complete moving packages and styles around
This commit is contained in:
Axel Kohlmeyer
@ -1,714 +0,0 @@
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// clang-format off
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/* ----------------------------------------------------------------------
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LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
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https://www.lammps.org/, Sandia National Laboratories
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Steve Plimpton, sjplimp@sandia.gov
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Copyright (2003) Sandia Corporation. Under the terms of Contract
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DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
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certain rights in this software. This software is distributed under
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the GNU General Public License.
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See the README file in the top-level LAMMPS directory.
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------------------------------------------------------------------------- */
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/* ----------------------------------------------------------------------
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Contributing author: Aidan Thompson (SNL)
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Axel Kohlmeyer (Temple U)
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------------------------------------------------------------------------- */
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#include "compute_orientorder_atom.h"
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#include "atom.h"
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#include "comm.h"
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#include "error.h"
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#include "force.h"
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#include "math_const.h"
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#include "math_special.h"
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#include "memory.h"
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#include "modify.h"
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#include "neigh_list.h"
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#include "neigh_request.h"
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#include "neighbor.h"
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#include "pair.h"
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#include "update.h"
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#include <cstring>
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#include <cmath>
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using namespace LAMMPS_NS;
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using namespace MathConst;
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using namespace MathSpecial;
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#ifdef DBL_EPSILON
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#define MY_EPSILON (10.0*DBL_EPSILON)
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#else
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#define MY_EPSILON (10.0*2.220446049250313e-16)
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#endif
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#define QEPSILON 1.0e-6
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/* ---------------------------------------------------------------------- */
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ComputeOrientOrderAtom::ComputeOrientOrderAtom(LAMMPS *lmp, int narg, char **arg) :
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Compute(lmp, narg, arg),
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qlist(nullptr), distsq(nullptr), nearest(nullptr), rlist(nullptr),
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qnarray(nullptr), qnm_r(nullptr), qnm_i(nullptr), cglist(nullptr)
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{
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if (narg < 3 ) error->all(FLERR,"Illegal compute orientorder/atom command");
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// set default values for optional args
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nnn = 12;
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cutsq = 0.0;
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wlflag = 0;
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wlhatflag = 0;
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qlcompflag = 0;
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chunksize = 16384;
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// specify which orders to request
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nqlist = 5;
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memory->create(qlist,nqlist,"orientorder/atom:qlist");
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qlist[0] = 4;
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qlist[1] = 6;
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qlist[2] = 8;
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qlist[3] = 10;
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qlist[4] = 12;
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qmax = 12;
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// process optional args
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int iarg = 3;
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while (iarg < narg) {
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if (strcmp(arg[iarg],"nnn") == 0) {
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if (iarg+2 > narg)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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if (strcmp(arg[iarg+1],"NULL") == 0) {
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nnn = 0;
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} else {
