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fix_rigid.cpp
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Wed, Jun 26, 17:31

fix_rigid.cpp
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/* ----------------------------------------------------------------------
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.
------------------------------------------------------------------------- */
#include "math.h"
#include "stdio.h"
#include "string.h"
#include "fix_rigid.h"
#include "atom.h"
#include "domain.h"
#include "update.h"
#include "respa.h"
#include "modify.h"
#include "group.h"
#include "comm.h"
#include "force.h"
#include "output.h"
#include "memory.h"
#include "error.h"
using namespace LAMMPS_NS;
#define TOLERANCE 1.0e-6
#define EPSILON 1.0e-7
#define MAXJACOBI 50
#define MIN(A,B) ((A) < (B)) ? (A) : (B)
#define MAX(A,B) ((A) > (B)) ? (A) : (B)
/* ---------------------------------------------------------------------- */
FixRigid::FixRigid(LAMMPS *lmp, int narg, char **arg) :
Fix(lmp, narg, arg)
{
int i,ibody;
rigid_flag = 1;
virial_flag = 1;
// perform initial allocation of atom-based arrays
// register with Atom class
body = NULL;
displace = NULL;
grow_arrays(atom->nmax);
atom->add_callback(0);
// parse command-line args
// set nbody and body[i] for each atom
if (narg < 4) error->all("Illegal fix rigid command");
// single rigid body
// nbody = 1
// all atoms in fix group are part of body
if (strcmp(arg[3],"single") == 0) {
if (narg != 4) error->all("Illegal fix rigid command");
nbody = 1;
int *mask = atom->mask;
int nlocal = atom->nlocal;
for (i = 0; i < nlocal; i++) {
body[i] = -1;
if (mask[i] & groupbit) body[i] = 0;
}
// each molecule in fix group is a rigid body
// maxmol = largest molecule #
// ncount = # of atoms in each molecule (have to sum across procs)
// nbody = # of non-zero ncount values
// use nall as incremented ptr to set body[] values for each atom
} else if (strcmp(arg[3],"molecule") == 0) {
if (narg != 4) error->all("Illegal fix rigid command");
if (atom->molecular == 0)
error->all("Must use a molecular atom style with fix rigid molecule");
int *mask = atom->mask;
int *molecule = atom->molecule;
int nlocal = atom->nlocal;
int maxmol = -1;
for (i = 0; i < nlocal; i++)
if (mask[i] & groupbit) maxmol = MAX(maxmol,molecule[i]);
int itmp;
MPI_Allreduce(&maxmol,&itmp,1,MPI_INT,MPI_MAX,world);
maxmol = itmp + 1;
int *ncount = new int[maxmol];
for (i = 0; i < maxmol; i++) ncount[i] = 0;
for (i = 0; i < nlocal; i++)
if (mask[i] & groupbit) ncount[molecule[i]]++;
int *nall = new int[maxmol];
MPI_Allreduce(ncount,nall,maxmol,MPI_INT,MPI_SUM,world);
nbody = 0;
for (i = 0; i < maxmol; i++)
if (nall[i]) nall[i] = nbody++;
else nall[i] = -1;
for (i = 0; i < nlocal; i++) {
body[i] = -1;
if (mask[i] & groupbit) body[i] = nall[molecule[i]];
}
delete [] ncount;
delete [] nall;
// each listed group is a rigid body
// check if all listed groups exist
// an atom must belong to fix group and listed group to be in rigid body
// error if atom belongs to more than 1 rigid body
} else if (strcmp(arg[3],"group") == 0) {
nbody = narg-4;
if (nbody <= 0) error->all("Illegal fix rigid command");
int *igroups = new int[nbody];
for (ibody = 0; ibody < nbody; ibody++) {
igroups[ibody] = group->find(arg[ibody+4]);
if (igroups[ibody] == -1)
error->all("Could not find fix rigid group ID");
}
int *mask = atom->mask;
int nlocal = atom->nlocal;
int flag = 0;
for (i = 0; i < nlocal; i++) {
body[i] = -1;
if (mask[i] & groupbit)
for (ibody = 0; ibody < nbody; ibody++)
if (mask[i] & group->bitmask[igroups[ibody]]) {
if (body[i] >= 0) flag = 1;
body[i] = ibody;
}
}
int flagall;
MPI_Allreduce(&flag,&flagall,1,MPI_INT,MPI_SUM,world);
if (flagall)
error->all("One or more atoms belong to multiple rigid bodies");
delete [] igroups;
} else error->all("Illegal fix rigid command");
// error check on nbody
if (nbody == 0) error->all("No rigid bodies defined");
// create all nbody-length arrays
nrigid = (int *) memory->smalloc(nbody*sizeof(int),"rigid:nrigid");
masstotal = (double *)
memory->smalloc(nbody*sizeof(double),"rigid:masstotal");
xcm = memory->create_2d_double_array(nbody,3,"rigid:xcm");
vcm = memory->create_2d_double_array(nbody,3,"rigid:vcm");
fcm = memory->create_2d_double_array(nbody,3,"rigid:fcm");
inertia = memory->create_2d_double_array(nbody,3,"rigid:inertia");
ex_space = memory->create_2d_double_array(nbody,3,"rigid:ex_space");
