  memory->create(fglobal,4,3,"pair:fglobal");
  memory->create(basis,3,3,"pair:basis");
}

/* ----------------------------------------------------------------------
   global settings
------------------------------------------------------------------------- */

void PairMesoCNT::settings(int narg, char ** /* arg */)
{
  if (narg != 0) error->all(FLERR,"Illegal pair_style command");
}

/* ----------------------------------------------------------------------
   set coeffs for one or more type pairs
------------------------------------------------------------------------- */

void PairMesoCNT::coeff(int narg, char **arg)
{
  if (narg != 3) error->all(FLERR,"Incorrect args for pair coefficients");
  file = arg[2];
  read_file();
  if (!allocated) allocate();

  // units, eV to energy unit conversion
  ang = force->angstrom;
  ang_inv = 1.0 / ang;
  if (strcmp(update->unit_style,"lj") == 0)
    error->all(FLERR,"Pair style mesocnt does not support lj units");
  else if (strcmp(update->unit_style,"real") == 0) eunit = 23.06054966;
  else if (strcmp(update->unit_style,"metal") == 0) eunit = 1.0;
  else if (strcmp(update->unit_style,"si") == 0) eunit = 1.6021765e-19;
  else if (strcmp(update->unit_style,"cgs") == 0) eunit = 1.6021765e-12;
  else if (strcmp(update->unit_style,"electron") == 0) eunit = 3.674932248e-2;
  else if (strcmp(update->unit_style,"micro") == 0) eunit = 1.6021765e-4;
  else if (strcmp(update->unit_style,"nano") == 0) eunit = 1.6021765e2;
  else error->all(FLERR,"Pair style mesocnt does not recognize this units style");
  funit = eunit * ang_inv;

  // potential variables
  sig = sig_ang * ang;
  r = r_ang * ang;
  rsq = r * r;
  d = 2.0 * r;
  d_ang = 2.0 * r_ang;
  rc = 3.0 * sig;
  cutoff = rc + d;
  cutoffsq = cutoff * cutoff;
  cutoff_ang = cutoff * ang_inv;
  cutoffsq_ang = cutoff_ang * cutoff_ang;
  comega = 0.275 * (1.0 - 1.0/(1.0 + 0.59*r_ang));
  ctheta = 0.35 + 0.0226*(r_ang - 6.785);

  // compute spline coefficients
  spline_coeff(uinf_data,uinf_coeff,delh_uinf,uinf_points);
  spline_coeff(gamma_data,gamma_coeff,delh_gamma,gamma_points);
  spline_coeff(phi_data,phi_coeff,delh_phi,delpsi_phi,phi_points);
  spline_coeff(usemi_data,usemi_coeff,delh_usemi,delxi_usemi,usemi_points);

  memory->destroy(uinf_data);
  memory->destroy(gamma_data);
  memory->destroy(phi_data);
  memory->destroy(usemi_data);

  int ntypes = atom->ntypes;
  for (int i = 1; i <= ntypes; i++)
    for (int j = i; j <= ntypes; j++)
      setflag[i][j] = 1;
}

/* ----------------------------------------------------------------------
   init specific to this pair style
------------------------------------------------------------------------- */

void PairMesoCNT::init_style()
{
  if (atom->tag_enable == 0)
    error->all(FLERR,"Pair style mesocnt requires atom IDs");
  if (force->newton_pair == 0)
    error->all(FLERR,"Pair style mesocnt requires newton pair on");

  // need a full neighbor list

  int irequest = neighbor->request(this,instance_me);
  neighbor->requests[irequest]->half = 0;
  neighbor->requests[irequest]->full = 1;
}

/* ----------------------------------------------------------------------
   init for one type pair i,j and corresponding j,i
------------------------------------------------------------------------- */

double PairMesoCNT::init_one(int /* i */, int /* j */)
{
  return cutoff;
}

/* ----------------------------------------------------------------------
   update bond neighbor lists
------------------------------------------------------------------------- */

void PairMesoCNT::bond_neigh()
{
  int **bondlist = neighbor->bondlist;
  int nbondlist = neighbor->nbondlist;
  int nlocal = atom->nlocal;

  int update_memory = 0;
  if (nbondlist > nlocal_size) {
    nlocal_size = 2 * nbondlist;
    update_memory = 1;
  }
  int *numneigh = list->numneigh;
  int numneigh_max = 0;
  for (int i = 0; i < nbondlist; i++) {
    int i1 = bondlist[i][0];
    int i2 = bondlist[i][1];
    int numneigh1,numneigh2;
    if (i1 > nlocal-1 && false) numneigh1 = 0;
    else numneigh1 = numneigh[i1];
    if (i2 > nlocal-1 && false) numneigh2 = 0;
    else numneigh2 = numneigh[i2];

    int numneigh_max_local = numneigh1 + numneigh1;
    if (numneigh_max_local > numneigh_max) numneigh_max = numneigh_max_local;
  }
  if (numneigh_max > reduced_neigh_size) {
    reduced_neigh_size = 2 * numneigh_max;
    update_memory = 1;
  }

  // grow arrays if necessary

  if (update_memory) {
    memory->destroy(reduced_neighlist);
    memory->destroy(numchainlist);
    memory->destroy(reduced_nlist);
    memory->destroy(nchainlist);
    memory->destroy(endlist);
    memory->destroy(chainlist);

    memory->create(reduced_nlist,nlocal_size,"pair:reduced_nlist");
    memory->create(numchainlist,nlocal_size,"pair:numchainlist");
    memory->create(reduced_neighlist,
                  nlocal_size,reduced_neigh_size,"pair:reduced_neighlist");
    memory->create(nchainlist,nlocal_size,reduced_neigh_size,"pair:nchainlist");
    memory->create(endlist,nlocal_size,reduced_neigh_size,"pair:endlist");
    memory->create(chainlist,nlocal_size,
                  reduced_neigh_size,reduced_neigh_size,"pair:chainlist");

    memory->grow(w,reduced_neigh_size,"pair:w");
    memory->grow(wnode,reduced_neigh_size,"pair:wnode");
    memory->grow(dq_w,reduced_neigh_size,3,"pair:dq_w");
    memory->grow(q1_dq_w,reduced_neigh_size,3,3,"pair:q1_dq_w");
    memory->grow(q2_dq_w,reduced_neigh_size,3,3,"pair:q2_dq_w");
  }

  for (int i = 0; i < nbondlist; i++) {
    int i1 = bondlist[i][0];
    int i2 = bondlist[i][1];

    int *reduced_neigh = reduced_neighlist[i];
    int *end = endlist[i];
    int *nchain = nchainlist[i];
    int **chain = chainlist[i];