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nnn = utils::numeric(FLERR,arg[iarg+1],false,lmp);
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if (nnn <= 0)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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}
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iarg += 2;
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} else if (strcmp(arg[iarg],"degrees") == 0) {
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if (iarg+2 > narg)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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nqlist = utils::numeric(FLERR,arg[iarg+1],false,lmp);
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if (nqlist <= 0)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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memory->destroy(qlist);
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memory->create(qlist,nqlist,"orientorder/atom:qlist");
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iarg += 2;
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if (iarg+nqlist > narg)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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qmax = 0;
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for (int il = 0; il < nqlist; il++) {
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qlist[il] = utils::numeric(FLERR,arg[iarg+il],false,lmp);
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if (qlist[il] < 0)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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if (qlist[il] > qmax) qmax = qlist[il];
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}
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iarg += nqlist;
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} else if (strcmp(arg[iarg],"wl") == 0) {
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if (iarg+2 > narg)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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if (strcmp(arg[iarg+1],"yes") == 0) wlflag = 1;
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else if (strcmp(arg[iarg+1],"no") == 0) wlflag = 0;
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else error->all(FLERR,"Illegal compute orientorder/atom command");
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iarg += 2;
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} else if (strcmp(arg[iarg],"wl/hat") == 0) {
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if (iarg+2 > narg)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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if (strcmp(arg[iarg+1],"yes") == 0) wlhatflag = 1;
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else if (strcmp(arg[iarg+1],"no") == 0) wlhatflag = 0;
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else error->all(FLERR,"Illegal compute orientorder/atom command");
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iarg += 2;
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} else if (strcmp(arg[iarg],"components") == 0) {
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qlcompflag = 1;
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if (iarg+2 > narg)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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qlcomp = utils::numeric(FLERR,arg[iarg+1],false,lmp);
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iqlcomp = -1;
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for (int il = 0; il < nqlist; il++)
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if (qlcomp == qlist[il]) {
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iqlcomp = il;
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break;
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}
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if (iqlcomp == -1)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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iarg += 2;
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} else if (strcmp(arg[iarg],"cutoff") == 0) {
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if (iarg+2 > narg)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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double cutoff = utils::numeric(FLERR,arg[iarg+1],false,lmp);
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if (cutoff <= 0.0)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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cutsq = cutoff*cutoff;
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iarg += 2;
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} else if (strcmp(arg[iarg],"chunksize") == 0) {
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if (iarg+2 > narg)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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chunksize = utils::numeric(FLERR,arg[iarg+1],false,lmp);
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if (chunksize <= 0)
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error->all(FLERR,"Illegal compute orientorder/atom command");
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iarg += 2;
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} else error->all(FLERR,"Illegal compute orientorder/atom command");
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}
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ncol = nqlist;
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if (wlflag) ncol += nqlist;
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if (wlhatflag) ncol += nqlist;
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if (qlcompflag) ncol += 2*(2*qlcomp+1);
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peratom_flag = 1;
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size_peratom_cols = ncol;
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nmax = 0;
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maxneigh = 0;
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}
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/* ---------------------------------------------------------------------- */
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ComputeOrientOrderAtom::~ComputeOrientOrderAtom()
