Added Clebsch-Gordan coefficients
This commit is contained in:
Aidan Thompson
@ -56,6 +56,7 @@ ComputeOrientOrderAtom::ComputeOrientOrderAtom(LAMMPS *lmp, int narg, char **arg
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nnn = 12;
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cutsq = 0.0;
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wlflag = 0;
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qlcompflag = 0;
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// specify which orders to request
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@ -103,6 +104,13 @@ ComputeOrientOrderAtom::ComputeOrientOrderAtom(LAMMPS *lmp, int narg, char **arg
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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],"wlparams") == 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],"components") == 0) {
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qlcompflag = 1;
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if (iarg+2 > narg)
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@ -130,8 +138,9 @@ ComputeOrientOrderAtom::ComputeOrientOrderAtom(LAMMPS *lmp, int narg, char **arg
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} else error->all(FLERR,"Illegal compute orientorder/atom command");
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}
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if (qlcompflag) ncol = nqlist + 2*(2*qlcomp+1);
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else ncol = nqlist;
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ncol = nqlist;
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if (wlflag) ncol += nqlist;
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if (qlcompflag) ncol += nqlist + 2*(2*qlcomp+1);
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peratom_flag = 1;
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size_peratom_cols = ncol;
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@ -151,7 +160,7 @@ ComputeOrientOrderAtom::~ComputeOrientOrderAtom()
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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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@ -183,6 +192,8 @@ void ComputeOrientOrderAtom::init()
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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) init_clebsch_gordan();
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}
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/* ---------------------------------------------------------------------- */
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@ -274,8 +285,8 @@ void ComputeOrientOrderAtom::compute_peratom()
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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 (int il = 0; il < nqlist; il++)
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qn[il] = 0.0;
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for (int 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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@ -461,52 +472,71 @@ void ComputeOrientOrderAtom::calc_boop(double **rlist,
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}
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}
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// convert sums to averages
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double facn = 1.0 / ncount;
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for (int il = 0; il < nqlist; il++) {
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int l = qlist[il];
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for(int m = 0; m < 2*l+1; m++) {
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qnm_r[il][m] *= facn;
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qnm_i[il][m] *= facn;
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}
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}
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// calculate Q_l
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double fac = sqrt(MY_4PI) / ncount;
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double facpi = sqrt(MY_4PI);
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double normfac = 0.0;
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int jcount = 0;
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int jj = 0;
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for (int il = 0; il < nqlist; il++) {
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int l = qlist[il];
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double qm_sum = 0.0;
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for(int m = 0; m < 2*l+1; m++)
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qm_sum += qnm_r[il][m]*qnm_r[il][m] + qnm_i[il][m]*qnm_i[il][m];
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qn[jcount++] = fac * sqrt(qm_sum / (2*l+1));
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for(int m = 0; m < 2*l+1; m++)
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printf("Q_l = %d %g %g\n",l, qnm_r[il][m], qnm_i[il][m]);
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qn[jj++] = facpi * sqrt(qm_sum / (2*l+1) );
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if (qlcompflag && iqlcomp == il) normfac = 1.0/sqrt(qm_sum);
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}
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// TODO:
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// 1. Need to allocate extra memory in qn[] for this option
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// 2. Need to add keyword option