    // reduce neighbors to common list

    neigh_common(i1,i2,reduced_nlist[i],reduced_neigh);

    // sort list according to atom-id

    sort(reduced_neigh,reduced_nlist[i]);

    // set up connected chains

    chain_split(reduced_neigh,
                  reduced_nlist[i],numchainlist[i],chain,nchain,end);
  }
}

/* ----------------------------------------------------------------------
   extract common neighbor list for bond
------------------------------------------------------------------------- */

void PairMesoCNT::neigh_common(int i1, int i2, int &numred, int *redlist)
{
  int nlocal = atom->nlocal;
  tagint *tag = atom->tag;
  tagint *mol = atom->molecule;
  int *numneigh = list->numneigh;
  int **firstneigh = list->firstneigh;
  int numneigh1,numneigh2;
  int *neighlist1,*neighlist2;

  if (i1 > nlocal-1) {
    numneigh1 = 0;
  } else {
    neighlist1 = firstneigh[i1];
    numneigh1 = numneigh[i1];
  }
  if (i2 > nlocal-1) {
    numneigh2 = 0;
  } else {
    neighlist2 = firstneigh[i2];
    numneigh2 = numneigh[i2];
  }

  int numneigh_max = numneigh1 + numneigh2;
  numred = 0;
  if (numneigh_max < 2) return;

  for (int j = 0; j < numneigh1; j++) {
    int ind = neighlist1[j];
    if (mol[ind] == mol[i1] && abs(tag[ind] - tag[i1]) < SELF_CUTOFF)
            continue;
    redlist[numred++] = ind;
  }
  int inflag = 0;
  for (int j2 = 0; j2 < numneigh2; j2++) {
    for (int j1 = 0; j1 < numneigh1; j1++) {
      if (neighlist1[j1] == neighlist2[j2]) {
        inflag = 1;
              break;
      }
    }
    if (inflag) {
      inflag = 0;
      continue;
    }
    int ind = neighlist2[j2];
    if (mol[ind] == mol[i2] && abs(tag[ind] - tag[i2]) < SELF_CUTOFF)
            continue;
    redlist[numred++] = ind;
  }
}

/* ----------------------------------------------------------------------
   split neighbors into chains and identify ends
------------------------------------------------------------------------- */

void PairMesoCNT::chain_split(int *redlist, int numred,
                int &numchain, int **chain, int *nchain, int *end)
{
  // empty neighbor list

  if (numred == 0) {
    numchain = 0;
    return;
  }

  tagint *tag = atom->tag;
  tagint *mol = atom->molecule;
  int clen = 0;
  int cid = 0;

  // split neighbor list into connected chains

  for (int j = 0; j < numred-1; j++) {
    int j1 = redlist[j];
    int j2 = redlist[j+1];
    chain[cid][clen++] = j1;
    if (tag[j2] - tag[j1] != 1 || mol[j1] != mol[j2]) {
      nchain[cid++] = clen;
      clen = 0;
    }
  }
  chain[cid][clen++] = redlist[numred-1];
  nchain[cid++] = clen;

  // check for chain ends

  for (int j = 0; j < cid; j++) {
    int cstart = chain[j][0];
    int cend = chain[j][nchain[j]-1];
    tagint tagstart = tag[cstart];
    tagint tagend = tag[cend];
    end[j] = 0;
    if (tagstart == 1) {
      end[j] = 1;
    } else {
      int idprev = atom->map(tagstart-1);
      if (mol[cstart] != mol[idprev]) end[j] = 1;
    }
    if (tagend == atom->natoms) {
      end[j] = 2;
    } else {
      int idnext = atom->map(tagend+1);
      if (mol[cend] != mol[idnext]) end[j] = 2;
    }
  }

  numchain = cid;
}

/* ----------------------------------------------------------------------
   insertion sort list according to corresponding atom ID
------------------------------------------------------------------------- */

void PairMesoCNT::sort(int *list, int size)
{
  int i,j,temp1,temp2;
  tagint *tag = atom->tag;
  for (i = 1; i < size; i++) {
    j = i;
    temp1 = list[j-1];
    temp2 = list[j];
    while (j > 0 && tag[temp1] > tag[temp2]) {
      list[j] = temp1;
      list[j-1] = temp2;
      j--;
      temp1 = list[j-1];
      temp2 = list[j];
    }
  }
}

/* ----------------------------------------------------------------------
   read mesocnt potential file
------------------------------------------------------------------------- */

void PairMesoCNT::read_file()
{
  int me, num;
  MPI_Comm_rank(world,&me);

  FILE *fp;

  if (me == 0) {
     char line[MAXLINE];

    // open file

    fp = force->open_potential(file);
    if (fp == NULL)
      error->one(FLERR,fmt::format("Cannot open mesocnt file: {}",file));

    utils::sfgets(FLERR,line,MAXLINE,fp,file,error);

    // potential parameters

    utils::sfgets(FLERR,line,MAXLINE,fp,file,error);
    num = sscanf(line,"%d %d %d %d",
                 &uinf_points,&gamma_points,&phi_points,&usemi_points);
    if (num != 4)
      error->one(FLERR,fmt::format("Could not correctly parse line 2 in "
                                   "mesocnt file: {}",file));

    utils::sfgets(FLERR,line,MAXLINE,fp,file,error);
    num = sscanf(line,"%lg %lg %lg %lg",&r_ang,&sig_ang,&delta1,&delta2);
    if (num != 4)
      error->one(FLERR,fmt::format("Could not correctly parse line 3 in "
                                   "mesocnt file: {}",file));
  }

  MPI_Bcast(&uinf_points,1,MPI_INT,0,world);
  MPI_Bcast(&gamma_points,1,MPI_INT,0,world);
  MPI_Bcast(&phi_points,1,MPI_INT,0,world);
  MPI_Bcast(&usemi_points,1,MPI_INT,0,world);
  MPI_Bcast(&r_ang,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&sig_ang,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&delta1,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&delta2,1,MPI_DOUBLE,0,world);

