static void power_fit(int n,int nset,real **val,real *t)
{
real *x,*y,quality,a,b,r;
int s,i;
snew(x,n);
snew(y,n);
if (t[0]>0) {
for(i=0; i<n; i++)
if (t[0]>0)
x[i] = log(t[i]);
} else {
fprintf(stdout,"First time is not larger than 0, using index number as time for power fit\n");
for(i=0; i<n; i++)
x[i] = log(i+1);
}
for(s=0; s<nset; s++) {
i=0;
for(i=0; i<n && val[s][i]>=0; i++)
y[i] = log(val[s][i]);
if (i < n)
fprintf(stdout,"Will power fit up to point %d, since it is not larger than 0\n",i);
lsq_y_ax_b(i,x,y,&a,&b,&r,&quality);
fprintf(stdout,"Power fit set %3d: error %.3f a %g b %g\n",
s+1,quality,a,exp(b));
}
sfree(y);
sfree(x);
}
static void regression_analysis(int n,bool bXYdy,real *x,real **val)
{
real S,chi2,a,b,da,db,r=0;
printf("Fitting data to a function f(x) = ax + b\n");
printf("Minimizing residual chi2 = Sum_i w_i [f(x_i) - y_i]2\n");
printf("Error estimates will be given if w_i (sigma) values are given\n");
printf("(use option -xydy).\n\n");
if (bXYdy)
lsq_y_ax_b_error(n,x,val[0],val[1],&a,&b,&da,&db,&r,&S);
else
lsq_y_ax_b(n,x,val[0],&a,&b,&r,&S);
chi2 = sqr((n-2)*S);
printf("Chi2 = %g\n",chi2);
printf("S (Sqrt(Chi2/(n-2)) = %g\n",S);
printf("Correlation coefficient = %.1f%%\n",100*r);
printf("\n");
if (bXYdy) {
printf("a = %g +/- %g\n",a,da);
printf("b = %g +/- %g\n",b,db);
}
else {
printf("a = %g\n",a);
printf("b = %g\n",b);
}
}
static void dielectric(FILE *fmj, FILE *fmd, FILE *outf, FILE *fcur, FILE *mcor,
FILE *fmjdsp, gmx_bool bNoJump, gmx_bool bACF, gmx_bool bINT,
int ePBC, t_topology top, t_trxframe fr, real temp,
real bfit, real efit, real bvit, real evit,
t_trxstatus *status, int isize, int nmols, int nshift,
int *index0, int indexm[], real mass2[],
real qmol[], real eps_rf, const gmx_output_env_t *oenv)
{
int i, j;
int valloc, nalloc, nfr, nvfr;
int vshfr;
real *xshfr = NULL;
int *vfr = NULL;
real refr = 0.0;
real *cacf = NULL;
real *time = NULL;
real *djc = NULL;
real corint = 0.0;
real prefactorav = 0.0;
real prefactor = 0.0;
real volume;
real volume_av = 0.0;
real dk_s, dk_d, dk_f;
real mj = 0.0;
real mj2 = 0.0;
real mjd = 0.0;
real mjdav = 0.0;
real md2 = 0.0;
real mdav2 = 0.0;
real sgk;
rvec mja_tmp;
rvec mjd_tmp;
rvec mdvec;
rvec *mu = NULL;
rvec *xp = NULL;
rvec *v0 = NULL;
rvec *mjdsp = NULL;
real *dsp2 = NULL;
real t0;
real rtmp;
rvec tmp;
rvec *mtrans = NULL;
/*
* Variables for the least-squares fit for Einstein-Helfand and Green-Kubo
*/
int bi, ei, ie, ii;
real rest = 0.0;
real sigma = 0.0;
real malt = 0.0;
real err = 0.0;
real *xfit;
real *yfit;
gmx_rmpbc_t gpbc = NULL;
/*
* indices for EH
*/
ei = 0;
bi = 0;
/*
* indices for GK
*/
ii = 0;
ie = 0;
t0 = 0;
sgk = 0.0;
/* This is the main loop over frames */
nfr = 0;
nvfr = 0;
vshfr = 0;
nalloc = 0;
valloc = 0;
clear_rvec(mja_tmp);
clear_rvec(mjd_tmp);
clear_rvec(mdvec);
clear_rvec(tmp);
gpbc = gmx_rmpbc_init(&top.idef, ePBC, fr.natoms);