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// 1. [done]Need to allocate extra memory in qnarray[] for this option
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// 2. [done]Need to add keyword option
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// 3. Need to caclulate Clebsch-Gordan/Wigner 3j coefficients
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// 4. Compate to bcc values in /Users/athomps/netapp/codes/MatMiner/matminer/matminer/featurizers/boop
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// (Can try getting them from boop.py first)
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// 5. Compate to bcc values in /Users/athomps/netapp/codes/MatMiner/matminer/matminer/featurizers/boop.py
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// // calculate W_l
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// calculate W_l
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// if (wlflag) {
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// for (int il = 0; il < nqlist; il++) {
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// int l = qlist[il];
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// double wlsum = 0.0;
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// for(int m1 = 0; m1 < 2*l+1; m1++) {
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// for(int m2 = MAX(0,l-m1); m2 < MIN(2*l+1,3*l-m1; m2++)) {
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// int m = m1 + m2 - l;
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// qm1qm2_r = qnm_r[il][m1]*qnm_r[il][m2] - qnm_i[il][m1]*qnm_i[il][m2];
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// qm1qm2_i = qnm_r[il][m1]*qnm_i[il][m2] + qnm_i[il][m1]*qnm_r[il][m2];
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// wlsum += (qm1qm2_r*qnm_r[il][m] + qm1qm2_i*qnm_i[il][m])*cg;
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// }
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// }
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// qn[jcount++] = wlsum;
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// }
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// }
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if (wlflag) {
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int idxcg_count = 0;
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for (int il = 0; il < nqlist; il++) {
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int l = qlist[il];
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double wlsum = 0.0;
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for(int m1 = 0; m1 < 2*l+1; m1++) {
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for(int m2 = MAX(0,l-m1); m2 < MIN(2*l+1,3*l-m1+1); m2++) {
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int m = m1 + m2 - l;
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double qm1qm2_r = qnm_r[il][m1]*qnm_r[il][m2] - qnm_i[il][m1]*qnm_i[il][m2];
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double qm1qm2_i = qnm_r[il][m1]*qnm_i[il][m2] + qnm_i[il][m1]*qnm_r[il][m2];
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wlsum += (qm1qm2_r*qnm_r[il][m] + qm1qm2_i*qnm_i[il][m])*cglist[idxcg_count];
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idxcg_count++;
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}
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}
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// This matches boop.py output, with cg==1
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printf("W_l = %d %g\n",l,wlsum);
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qn[jj++] = wlsum/sqrt(2*l+1);
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}
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}
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// output of the complex vector
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if (qlcompflag) {
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for(int m = 0; m < 2*qlcomp+1; m++) {
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qn[jcount++] = qnm_r[iqlcomp][m] * normfac;
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qn[jcount++] = qnm_i[iqlcomp][m] * normfac;
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qn[jj++] = qnm_r[iqlcomp][m] * normfac;
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qn[jj++] = qnm_i[iqlcomp][m] * normfac;
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}
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}
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@ -567,3 +597,272 @@ double ComputeOrientOrderAtom::associated_legendre(int l, int m, double x)
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return p;
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}
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/* ----------------------------------------------------------------------
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assign Clebsch-Gordan coefficients with l1=l2=l
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using the quasi-binomial formula VMK 8.2.1(3)
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------------------------------------------------------------------------- */
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void ComputeOrientOrderAtom::init_clebsch_gordan()
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{
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double sum,dcg,sfaccg;
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int m, aa2, bb2, cc2, j1, j2, j;
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int ifac, idxcg_count;
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idxcg_count = 0;