  // potential tables

  memory->create(uinf_data,uinf_points,"pair:uinf_data");
  memory->create(gamma_data,gamma_points,"pair:gamma_data");
  memory->create(phi_data,phi_points,phi_points,"pair:phi_data");
  memory->create(usemi_data,usemi_points,usemi_points,"pair:usemi_data");

  if (me == 0) {
    read_data(fp,uinf_data,hstart_uinf,delh_uinf,uinf_points);
    read_data(fp,gamma_data,hstart_gamma,delh_gamma,gamma_points);
    read_data(fp,phi_data,hstart_phi,psistart_phi,
                  delh_phi,delpsi_phi,phi_points);
    read_data(fp,usemi_data,hstart_usemi,xistart_usemi,
                  delh_usemi,delxi_usemi,usemi_points);

    fclose(fp);
  }

  MPI_Bcast(&hstart_uinf,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&hstart_gamma,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&hstart_phi,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&psistart_phi,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&hstart_usemi,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&xistart_usemi,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&delh_uinf,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&delh_gamma,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&delh_phi,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&delpsi_phi,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&delh_usemi,1,MPI_DOUBLE,0,world);
  MPI_Bcast(&delxi_usemi,1,MPI_DOUBLE,0,world);

  MPI_Bcast(uinf_data,uinf_points,MPI_DOUBLE,0,world);
  MPI_Bcast(gamma_data,gamma_points,MPI_DOUBLE,0,world);
  for (int i = 0; i < phi_points; i++)
    MPI_Bcast(phi_data[i],phi_points,MPI_DOUBLE,0,world);
  for (int i = 0; i < usemi_points; i++)
    MPI_Bcast(usemi_data[i],usemi_points,MPI_DOUBLE,0,world);
}

/* ----------------------------------------------------------------------
   read 1D data file
------------------------------------------------------------------------- */

void PairMesoCNT::read_data(FILE *fp, double *data,
                            double &xstart, double &dx, int ninput)
{
  char line[MAXLINE];
  utils::sfgets(FLERR,line,MAXLINE,fp,file,error);

  // read values from file

  int cerror = 0;
  int serror = 0;
  double x,xtemp,dxtemp;

  for (int i = 0; i < ninput; i++) {
    if (NULL == fgets(line,MAXLINE,fp))
      error->one(FLERR,fmt::format("Premature end of file in pair table: {}",file));

    if (i > 0) xtemp = x;
    if (2 != sscanf(line,"%lg %lg",&x,&data[i])) cerror++;
    if (i == 0) {
      xstart = x;
    } else {
      dxtemp = x - xtemp;
      if (i == 1) dx = dxtemp;
      if (fabs(dxtemp - dx)/dx > SMALL) serror++;
    }
  }

  // warn if data was read incompletely, e.g. columns were missing

  if (cerror) {
    std::string mesg = fmt::format("{} of {} lines were incomplete or could "
                                   "or could not be parsed completely in "
                                   "  pair table: {}",cerror,ninput,file);
    error->warning(FLERR,mesg);
  }

  // warn if spacing between data points is not constant

  if (serror) {
    std::string mesg = fmt::format("{} spacings in first column were different "
                                   " from first spacing in pair table: {}",serror,file);
    error->warning(FLERR,mesg);
  }
}

/* ----------------------------------------------------------------------
   read 2D data file
------------------------------------------------------------------------- */

void PairMesoCNT::read_data(FILE *fp, double **data,
                double &xstart, double &ystart,
                double &dx, double &dy, int ninput)
{
  char line[MAXLINE];
  fgets(line,MAXLINE,fp);

  // read values from file

  int cerror = 0;
  int sxerror = 0;
  int syerror = 0;
  double x,y,xtemp,ytemp,dxtemp,dytemp;

  for (int i = 0; i < ninput; i++) {
    if (i > 0) xtemp = x;
    for (int j = 0; j < ninput; j++) {
      if (NULL == fgets(line,MAXLINE,fp))
        error->one(FLERR,fmt::format("Premature end of file in pair table: {}",file));

      if (j > 0) ytemp = y;
      if (3 != sscanf(line,"%lg %lg %lg",&x,&y,&data[i][j])) cerror++;
      if (i == 0 && j == 0) ystart = y;
      if (j > 0) {
              dytemp = y - ytemp;
          if (j == 1) dy = dytemp;
              if (fabs(dytemp - dy)/dy > SMALL) syerror++;
      }
    }
    if (i == 0) {
      xstart = x;
    } else {
      dxtemp = x - xtemp;
      if (i == 1) dx = dxtemp;
      if (fabs(dxtemp - dx)/dx > SMALL) sxerror++;
    }
  }

  // warn if data was read incompletely, e.g. columns were missing

  if (cerror)
    error->warning(FLERR,fmt::format("{} of {} lines were incomplete or could "
                                     "not be parsed completely in pair table: {}",
                                     cerror,ninput*ninput,file));

  // warn if spacing between data points is not constant

  if (sxerror)
    error->warning(FLERR,fmt::format("{} spacings in first column were different "
                                     " from first spacing in pair table: {}",
                                     sxerror,file));
  if (syerror)
    error->warning(FLERR,fmt::format("{} spacings in second column were different "
                                     " from first spacing in pair table: {}",
                                     syerror,file));
}

/* ----------------------------------------------------------------------
   compute cubic spline coefficients
------------------------------------------------------------------------- */

void PairMesoCNT::spline_coeff(double *data, double **coeff,
                double dx, int size)
{
  double *u = data;
  double **g = coeff;
  int n = size;

  double d,*p,*bprime,*dprime,**b;
  memory->create(p,n,"pair:p");
  memory->create(b,n,n,"pair:b");
  memory->create(bprime,n,"pair:bprime");
  memory->create(dprime,n,"pair:dprime");

  double dx_inv = 1.0 / dx;
  double dxsq_inv = dx_inv * dx_inv;
  double dxcb_inv = dx_inv * dxsq_inv;

  double ax[4][4] =
  {
    {1, 0, 0, 0},
    {0, 1, 0, 0},
    {-3*dxsq_inv, -2*dx_inv, 3*dxsq_inv, -dx_inv},
    {2*dxcb_inv, dxsq_inv, -2*dxcb_inv, dxsq_inv}
  };