ey_space = memory->create_2d_double_array(nbody,3,"rigid:ey_space");
ez_space = memory->create_2d_double_array(nbody,3,"rigid:ez_space");
angmom = memory->create_2d_double_array(nbody,3,"rigid:angmom");
omega = memory->create_2d_double_array(nbody,3,"rigid:omega");
torque = memory->create_2d_double_array(nbody,3,"rigid:torque");
quat = memory->create_2d_double_array(nbody,4,"rigid:quat");
sum = memory->create_2d_double_array(nbody,6,"rigid:sum");
all = memory->create_2d_double_array(nbody,6,"rigid:all");
// nrigid[n] = # of atoms in Nth rigid body
// error if one or zero atoms
int *ncount = new int[nbody];
for (ibody = 0; ibody < nbody; ibody++) ncount[ibody] = 0;
int nlocal = atom->nlocal;
for (i = 0; i < nlocal; i++)
if (body[i] >= 0) ncount[body[i]]++;
MPI_Allreduce(ncount,nrigid,nbody,MPI_INT,MPI_SUM,world);
delete [] ncount;
for (ibody = 0; ibody < nbody; ibody++)
if (nrigid[ibody] <= 1) error->all("One or zero atoms in rigid body");
// print statistics
int nsum = 0;
for (ibody = 0; ibody < nbody; ibody++) nsum += nrigid[ibody];
if (comm->me == 0) {
if (screen) fprintf(screen,"%d rigid bodies with %d atoms\n",nbody,nsum);
if (logfile) fprintf(logfile,"%d rigid bodies with %d atoms\n",nbody,nsum);
}
// zero fix_rigid virial in case pressure uses it before 1st fix_rigid call
for (int n = 0; n < 6; n++) virial[n] = 0.0;
}
/* ---------------------------------------------------------------------- */
FixRigid::~FixRigid()
{
// unregister callbacks to this fix from Atom class
atom->delete_callback(id,0);
// delete locally stored arrays
memory->sfree(body);
memory->destroy_2d_double_array(displace);
// delete nbody-length arrays
memory->sfree(nrigid);
memory->sfree(masstotal);
memory->destroy_2d_double_array(xcm);
memory->destroy_2d_double_array(vcm);
memory->destroy_2d_double_array(fcm);
memory->destroy_2d_double_array(inertia);
memory->destroy_2d_double_array(ex_space);
memory->destroy_2d_double_array(ey_space);
memory->destroy_2d_double_array(ez_space);
memory->destroy_2d_double_array(angmom);
memory->destroy_2d_double_array(omega);
memory->destroy_2d_double_array(torque);
memory->destroy_2d_double_array(quat);
memory->destroy_2d_double_array(sum);
memory->destroy_2d_double_array(all);
}
/* ---------------------------------------------------------------------- */
int FixRigid::setmask()
{
int mask = 0;
mask |= INITIAL_INTEGRATE;
mask |= FINAL_INTEGRATE;
mask |= INITIAL_INTEGRATE_RESPA;
mask |= FINAL_INTEGRATE_RESPA;
return mask;
}
/* ---------------------------------------------------------------------- */
void FixRigid::init()
{
int i,ibody;
// warn if more than one rigid fix
int count = 0;
for (int i = 0; i < modify->nfix; i++)
if (strcmp(modify->fix[i]->style,"rigid") == 0) count++;
if (count > 1 && comm->me == 0) error->warning("More than one fix rigid");
// error if npt,nph fix comes before rigid fix
for (i = 0; i < modify->nfix; i++) {
if (strcmp(modify->fix[i]->style,"npt") == 0) break;
if (strcmp(modify->fix[i]->style,"nph") == 0) break;
}
if (i < modify->nfix) {
for (int j = i; j < modify->nfix; j++)
if (strcmp(modify->fix[j]->style,"rigid") == 0)
error->all("Rigid fix must come before NPT/NPH fix");
}
// compute rigid contribution to virial every step if fix NPT,NPH exists
pressure_flag = 0;
for (int i = 0; i < modify->nfix; i++) {
if (strcmp(modify->fix[i]->style,"npt") == 0) pressure_flag = 1;
if (strcmp(modify->fix[i]->style,"nph") == 0) pressure_flag = 1;
}
// timestep info
dtv = update->dt;
dtf = 0.5 * update->dt * force->ftm2v;
dtq = 0.5 * update->dt;
if (strcmp(update->integrate_style,"respa") == 0)
step_respa = ((Respa *) update->integrate)->step;
// compute masstotal & center-of-mass of each rigid body
int *type = atom->type;
int *image = atom->image;
double *mass = atom->mass;
double **x = atom->x;
int nlocal = atom->nlocal;
double xprd = domain->xprd;
double yprd = domain->yprd;
double zprd = domain->zprd;
for (ibody = 0; ibody < nbody; ibody++)
for (i = 0; i < 6; i++) sum[ibody][i] = 0.0;
int xbox,ybox,zbox;
double massone;
for (i = 0; i < nlocal; i++) {
if (body[i] < 0) continue;
ibody = body[i];
xbox = (image[i] & 1023) - 512;
ybox = (image[i] >> 10 & 1023) - 512;
zbox = (image[i] >> 20) - 512;
massone = mass[type[i]];
sum[ibody][0] += (x[i][0] + xbox*xprd) * massone;
sum[ibody][1] += (x[i][1] + ybox*yprd) * massone;
sum[ibody][2] += (x[i][2] + zbox*zprd) * massone;
sum[ibody][3] += massone;
}