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{
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if (copymode) return;
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memory->destroy(qnarray);
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memory->destroy(distsq);
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memory->destroy(rlist);
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memory->destroy(nearest);
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memory->destroy(qlist);
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memory->destroy(qnm_r);
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memory->destroy(qnm_i);
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memory->destroy(cglist);
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}
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/* ---------------------------------------------------------------------- */
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void ComputeOrientOrderAtom::init()
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{
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if (force->pair == nullptr)
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error->all(FLERR,"Compute orientorder/atom requires a "
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"pair style be defined");
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if (cutsq == 0.0) cutsq = force->pair->cutforce * force->pair->cutforce;
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else if (sqrt(cutsq) > force->pair->cutforce)
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error->all(FLERR,"Compute orientorder/atom cutoff is "
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"longer than pairwise cutoff");
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memory->create(qnm_r,nqlist,2*qmax+1,"orientorder/atom:qnm_r");
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memory->create(qnm_i,nqlist,2*qmax+1,"orientorder/atom:qnm_i");
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// need an occasional full neighbor list
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int irequest = neighbor->request(this,instance_me);
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neighbor->requests[irequest]->pair = 0;
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neighbor->requests[irequest]->compute = 1;
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neighbor->requests[irequest]->half = 0;
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neighbor->requests[irequest]->full = 1;
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neighbor->requests[irequest]->occasional = 1;
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int count = 0;
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for (int i = 0; i < modify->ncompute; i++)
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if (strcmp(modify->compute[i]->style,"orientorder/atom") == 0) count++;
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if (count > 1 && comm->me == 0)
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error->warning(FLERR,"More than one compute orientorder/atom");
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if (wlflag || wlhatflag) init_clebsch_gordan();
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}
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/* ---------------------------------------------------------------------- */
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void ComputeOrientOrderAtom::init_list(int /*id*/, NeighList *ptr)
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{
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list = ptr;
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}
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/* ---------------------------------------------------------------------- */
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void ComputeOrientOrderAtom::compute_peratom()
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{
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int i,j,ii,jj,inum,jnum;
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double xtmp,ytmp,ztmp,delx,dely,delz,rsq;
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int *ilist,*jlist,*numneigh,**firstneigh;
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invoked_peratom = update->ntimestep;
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// grow order parameter array if necessary
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if (atom->nmax > nmax) {
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memory->destroy(qnarray);
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nmax = atom->nmax;
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memory->create(qnarray,nmax,ncol,"orientorder/atom:qnarray");
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array_atom = qnarray;
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}
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// invoke full neighbor list (will copy or build if necessary)
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neighbor->build_one(list);
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inum = list->inum;
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ilist = list->ilist;
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numneigh = list->numneigh;
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firstneigh = list->firstneigh;
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// compute order parameter for each atom in group
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// use full neighbor list to count atoms less than cutoff
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double **x = atom->x;
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int *mask = atom->mask;
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memset(&qnarray[0][0],0,sizeof(double)*nmax*ncol);
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for (ii = 0; ii < inum; ii++) {
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i = ilist[ii];
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double* qn = qnarray[i];
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if (mask[i] & groupbit) {