do
{
refr = (nfr+1);
if (nfr >= nalloc)
{
nalloc += 100;
srenew(time, nalloc);
srenew(mu, nalloc);
srenew(mjdsp, nalloc);
srenew(dsp2, nalloc);
srenew(mtrans, nalloc);
srenew(xshfr, nalloc);
for (i = nfr; i < nalloc; i++)
{
clear_rvec(mjdsp[i]);
clear_rvec(mu[i]);
clear_rvec(mtrans[i]);
dsp2[i] = 0.0;
xshfr[i] = 0.0;
}
}
GMX_RELEASE_ASSERT(time != NULL, "Memory not allocated correctly - time array is NULL");
if (nfr == 0)
{
t0 = fr.time;
}
time[nfr] = fr.time-t0;
if (time[nfr] <= bfit)
{
bi = nfr;
}
if (time[nfr] <= efit)
{
ei = nfr;
}
if (bNoJump)
{
if (xp)
{
remove_jump(fr.box, fr.natoms, xp, fr.x);
}
else
{
snew(xp, fr.natoms);
}
for (i = 0; i < fr.natoms; i++)
{
copy_rvec(fr.x[i], xp[i]);
}
}
gmx_rmpbc_trxfr(gpbc, &fr);
calc_mj(top, ePBC, fr.box, bNoJump, nmols, indexm, fr.x, mtrans[nfr], mass2, qmol);
for (i = 0; i < isize; i++)
{
j = index0[i];
svmul(top.atoms.atom[j].q, fr.x[j], fr.x[j]);
rvec_inc(mu[nfr], fr.x[j]);
}
/*if(mod(nfr,nshift)==0){*/
if (nfr%nshift == 0)
{
for (j = nfr; j >= 0; j--)
{
rvec_sub(mtrans[nfr], mtrans[j], tmp);
dsp2[nfr-j] += norm2(tmp);
xshfr[nfr-j] += 1.0;
}
}
if (fr.bV)
{
if (nvfr >= valloc)
{
valloc += 100;
srenew(vfr, valloc);
if (bINT)
{
srenew(djc, valloc);
}
srenew(v0, valloc);
if (bACF)
{
srenew(cacf, valloc);
}
}
if (time[nfr] <= bvit)
{
ii = nvfr;
}
if (time[nfr] <= evit)
{
ie = nvfr;
}
vfr[nvfr] = nfr;
clear_rvec(v0[nvfr]);
if (bACF)
{
cacf[nvfr] = 0.0;
}
if (bINT)
{
djc[nvfr] = 0.0;
}
for (i = 0; i < isize; i++)
{
j = index0[i];
svmul(mass2[j], fr.v[j], fr.v[j]);
svmul(qmol[j], fr.v[j], fr.v[j]);
rvec_inc(v0[nvfr], fr.v[j]);
}
fprintf(fcur, "%.3f\t%.6f\t%.6f\t%.6f\n", time[nfr], v0[nfr][XX], v0[nfr][YY], v0[nfr][ZZ]);
if (bACF || bINT)
{
/*if(mod(nvfr,nshift)==0){*/
if (nvfr%nshift == 0)
{
for (j = nvfr; j >= 0; j--)
{
if (bACF)
{
cacf[nvfr-j] += iprod(v0[nvfr], v0[j]);
}
if (bINT)
{
djc[nvfr-j] += iprod(mu[vfr[j]], v0[nvfr]);
}
}
vshfr++;
}
}
nvfr++;
}
volume = det(fr.box);
volume_av += volume;
rvec_inc(mja_tmp, mtrans[nfr]);
mjd += iprod(mu[nfr], mtrans[nfr]);
rvec_inc(mdvec, mu[nfr]);
mj2 += iprod(mtrans[nfr], mtrans[nfr]);
md2 += iprod(mu[nfr], mu[nfr]);
fprintf(fmj, "%.3f\t%8.5f\t%8.5f\t%8.5f\t%8.5f\t%8.5f\n", time[nfr], mtrans[nfr][XX], mtrans[nfr][YY], mtrans[nfr][ZZ], mj2/refr, norm(mja_tmp)/refr);
fprintf(fmd, "%.3f\t%8.5f\t%8.5f\t%8.5f\t%8.5f\t%8.5f\n", \
time[nfr], mu[nfr][XX], mu[nfr][YY], mu[nfr][ZZ], md2/refr, norm(mdvec)/refr);
nfr++;
}
while (read_next_frame(oenv, status, &fr));
gmx_rmpbc_done(gpbc);
volume_av /= refr;
prefactor = 1.0;
prefactor /= 3.0*EPSILON0*volume_av*BOLTZ*temp;
prefactorav = E_CHARGE*E_CHARGE;
prefactorav /= volume_av*BOLTZMANN*temp*NANO*6.0;
fprintf(stderr, "Prefactor fit E-H: 1 / 6.0*V*k_B*T: %g\n", prefactorav);
calc_mjdsp(fmjdsp, prefactorav, dsp2, time, nfr, xshfr);
/*
* Now we can average and calculate the correlation functions