  // compute finite difference derivatives at boundaries

  p[0] = (u[1] - u[0]) * dx_inv;
  p[n-1] = (u[n-1] - u[n-2]) * dx_inv;

  // compute derivatives inside domain

  for (int i = 1; i < n-1; i++) {
    if (i > 1) b[i][i-1] = dx;
    b[i][i] = 4 * dx;
    if (i < n-2) b[i][i+1] = dx;
  }
  bprime[1] = b[1][1];
  for (int i = 2; i < n-1; i++)
    bprime[i] = b[i][i] - b[i][i-1]*b[i-1][i]/bprime[i-1];

  for (int i = 1; i < n-1; i++) {
    d = 3 * (u[i+1] - u[i-1]);
    if (i == 1) d -= dx * p[i-1];
    if (i == n-2) d -= dx * p[i+1];
    dprime[i] = d;
    if (i != 1) dprime[i] -= b[i][i-1] * dprime[i-1] / bprime[i-1];
  }

  p[n-2] = dprime[n-2] / bprime[n-2];
  for (int i = n-3; i > 0; i--)
    p[i] = (dprime[i] - b[i][i+1]*p[i+1]) / bprime[i];

  // compute spline coefficients

  for (int i = 1; i < n; i++) {
    for (int j = 0; j < 4; j++)
      g[i][j] = 0;

    double k[4] = {u[i-1], p[i-1], u[i], p[i]};

    for (int j = 0; j < 4; j++)
      for (int l = 0; l < 4; l++)
        g[i][j] += ax[j][l] * k[l];
  }

  memory->destroy(p);
  memory->destroy(b);
  memory->destroy(bprime);
  memory->destroy(dprime);
}

/* ----------------------------------------------------------------------
   compute bicubic spline coefficients
------------------------------------------------------------------------- */

void PairMesoCNT::spline_coeff(double **data, double ****coeff,
                double dx, double dy, int size)
{
  double **u = data;
  double ****g = coeff;
  int n = size;

  double d,*bprime,*dprime,**p,**q,**s,**b;
  memory->create(p,n,n,"pair:p");
  memory->create(q,n,n,"pair:q");
  memory->create(s,n,n,"pair:s");
  memory->create(b,n,n,"pair:b");
  memory->create(bprime,n,"pair:bprime");
  memory->create(dprime,n,"pair:dprime");

  double dx_inv = 1.0 / dx;
  double dy_inv = 1.0 / dy;
  double dxsq_inv = dx_inv * dx_inv;
  double dysq_inv = dy_inv * dy_inv;
  double dxcb_inv = dx_inv * dxsq_inv;
  double dycb_inv = dy_inv * dysq_inv;

  double ax[4][4] =
  {
    {1, 0, 0, 0},
    {0, 1, 0, 0},
    {-3*dxsq_inv, -2*dx_inv, 3*dxsq_inv, -dx_inv},
    {2*dxcb_inv, dxsq_inv, -2*dxcb_inv, dxsq_inv}
  };
  double ay[4][4] =
  {
    {1, 0, 0, 0},
    {0, 1, 0, 0},
    {-3*dysq_inv, -2*dy_inv, 3*dysq_inv, -dy_inv},
    {2*dycb_inv, dysq_inv, -2*dycb_inv, dysq_inv}
  };

  // compute finite difference derivatives at boundaries

  for (int i = 0; i < n; i++) {
    p[0][i] = (u[1][i] - u[0][i]) * dx_inv;
    p[n-1][i] = (u[n-1][i] - u[n-2][i]) * dx_inv;
  }

  for (int i = 0; i < n; i++) {
    q[i][0] = (u[i][1] - u[i][0]) * dy_inv;
    q[i][n-1] = (u[i][n-1] - u[i][n-2]) * dy_inv;
  }

  s[0][0] = (p[0][1] - p[0][0]) * dy_inv;
  s[0][n-1] = (p[0][n-1] - p[0][n-2]) * dy_inv;
  s[n-1][0] = (p[n-1][1] - p[n-1][0]) * dy_inv;
  s[n-1][n-1] = (p[n-1][n-1] - p[n-1][n-2]) * dy_inv;

  // compute derivatives inside domain

  // sweep in x

  for (int i = 1; i < n-1; i++) {
    if (i > 1) b[i][i-1] = dx;
    b[i][i] = 4 * dx;
    if (i < n-2) b[i][i+1] = dx;
  }
  bprime[1] = b[1][1];
  for (int i = 2; i < n-1; i++)
    bprime[i] = b[i][i] - b[i][i-1]*b[i-1][i]/bprime[i-1];

  // compute p

  for (int j = 0; j < n; j++) {
    for (int i = 1; i < n-1; i++) {
      d = 3 * (u[i+1][j] - u[i-1][j]);
      if (i == 1) d -= dx * p[i-1][j];
      if (i == n-2) d -= dx * p[i+1][j];
      dprime[i] = d;
      if (i != 1) dprime[i] -= b[i][i-1] * dprime[i-1] / bprime[i-1];
    }

    p[n-2][j] = dprime[n-2] / bprime[n-2];
    for (int i = n-3; i > 0; i--)
      p[i][j] = (dprime[i] - b[i][i+1]*p[i+1][j]) / bprime[i];
  }

  // compute s

  for (int j = 0; j < n; j += n-1) {
    for (int i = 1; i < n-1; i++) {
      d = 3 * (q[i+1][j] - q[i-1][j]);
      if (i == 1) d -= dx * s[i-1][j];
      if (i == n-2) d -= dx * s[i+1][j];
      dprime[i] = d;
      if (i != 1) dprime[i] -= b[i][i-1] * dprime[i-1] / bprime[i-1];
    }

    s[n-2][j] = dprime[n-2] / bprime[n-2];
    for (int i = n-3; i > 0; i--)
      s[i][j] = (dprime[i] - b[i][i+1]*s[i+1][j]) / bprime[i];
  }

