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ffcb07d0b873bf427651081b7c8cc41d13fc88bf
lammps/src/group.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 "mpi.h"
#include "stdio.h"
#include "string.h"
#include "stdlib.h"
#include "group.h"
#include "domain.h"
#include "atom.h"
#include "atom_vec_hybrid.h"
#include "region.h"
#include "memory.h"
#include "error.h"
using namespace LAMMPS_NS;
#define MAX_GROUP 32
#define TYPE 1
#define MOLECULE 2
#define ID 3
#define LESS_THAN 1
#define GREATER_THAN 2
#define LESS_EQUAL 3
#define GREATER_EQUAL 4
#define BETWEEN 5
#define BIG 1.0e20
#define MIN(a,b) ((a) < (b) ? (a) : (b))
#define MAX(a,b) ((a) > (b) ? (a) : (b))
/* ----------------------------------------------------------------------
initialize group memory
------------------------------------------------------------------------- */
Group::Group(LAMMPS *lmp) : Pointers(lmp)
{
MPI_Comm_rank(world,&me);
names = (char **) memory->smalloc(MAX_GROUP*sizeof(char *),"group:names");
bitmask = new int[MAX_GROUP];
inversemask = new int[MAX_GROUP];
for (int i = 0; i < MAX_GROUP; i++) bitmask[i] = 1 << i;
for (int i = 0; i < MAX_GROUP; i++) inversemask[i] = bitmask[i] ^ ~0;
// create "all" group
char *str = "all";
int n = strlen(str) + 1;
names[0] = (char *) memory->smalloc(n*sizeof(char),"group:names[]");
strcpy(names[0],str);
ngroup = 1;
}
/* ----------------------------------------------------------------------
free all memory
------------------------------------------------------------------------- */
Group::~Group()
{
for (int i = 0; i < ngroup; i++) memory->sfree(names[i]);
memory->sfree(names);
delete [] bitmask;
delete [] inversemask;
}
/* ----------------------------------------------------------------------
assign atoms to a new or existing group
------------------------------------------------------------------------- */
void Group::assign(int narg, char **arg)
{
int i;
if (domain->box_exist == 0)
error->all("Group command before simulation box is defined");
if (narg < 2) error->all("Illegal group command");
// find group in existing list
// igroup = -1 is a new group name, add it
int igroup = find(arg[0]);
if (igroup == -1) {
if (ngroup == MAX_GROUP) error->all("Too many groups");
igroup = ngroup;
ngroup++;
int n = strlen(arg[0]) + 1;
names[igroup] = (char *) memory->smalloc(n*sizeof(char),"group:names[]");
strcpy(names[igroup],arg[0]);
}
double **x = atom->x;
int *mask = atom->mask;
int nlocal = atom->nlocal;
int bit = bitmask[igroup];
// style = region
if (strcmp(arg[1],"region") == 0) {
if (narg != 3) error->all("Illegal group command");
int iregion;
for (iregion = 0; iregion < domain->nregion; iregion++)
if (strcmp(arg[2],domain->regions[iregion]->id) == 0) break;
if (iregion == domain->nregion)
error->all("Group region ID does not exist");
// add to group if atom is in region
for (i = 0; i < nlocal; i++)
if (domain->regions[iregion]->match(x[i][0],x[i][1],x[i][2]))
mask[i] |= bit;
// style = hybrid
} else if (strcmp(arg[1],"hybrid") == 0) {
if (narg != 3) error->all("Illegal group command");
if (strcmp(atom->atom_style,"hybrid") != 0)
error->all("Group hybrid command requires atom style hybrid");
AtomVecHybrid *avec_hybrid = (AtomVecHybrid *) atom->avec;
int ihybrid;
for (ihybrid = 0; ihybrid < avec_hybrid->nstyles; ihybrid++)
if (strcmp(avec_hybrid->keywords[ihybrid],arg[2]) == 0) break;
if (ihybrid == avec_hybrid->nstyles)
error->all("Group hybrid sub-style does not exist");
// add to group if atom matches hybrid sub-style
int *hybrid = atom->hybrid;
for (i = 0; i < nlocal; i++)
if (hybrid[i] == ihybrid) mask[i] |= bit;
// style = logical condition