*/
mj2 /= refr;
mjd /= refr;
md2 /= refr;
svmul(1.0/refr, mdvec, mdvec);
svmul(1.0/refr, mja_tmp, mja_tmp);
mdav2 = norm2(mdvec);
mj = norm2(mja_tmp);
mjdav = iprod(mdvec, mja_tmp);
printf("\n\nAverage translational dipole moment M_J [enm] after %d frames (|M|^2): %f %f %f (%f)\n", nfr, mja_tmp[XX], mja_tmp[YY], mja_tmp[ZZ], mj2);
printf("\n\nAverage molecular dipole moment M_D [enm] after %d frames (|M|^2): %f %f %f (%f)\n", nfr, mdvec[XX], mdvec[YY], mdvec[ZZ], md2);
if (v0 != NULL)
{
if (bINT)
{
printf("\nCalculating M_D - current correlation integral ... \n");
corint = calc_cacf(mcor, prefactorav/EPSI0, djc, time, nvfr, vfr, ie, nshift);
}
if (bACF)
{
printf("\nCalculating current autocorrelation ... \n");
sgk = calc_cacf(outf, prefactorav/PICO, cacf, time, nvfr, vfr, ie, nshift);
if (ie > ii)
{
snew(xfit, ie-ii+1);
snew(yfit, ie-ii+1);
for (i = ii; i <= ie; i++)
{
xfit[i-ii] = std::log(time[vfr[i]]);
rtmp = std::abs(cacf[i]);
yfit[i-ii] = std::log(rtmp);
}
lsq_y_ax_b(ie-ii, xfit, yfit, &sigma, &malt, &err, &rest);
malt = std::exp(malt);
sigma += 1.0;
malt *= prefactorav*2.0e12/sigma;
sfree(xfit);
sfree(yfit);
}
}
}
/* Calculation of the dielectric constant */
fprintf(stderr, "\n********************************************\n");
dk_s = calceps(prefactor, md2, mj2, mjd, eps_rf, FALSE);
fprintf(stderr, "\nAbsolute values:\n epsilon=%f\n", dk_s);
fprintf(stderr, " <M_D^2> , <M_J^2>, <(M_J*M_D)^2>: (%f, %f, %f)\n\n", md2, mj2, mjd);
fprintf(stderr, "********************************************\n");
dk_f = calceps(prefactor, md2-mdav2, mj2-mj, mjd-mjdav, eps_rf, FALSE);
fprintf(stderr, "\n\nFluctuations:\n epsilon=%f\n\n", dk_f);
fprintf(stderr, "\n deltaM_D , deltaM_J, deltaM_JD: (%f, %f, %f)\n", md2-mdav2, mj2-mj, mjd-mjdav);
fprintf(stderr, "\n********************************************\n");
if (bINT)
{
dk_d = calceps(prefactor, md2-mdav2, mj2-mj, corint, eps_rf, TRUE);
fprintf(stderr, "\nStatic dielectric constant using integral and fluctuations: %f\n", dk_d);
fprintf(stderr, "\n < M_JM_D > via integral: %.3f\n", -1.0*corint);
}
fprintf(stderr, "\n***************************************************");
fprintf(stderr, "\n\nAverage volume V=%f nm^3 at T=%f K\n", volume_av, temp);
fprintf(stderr, "and corresponding refactor 1.0 / 3.0*V*k_B*T*EPSILON_0: %f \n", prefactor);
if (bACF && (ii < nvfr))
{
fprintf(stderr, "Integral and integrated fit to the current acf yields at t=%f:\n", time[vfr[ii]]);
fprintf(stderr, "sigma=%8.3f (pure integral: %.3f)\n", sgk-malt*std::pow(time[vfr[ii]], sigma), sgk);
}
if (ei > bi)
{
fprintf(stderr, "\nStart fit at %f ps (%f).\n", time[bi], bfit);
fprintf(stderr, "End fit at %f ps (%f).\n\n", time[ei], efit);
snew(xfit, ei-bi+1);
snew(yfit, ei-bi+1);
for (i = bi; i <= ei; i++)
{
xfit[i-bi] = time[i];
yfit[i-bi] = dsp2[i];
}