MPI_Allreduce(sum[0],all[0],6*nbody,MPI_DOUBLE,MPI_SUM,world);
for (ibody = 0; ibody < nbody; ibody++) {
masstotal[ibody] = all[ibody][3];
xcm[ibody][0] = all[ibody][0]/masstotal[ibody];
xcm[ibody][1] = all[ibody][1]/masstotal[ibody];
xcm[ibody][2] = all[ibody][2]/masstotal[ibody];
}
// compute 6 moments of inertia of each body
// dx,dy,dz = coords relative to center-of-mass
for (ibody = 0; ibody < nbody; ibody++)
for (i = 0; i < 6; i++) sum[ibody][i] = 0.0;
double dx,dy,dz;
for (i = 0; i < nlocal; i++) {
if (body[i] < 0) continue;
ibody = body[i];
xbox = (image[i] & 1023) - 512;
ybox = (image[i] >> 10 & 1023) - 512;
zbox = (image[i] >> 20) - 512;
dx = x[i][0] + xbox*xprd - xcm[ibody][0];
dy = x[i][1] + ybox*yprd - xcm[ibody][1];
dz = x[i][2] + zbox*zprd - xcm[ibody][2];
massone = mass[type[i]];
sum[ibody][0] += massone * (dy*dy + dz*dz);
sum[ibody][1] += massone * (dx*dx + dz*dz);
sum[ibody][2] += massone * (dx*dx + dy*dy);
sum[ibody][3] -= massone * dx*dy;
sum[ibody][4] -= massone * dy*dz;
sum[ibody][5] -= massone * dx*dz;
}
MPI_Allreduce(sum[0],all[0],6*nbody,MPI_DOUBLE,MPI_SUM,world);
// inertia = 3 eigenvalues = principal moments of inertia
// ex_space,ey_space,ez_space = 3 eigenvectors = principal axes of rigid body
double **tensor = memory->create_2d_double_array(3,3,"fix_rigid:tensor");
double **evectors = memory->create_2d_double_array(3,3,"fix_rigid:evectors");
int ierror;
double ez0,ez1,ez2;
for (ibody = 0; ibody < nbody; ibody++) {
tensor[0][0] = all[ibody][0];
tensor[1][1] = all[ibody][1];
tensor[2][2] = all[ibody][2];
tensor[0][1] = tensor[1][0] = all[ibody][3];
tensor[1][2] = tensor[2][1] = all[ibody][4];
tensor[0][2] = tensor[2][0] = all[ibody][5];
ierror = jacobi(tensor,inertia[ibody],evectors);
if (ierror) error->all("Insufficient Jacobi rotations for rigid body");
ex_space[ibody][0] = evectors[0][0];
ex_space[ibody][1] = evectors[1][0];
ex_space[ibody][2] = evectors[2][0];
ey_space[ibody][0] = evectors[0][1];
ey_space[ibody][1] = evectors[1][1];
ey_space[ibody][2] = evectors[2][1];
ez_space[ibody][0] = evectors[0][2];
ez_space[ibody][1] = evectors[1][2];
ez_space[ibody][2] = evectors[2][2];
// if any principal moment < scaled EPSILON, set to 0.0
double max;
max = MAX(inertia[ibody][0],inertia[ibody][1]);
max = MAX(max,inertia[ibody][2]);
if (inertia[ibody][0] < EPSILON*max) inertia[ibody][0] = 0.0;
if (inertia[ibody][1] < EPSILON*max) inertia[ibody][1] = 0.0;
if (inertia[ibody][2] < EPSILON*max) inertia[ibody][2] = 0.0;
// enforce 3 evectors as a right-handed coordinate system
// flip 3rd evector if needed
ez0 = ex_space[ibody][1]*ey_space[ibody][2] -
ex_space[ibody][2]*ey_space[ibody][1];
ez1 = ex_space[ibody][2]*ey_space[ibody][0] -
ex_space[ibody][0]*ey_space[ibody][2];
ez2 = ex_space[ibody][0]*ey_space[ibody][1] -
ex_space[ibody][1]*ey_space[ibody][0];
if (ez0*ez_space[ibody][0] + ez1*ez_space[ibody][1] +
ez2*ez_space[ibody][2] < 0.0) {
ez_space[ibody][0] = -ez_space[ibody][0];
ez_space[ibody][1] = -ez_space[ibody][1];
ez_space[ibody][2] = -ez_space[ibody][2];
}
// create initial quaternion
qcreate(evectors,quat[ibody]);
}
// free temporary memory
memory->destroy_2d_double_array(tensor);
memory->destroy_2d_double_array(evectors);
// displace = initial atom coords in basis of principal axes
// set displace = 0.0 for atoms not in any rigid body
for (i = 0; i < nlocal; i++) {
if (body[i] < 0) displace[i][0] = displace[i][1] = displace[i][2] = 0.0;
else {
ibody = body[i];
xbox = (image[i] & 1023) - 512;
ybox = (image[i] >> 10 & 1023) - 512;
zbox = (image[i] >> 20) - 512;
dx = x[i][0] + xbox*xprd - xcm[ibody][0];
dy = x[i][1] + ybox*yprd - xcm[ibody][1];
dz = x[i][2] + zbox*zprd - xcm[ibody][2];
displace[i][0] = dx*ex_space[ibody][0] + dy*ex_space[ibody][1] +
dz*ex_space[ibody][2];
displace[i][1] = dx*ey_space[ibody][0] + dy*ey_space[ibody][1] +
dz*ey_space[ibody][2];
displace[i][2] = dx*ez_space[ibody][0] + dy*ez_space[ibody][1] +
dz*ez_space[ibody][2];
}
}
// test for valid principal moments & axes
// recompute moments of inertia around new axes
// 3 diagonal moments should equal principal moments
// 3 off-diagonal moments should be 0.0
for (ibody = 0; ibody < nbody; ibody++)
for (i = 0; i < 6; i++) sum[ibody][i] = 0.0;
for (i = 0; i < nlocal; i++) {
if (body[i] < 0) continue;
ibody = body[i];
massone = mass[type[i]];
sum[ibody][0] += massone *
(displace[i][1]*displace[i][1] + displace[i][2]*displace[i][2]);
sum[ibody][1] += massone *