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for (int il = 0; il < nqlist; il++) {
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int l = qlist[il];
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for(int m1 = 0; m1 < 2*l+1; m1++) {
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for(int m2 = MAX(0,l-m1); m2 < MIN(2*l+1,3*l-m1+1); m2++) {
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idxcg_count++;
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}
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}
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}
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idxcg_max = idxcg_count;
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memory->create(cglist, idxcg_max, "computeorientorderatom:cglist");
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idxcg_count = 0;
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for (int il = 0; il < nqlist; il++) {
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int l = qlist[il];
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j1 = j2 = j = l;
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for(int m1 = 0; m1 < 2*l+1; m1++) {
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aa2 = m1 - j1;
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for(int m2 = MAX(0,l-m1); m2 < MIN(2*l+1,3*l-m1+1); m2++) {
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bb2 = m2 - j2;
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m = (aa2 + bb2 + j) / 2;
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sum = 0.0;
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for (int z = MAX(0, MAX(-(j - j2 + aa2)
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, -(j - j1 - bb2) ));
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z <= MIN((j1 + j2 - j),
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MIN((j1 - aa2), (j2 + bb2)));
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z++) {
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ifac = z % 2 ? -1 : 1;
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sum += ifac /
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(factorial(z) *
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factorial((j1 + j2 - j) - z) *
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factorial((j1 - aa2) - z) *
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factorial((j2 + bb2) - z) *
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factorial((j - j2 + aa2) + z) *
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factorial((j - j1 - bb2) + z));
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}
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cc2 = m - j;
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dcg = deltacg(j1, j2, j);
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sfaccg = sqrt(factorial((j1 + aa2)) *
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factorial((j1 - aa2)) *
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factorial((j2 + bb2)) *
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factorial((j2 - bb2)) *
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factorial((j + cc2)) *
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factorial((j - cc2)) *
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(j + 1));
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cglist[idxcg_count] = sum * dcg * sfaccg;
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idxcg_count++;
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}
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}
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}
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}
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/* ----------------------------------------------------------------------
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factorial n, wrapper for precomputed table
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------------------------------------------------------------------------- */
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double ComputeOrientOrderAtom::factorial(int n)
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{
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if (n < 0 || n > nmaxfactorial) {
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char str[128];
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sprintf(str, "Invalid argument to factorial %d", n);
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error->all(FLERR, str);
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}
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return nfac_table[n];
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}
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/* ----------------------------------------------------------------------
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factorial n table, size SNA::nmaxfactorial+1
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------------------------------------------------------------------------- */
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const double ComputeOrientOrderAtom::nfac_table[] = {
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1,
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1,
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2,
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6,
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24,
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120,
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720,