lsq_y_ax_b(ei-bi, xfit, yfit, &sigma, &malt, &err, &rest);
sigma *= 1e12;
dk_d = calceps(prefactor, md2, 0.5*malt/prefactorav, corint, eps_rf, TRUE);
fprintf(stderr, "Einstein-Helfand fit to the MSD of the translational dipole moment yields:\n\n");
fprintf(stderr, "sigma=%.4f\n", sigma);
fprintf(stderr, "translational fraction of M^2: %.4f\n", 0.5*malt/prefactorav);
fprintf(stderr, "Dielectric constant using EH: %.4f\n", dk_d);
sfree(xfit);
sfree(yfit);
}
else
{
fprintf(stderr, "Too few points for a fit.\n");
}
if (v0 != NULL)
{
sfree(v0);
}
if (bACF)
{
sfree(cacf);
}
if (bINT)
{
sfree(djc);
}
sfree(time);
sfree(mjdsp);
sfree(mu);
}
static void regression_analysis(int n, gmx_bool bXYdy,
real *x, int nset, real **val)
{
real S, chi2, a, b, da, db, r = 0;
int ok;
if (bXYdy || (nset == 1))
{
printf("Fitting data to a function f(x) = ax + b\n");
printf("Minimizing residual chi2 = Sum_i w_i [f(x_i) - y_i]2\n");
printf("Error estimates will be given if w_i (sigma) values are given\n");
printf("(use option -xydy).\n\n");
if (bXYdy)
{
if ((ok = lsq_y_ax_b_error(n, x, val[0], val[1], &a, &b, &da, &db, &r, &S)) != estatsOK)
{
gmx_fatal(FARGS, "Error fitting the data: %s",
gmx_stats_message(ok));
}
}
else
{
if ((ok = lsq_y_ax_b(n, x, val[0], &a, &b, &r, &S)) != estatsOK)
{
gmx_fatal(FARGS, "Error fitting the data: %s",
gmx_stats_message(ok));
}
}
chi2 = sqr((n-2)*S);
printf("Chi2 = %g\n", chi2);
printf("S (Sqrt(Chi2/(n-2)) = %g\n", S);
printf("Correlation coefficient = %.1f%%\n", 100*r);
printf("\n");
if (bXYdy)
{
printf("a = %g +/- %g\n", a, da);
printf("b = %g +/- %g\n", b, db);
}
else
{
printf("a = %g\n", a);
printf("b = %g\n", b);
}
}
else
{
double chi2, *a, **xx, *y;
int i, j;
snew(y, n);
snew(xx, nset-1);
for (j = 0; (j < nset-1); j++)
{
snew(xx[j], n);
}
for (i = 0; (i < n); i++)
{
y[i] = val[0][i];
for (j = 1; (j < nset); j++)
{
xx[j-1][i] = val[j][i];
}
}
snew(a, nset-1);
chi2 = multi_regression(NULL, n, y, nset-1, xx, a);
printf("Fitting %d data points in %d sets\n", n, nset-1);
printf("chi2 = %g\n", chi2);
printf("A =");
for (i = 0; (i < nset-1); i++)
{
printf(" %g", a[i]);
sfree(xx[i]);
}
printf("\n");
sfree(xx);
sfree(y);
sfree(a);
}
}
void do_corr(const char *trx_file, const char *ndx_file, const char *msd_file,
const char *mol_file, const char *pdb_file, real t_pdb,
int nrgrp, t_topology *top, int ePBC,
gmx_bool bTen, gmx_bool bMW, gmx_bool bRmCOMM,
int type, real dim_factor, int axis,
real dt, real beginfit, real endfit, const output_env_t oenv)
{
t_corr *msd;
int *gnx; /* the selected groups' sizes */
atom_id **index; /* selected groups' indices */
char **grpname;
int i, i0, i1, j, N, nat_trx;
real *DD, *SigmaD, a, a2, b, r, chi2;
rvec *x;
matrix box;
int *gnx_com = NULL; /* the COM removal group size */
atom_id **index_com = NULL; /* the COM removal group atom indices */
char **grpname_com = NULL; /* the COM removal group name */