(displace[i][0]*displace[i][0] + displace[i][2]*displace[i][2]);
sum[ibody][2] += massone *
(displace[i][0]*displace[i][0] + displace[i][1]*displace[i][1]);
sum[ibody][3] -= massone * displace[i][0]*displace[i][1];
sum[ibody][4] -= massone * displace[i][1]*displace[i][2];
sum[ibody][5] -= massone * displace[i][0]*displace[i][2];
}
MPI_Allreduce(sum[0],all[0],6*nbody,MPI_DOUBLE,MPI_SUM,world);
for (ibody = 0; ibody < nbody; ibody++) {
if (fabs(all[ibody][0]-inertia[ibody][0]) > TOLERANCE ||
fabs(all[ibody][1]-inertia[ibody][1]) > TOLERANCE ||
fabs(all[ibody][2]-inertia[ibody][2]) > TOLERANCE)
error->all("Bad principal moments");
if (fabs(all[ibody][3]) > TOLERANCE ||
fabs(all[ibody][4]) > TOLERANCE ||
fabs(all[ibody][5]) > TOLERANCE)
error->all("Bad principal moments");
}
}
/* ---------------------------------------------------------------------- */
void FixRigid::setup()
{
int i,ibody;
// vcm = velocity of center-of-mass of each rigid body
// fcm = force on center-of-mass of each rigid body
int *type = atom->type;
double **v = atom->v;
double **f = atom->f;
double *mass = atom->mass;
int nlocal = atom->nlocal;
for (ibody = 0; ibody < nbody; ibody++)
for (i = 0; i < 6; i++) sum[ibody][i] = 0.0;
double massone;
for (i = 0; i < nlocal; i++) {
if (body[i] < 0) continue;
ibody = body[i];
massone = mass[type[i]];
sum[ibody][0] += v[i][0] * massone;
sum[ibody][1] += v[i][1] * massone;
sum[ibody][2] += v[i][2] * massone;
sum[ibody][3] += f[i][0];
sum[ibody][4] += f[i][1];
sum[ibody][5] += f[i][2];
}
MPI_Allreduce(sum[0],all[0],6*nbody,MPI_DOUBLE,MPI_SUM,world);
for (ibody = 0; ibody < nbody; ibody++) {
vcm[ibody][0] = all[ibody][0]/masstotal[ibody];
vcm[ibody][1] = all[ibody][1]/masstotal[ibody];
vcm[ibody][2] = all[ibody][2]/masstotal[ibody];
fcm[ibody][0] = all[ibody][3];
fcm[ibody][1] = all[ibody][4];
fcm[ibody][2] = all[ibody][5];
}
// angmom = angular momentum of each rigid body
// torque = torque on each rigid body
int *image = atom->image;
double **x = atom->x;
double xprd = domain->xprd;
double yprd = domain->yprd;
double zprd = domain->zprd;
for (ibody = 0; ibody < nbody; ibody++)
for (i = 0; i < 6; i++) sum[ibody][i] = 0.0;
int xbox,ybox,zbox;
double dx,dy,dz;
for (i = 0; i < nlocal; i++) {
if (body[i] < 0) continue;
ibody = body[i];
xbox = (image[i] & 1023) - 512;
ybox = (image[i] >> 10 & 1023) - 512;
zbox = (image[i] >> 20) - 512;
dx = x[i][0] + xbox*xprd - xcm[ibody][0];
dy = x[i][1] + ybox*yprd - xcm[ibody][1];
dz = x[i][2] + zbox*zprd - xcm[ibody][2];
massone = mass[type[i]];
sum[ibody][0] += dy * massone*v[i][2] - dz * massone*v[i][1];
sum[ibody][1] += dz * massone*v[i][0] - dx * massone*v[i][2];
sum[ibody][2] += dx * massone*v[i][1] - dy * massone*v[i][0];
sum[ibody][3] += dy * f[i][2] - dz * f[i][1];
sum[ibody][4] += dz * f[i][0] - dx * f[i][2];
sum[ibody][5] += dx * f[i][1] - dy * f[i][0];
}
MPI_Allreduce(sum[0],all[0],6*nbody,MPI_DOUBLE,MPI_SUM,world);
for (ibody = 0; ibody < nbody; ibody++) {
angmom[ibody][0] = all[ibody][0];
angmom[ibody][1] = all[ibody][1];
angmom[ibody][2] = all[ibody][2];
torque[ibody][0] = all[ibody][3];
torque[ibody][1] = all[ibody][4];
torque[ibody][2] = all[ibody][5];
}
// set velocities from angmom & omega
// guestimate virial as 2x the set_v contribution
for (ibody = 0; ibody < nbody; ibody++)
omega_from_mq(angmom[ibody],ex_space[ibody],ey_space[ibody],
ez_space[ibody],inertia[ibody],omega[ibody]);
for (int n = 0; n < 6; n++) virial[n] = 0.0;
set_v(1);
for (int n = 0; n < 6; n++) virial[n] *= 2.0;
}
/* ---------------------------------------------------------------------- */
void FixRigid::initial_integrate()
{
double dtfm;
for (int ibody = 0; ibody < nbody; ibody++) {
// update vcm by 1/2 step
dtfm = dtf / masstotal[ibody];
vcm[ibody][0] += dtfm * fcm[ibody][0];
vcm[ibody][1] += dtfm * fcm[ibody][1];
vcm[ibody][2] += dtfm * fcm[ibody][2];
// update xcm by full step
xcm[ibody][0] += dtv * vcm[ibody][0];
xcm[ibody][1] += dtv * vcm[ibody][1];
xcm[ibody][2] += dtv * vcm[ibody][2];
// update angular momentum by 1/2 step
angmom[ibody][0] += dtf * torque[ibody][0];
angmom[ibody][1] += dtf * torque[ibody][1];
angmom[ibody][2] += dtf * torque[ibody][2];
// update quaternion a full step
// returns new normalized quat
// returns ex_space,ey_space,ez_space for new quat
// returns omega at 1/2 step (depends on angmom and quat)
richardson(quat[ibody],omega[ibody],angmom[ibody],inertia[ibody],