} else if (strcmp(arg[2],"<") == 0 || strcmp(arg[2],">") == 0 ||
strcmp(arg[2],"<=") == 0 || strcmp(arg[2],">=") == 0 ||
strcmp(arg[2],"<>") == 0) {
if (narg < 4 || narg > 5) error->all("Illegal group command");
int category,condition,bound1,bound2;
if (strcmp(arg[1],"type") == 0) category = TYPE;
else if (strcmp(arg[1],"molecule") == 0) category = MOLECULE;
else if (strcmp(arg[1],"id") == 0) category = ID;
else error->all("Illegal group command");
if (strcmp(arg[2],"<") == 0) condition = LESS_THAN;
else if (strcmp(arg[2],">") == 0) condition = GREATER_THAN;
else if (strcmp(arg[2],"<=") == 0) condition = LESS_EQUAL;
else if (strcmp(arg[2],">=") == 0) condition = GREATER_EQUAL;
else if (strcmp(arg[2],"<>") == 0) condition = BETWEEN;
else error->all("Illegal group command");
bound1 = atoi(arg[3]);
bound2 = -1;
if (condition == BETWEEN) {
if (narg != 5) error->all("Illegal group command");
bound2 = atoi(arg[4]);
}
int *attribute;
if (category == TYPE) attribute = atom->type;
else if (category == MOLECULE) attribute = atom->molecule;
else if (category == ID) attribute = atom->tag;
// add to group if meets condition
if (condition == LESS_THAN) {
for (i = 0; i < nlocal; i++) if (attribute[i] < bound1) mask[i] |= bit;
} else if (condition == GREATER_THAN) {
for (i = 0; i < nlocal; i++) if (attribute[i] > bound1) mask[i] |= bit;
} else if (condition == LESS_EQUAL) {
for (i = 0; i < nlocal; i++) if (attribute[i] <= bound1) mask[i] |= bit;
} else if (condition == GREATER_EQUAL) {
for (i = 0; i < nlocal; i++) if (attribute[i] >= bound1) mask[i] |= bit;
} else if (condition == BETWEEN) {
for (i = 0; i < nlocal; i++)
if (attribute[i] >= bound1 && attribute[i] <= bound2) mask[i] |= bit;
}
// style = list of values
} else if (strcmp(arg[1],"type") == 0 || strcmp(arg[1],"molecule") == 0 ||
strcmp(arg[1],"id") == 0) {
if (narg < 3) error->all("Illegal group command");
int length = narg-2;
int *list = new int[length];
int category;
if (strcmp(arg[1],"type") == 0) category = TYPE;
else if (strcmp(arg[1],"molecule") == 0) category = MOLECULE;
else if (strcmp(arg[1],"id") == 0) category = ID;
else error->all("Illegal group command");
length = narg - 2;
for (int iarg = 2; iarg < narg; iarg++) list[iarg-2] = atoi(arg[iarg]);
int *attribute;
if (category == TYPE) attribute = atom->type;
else if (category == MOLECULE) attribute = atom->molecule;
else if (category == ID) attribute = atom->tag;
// add to group if attribute is any in list
for (int ilist = 0; ilist < length; ilist++)
for (i = 0; i < nlocal; i++)
if (attribute[i] == list[ilist]) mask[i] |= bit;
delete [] list;
// style = subtract
} else if (strcmp(arg[1],"subtract") == 0) {
if (narg < 4) error->all("Illegal group command");
int length = narg-2;
int *list = new int[length];
int jgroup;
for (int iarg = 2; iarg < narg; iarg++) {
jgroup = find(arg[iarg]);
if (jgroup == -1) error->all("Group ID does not exist");
list[iarg-2] = jgroup;
}
// add to group if in 1st group in list
int otherbit = bitmask[list[0]];
for (i = 0; i < nlocal; i++)
if (mask[i] & otherbit) mask[i] |= bit;
// remove atoms if they are in any of the other groups
// AND with inverse mask removes the atom from group
int inverse = inversemask[igroup];
for (int ilist = 1; ilist < length; ilist++) {
otherbit = bitmask[list[ilist]];
for (i = 0; i < nlocal; i++)
if (mask[i] & otherbit) mask[i] &= inverse;
}
delete [] list;
// style = union
} else if (strcmp(arg[1],"union") == 0) {
if (narg < 3) error->all("Illegal group command");
int length = narg-2;
int *list = new int[length];
int jgroup;
for (int iarg = 2; iarg < narg; iarg++) {
jgroup = find(arg[iarg]);
if (jgroup == -1) error->all("Group ID does not exist");