snew(gnx, nrgrp);
snew(index, nrgrp);
snew(grpname, nrgrp);
fprintf(stderr, "\nSelect a group to calculate mean squared displacement for:\n");
get_index(&top->atoms, ndx_file, nrgrp, gnx, index, grpname);
if (bRmCOMM)
{
snew(gnx_com, 1);
snew(index_com, 1);
snew(grpname_com, 1);
fprintf(stderr, "\nNow select a group for center of mass removal:\n");
get_index(&top->atoms, ndx_file, 1, gnx_com, index_com, grpname_com);
}
if (mol_file)
{
index_atom2mol(&gnx[0], index[0], &top->mols);
}
msd = init_corr(nrgrp, type, axis, dim_factor,
mol_file == NULL ? 0 : gnx[0], bTen, bMW, dt, top,
beginfit, endfit);
nat_trx =
corr_loop(msd, trx_file, top, ePBC, mol_file ? gnx[0] : 0, gnx, index,
(mol_file != NULL) ? calc1_mol : (bMW ? calc1_mw : calc1_norm),
bTen, gnx_com, index_com, dt, t_pdb,
pdb_file ? &x : NULL, box, oenv);
/* Correct for the number of points */
for (j = 0; (j < msd->ngrp); j++)
{
for (i = 0; (i < msd->nframes); i++)
{
msd->data[j][i] /= msd->ndata[j][i];
if (bTen)
{
msmul(msd->datam[j][i], 1.0/msd->ndata[j][i], msd->datam[j][i]);
}
}
}
if (mol_file)
{
if (pdb_file && x == NULL)
{
fprintf(stderr, "\nNo frame found need time tpdb = %g ps\n"
"Can not write %s\n\n", t_pdb, pdb_file);
}
i = top->atoms.nr;
top->atoms.nr = nat_trx;
printmol(msd, mol_file, pdb_file, index[0], top, x, ePBC, box, oenv);
top->atoms.nr = i;
}
DD = NULL;
SigmaD = NULL;
if (beginfit == -1)
{
i0 = static_cast<int>(0.1*(msd->nframes - 1) + 0.5);
beginfit = msd->time[i0];
}
else
{
for (i0 = 0; i0 < msd->nframes && msd->time[i0] < beginfit; i0++)
{
;
}
}
if (endfit == -1)
{
i1 = static_cast<int>(0.9*(msd->nframes - 1) + 0.5) + 1;
endfit = msd->time[i1-1];
}
else
{
for (i1 = i0; i1 < msd->nframes && msd->time[i1] <= endfit; i1++)
{
;
}
}
fprintf(stdout, "Fitting from %g to %g %s\n\n", beginfit, endfit,
output_env_get_time_unit(oenv));
N = i1-i0;
if (N <= 2)
{
fprintf(stdout, "Not enough points for fitting (%d).\n"
"Can not determine the diffusion constant.\n", N);
}
else
{
snew(DD, msd->ngrp);
snew(SigmaD, msd->ngrp);
for (j = 0; j < msd->ngrp; j++)
{
if (N >= 4)
{
lsq_y_ax_b(N/2, &(msd->time[i0]), &(msd->data[j][i0]), &a, &b, &r, &chi2);
lsq_y_ax_b(N/2, &(msd->time[i0+N/2]), &(msd->data[j][i0+N/2]), &a2, &b, &r, &chi2);
SigmaD[j] = std::abs(a-a2);
}
else
{
SigmaD[j] = 0;
}
lsq_y_ax_b(N, &(msd->time[i0]), &(msd->data[j][i0]), &(DD[j]), &b, &r, &chi2);
DD[j] *= FACTOR/msd->dim_factor;
SigmaD[j] *= FACTOR/msd->dim_factor;
if (DD[j] > 0.01 && DD[j] < 1e4)
{
fprintf(stdout, "D[%10s] %.4f (+/- %.4f) 1e-5 cm^2/s\n",
grpname[j], DD[j], SigmaD[j]);
}
else
{
fprintf(stdout, "D[%10s] %.4g (+/- %.4g) 1e-5 cm^2/s\n",
grpname[j], DD[j], SigmaD[j]);
}
}
}
/* Print mean square displacement */
corr_print(msd, bTen, msd_file,
"Mean Square Displacement",
"MSD (nm\\S2\\N)",
msd->time[msd->nframes-1], beginfit, endfit, DD, SigmaD, grpname, oenv);
}