  // sweep in y

  for (int i = 1; i < n-1; i++) {
    if (i > 1) b[i][i-1] = dy;
    b[i][i] = 4 * dy;
    if (i < n-2) b[i][i+1] = dy;
  }
  bprime[1] = b[1][1];
  for (int i = 2; i < n-1; i++)
    bprime[i] = b[i][i] - b[i][i-1]*b[i-1][i]/bprime[i-1];

  // compute q

  for (int i = 0; i < n; i++) {
    for (int j = 1; j < n-1; j++) {
      d = 3 * (u[i][j+1] - u[i][j-1]);
      if (j == 1) d -= dy * q[i][j-1];
      if (j == n-2) d -= dy * q[i][j+1];
      dprime[j] = d;
      if (j != 1) dprime[j] -= b[j][j-1] * dprime[j-1] / bprime[j-1];
    }

    q[i][n-2] = dprime[n-2] / bprime[n-2];
    for (int j = n-3; j > 0; j--)
      q[i][j] = (dprime[j] - b[j][j+1]*q[i][j+1]) / bprime[j];
  }

  // compute s

  for (int i = 0; i < n; i++) {
    for (int j = 1; j < n-1; j++) {
      d = 3 * (p[i][j+1] - p[i][j-1]);
      if (j == 1) d -= dy * s[i][j-1];
      if (j == n-2) d -= dy * s[i][j+1];
      dprime[j] = d;
      if (j != 1) dprime[j] -= b[j][j-1] * dprime[j-1] / bprime[j-1];
    }

    s[i][n-2] = dprime[n-2] / bprime[n-2];
    for (int j = n-3; j > 0; j--)
      s[i][j] = (dprime[j] - b[j][j+1]*s[i][j+1]) / bprime[j];
  }

  for (int i = 1; i < n; i++)
    for (int j = 1; j < n; j++) {
      for (int l = 0; l < 4; l++)
        for (int m = 0; m < 4; m++)
                g[i][j][l][m] = 0;

      double k[4][4] =
      {
        {u[i-1][j-1], q[i-1][j-1], u[i-1][j], q[i-1][j]},
        {p[i-1][j-1], s[i-1][j-1], p[i-1][j], s[i-1][j]},
        {u[i][j-1], q[i][j-1], u[i][j], q[i][j]},
        {p[i][j-1], s[i][j-1], p[i][j], s[i][j]}
      };

      for (int l = 0; l < 4; l++)
        for (int m = 0; m < 4; m++)
          for (int n = 0; n < 4; n++)
                  for (int o = 0; o < 4; o++)
                    g[i][j][l][m] += ax[l][n] * k[n][o] * ay[m][o];
    }

  memory->destroy(p);
  memory->destroy(q);
  memory->destroy(s);
  memory->destroy(b);
  memory->destroy(bprime);
  memory->destroy(dprime);
}


/* ----------------------------------------------------------------------
   cubic spline evaluation
------------------------------------------------------------------------- */

double PairMesoCNT::spline(double x, double xstart, double dx,
                double **coeff, int coeff_size)
{
  int i = ceil((x - xstart)/dx);

  // linear extrapolation

  if (i < 1) {
    return coeff[1][0] + coeff[1][1]*(x - xstart);

  // constant extrapolation

  } else if (i > coeff_size-1) {
    i = coeff_size - 1;
    x = xstart + (coeff_size-1)*dx;
  }

  // cubic interpolation

  double xlo = xstart + (i-1)*dx;
  double xbar = x - xlo;

  return coeff[i][0]
          + xbar*(coeff[i][1] + xbar*(coeff[i][2] + xbar*coeff[i][3]));
}

/* ----------------------------------------------------------------------
   cubic spline derivative
------------------------------------------------------------------------- */

double PairMesoCNT::dspline(double x, double xstart, double dx,
                double **coeff, int coeff_size)
{
  int i = ceil((x - xstart)/dx);

  // constant extrapolation

  if (i < 1) {
    return coeff[1][1];

  // constant extrapolation

  } else if (i > coeff_size-1) {
    i = coeff_size - 1;
    x = xstart + (coeff_size-1)*dx;
  }

  // cubic interpolation

  double xlo = xstart + (i-1)*dx;
  double xbar = x - xlo;

  return coeff[i][1] + xbar*(2*coeff[i][2] + 3*xbar*coeff[i][3]);
}

/* ----------------------------------------------------------------------
   bicubic spline evaluation
------------------------------------------------------------------------- */

double PairMesoCNT::spline(double x, double y,
                double xstart, double ystart,
                double dx, double dy,
                double ****coeff, int coeff_size)
{
  int i = ceil((x - xstart)/dx);
  int j = ceil((y - ystart)/dy);

  // constant extrapolation

  if (i < 1) {
    i = 1;
    x = xstart;
  } else if (i > coeff_size-1) {
    i = coeff_size - 1;
    x = xstart + (coeff_size-1)*dx;
  }

  if (j < 1) {
    j = 1;
    y = ystart;
  } else if (j > coeff_size-1) {
    j = coeff_size - 1;
    y = ystart + (coeff_size-1)*dy;
  }

  // cubic interpolation

  double xlo = xstart + (i-1)*dx;
  double ylo = ystart + (j-1)*dy;
  double xbar = x - xlo;
  double ybar = y - ylo;

  double y0 = coeff[i][j][0][0]
          + ybar*(coeff[i][j][0][1]
          + ybar*(coeff[i][j][0][2]
          + ybar*(coeff[i][j][0][3])));
  double y1 = coeff[i][j][1][0]
          + ybar*(coeff[i][j][1][1]
          + ybar*(coeff[i][j][1][2]
          + ybar*(coeff[i][j][1][3])));
  double y2 = coeff[i][j][2][0]
          + ybar*(coeff[i][j][2][1]
          + ybar*(coeff[i][j][2][2]
          + ybar*(coeff[i][j][2][3])));
  double y3 = coeff[i][j][3][0]
          + ybar*(coeff[i][j][3][1]
          + ybar*(coeff[i][j][3][2]
          + ybar*(coeff[i][j][3][3])));

  return y0 + xbar*(y1 + xbar*(y2 + xbar*y3));
}

/* ----------------------------------------------------------------------
   bicubic spline partial x derivative
------------------------------------------------------------------------- */

double PairMesoCNT::dxspline(double x, double y,
                double xstart, double ystart,
                double dx, double dy,
                double ****coeff, int coeff_size)
{
  int i = ceil((x - xstart)/dx);
  int j = ceil((y - ystart)/dy);