list[iarg-2] = jgroup;
}
// add to group if in any other group in list
int otherbit;
for (int ilist = 0; ilist < length; ilist++) {
otherbit = bitmask[list[ilist]];
for (i = 0; i < nlocal; i++)
if (mask[i] & otherbit) mask[i] |= bit;
}
delete [] list;
// style = intersect
} else if (strcmp(arg[1],"intersect") == 0) {
if (narg < 4) error->all("Illegal group command");
int length = narg-2;
int *list = new int[length];
int jgroup;
for (int iarg = 2; iarg < narg; iarg++) {
jgroup = find(arg[iarg]);
if (jgroup == -1) error->all("Group ID does not exist");
list[iarg-2] = jgroup;
}
// add to group if in all groups in list
int otherbit,ok,ilist;
for (i = 0; i < nlocal; i++) {
ok = 1;
for (ilist = 0; ilist < length; ilist++) {
otherbit = bitmask[list[ilist]];
if ((mask[i] & otherbit) == 0) ok = 0;
}
if (ok) mask[i] |= bit;
}
delete [] list;
// not a valid group style
} else error->all("Illegal group command");
// print stats for changed group
int n,all;
n = 0;
for (i = 0; i < nlocal; i++) if (mask[i] & bit) n++;
MPI_Allreduce(&n,&all,1,MPI_INT,MPI_SUM,world);
if (me == 0) {
if (screen) fprintf(screen,"%d atoms in group %s\n",all,names[igroup]);
if (logfile) fprintf(logfile,"%d atoms in group %s\n",all,names[igroup]);
}
}
/* ----------------------------------------------------------------------
add flagged atoms to a new or existing group
------------------------------------------------------------------------- */
void Group::create(char *name, int *flag)
{
int i;
// find group in existing list
// igroup = -1 is a new group name, add it
int igroup = find(name);
if (igroup == -1) {
if (ngroup == MAX_GROUP) error->all("Too many groups");
igroup = ngroup;
ngroup++;
int n = strlen(name) + 1;
names[igroup] = (char *) memory->smalloc(n*sizeof(char),"group:names[]");
strcpy(names[igroup],name);
}
// add atom to group if flag is set
int *mask = atom->mask;
int nlocal = atom->nlocal;
int bit = bitmask[igroup];
for (i = 0; i < nlocal; i++)
if (flag[i]) mask[i] |= bit;
}
/* ----------------------------------------------------------------------
return group index if name matches existing group, -1 if no such group
------------------------------------------------------------------------- */
int Group::find(char *name)
{
for (int igroup = 0; igroup < ngroup; igroup++)
if (strcmp(name,names[igroup]) == 0) return igroup;
return -1;
}
/* ----------------------------------------------------------------------
write group info to a restart file
only called by proc 0
------------------------------------------------------------------------- */
void Group::write_restart(FILE *fp)
{
fwrite(&ngroup,sizeof(int),1,fp);
int n;
for (int i = 0; i < ngroup; i++) {
n = strlen(names[i]) + 1;
fwrite(&n,sizeof(int),1,fp);
fwrite(names[i],sizeof(char),n,fp);
}
}
/* ----------------------------------------------------------------------
read group info from a restart file
proc 0 reads, bcast to all procs
------------------------------------------------------------------------- */
void Group::read_restart(FILE *fp)
{
int i,n;
for (i = 0; i < ngroup; i++) memory->sfree(names[i]);
if (me == 0) fread(&ngroup,sizeof(int),1,fp);
MPI_Bcast(&ngroup,1,MPI_INT,0,world);
for (i = 0; i < ngroup; i++) {
if (me == 0) fread(&n,sizeof(int),1,fp);
MPI_Bcast(&n,1,MPI_INT,0,world);
names[i] = (char *) memory->smalloc(n*sizeof(char),"group:names[]");
if (me == 0) fread(names[i],sizeof(char),n,fp);
MPI_Bcast(names[i],n,MPI_CHAR,0,world);
}
}
// ----------------------------------------------------------------------
// computations on a group of atoms
// ----------------------------------------------------------------------