ex_space[ibody],ey_space[ibody],ez_space[ibody]);
}
// set coords and velocities if atoms in rigid bodies
// from quarternion and omega
int vflag = 0;
if (pressure_flag || output->next_thermo == update->ntimestep) vflag = 1;
set_xv(vflag);
}
/* ---------------------------------------------------------------------- */
void FixRigid::richardson(double *q, double *w,
double *m, double *moments,
double *ex, double *ey, double *ez)
{
// compute omega at 1/2 step from m at 1/2 step and q at 0
omega_from_mq(m,ex,ey,ez,moments,w);
// full update from dq/dt = 1/2 w q
double wq[4];
multiply(w,q,wq);
double qfull[4];
qfull[0] = q[0] + dtq * wq[0];
qfull[1] = q[1] + dtq * wq[1];
qfull[2] = q[2] + dtq * wq[2];
qfull[3] = q[3] + dtq * wq[3];
normalize(qfull);
// 1st half update from dq/dt = 1/2 w q
double qhalf[4];
qhalf[0] = q[0] + 0.5*dtq * wq[0];
qhalf[1] = q[1] + 0.5*dtq * wq[1];
qhalf[2] = q[2] + 0.5*dtq * wq[2];
qhalf[3] = q[3] + 0.5*dtq * wq[3];
normalize(qhalf);
// udpate ex,ey,ez from qhalf
// re-compute omega at 1/2 step from m at 1/2 step and q at 1/2 step
// recompute wq
exyz_from_q(qhalf,ex,ey,ez);
omega_from_mq(m,ex,ey,ez,moments,w);
multiply(w,qhalf,wq);
// 2nd half update from dq/dt = 1/2 w q
qhalf[0] += 0.5*dtq * wq[0];
qhalf[1] += 0.5*dtq * wq[1];
qhalf[2] += 0.5*dtq * wq[2];
qhalf[3] += 0.5*dtq * wq[3];
normalize(qhalf);
// corrected Richardson update
q[0] = 2.0*qhalf[0] - qfull[0];
q[1] = 2.0*qhalf[1] - qfull[1];
q[2] = 2.0*qhalf[2] - qfull[2];
q[3] = 2.0*qhalf[3] - qfull[3];
normalize(q);
exyz_from_q(q,ex,ey,ez);
}
/* ---------------------------------------------------------------------- */
void FixRigid::final_integrate()
{
int i,ibody;
double dtfm;
// sum forces and torques on atoms in rigid body
int *image = atom->image;
double **x = atom->x;
double **f = atom->f;
int nlocal = atom->nlocal;
double xprd = domain->xprd;
double yprd = domain->yprd;
double zprd = domain->zprd;
int xbox,ybox,zbox;
double dx,dy,dz;
for (ibody = 0; ibody < nbody; ibody++)
for (i = 0; i < 6; i++) sum[ibody][i] = 0.0;
for (i = 0; i < nlocal; i++) {
if (body[i] < 0) continue;
ibody = body[i];
sum[ibody][0] += f[i][0];
sum[ibody][1] += f[i][1];
sum[ibody][2] += f[i][2];
xbox = (image[i] & 1023) - 512;
ybox = (image[i] >> 10 & 1023) - 512;
zbox = (image[i] >> 20) - 512;
dx = x[i][0] + xbox*xprd - xcm[ibody][0];
dy = x[i][1] + ybox*yprd - xcm[ibody][1];
dz = x[i][2] + zbox*zprd - xcm[ibody][2];
sum[ibody][3] += dy*f[i][2] - dz*f[i][1];
sum[ibody][4] += dz*f[i][0] - dx*f[i][2];
sum[ibody][5] += dx*f[i][1] - dy*f[i][0];
}
MPI_Allreduce(sum[0],all[0],6*nbody,MPI_DOUBLE,MPI_SUM,world);
for (ibody = 0; ibody < nbody; ibody++) {
fcm[ibody][0] = all[ibody][0];
fcm[ibody][1] = all[ibody][1];
fcm[ibody][2] = all[ibody][2];
torque[ibody][0] = all[ibody][3];
torque[ibody][1] = all[ibody][4];
torque[ibody][2] = all[ibody][5];
// update vcm by 1/2 step
dtfm = dtf / masstotal[ibody];
vcm[ibody][0] += dtfm * fcm[ibody][0];
vcm[ibody][1] += dtfm * fcm[ibody][1];
vcm[ibody][2] += dtfm * fcm[ibody][2];
// update angular momentum by 1/2 step
angmom[ibody][0] += dtf * torque[ibody][0];
angmom[ibody][1] += dtf * torque[ibody][1];
angmom[ibody][2] += dtf * torque[ibody][2];
}
// set velocities from angmom & omega
for (ibody = 0; ibody < nbody; ibody++)
omega_from_mq(angmom[ibody],ex_space[ibody],ey_space[ibody],
ez_space[ibody],inertia[ibody],omega[ibody]);
int vflag = 0;
if (pressure_flag || output->next_thermo == update->ntimestep) vflag = 1;
set_v(vflag);
}
/* ---------------------------------------------------------------------- */
void FixRigid::initial_integrate_respa(int ilevel, int flag)
{
if (flag) return; // only used by NPT,NPH
dtv = step_respa[ilevel];
dtf = 0.5 * step_respa[ilevel] * force->ftm2v;
dtq = 0.5 * step_respa[ilevel];
if (ilevel == 0) initial_integrate();
else final_integrate();
}
/* ---------------------------------------------------------------------- */
void FixRigid::final_integrate_respa(int ilevel)
{
dtf = 0.5 * step_respa[ilevel] * force->ftm2v;
final_integrate();
}
/* ----------------------------------------------------------------------
count # of degrees-of-freedom removed by fix_rigid for atoms in igroup
------------------------------------------------------------------------- */
int FixRigid::dof(int igroup)
{
int groupbit = group->bitmask[igroup];
// ncount = # of atoms in each rigid body that are also in group
int *mask = atom->mask;
int nlocal = atom->nlocal;