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5040,
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40320,
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362880,
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3628800,
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39916800,
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479001600,
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6227020800,
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87178291200,
|
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1307674368000,
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20922789888000,
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355687428096000,
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6.402373705728e+15,
|
||||
1.21645100408832e+17,
|
||||
2.43290200817664e+18,
|
||||
5.10909421717094e+19,
|
||||
1.12400072777761e+21,
|
||||
2.5852016738885e+22,
|
||||
6.20448401733239e+23,
|
||||
1.5511210043331e+25,
|
||||
4.03291461126606e+26,
|
||||
1.08888694504184e+28,
|
||||
3.04888344611714e+29,
|
||||
8.8417619937397e+30,
|
||||
2.65252859812191e+32,
|
||||
8.22283865417792e+33,
|
||||
2.63130836933694e+35,
|
||||
8.68331761881189e+36,
|
||||
2.95232799039604e+38,
|
||||
1.03331479663861e+40,
|
||||
3.71993326789901e+41,
|
||||
1.37637530912263e+43,
|
||||
5.23022617466601e+44,
|
||||
2.03978820811974e+46,
|
||||
8.15915283247898e+47,
|
||||
3.34525266131638e+49,
|
||||
1.40500611775288e+51,
|
||||
6.04152630633738e+52,
|
||||
2.65827157478845e+54,
|
||||
1.1962222086548e+56,
|
||||
5.50262215981209e+57,
|
||||
2.58623241511168e+59,
|
||||
1.24139155925361e+61,
|
||||
6.08281864034268e+62,
|
||||
3.04140932017134e+64,
|
||||
1.55111875328738e+66,
|
||||
8.06581751709439e+67,
|
||||
4.27488328406003e+69,
|
||||
2.30843697339241e+71,
|
||||
1.26964033536583e+73,
|
||||
7.10998587804863e+74,
|
||||
4.05269195048772e+76,
|
||||
2.35056133128288e+78,
|
||||
1.3868311854569e+80,
|
||||
8.32098711274139e+81,
|
||||
5.07580213877225e+83,
|
||||
3.14699732603879e+85,
|
||||
1.98260831540444e+87,
|
||||
1.26886932185884e+89,
|
||||
8.24765059208247e+90,
|
||||
5.44344939077443e+92,
|
||||
3.64711109181887e+94,
|
||||
2.48003554243683e+96,
|
||||
1.71122452428141e+98,
|
||||
1.19785716699699e+100,
|
||||
8.50478588567862e+101,
|
||||
6.12344583768861e+103,
|
||||
4.47011546151268e+105,
|
||||
3.30788544151939e+107,
|
||||
2.48091408113954e+109,
|
||||
1.88549470166605e+111,
|
||||
1.45183092028286e+113,
|
||||
1.13242811782063e+115,
|
||||
8.94618213078297e+116,
|
||||
7.15694570462638e+118,
|
||||
5.79712602074737e+120,
|
||||
4.75364333701284e+122,
|
||||
3.94552396972066e+124,
|
||||
3.31424013456535e+126,
|
||||
2.81710411438055e+128,
|
||||
2.42270953836727e+130,
|
||||
2.10775729837953e+132,
|
||||
1.85482642257398e+134,
|
||||
1.65079551609085e+136,
|
||||
1.48571596448176e+138,
|
||||
1.3520015276784e+140,
|
||||
1.24384140546413e+142,
|
||||
1.15677250708164e+144,
|
||||
1.08736615665674e+146,
|
||||
1.03299784882391e+148,
|
||||
9.91677934870949e+149,
|
||||
9.61927596824821e+151,
|
||||
9.42689044888324e+153,
|
||||
9.33262154439441e+155,
|
||||
9.33262154439441e+157,
|
||||
9.42594775983835e+159,
|
||||
9.61446671503512e+161,
|
||||
9.90290071648618e+163,
|
||||
1.02990167451456e+166,
|
||||
1.08139675824029e+168,
|
||||
1.14628056373471e+170,
|
||||
1.22652020319614e+172,
|
||||
1.32464181945183e+174,
|
||||
1.44385958320249e+176,
|
||||
1.58824554152274e+178,
|
||||
1.76295255109024e+180,
|
||||
1.97450685722107e+182,
|
||||
2.23119274865981e+184,
|
||||
2.54355973347219e+186,
|
||||
2.92509369349301e+188,
|
||||
3.3931086844519e+190,
|
||||
3.96993716080872e+192,
|
||||
4.68452584975429e+194,
|
||||
5.5745857612076e+196,
|
||||
6.68950291344912e+198,
|
||||
8.09429852527344e+200,
|
||||
9.8750442008336e+202,
|
||||
1.21463043670253e+205,
|
||||
1.50614174151114e+207,
|
||||
1.88267717688893e+209,
|
||||
2.37217324288005e+211,
|
||||
3.01266001845766e+213,
|
||||
3.8562048236258e+215,
|
||||
4.97450422247729e+217,
|
||||
6.46685548922047e+219,
|
||||
8.47158069087882e+221,
|
||||
1.118248651196e+224,
|
||||
1.48727070609069e+226,
|
||||
1.99294274616152e+228,
|
||||
2.69047270731805e+230,
|
||||
3.65904288195255e+232,
|
||||
5.01288874827499e+234,
|
||||
6.91778647261949e+236,
|
||||
9.61572319694109e+238,
|
||||
1.34620124757175e+241,
|
||||
1.89814375907617e+243,
|
||||
2.69536413788816e+245,
|
||||
3.85437071718007e+247,
|
||||
5.5502938327393e+249,
|
||||
8.04792605747199e+251,
|
||||
1.17499720439091e+254,
|
||||
1.72724589045464e+256,
|
||||
2.55632391787286e+258,
|
||||
3.80892263763057e+260,
|
||||
5.71338395644585e+262,
|
||||
8.62720977423323e+264,
|
||||
1.31133588568345e+267,
|
||||
2.00634390509568e+269,
|
||||
3.08976961384735e+271,
|
||||
4.78914290146339e+273,
|
||||
7.47106292628289e+275,
|
||||
1.17295687942641e+278,
|
||||
1.85327186949373e+280,
|
||||
2.94670227249504e+282,
|
||||
4.71472363599206e+284,
|
||||
7.59070505394721e+286,
|
||||
1.22969421873945e+289,
|
||||
2.0044015765453e+291,
|
||||
3.28721858553429e+293,
|
||||
5.42391066613159e+295,
|
||||
9.00369170577843e+297,
|
||||
1.503616514865e+300, // nmaxfactorial = 167
|
||||
};
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
the function delta given by VMK Eq. 8.2(1)
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
double ComputeOrientOrderAtom::deltacg(int j1, int j2, int j)
|
||||
{
|
||||
double sfaccg = factorial((j1 + j2 + j) + 1);
|
||||
return sqrt(factorial((j1 + j2 - j)) *
|
||||
factorial((j1 - j2 + j)) *
|
||||
factorial((-j1 + j2 + j)) / sfaccg);
|
||||
}
|
||||
|
||||
|
||||
Reference in New Issue
Block a user