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xtmp = x[i][0];
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ytmp = x[i][1];
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ztmp = x[i][2];
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jlist = firstneigh[i];
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jnum = numneigh[i];
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// insure distsq and nearest arrays are long enough
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if (jnum > maxneigh) {
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memory->destroy(distsq);
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memory->destroy(rlist);
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memory->destroy(nearest);
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maxneigh = jnum;
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memory->create(distsq,maxneigh,"orientorder/atom:distsq");
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memory->create(rlist,maxneigh,3,"orientorder/atom:rlist");
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memory->create(nearest,maxneigh,"orientorder/atom:nearest");
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}
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// loop over list of all neighbors within force cutoff
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// distsq[] = distance sq to each
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// rlist[] = distance vector to each
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// nearest[] = atom indices of neighbors
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int ncount = 0;
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for (jj = 0; jj < jnum; jj++) {
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j = jlist[jj];
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j &= NEIGHMASK;
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delx = xtmp - x[j][0];
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dely = ytmp - x[j][1];
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delz = ztmp - x[j][2];
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rsq = delx*delx + dely*dely + delz*delz;
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if (rsq < cutsq) {
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distsq[ncount] = rsq;
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rlist[ncount][0] = delx;
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rlist[ncount][1] = dely;
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rlist[ncount][2] = delz;
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nearest[ncount++] = j;
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}
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}
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// if not nnn neighbors, order parameter = 0;
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if ((ncount == 0) || (ncount < nnn)) {
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for (jj = 0; jj < ncol; jj++)
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qn[jj] = 0.0;
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continue;
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}
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// if nnn > 0, use only nearest nnn neighbors
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if (nnn > 0) {
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select3(nnn,ncount,distsq,nearest,rlist);
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ncount = nnn;
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}
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calc_boop(rlist, ncount, qn, qlist, nqlist);
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}
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}
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}
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/* ----------------------------------------------------------------------
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memory usage of local atom-based array
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------------------------------------------------------------------------- */
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double ComputeOrientOrderAtom::memory_usage()
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{
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double bytes = (double)ncol*nmax * sizeof(double);
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bytes += (double)(qmax*(2*qmax+1)+maxneigh*4) * sizeof(double);
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bytes += (double)(nqlist+maxneigh) * sizeof(int);
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return bytes;
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}
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/* ----------------------------------------------------------------------
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select3 routine from Numerical Recipes (slightly modified)
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find k smallest values in array of length n
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sort auxiliary arrays at same time
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------------------------------------------------------------------------- */
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// Use no-op do while to create single statement
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#define SWAP(a,b) do { \
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tmp = a; a = b; b = tmp; \
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} while (0)
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#define ISWAP(a,b) do { \
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itmp = a; a = b; b = itmp; \
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} while (0)
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#define SWAP3(a,b) do { \
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tmp = a[0]; a[0] = b[0]; b[0] = tmp; \
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tmp = a[1]; a[1] = b[1]; b[1] = tmp; \