/* ----------------------------------------------------------------------
count atoms in group
compute in double precision in case system is huge
------------------------------------------------------------------------- */
double Group::count(int igroup)
{
int groupbit = bitmask[igroup];
int *mask = atom->mask;
int nlocal = atom->nlocal;
int n = 0;
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit) n++;
double nsingle = n;
double nall;
MPI_Allreduce(&nsingle,&nall,1,MPI_DOUBLE,MPI_SUM,world);
return nall;
}
/* ----------------------------------------------------------------------
compute the total mass of group of atoms
use either per-type mass or per-atom rmass
------------------------------------------------------------------------- */
double Group::mass(int igroup)
{
int groupbit = bitmask[igroup];
int *mask = atom->mask;
int *type = atom->type;
double *mass = atom->mass;
double *rmass = atom->rmass;
int nlocal = atom->nlocal;
double m = 0.0;
if (mass) {
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit) m += mass[type[i]];
} else {
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit) m += rmass[i];
}
double mall;
MPI_Allreduce(&m,&mall,1,MPI_DOUBLE,MPI_SUM,world);
return mall;
}
/* ----------------------------------------------------------------------
compute the total charge of group of atoms
------------------------------------------------------------------------- */
double Group::charge(int igroup)
{
int groupbit = bitmask[igroup];
int *mask = atom->mask;
double *q = atom->q;
int nlocal = atom->nlocal;
double qone = 0.0;
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit) qone += q[i];
double qall;
MPI_Allreduce(&qone,&qall,1,MPI_DOUBLE,MPI_SUM,world);
return qall;
}
/* ----------------------------------------------------------------------
compute the coordinate bounds of the group of atoms
periodic images are not considered, so atoms are NOT unwrapped
------------------------------------------------------------------------- */
void Group::bounds(int igroup, double *minmax)
{
int groupbit = bitmask[igroup];
double extent[6];
extent[0] = extent[2] = extent[4] = BIG;
extent[1] = extent[3] = extent[5] = -BIG;
double **x = atom->x;
int *mask = atom->mask;
int nlocal = atom->nlocal;
for (int i = 0; i < nlocal; i++) {
if (mask[i] & groupbit) {
extent[0] = MIN(extent[0],x[i][0]);
extent[1] = MAX(extent[1],x[i][0]);
extent[2] = MIN(extent[2],x[i][1]);
extent[3] = MAX(extent[3],x[i][1]);
extent[4] = MIN(extent[4],x[i][2]);
extent[5] = MAX(extent[5],x[i][2]);
}
}
// compute extent across all procs
// flip sign of MIN to do it in one Allreduce MAX
// set box by extent in shrink-wrapped dims
extent[0] = -extent[0];
extent[2] = -extent[2];
extent[4] = -extent[4];
MPI_Allreduce(extent,minmax,6,MPI_DOUBLE,MPI_MAX,world);
extent[0] = -extent[0];
extent[2] = -extent[2];
extent[4] = -extent[4];
}
/* ----------------------------------------------------------------------
compute the center-of-mass coords of group with total mass = masstotal
return center-of-mass coords in cm[]
must unwrap atoms to compute center-of-mass correctly
------------------------------------------------------------------------- */
void Group::xcm(int igroup, double masstotal, double *cm)
{
int groupbit = bitmask[igroup];
double **x = atom->x;
int *mask = atom->mask;
int *type = atom->type;
int *image = atom->image;
double *mass = atom->mass;
double *rmass = atom->rmass;
int nlocal = atom->nlocal;
double cmone[3];
cmone[0] = cmone[1] = cmone[2] = 0.0;
double xprd = domain->xprd;
double yprd = domain->yprd;
double zprd = domain->zprd;
int xbox,ybox,zbox;
double massone;
if (mass) {
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit) {