  // constant extrapolation

  if (i < 1) {
    i = 1;
    x = xstart;
  } else if (i > coeff_size-1) {
    i = coeff_size - 1;
    x = xstart + (coeff_size-1)*dx;
  }

  if (j < 1) {
    j = 1;
    y = ystart;
  } else if (j > coeff_size-1) {
    j = coeff_size - 1;
    y = ystart + (coeff_size-1)*dy;
  }

  // cubic interpolation

  double xlo = xstart + (i-1)*dx;
  double ylo = ystart + (j-1)*dy;
  double xbar = x - xlo;
  double ybar = y - ylo;

  double y1 = coeff[i][j][1][0]
          + ybar*(coeff[i][j][1][1]
          + ybar*(coeff[i][j][1][2]
          + ybar*(coeff[i][j][1][3])));
  double y2 = coeff[i][j][2][0]
          + ybar*(coeff[i][j][2][1]
          + ybar*(coeff[i][j][2][2]
          + ybar*(coeff[i][j][2][3])));
  double y3 = coeff[i][j][3][0]
          + ybar*(coeff[i][j][3][1]
          + ybar*(coeff[i][j][3][2]
          + ybar*(coeff[i][j][3][3])));

  return y1 + xbar*(2*y2 + 3*xbar*y3);
}

/* ----------------------------------------------------------------------
   bicubic spline partial y derivative
------------------------------------------------------------------------- */

double PairMesoCNT::dyspline(double x, double y,
                double xstart, double ystart,
                double dx, double dy,
                double ****coeff, int coeff_size)
{
  int i = ceil((x - xstart)/dx);
  int j = ceil((y - ystart)/dy);

  // constant extrapolation

  if (i < 1) {
    i = 1;
    x = xstart;
  } else if (i > coeff_size-1) {
    i = coeff_size - 1;
    x = xstart + (coeff_size-1)*dx;
  }

  if (j < 1) {
    j = 1;
    y = ystart;
  } else if (j > coeff_size-1) {
    j = coeff_size - 1;
    y = ystart + (coeff_size-1)*dy;
  }

  // cubic interpolation

  double xlo = xstart + (i-1)*dx;
  double ylo = ystart + (j-1)*dy;
  double xbar = x - xlo;
  double ybar = y - ylo;

  double y0 = coeff[i][j][0][1]
          + ybar*(2*coeff[i][j][0][2]
          + 3*ybar*coeff[i][j][0][3]);
  double y1 = coeff[i][j][1][1]
          + ybar*(2*coeff[i][j][1][2]
          + 3*ybar*coeff[i][j][1][3]);
  double y2 = coeff[i][j][2][1]
          + ybar*(2*coeff[i][j][2][2]
          + 3*ybar*coeff[i][j][2][3]);
  double y3 = coeff[i][j][3][1]
          + ybar*(2*coeff[i][j][3][2]
          + 3*ybar*coeff[i][j][3][3]);

  return y0 + xbar*(y1 + xbar*(y2 + xbar*y3));
}

/* ----------------------------------------------------------------------
   compute local geometric parameters
------------------------------------------------------------------------- */

void PairMesoCNT::geometry(const double *r1, const double *r2,
                const double *p1, const double *p2, const double *qe,
    double *p, double *m, double *param, double **basis)
{
  double r[3],delr[3],l[3],rbar[3],pbar[3],delrbar[3];
  double psil[3],psim[3],dell_psim[3],delpsil_m[3];
  double delr1[3],delr2[3],delp1[3],delp2[3],delpqe[3];

  double *ex = basis[0];
  double *ey = basis[1];
  double *ez = basis[2];

  add3(r1,r2,r);
  scale3(0.5,r);
  add3(p1,p2,p);
  scale3(0.5,p);

  sub3(p,r,delr);

  sub3(r2,r1,l);
  norm3(l);
  sub3(p2,p1,m);
  norm3(m);

  double psi = dot3(l,m);
  if (psi > 1.0) psi = 1.0;
  else if (psi < -1.0) psi = -1.0;
  double denom = 1.0 - psi*psi;

  copy3(l,psil);
  scale3(psi,psil);
  copy3(m,psim);
  scale3(psi,psim);

  double rhoe,etae,taur,taup;
  if (qe) {
    sub3(p,qe,delpqe);
    rhoe = dot3(delpqe,m);
  } else rhoe = 0;

  // parallel case

  if (denom < SWITCH) {
    taur = dot3(delr,l) - rhoe*psi;
    taup = -rhoe;
    etae = 0;

  // non-parallel case

  } else {
    double frac = 1.0 / denom;
    sub3(l,psim,dell_psim);
    sub3(psil,m,delpsil_m);
    taur = dot3(delr,dell_psim) * frac;
    taup = dot3(delr,delpsil_m) * frac;
    etae = -rhoe - taup;
  }

  scaleadd3(taur,l,r,rbar);
  scaleadd3(taup,m,p,pbar);
  sub3(pbar,rbar,delrbar);

  double h = len3(delrbar);

  copy3(delrbar,ex);
  copy3(l,ez);
  scale3(1.0/h,ex);
  cross3(ez,ex,ey);

  double alpha;
  alpha = (dot3(m,ey) < 0) ? acos(psi) : MY_2PI - acos(psi);

  sub3(r1,rbar,delr1);
  sub3(r2,rbar,delr2);
  sub3(p1,pbar,delp1);
  sub3(p2,pbar,delp2);
  double xi1 = dot3(delr1,l);
  double xi2 = dot3(delr2,l);
  double eta1 = dot3(delp1,m);
  double eta2 = dot3(delp2,m);

  param[0] = h;
  param[1] = alpha;
  param[2] = xi1;
  param[3] = xi2;
  param[4] = eta1;
  param[5] = eta2;
  param[6] = etae;
}