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tmp = a[2]; a[2] = b[2]; b[2] = tmp; \
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} while (0)
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/* ---------------------------------------------------------------------- */
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void ComputeOrientOrderAtom::select3(int k, int n, double *arr, int *iarr, double **arr3)
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{
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int i,ir,j,l,mid,ia,itmp;
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double a,tmp,a3[3];
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arr--;
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iarr--;
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arr3--;
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l = 1;
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ir = n;
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for (;;) {
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||||
if (ir <= l+1) {
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||||
if (ir == l+1 && arr[ir] < arr[l]) {
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SWAP(arr[l],arr[ir]);
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ISWAP(iarr[l],iarr[ir]);
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SWAP3(arr3[l],arr3[ir]);
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}
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||||
return;
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||||
} else {
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||||
mid=(l+ir) >> 1;
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SWAP(arr[mid],arr[l+1]);
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ISWAP(iarr[mid],iarr[l+1]);
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SWAP3(arr3[mid],arr3[l+1]);
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||||
if (arr[l] > arr[ir]) {
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||||
SWAP(arr[l],arr[ir]);
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ISWAP(iarr[l],iarr[ir]);
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SWAP3(arr3[l],arr3[ir]);
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||||
}
|
||||
if (arr[l+1] > arr[ir]) {
|
||||
SWAP(arr[l+1],arr[ir]);
|
||||
ISWAP(iarr[l+1],iarr[ir]);
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||||
SWAP3(arr3[l+1],arr3[ir]);
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||||
}
|
||||
if (arr[l] > arr[l+1]) {
|
||||
SWAP(arr[l],arr[l+1]);
|
||||
ISWAP(iarr[l],iarr[l+1]);
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||||
SWAP3(arr3[l],arr3[l+1]);
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||||
}
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||||
i = l+1;
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||||
j = ir;
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||||
a = arr[l+1];
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||||
ia = iarr[l+1];
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||||
a3[0] = arr3[l+1][0];
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||||
a3[1] = arr3[l+1][1];
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||||
a3[2] = arr3[l+1][2];
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||||
for (;;) {
|
||||
do i++; while (arr[i] < a);
|
||||
do j--; while (arr[j] > a);
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||||
if (j < i) break;
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||||
SWAP(arr[i],arr[j]);
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||||
ISWAP(iarr[i],iarr[j]);
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||||
SWAP3(arr3[i],arr3[j]);
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||||
}
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||||
arr[l+1] = arr[j];
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||||
arr[j] = a;
|
||||
iarr[l+1] = iarr[j];
|
||||
iarr[j] = ia;
|
||||
arr3[l+1][0] = arr3[j][0];
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||||
arr3[l+1][1] = arr3[j][1];
|
||||
arr3[l+1][2] = arr3[j][2];
|
||||
arr3[j][0] = a3[0];
|
||||
arr3[j][1] = a3[1];
|
||||
arr3[j][2] = a3[2];
|
||||
if (j >= k) ir = j-1;
|
||||
if (j <= k) l = i;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
calculate the bond orientational order parameters
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void ComputeOrientOrderAtom::calc_boop(double **rlist,
|
||||
int ncount, double qn[],
|
||||
int qlist[], int nqlist) {
|
||||
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
for (int m = 0; m < 2*l+1; m++) {
|
||||
qnm_r[il][m] = 0.0;
|
||||
qnm_i[il][m] = 0.0;
|
||||
}
|
||||
}
|
||||
|
||||
for (int ineigh = 0; ineigh < ncount; ineigh++) {
|
||||
const double * const r = rlist[ineigh];
|
||||
double rmag = dist(r);
|
||||
if (rmag <= MY_EPSILON) {
|
||||
return;
|
||||
}
|
||||
|
||||
double costheta = r[2] / rmag;
|
||||
double expphi_r = r[0];
|
||||
double expphi_i = r[1];
|
||||
double rxymag = sqrt(expphi_r*expphi_r+expphi_i*expphi_i);
|
||||
if (rxymag <= MY_EPSILON) {
|
||||
expphi_r = 1.0;
|
||||
expphi_i = 0.0;
|
||||
} else {
|
||||
double rxymaginv = 1.0/rxymag;
|
||||
expphi_r *= rxymaginv;
|
||||
expphi_i *= rxymaginv;
|
||||
}
|
||||
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
|
||||
// calculate spherical harmonics
|
||||
// Ylm, -l <= m <= l
|
||||
// sign convention: sign(Yll(0,0)) = (-1)^l
|
||||
|
||||
qnm_r[il][l] += polar_prefactor(l, 0, costheta);
|
||||
double expphim_r = expphi_r;
|
||||
double expphim_i = expphi_i;
|
||||
for (int m = 1; m <= +l; m++) {
|
||||
|
||||
double prefactor = polar_prefactor(l, m, costheta);
|
||||
double ylm_r = prefactor * expphim_r;
|
||||
double ylm_i = prefactor * expphim_i;
|
||||
qnm_r[il][m+l] += ylm_r;
|
||||
qnm_i[il][m+l] += ylm_i;
|
||||
if (m & 1) {
|
||||
qnm_r[il][-m+l] -= ylm_r;
|
||||
qnm_i[il][-m+l] += ylm_i;
|
||||
} else {
|
||||
qnm_r[il][-m+l] += ylm_r;
|
||||
qnm_i[il][-m+l] -= ylm_i;
|
||||
}
|
||||
double tmp_r = expphim_r*expphi_r - expphim_i*expphi_i;
|
||||
double tmp_i = expphim_r*expphi_i + expphim_i*expphi_r;
|
||||
expphim_r = tmp_r;
|
||||
expphim_i = tmp_i;