xbox = (image[i] & 1023) - 512;
ybox = (image[i] >> 10 & 1023) - 512;
zbox = (image[i] >> 20) - 512;
massone = mass[type[i]];
cmone[0] += (x[i][0] + xbox*xprd) * massone;
cmone[1] += (x[i][1] + ybox*yprd) * massone;
cmone[2] += (x[i][2] + zbox*zprd) * massone;
}
} else {
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit) {
xbox = (image[i] & 1023) - 512;
ybox = (image[i] >> 10 & 1023) - 512;
zbox = (image[i] >> 20) - 512;
massone = rmass[i];
cmone[0] += (x[i][0] + xbox*xprd) * massone;
cmone[1] += (x[i][1] + ybox*yprd) * massone;
cmone[2] += (x[i][2] + zbox*zprd) * massone;
}
}
MPI_Allreduce(cmone,cm,3,MPI_DOUBLE,MPI_SUM,world);
cm[0] /= masstotal;
cm[1] /= masstotal;
cm[2] /= masstotal;
}
/* ----------------------------------------------------------------------
compute the center-of-mass velocity of group with total mass = masstotal
return center-of-mass velocity in cm[]
------------------------------------------------------------------------- */
void Group::vcm(int igroup, double masstotal, double *cm)
{
int groupbit = bitmask[igroup];
double **v = atom->v;
int *mask = atom->mask;
int *type = atom->type;
double *mass = atom->mass;
double *rmass = atom->rmass;
int nlocal = atom->nlocal;
double p[3],massone;
p[0] = p[1] = p[2] = 0.0;
if (mass) {
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit) {
massone = mass[type[i]];
p[0] += v[i][0]*massone;
p[1] += v[i][1]*massone;
p[2] += v[i][2]*massone;
}
} else {
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit) {
massone = rmass[i];
p[0] += v[i][0]*massone;
p[1] += v[i][1]*massone;
p[2] += v[i][2]*massone;
}
}
MPI_Allreduce(p,cm,3,MPI_DOUBLE,MPI_SUM,world);
cm[0] /= masstotal;
cm[1] /= masstotal;
cm[2] /= masstotal;
}
/* ----------------------------------------------------------------------
compute the radius-of-gyration of group around center-of-mass cm
must unwrap atoms to compute Rg correctly
------------------------------------------------------------------------- */
double Group::gyration(int igroup, double masstotal, double *cm)
{
int groupbit = bitmask[igroup];
double **x = atom->x;
int *mask = atom->mask;
int *type = atom->type;
int *image = atom->image;
double *mass = atom->mass;
double *rmass = atom->rmass;
int nlocal = atom->nlocal;
int xbox,ybox,zbox;
double dx,dy,dz,massone;
double xprd = domain->xprd;
double yprd = domain->yprd;
double zprd = domain->zprd;
double rg = 0.0;
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit) {
xbox = (image[i] & 1023) - 512;
ybox = (image[i] >> 10 & 1023) - 512;
zbox = (image[i] >> 20) - 512;
dx = (x[i][0] + xbox*xprd) - cm[0];
dy = (x[i][1] + ybox*yprd) - cm[1];
dz = (x[i][2] + zbox*zprd) - cm[2];
if (mass) massone = mass[type[i]];
else massone = rmass[i];
rg += (dx*dx + dy*dy + dz*dz) * massone;
}
double rg_all;
MPI_Allreduce(&rg,&rg_all,1,MPI_DOUBLE,MPI_SUM,world);
return sqrt(rg_all/masstotal);
}
/* ----------------------------------------------------------------------
compute the angular momentum L (lmom) of group around center-of-mass cm
must unwrap atoms to compute L correctly
------------------------------------------------------------------------- */
void Group::angmom(int igroup, double *cm, double *lmom)
{
int groupbit = bitmask[igroup];
double **x = atom->x;
double **v = atom->v;
int *mask = atom->mask;
int *type = atom->type;
int *image = atom->image;
double *mass = atom->mass;
double *rmass = atom->rmass;
int nlocal = atom->nlocal;
int xbox,ybox,zbox;
double dx,dy,dz,massone;
double xprd = domain->xprd;
double yprd = domain->yprd;
double zprd = domain->zprd;
double p[3];
p[0] = p[1] = p[2] = 0.0;
for (int i = 0; i < nlocal; i++)
if (mask[i] & groupbit) {