/* ----------------------------------------------------------------------
   weight for substitute CNT chain
------------------------------------------------------------------------- */

void PairMesoCNT::weight(const double *r1, const double *r2,
                                     const double *p1, const double *p2, double &w,
                         double *dr1_w, double *dr2_w,
                         double *dp1_w, double *dp2_w)
{
  double dr,dp,rhoc,rhomin,rho,frac,arg,factor;
  double r[3],p[3];
  double dr_rho[3],dr_rhoc[3],dp_rhoc[3];

  add3(r1,r2,r);
  add3(p1,p2,p);
  scale3(0.5,r);
  scale3(0.5,p);

  dr = sqrt(0.25*distsq3(r1,r2) + rsq);
  dp = sqrt(0.25*distsq3(p1,p2) + rsq);
  rhoc = dr + dp + rc;
  rhomin = 20.0 * ang;
  rho = sqrt(distsq3(r,p));

  frac = 1.0 / (rhoc - rhomin);
  arg = frac * (rho - rhomin);
  w = s(arg);

  if (w == 0.0 || w == 1.0) {
    zero3(dr1_w);
    zero3(dr2_w);
    zero3(dp1_w);
    zero3(dp2_w);
  } else {
    factor = ds(arg) * frac;

    sub3(r,p,dr_rho);
    sub3(r1,r2,dr_rhoc);
    sub3(p1,p2,dp_rhoc);
    scale3(0.5/rho,dr_rho);
    scale3(0.25/dr,dr_rhoc);
    scale3(0.25/dp,dp_rhoc);

    scaleadd3(-arg,dr_rhoc,dr_rho,dr1_w);
    scaleadd3(arg,dr_rhoc,dr_rho,dr2_w);
    negate3(dr_rho);
    scaleadd3(-arg,dp_rhoc,dr_rho,dp1_w);
    scaleadd3(arg,dp_rhoc,dr_rho,dp2_w);
    scale3(factor,dr1_w);
    scale3(factor,dr2_w);
    scale3(factor,dp1_w);
    scale3(factor,dp2_w);
  }
}

/* ----------------------------------------------------------------------
   forces for infinite CNT case
------------------------------------------------------------------------- */

void PairMesoCNT::finf(const double *param, double &evdwl, double **f)
{
  double h = param[0] * ang_inv;
  double alpha = param[1];
  double xi1 = param[2] * ang_inv;
  double xi2 = param[3] * ang_inv;

  double sin_alpha = sin(alpha);
  double sin_alphasq = sin_alpha * sin_alpha;

  // parallel case

  if (sin_alphasq < SWITCH) {
    double ubar = spline(h,hstart_uinf,delh_uinf,uinf_coeff,uinf_points);
    double delxi = xi2 - xi1;
    f[0][0] = 0.5 * delxi
            * dspline(h,hstart_uinf,delh_uinf,uinf_coeff,uinf_points)
            * funit;
    f[1][0] = f[0][0];
    f[0][1] = 0;
    f[1][1] = 0;
    f[0][2] = ubar * funit;
    f[1][2] = -f[0][2];
    evdwl = ubar * delxi * eunit;

  // non-parallel case

  } else {
    double sin_alpha_inv = 1.0 / sin_alpha;
    double sin_alphasq_inv = sin_alpha_inv * sin_alpha_inv;
    double cos_alpha = cos(alpha);
    double cot_alpha = cos_alpha * sin_alpha_inv;

    double omega = 1.0 / (1.0 - comega*sin_alphasq);
    double c1 = omega * sin_alpha;
    double c1_inv = 1.0 / c1;
    double domega = 2 * comega * cos_alpha * c1 * omega;

    double gamma_orth =
            spline(h,hstart_gamma,delh_gamma,gamma_coeff,gamma_points);
    double dgamma_orth =
            dspline(h,hstart_gamma,delh_gamma,gamma_coeff,gamma_points);
    double gamma = 1.0 + (gamma_orth - 1.0)*sin_alphasq;
    double gamma_inv = 1.0 / gamma;
    double dalpha_gamma = 2 * (gamma_orth - 1) * sin_alpha * cos_alpha;
    double dh_gamma = dgamma_orth * sin_alphasq;

    double zeta1 = xi1 * c1;
    double zeta2 = xi2 * c1;

    double smooth = s5((h-d_ang-delta1)/(delta2-delta1));
    double dsmooth = ds5((h-d_ang-delta1)/(delta2-delta1));
    double g = d_ang + delta2;
    double hsq = h * h;

    double zetaminbar;
    if (h >= g) zetaminbar = 0;
    else zetaminbar = sqrt(g*g - hsq);
    double zetamin = smooth * zetaminbar;
    double zetamax = sqrt(cutoffsq_ang - hsq);

    double dzetaminbar;
    if (h >= g) dzetaminbar = 0;
    else dzetaminbar = -h / zetaminbar;
    double dzetamin =
            dzetaminbar*smooth + zetaminbar*dsmooth/(delta2-delta1);
    double dzetamax = -h / zetamax;

    double zeta_range_inv = 1.0 / (zetamax - zetamin);
    double delzeta1 = fabs(zeta1) - zetamin;
    double delzeta2 = fabs(zeta2) - zetamin;

    double psi1 = delzeta1 * zeta_range_inv;
    double psi2 = delzeta2 * zeta_range_inv;

    double phi1 = spline(h,psi1,hstart_phi,psistart_phi,
                  delh_phi,delpsi_phi,phi_coeff,phi_points);
    double dh_phibar1 = dxspline(h,psi1,hstart_phi,psistart_phi,
                  delh_phi,delpsi_phi,phi_coeff,phi_points);
    double dpsi_phibar1 = dyspline(h,psi1,hstart_phi,psistart_phi,
                  delh_phi,delpsi_phi,phi_coeff,phi_points);
    double phi2 = spline(h,psi2,hstart_phi,psistart_phi,
                  delh_phi,delpsi_phi,phi_coeff,phi_points);
    double dh_phibar2 = dxspline(h,psi2,hstart_phi,psistart_phi,
                  delh_phi,delpsi_phi,phi_coeff,phi_points);
    double dpsi_phibar2 = dyspline(h,psi2,hstart_phi,psistart_phi,
                  delh_phi,delpsi_phi,phi_coeff,phi_points);

    double dzeta_range = dzetamax - dzetamin;
    double dh_psi1 = -zeta_range_inv * (dzetamin + dzeta_range*psi1);
    double dh_psi2 = -zeta_range_inv * (dzetamin + dzeta_range*psi2);
    double dh_phi1 = dh_phibar1 + dpsi_phibar1*dh_psi1;
    double dh_phi2 = dh_phibar2 + dpsi_phibar2*dh_psi2;