int *ncount = new int[nbody];
for (int ibody = 0; ibody < nbody; ibody++) ncount[ibody] = 0;
for (int i = 0; i < nlocal; i++)
if (body[i] >= 0 && mask[i] & groupbit) ncount[body[i]]++;
int *nall = new int[nbody];
MPI_Allreduce(ncount,nall,nbody,MPI_INT,MPI_SUM,world);
// remove 3N - 6 dof for each rigid body if more than 2 atoms in igroup
// remove 3N - 5 dof for each diatomic rigid body in igroup
int n = 0;
for (int ibody = 0; ibody < nbody; ibody++) {
if (nall[ibody] > 2) n += 3*nall[ibody] - 6;
else if (nall[ibody] == 2) n++;
}
delete [] ncount;
delete [] nall;
return n;
}
/* ----------------------------------------------------------------------
adjust xcm of each rigid body due to box deformation
called by various fixes that change box size/shape
flag = 0/1 means map from box to lamda coords or vice versa
------------------------------------------------------------------------- */
void FixRigid::deform(int flag)
{
if (flag == 0)
for (int ibody = 0; ibody < nbody; ibody++)
domain->x2lamda(xcm[ibody],xcm[ibody]);
else
for (int ibody = 0; ibody < nbody; ibody++)
domain->lamda2x(xcm[ibody],xcm[ibody]);
}
/* ----------------------------------------------------------------------
compute evalues and evectors of 3x3 real symmetric matrix
based on Jacobi rotations
adapted from Numerical Recipes jacobi() function
------------------------------------------------------------------------- */
int FixRigid::jacobi(double **matrix, double *evalues, double **evectors)
{
int i,j,k;
double tresh,theta,tau,t,sm,s,h,g,c,b[3],z[3];
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) evectors[i][j] = 0.0;
evectors[i][i] = 1.0;
}
for (i = 0; i < 3; i++) {
b[i] = evalues[i] = matrix[i][i];
z[i] = 0.0;
}
for (int iter = 1; iter <= MAXJACOBI; iter++) {
sm = 0.0;
for (i = 0; i < 2; i++)
for (j = i+1; j < 3; j++)
sm += fabs(matrix[i][j]);
if (sm == 0.0) return 0;
if (iter < 4) tresh = 0.2*sm/(3*3);
else tresh = 0.0;
for (i = 0; i < 2; i++) {
for (j = i+1; j < 3; j++) {
g = 100.0*fabs(matrix[i][j]);
if (iter > 4 && fabs(evalues[i])+g == fabs(evalues[i])
&& fabs(evalues[j])+g == fabs(evalues[j]))
matrix[i][j] = 0.0;
else if (fabs(matrix[i][j]) > tresh) {
h = evalues[j]-evalues[i];
if (fabs(h)+g == fabs(h)) t = (matrix[i][j])/h;
else {
theta = 0.5*h/(matrix[i][j]);
t = 1.0/(fabs(theta)+sqrt(1.0+theta*theta));
if (theta < 0.0) t = -t;
}
c = 1.0/sqrt(1.0+t*t);
s = t*c;
tau = s/(1.0+c);
h = t*matrix[i][j];
z[i] -= h;
z[j] += h;
evalues[i] -= h;
evalues[j] += h;
matrix[i][j] = 0.0;
for (k = 0; k < i; k++) rotate(matrix,k,i,k,j,s,tau);
for (k = i+1; k < j; k++) rotate(matrix,i,k,k,j,s,tau);
for (k = j+1; k < 3; k++) rotate(matrix,i,k,j,k,s,tau);
for (k = 0; k < 3; k++) rotate(evectors,k,i,k,j,s,tau);
}
}
}
for (i = 0; i < 3; i++) {
evalues[i] = b[i] += z[i];
z[i] = 0.0;
}
}
return 1;
}
/* ----------------------------------------------------------------------
perform a single Jacobi rotation
------------------------------------------------------------------------- */
void FixRigid::rotate(double **matrix, int i, int j, int k, int l,
double s, double tau)
{
double g = matrix[i][j];
double h = matrix[k][l];
matrix[i][j] = g-s*(h+g*tau);
matrix[k][l] = h+s*(g-h*tau);
}
/* ----------------------------------------------------------------------
create quaternion from rotation matrix (evectors)
------------------------------------------------------------------------- */
void FixRigid::qcreate(double **a, double *q)
{
// squares of quaternion components
double q0sq = 0.25 * (a[0][0] + a[1][1] + a[2][2] + 1.0);
double q1sq = q0sq - 0.5 * (a[1][1] + a[2][2]);
double q2sq = q0sq - 0.5 * (a[0][0] + a[2][2]);
double q3sq = q0sq - 0.5 * (a[0][0] + a[1][1]);
// some component must be greater than 1/4 since they sum to 1
// compute other components from it
if (q0sq >= 0.25) {
q[0] = sqrt(q0sq);
q[1] = (a[2][1] - a[1][2]) / (4.0*q[0]);
q[2] = (a[0][2] - a[2][0]) / (4.0*q[0]);
q[3] = (a[1][0] - a[0][1]) / (4.0*q[0]);
} else if (q1sq >= 0.25) {
q[1] = sqrt(q1sq);
q[0] = (a[2][1] - a[1][2]) / (4.0*q[1]);
q[2] = (a[0][1] + a[1][0]) / (4.0*q[1]);
q[3] = (a[2][0] + a[0][2]) / (4.0*q[1]);
} else if (q2sq >= 0.25) {
q[2] = sqrt(q2sq);
q[0] = (a[0][2] - a[2][0]) / (4.0*q[2]);
q[1] = (a[0][1] + a[1][0]) / (4.0*q[2]);
q[2] = (a[1][2] + a[2][1]) / (4.0*q[2]);
} else if (q3sq >= 0.25) {
q[3] = sqrt(q3sq);
q[0] = (a[1][0] - a[0][1]) / (4.0*q[3]);
q[1] = (a[0][2] + a[2][0]) / (4.0*q[3]);