xbox = (image[i] & 1023) - 512;
ybox = (image[i] >> 10 & 1023) - 512;
zbox = (image[i] >> 20) - 512;
dx = (x[i][0] + xbox*xprd) - cm[0];
dy = (x[i][1] + ybox*yprd) - cm[1];
dz = (x[i][2] + zbox*zprd) - cm[2];
if (mass) massone = mass[type[i]];
else massone = rmass[i];
p[0] += massone * (dy*v[i][2] - dz*v[i][1]);
p[1] += massone * (dz*v[i][0] - dx*v[i][2]);
p[2] += massone * (dx*v[i][1] - dy*v[i][0]);
}
MPI_Allreduce(p,lmom,3,MPI_DOUBLE,MPI_SUM,world);
}
/* ----------------------------------------------------------------------
compute moment of inertia tensor around center-of-mass cm
must unwrap atoms to compute itensor correctly
------------------------------------------------------------------------- */
void Group::inertia(int igroup, double *cm, double itensor[3][3])
{
int i,j;
int groupbit = bitmask[igroup];
double **x = atom->x;
int *mask = atom->mask;
int *type = atom->type;
int *image = atom->image;
double *mass = atom->mass;
double *rmass = atom->rmass;
int nlocal = atom->nlocal;
int xbox,ybox,zbox;
double dx,dy,dz,massone;
double xprd = domain->xprd;
double yprd = domain->yprd;
double zprd = domain->zprd;
double ione[3][3];
for (i = 0; i < 3; i++)
for (j = 0; j < 3; j++)
ione[i][j] = 0.0;
for (i = 0; i < nlocal; i++)
if (mask[i] & groupbit) {
xbox = (image[i] & 1023) - 512;
ybox = (image[i] >> 10 & 1023) - 512;
zbox = (image[i] >> 20) - 512;
dx = (x[i][0] + xbox*xprd) - cm[0];
dy = (x[i][1] + ybox*yprd) - cm[1];
dz = (x[i][2] + zbox*zprd) - cm[2];
if (mass) massone = mass[type[i]];
else massone = rmass[i];
ione[0][0] += massone * (dy*dy + dz*dz);
ione[1][1] += massone * (dx*dx + dz*dz);
ione[2][2] += massone * (dx*dx + dy*dy);
ione[0][1] -= massone * dx*dy;
ione[1][2] -= massone * dy*dz;
ione[0][2] -= massone * dx*dz;
}
ione[1][0] = ione[0][1];
ione[2][1] = ione[1][2];
ione[2][0] = ione[0][2];
MPI_Allreduce(&ione[0][0],&itensor[0][0],9,MPI_DOUBLE,MPI_SUM,world);
}
/* ----------------------------------------------------------------------
compute angular velocity omega from L = Iw, inverting I to solve for w
really not a group operation, but L and I were computed for a group
------------------------------------------------------------------------- */
void Group::omega(double *angmom, double inertia[3][3], double *w)
{
double inverse[3][3];
inverse[0][0] = inertia[1][1]*inertia[2][2] - inertia[1][2]*inertia[2][1];
inverse[0][1] = -(inertia[0][1]*inertia[2][2] - inertia[0][2]*inertia[2][1]);
inverse[0][2] = inertia[0][1]*inertia[1][2] - inertia[0][2]*inertia[1][1];
inverse[1][0] = -(inertia[1][0]*inertia[2][2] - inertia[1][2]*inertia[2][0]);
inverse[1][1] = inertia[0][0]*inertia[2][2] - inertia[0][2]*inertia[2][0];
inverse[1][2] = -(inertia[0][0]*inertia[1][2] - inertia[0][2]*inertia[1][0]);
inverse[2][0] = inertia[1][0]*inertia[2][1] - inertia[1][1]*inertia[2][0];
inverse[2][1] = -(inertia[0][0]*inertia[2][1] - inertia[0][1]*inertia[2][0]);
inverse[2][2] = inertia[0][0]*inertia[1][1] - inertia[0][1]*inertia[1][0];
double determinant = inertia[0][0]*inertia[1][1]*inertia[2][2] +
inertia[0][1]*inertia[1][2]*inertia[2][0] +
inertia[0][2]*inertia[1][0]*inertia[2][1] -
inertia[0][0]*inertia[1][2]*inertia[2][1] -
inertia[0][1]*inertia[1][0]*inertia[2][2] -
inertia[2][0]*inertia[1][1]*inertia[0][2];
int i,j;
for (i = 0; i < 3; i++)
for (j = 0; j < 3; j++)
inverse[i][j] /= determinant;
w[0] = inverse[0][0]*angmom[0] + inverse[0][1]*angmom[1] +
inverse[0][2]*angmom[2];
w[1] = inverse[1][0]*angmom[0] + inverse[1][1]*angmom[1] +
inverse[1][2]*angmom[2];
w[2] = inverse[2][0]*angmom[0] + inverse[2][1]*angmom[1] +
inverse[2][2]*angmom[2];
}
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