    double dzeta_phi1 = dpsi_phibar1 * zeta_range_inv;
    double dzeta_phi2 = dpsi_phibar2 * zeta_range_inv;

    if (zeta1 < 0) {
      phi1 *= -1;
      dh_phi1 *= -1;
    }

    if (zeta2 < 0) {
      phi2 *= -1;
      dh_phi2 *= -1;
    }

    double deldzeta_phi = dzeta_phi2 - dzeta_phi1;

    double c2 = gamma * c1_inv;
    double u = c2 * (phi2 - phi1);
    double c3 = u * gamma_inv;

    double dh_u = dh_gamma*c3 + c2*(dh_phi2 - dh_phi1);
    double dalpha_u = dalpha_gamma*c3
            + c1_inv*(domega*sin_alpha + omega*cos_alpha)
            * (gamma*(xi2*dzeta_phi2 - xi1*dzeta_phi1) - u);

    double lr_inv = 1.0 / (xi2 - xi1);
    double cx = h * gamma * sin_alphasq_inv * deldzeta_phi;
    double cy = gamma * cot_alpha * deldzeta_phi;

    f[0][0] = lr_inv * (xi2*dh_u - cx) * funit;
    f[1][0] = lr_inv * (-xi1*dh_u + cx) * funit;
    f[0][1] = lr_inv * (dalpha_u - xi2*cy) * funit;
    f[1][1] = lr_inv * (-dalpha_u + xi1*cy) * funit;
    f[0][2] = gamma * dzeta_phi1 * funit;
    f[1][2] = -gamma * dzeta_phi2 * funit;
    evdwl = u * eunit;
  }
}

/* ----------------------------------------------------------------------
   forces for semi-infinite CNT case
------------------------------------------------------------------------- */

void PairMesoCNT::fsemi(const double *param, double &evdwl,
                        double &fend, double **f)
{
  double h = param[0] * ang_inv;
  double alpha = param[1];
  double xi1 = param[2] * ang_inv;
  double xi2 = param[3] * ang_inv;
  double etae = param[6] * ang_inv;

  double sin_alpha = sin(alpha);
  double sin_alphasq = sin_alpha * sin_alpha;
  double cos_alpha = cos(alpha);

  double omega = 1.0 / (1.0 - comega*sin_alphasq);
  double omegasq = omega * omega;
  double domega = 2 * comega * sin_alpha * cos_alpha * omegasq;

  double theta = 1.0 - ctheta*sin_alphasq;
  double dtheta = -2 * ctheta * sin_alpha * cos_alpha;

  double c1 = omega * sin_alpha;
  double c1sq = c1 * c1;
  double c2 = theta * etae;

  double gamma_orth = spline(h,hstart_gamma,delh_gamma,
                             gamma_coeff,gamma_points);
  double dgamma_orth = dspline(h,hstart_gamma,delh_gamma,
                               gamma_coeff,gamma_points);
  double gamma = 1.0 + (gamma_orth - 1)*sin_alphasq;
  double gamma_inv = 1.0 / gamma;
  double dalpha_gamma = 2 * (gamma_orth - 1) * sin_alpha * cos_alpha;
  double dh_gamma = dgamma_orth * sin_alphasq;

  double delxi = (xi2 - xi1) / (QUADRATURE - 1);
  double c3 = delxi * gamma;

  double jh = 0;
  double jh1 = 0;
  double jh2 = 0;
  double jxi = 0;
  double jxi1 = 0;
  double ubar = 0;

  for (int i = 0; i < QUADRATURE; i++) {
    double xibar = xi1 + i*delxi;
    double g = xibar * c1;
    double hbar = sqrt(h*h + g*g);
    double thetabar = xibar*cos_alpha - c2;

    double c = 1.0;
    if (i == 0 || i == QUADRATURE-1) c = 0.5;

    double u = c * spline(hbar,thetabar,hstart_usemi,xistart_usemi,
                          delh_usemi,delxi_usemi,usemi_coeff,usemi_points);
    double uh;
    if (hbar == 0) uh = 0;
    else uh = c / hbar * dxspline(hbar,thetabar,hstart_usemi,xistart_usemi,
                                  delh_usemi,delxi_usemi,usemi_coeff,usemi_points);
    double uxi = c * dyspline(hbar,thetabar,hstart_usemi,xistart_usemi,
                              delh_usemi,delxi_usemi,usemi_coeff,usemi_points);

    double uh1 = xibar * uh;
    jh += uh;
    jh1 += uh1;
    jh2 += xibar * uh1;
    jxi += uxi;
    jxi1 += xibar * uxi;
    ubar += u;
  }

  jh *= c3;
  jh1 *= c3;
  jh2 *= c3;
  jxi *= c3;
  jxi1 *= c3;
  ubar *= c3;

  double c4 = gamma_inv * ubar;
  double dh_ubar = dh_gamma*c4 + h*jh;
  double dalpha_ubar = dalpha_gamma*c4
    + c1*(domega*sin_alpha + omega*cos_alpha)*jh2
    - sin_alpha*jxi1 - dtheta*etae*jxi;

  double cx = h * (omegasq*jh1 + cos_alpha*ctheta*jxi);
  double cy = sin_alpha * (cos_alpha*omegasq*jh1 + (ctheta-1)*jxi);
  double cz1 = c1sq*jh1 + cos_alpha*jxi;
  double cz2 = c1sq*jh2 + cos_alpha*jxi1;

  double l_inv = 1.0 / (xi2 - xi1);
  f[0][0] = l_inv * (xi2*dh_ubar - cx) * funit;
  f[1][0] = l_inv * (cx - xi1*dh_ubar) * funit;
  f[0][1] = l_inv * (dalpha_ubar - xi2*cy) * funit;
  f[1][1] = l_inv * (xi1*cy - dalpha_ubar) * funit;
  f[0][2] = l_inv * (cz2 + ubar - xi2*cz1) * funit;
  f[1][2] = l_inv * (xi1*cz1 - cz2 - ubar) * funit;
  evdwl = ubar * eunit;

  fend = theta * jxi * funit;
}