|
||||
}
|
||||
|
||||
}
|
||||
}
|
||||
|
||||
// convert sums to averages
|
||||
|
||||
double facn = 1.0 / ncount;
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
for (int m = 0; m < 2*l+1; m++) {
|
||||
qnm_r[il][m] *= facn;
|
||||
qnm_i[il][m] *= facn;
|
||||
}
|
||||
}
|
||||
|
||||
// calculate Q_l
|
||||
// NOTE: optional W_l_hat and components of Q_qlcomp use these stored Q_l values
|
||||
|
||||
int jj = 0;
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
double qnormfac = sqrt(MY_4PI/(2*l+1));
|
||||
double qm_sum = 0.0;
|
||||
for (int m = 0; m < 2*l+1; m++)
|
||||
qm_sum += qnm_r[il][m]*qnm_r[il][m] + qnm_i[il][m]*qnm_i[il][m];
|
||||
qn[jj++] = qnormfac * sqrt(qm_sum);
|
||||
}
|
||||
|
||||
// calculate W_l
|
||||
|
||||
if (wlflag) {
|
||||
int idxcg_count = 0;
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
double wlsum = 0.0;
|
||||
for (int m1 = 0; m1 < 2*l+1; m1++) {
|
||||
for (int m2 = MAX(0,l-m1); m2 < MIN(2*l+1,3*l-m1+1); m2++) {
|
||||
int m = m1 + m2 - l;
|
||||
double qm1qm2_r = qnm_r[il][m1]*qnm_r[il][m2] - qnm_i[il][m1]*qnm_i[il][m2];
|
||||
double qm1qm2_i = qnm_r[il][m1]*qnm_i[il][m2] + qnm_i[il][m1]*qnm_r[il][m2];
|
||||
wlsum += (qm1qm2_r*qnm_r[il][m] + qm1qm2_i*qnm_i[il][m])*cglist[idxcg_count];
|
||||
idxcg_count++;
|
||||
}
|
||||
}
|
||||
qn[jj++] = wlsum/sqrt(2*l+1);
|
||||
}
|
||||
}
|
||||
|
||||
// calculate W_l_hat
|
||||
|
||||
if (wlhatflag) {
|
||||
int idxcg_count = 0;
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
double wlsum = 0.0;
|
||||
for (int m1 = 0; m1 < 2*l+1; m1++) {
|
||||
for (int m2 = MAX(0,l-m1); m2 < MIN(2*l+1,3*l-m1+1); m2++) {
|
||||
int m = m1 + m2 - l;
|
||||
double qm1qm2_r = qnm_r[il][m1]*qnm_r[il][m2] - qnm_i[il][m1]*qnm_i[il][m2];
|
||||
double qm1qm2_i = qnm_r[il][m1]*qnm_i[il][m2] + qnm_i[il][m1]*qnm_r[il][m2];
|
||||
wlsum += (qm1qm2_r*qnm_r[il][m] + qm1qm2_i*qnm_i[il][m])*cglist[idxcg_count];
|
||||
idxcg_count++;
|
||||
}
|
||||
}
|
||||
if (qn[il] < QEPSILON)
|
||||
qn[jj++] = 0.0;
|
||||
else {
|
||||
double qnormfac = sqrt(MY_4PI/(2*l+1));
|
||||
double qnfac = qnormfac/qn[il];
|
||||
qn[jj++] = wlsum/sqrt(2*l+1)*(qnfac*qnfac*qnfac);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Calculate components of Q_l/|Q_l|, for l=qlcomp
|
||||
|
||||
if (qlcompflag) {
|
||||
int il = iqlcomp;
|
||||
int l = qlcomp;
|
||||
if (qn[il] < QEPSILON)
|
||||
for (int m = 0; m < 2*l+1; m++) {
|
||||
qn[jj++] = 0.0;
|
||||
qn[jj++] = 0.0;
|
||||
}
|
||||
else {
|
||||
double qnormfac = sqrt(MY_4PI/(2*l+1));
|
||||
double qnfac = qnormfac/qn[il];
|
||||
for (int m = 0; m < 2*l+1; m++) {
|
||||
qn[jj++] = qnm_r[il][m] * qnfac;
|
||||
qn[jj++] = qnm_i[il][m] * qnfac;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
calculate scalar distance
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
double ComputeOrientOrderAtom::dist(const double r[])
|
||||
{
|
||||
return sqrt(r[0]*r[0] + r[1]*r[1] + r[2]*r[2]);
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
polar prefactor for spherical harmonic Y_l^m, where
|
||||
Y_l^m (theta, phi) = prefactor(l, m, cos(theta)) * exp(i*m*phi)
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
double ComputeOrientOrderAtom::polar_prefactor(int l, int m, double costheta)
|
||||
{
|
||||
const int mabs = abs(m);
|
||||
|
||||
double prefactor = 1.0;
|
||||
for (int i=l-mabs+1; i < l+mabs+1; ++i)
|
||||
prefactor *= static_cast<double>(i);
|
||||
|
||||
prefactor = sqrt(static_cast<double>(2*l+1)/(MY_4PI*prefactor))
|
||||
* associated_legendre(l,mabs,costheta);
|
||||
|
||||
if ((m < 0) && (m % 2)) prefactor = -prefactor;
|
||||
|
||||
return prefactor;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
associated legendre polynomial
|
||||
sign convention: P(l,l) = (2l-1)!!(-sqrt(1-x^2))^l
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
double ComputeOrientOrderAtom::associated_legendre(int l, int m, double x)
|
||||
{
|
||||
if (l < m) return 0.0;
|
||||
|
||||
double p(1.0), pm1(0.0), pm2(0.0);
|
||||
|
||||
if (m != 0) {
|
||||
const double msqx = -sqrt(1.0-x*x);
|
||||
for (int i=1; i < m+1; ++i)
|
||||
p *= static_cast<double>(2*i-1) * msqx;
|
||||
}
|
||||
|
||||
for (int i=m+1; i < l+1; ++i) {
|
||||
pm2 = pm1;
|
||||
pm1 = p;
|
||||
p = (static_cast<double>(2*i-1)*x*pm1
|
||||
- static_cast<double>(i+m-1)*pm2) / static_cast<double>(i-m);
|
||||
}
|
||||
|
||||
return p;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
assign Clebsch-Gordan coefficients
|
||||
using the quasi-binomial formula VMK 8.2.1(3)
|
||||
specialized for case j1=j2=j=l
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void ComputeOrientOrderAtom::init_clebsch_gordan()
|
||||
{
|
||||
double sum,dcg,sfaccg, sfac1, sfac2;
|
||||
int m, aa2, bb2, cc2;
|
||||
int ifac, idxcg_count;
|
||||
|
||||
idxcg_count = 0;
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
for (int m1 = 0; m1 < 2*l+1; m1++)
|
||||
for (int m2 = MAX(0,l-m1); m2 < MIN(2*l+1,3*l-m1+1); m2++)
|
||||
idxcg_count++;
|
||||
}
|
||||
idxcg_max = idxcg_count;
|
||||
memory->create(cglist, idxcg_max, "computeorientorderatom:cglist");
|
||||
|
||||
idxcg_count = 0;
|
||||
for (int il = 0; il < nqlist; il++) {
|
||||
int l = qlist[il];
|
||||
for (int m1 = 0; m1 < 2*l+1; m1++) {
|
||||
aa2 = m1 - l;
|
||||
for (int m2 = MAX(0,l-m1); m2 < MIN(2*l+1,3*l-m1+1); m2++) {
|
||||
bb2 = m2 - l;
|
||||
m = aa2 + bb2 + l;
|
||||
|
||||
sum = 0.0;
|
||||
for (int z = MAX(0, MAX(-aa2, bb2));
|
||||
z <= MIN(l, MIN(l - aa2, l + bb2)); z++) {
|
||||
ifac = z % 2 ? -1 : 1;
|
||||
sum += ifac /
|
||||
(factorial(z) *
|
||||
factorial(l - z) *
|
||||
factorial(l - aa2 - z) *
|
||||
factorial(l + bb2 - z) *
|
||||
factorial(aa2 + z) *
|
||||
factorial(-bb2 + z));
|
||||
}
|
||||
|
||||
cc2 = m - l;
|
||||
sfaccg = sqrt(factorial(l + aa2) *
|
||||
factorial(l - aa2) *
|
||||
factorial(l + bb2) *
|
||||
factorial(l - bb2) *
|
||||
factorial(l + cc2) *
|
||||
factorial(l - cc2) *
|
||||
(2*l + 1));
|
||||
|
||||
sfac1 = factorial(3*l + 1);
|
||||
sfac2 = factorial(l);
|
||||
dcg = sqrt(sfac2*sfac2*sfac2 / sfac1);
|
||||
|
||||
cglist[idxcg_count] = sum * dcg * sfaccg;
|
||||
idxcg_count++;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user