q[2] = (a[1][2] + a[2][1]) / (4.0*q[3]);
} else
error->all("Quaternion creation numeric error");
normalize(q);
}
/* ----------------------------------------------------------------------
quaternion multiply: c = a*b where a = (0,a)
------------------------------------------------------------------------- */
void FixRigid::multiply(double *a, double *b, double *c)
{
c[0] = -(a[0]*b[1] + a[1]*b[2] + a[2]*b[3]);
c[1] = b[0]*a[0] + a[1]*b[3] - a[2]*b[2];
c[2] = b[0]*a[1] + a[2]*b[1] - a[0]*b[3];
c[3] = b[0]*a[2] + a[0]*b[2] - a[1]*b[1];
}
/* ----------------------------------------------------------------------
normalize a quaternion
------------------------------------------------------------------------- */
void FixRigid::normalize(double *q)
{
double norm = 1.0 / sqrt(q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
q[0] *= norm;
q[1] *= norm;
q[2] *= norm;
q[3] *= norm;
}
/* ----------------------------------------------------------------------
compute omega from angular momentum
w = omega = angular velocity in space frame
wbody = angular velocity in body frame
set wbody component to 0.0 if inertia component is 0.0
otherwise body can spin easily around that axis
project space-frame angular momentum onto body axes
and divide by principal moments
------------------------------------------------------------------------- */
void FixRigid::omega_from_mq(double *m, double *ex, double *ey, double *ez,
double *inertia, double *w)
{
double wbody[3];
if (inertia[0] == 0.0) wbody[0] = 0.0;
else wbody[0] = (m[0]*ex[0] + m[1]*ex[1] + m[2]*ex[2]) / inertia[0];
if (inertia[1] == 0.0) wbody[1] = 0.0;
else wbody[1] = (m[0]*ey[0] + m[1]*ey[1] + m[2]*ey[2]) / inertia[1];
if (inertia[2] == 0.0) wbody[2] = 0.0;
else wbody[2] = (m[0]*ez[0] + m[1]*ez[1] + m[2]*ez[2]) / inertia[2];
w[0] = wbody[0]*ex[0] + wbody[1]*ey[0] + wbody[2]*ez[0];
w[1] = wbody[0]*ex[1] + wbody[1]*ey[1] + wbody[2]*ez[1];
w[2] = wbody[0]*ex[2] + wbody[1]*ey[2] + wbody[2]*ez[2];
}
/* ----------------------------------------------------------------------
compute space-frame ex,ey,ez from current quaternion q
ex,ey,ez = space-frame coords of 1st,2nd,3rd principal axis
operation is ex = q' d q = Q d, where d is (1,0,0) = 1st axis in body frame
------------------------------------------------------------------------- */
void FixRigid::exyz_from_q(double *q, double *ex, double *ey, double *ez)
{
ex[0] = q[0]*q[0] + q[1]*q[1] - q[2]*q[2] - q[3]*q[3];
ex[1] = 2.0 * (q[1]*q[2] + q[0]*q[3]);
ex[2] = 2.0 * (q[1]*q[3] - q[0]*q[2]);
ey[0] = 2.0 * (q[1]*q[2] - q[0]*q[3]);
ey[1] = q[0]*q[0] - q[1]*q[1] + q[2]*q[2] - q[3]*q[3];
ey[2] = 2.0 * (q[2]*q[3] + q[0]*q[1]);
ez[0] = 2.0 * (q[1]*q[3] + q[0]*q[2]);
ez[1] = 2.0 * (q[2]*q[3] - q[0]*q[1]);
ez[2] = q[0]*q[0] - q[1]*q[1] - q[2]*q[2] + q[3]*q[3];
}
/* ----------------------------------------------------------------------
set space-frame coords and velocity of each atom in each rigid body
x = Q displace + Xcm, mapped back to periodic box
v = Vcm + (W cross (x - Xcm))
------------------------------------------------------------------------- */
void FixRigid::set_xv(int vflag)
{
int *image = atom->image;
double **x = atom->x;
double **v = atom->v;
int nlocal = atom->nlocal;
double xprd = domain->xprd;
double yprd = domain->yprd;
double zprd = domain->zprd;
int ibody;
int xbox,ybox,zbox;
double vold0,vold1,vold2,fc0,fc1,fc2,massone,x0,x1,x2;
double *mass = atom->mass;
double **f = atom->f;
int *type = atom->type;
// zero out fix_rigid virial
if (vflag) for (int n = 0; n < 6; n++) virial[n] = 0.0;
for (int i = 0; i < nlocal; i++) {
if (body[i] < 0) continue;
ibody = body[i];
xbox = (image[i] & 1023) - 512;
ybox = (image[i] >> 10 & 1023) - 512;
zbox = (image[i] >> 20) - 512;
// save old positions and velocities for virial contribution
if (vflag) {
x0 = x[i][0] + xbox*xprd;
x1 = x[i][1] + ybox*yprd;
x2 = x[i][2] + zbox*zprd;
vold0 = v[i][0];
vold1 = v[i][1];
vold2 = v[i][2];
}
x[i][0] = ex_space[ibody][0]*displace[i][0] +
ey_space[ibody][0]*displace[i][1] +
ez_space[ibody][0]*displace[i][2];
x[i][1] = ex_space[ibody][1]*displace[i][0] +
ey_space[ibody][1]*displace[i][1] +
ez_space[ibody][1]*displace[i][2];
x[i][2] = ex_space[ibody][2]*displace[i][0] +
ey_space[ibody][2]*displace[i][1] +
ez_space[ibody][2]*displace[i][2];
v[i][0] = omega[ibody][1]*x[i][2] - omega[ibody][2]*x[i][1] +
vcm[ibody][0];
v[i][1] = omega[ibody][2]*x[i][0] - omega[ibody][0]*x[i][2] +
vcm[ibody][1];
v[i][2] = omega[ibody][0]*x[i][1] - omega[ibody][1]*x[i][0] +
vcm[ibody][2];
x[i][0] += xcm[ibody][0] - xbox*xprd;
x[i][1] += xcm[ibody][1] - ybox*yprd;
x[i][2] += xcm[ibody][2] - zbox*zprd;
// compute body constraint forces for virial
if (vflag) {
massone = mass[type[i]];
fc0 = massone*(v[i][0] - vold0)/dtf - f[i][0];
fc1 = massone*(v[i][1] - vold1)/dtf - f[i][1];
fc2 = massone*(v[i][2] - vold2)/dtf - f[i][2];
virial[0] += 0.5*fc0*x0;
virial[1] += 0.5*fc1*x1;
virial[2] += 0.5*fc2*x2;
virial[3] += 0.5*fc1*x0;
virial[4] += 0.5*fc2*x0;
virial[5] += 0.5*fc2*x1;
}
}
}
/* ----------------------------------------------------------------------
set space-frame velocity of each atom in rigid body
v = Vcm + (W cross (x - Xcm))
------------------------------------------------------------------------- */
void FixRigid::set_v(int vflag)
{
double **v = atom->v;
int nlocal = atom->nlocal;
int ibody;
double dx,dy,dz;
double vold0,vold1,vold2,fc0,fc1,fc2,massone,x0,x1,x2;
double *mass = atom->mass;
double **f = atom->f;
double **x = atom->x;
int *type = atom->type;
int *image = atom->image;
double xprd = domain->xprd;
double yprd = domain->yprd;
double zprd = domain->zprd;
int xbox,ybox,zbox;
for (int i = 0; i < nlocal; i++) {
if (body[i] < 0) continue;
ibody = body[i];
dx = ex_space[ibody][0]*displace[i][0] +
ey_space[ibody][0]*displace[i][1] +
ez_space[ibody][0]*displace[i][2];
dy = ex_space[ibody][1]*displace[i][0] +
ey_space[ibody][1]*displace[i][1] +
ez_space[ibody][1]*displace[i][2];
dz = ex_space[ibody][2]*displace[i][0] +
ey_space[ibody][2]*displace[i][1] +
ez_space[ibody][2]*displace[i][2];
// save old velocities for virial
if (vflag) {
vold0 = v[i][0];
vold1 = v[i][1];
vold2 = v[i][2];
}
v[i][0] = omega[ibody][1]*dz - omega[ibody][2]*dy + vcm[ibody][0];
v[i][1] = omega[ibody][2]*dx - omega[ibody][0]*dz + vcm[ibody][1];
v[i][2] = omega[ibody][0]*dy - omega[ibody][1]*dx + vcm[ibody][2];
// compute body constraint forces for virial
// use unwrapped atom positions
if (vflag) {
massone = mass[type[i]];
fc0 = massone*(v[i][0] - vold0)/dtf - f[i][0];
fc1 = massone*(v[i][1] - vold1)/dtf - f[i][1];
fc2 = massone*(v[i][2] - vold2)/dtf - f[i][2];
xbox = (image[i] & 1023) - 512;
ybox = (image[i] >> 10 & 1023) - 512;
zbox = (image[i] >> 20) - 512;
x0 = x[i][0] + xbox*xprd;
x1 = x[i][1] + ybox*yprd;
x2 = x[i][2] + zbox*zprd;
virial[0] += 0.5*fc0*x0;
virial[1] += 0.5*fc1*x1;
virial[2] += 0.5*fc2*x2;
virial[3] += 0.5*fc1*x0;
virial[4] += 0.5*fc2*x0;
virial[5] += 0.5*fc2*x1;
}
}
}
/* ----------------------------------------------------------------------
memory usage of local atom-based arrays
------------------------------------------------------------------------- */
int FixRigid::memory_usage()
{
int nmax = atom->nmax;
int bytes = nmax * sizeof(int);
bytes += nmax*3 * sizeof(double);
return bytes;
}
/* ----------------------------------------------------------------------
allocate local atom-based arrays
------------------------------------------------------------------------- */
void FixRigid::grow_arrays(int nmax)
{
body = (int *) memory->srealloc(body,nmax*sizeof(int),"rigid:body");
displace = memory->grow_2d_double_array(displace,nmax,3,"rigid:displace");
}
/* ----------------------------------------------------------------------
copy values within local atom-based arrays
------------------------------------------------------------------------- */
void FixRigid::copy_arrays(int i, int j)
{
body[j] = body[i];
displace[j][0] = displace[i][0];
displace[j][1] = displace[i][1];
displace[j][2] = displace[i][2];
}
/* ----------------------------------------------------------------------
pack values in local atom-based arrays for exchange with another proc
------------------------------------------------------------------------- */
int FixRigid::pack_exchange(int i, double *buf)
{
buf[0] = body[i];
buf[1] = displace[i][0];
buf[2] = displace[i][1];
buf[3] = displace[i][2];
return 4;
}
/* ----------------------------------------------------------------------
unpack values in local atom-based arrays from exchange with another proc
------------------------------------------------------------------------- */
int FixRigid::unpack_exchange(int nlocal, double *buf)
{
body[nlocal] = static_cast<int> (buf[0]);
displace[nlocal][0] = buf[1];
displace[nlocal][1] = buf[2];
displace[nlocal][2] = buf[3];
return 4;
}

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