int gmx_dielectric(int argc, char *argv[])
{
const char *desc[] = {
"[THISMODULE] calculates frequency dependent dielectric constants",
"from the autocorrelation function of the total dipole moment in",
"your simulation. This ACF can be generated by [gmx-dipoles].",
"The functional forms of the available functions are:[PAR]",
"One parameter: y = [EXP]-a[SUB]1[sub] x[exp],[BR]",
"Two parameters: y = a[SUB]2[sub] [EXP]-a[SUB]1[sub] x[exp],[BR]",
"Three parameters: y = a[SUB]2[sub] [EXP]-a[SUB]1[sub] x[exp] + (1 - a[SUB]2[sub]) [EXP]-a[SUB]3[sub] x[exp].[BR]",
"Start values for the fit procedure can be given on the command line.",
"It is also possible to fix parameters at their start value, use [TT]-fix[tt]",
"with the number of the parameter you want to fix.",
"[PAR]",
"Three output files are generated, the first contains the ACF,",
"an exponential fit to it with 1, 2 or 3 parameters, and the",
"numerical derivative of the combination data/fit.",
"The second file contains the real and imaginary parts of the",
"frequency-dependent dielectric constant, the last gives a plot",
"known as the Cole-Cole plot, in which the imaginary",
"component is plotted as a function of the real component.",
"For a pure exponential relaxation (Debye relaxation) the latter",
"plot should be one half of a circle."
};
t_filenm fnm[] = {
{ efXVG, "-f", "dipcorr", ffREAD },
{ efXVG, "-d", "deriv", ffWRITE },
{ efXVG, "-o", "epsw", ffWRITE },
{ efXVG, "-c", "cole", ffWRITE }
};
#define NFILE asize(fnm)
output_env_t oenv;
int i, j, nx, ny, nxtail, eFitFn, nfitparm;
real dt, integral, fitintegral, *fitparms, fac, rffac;
double **yd;
real **y;
const char *legend[] = { "Correlation", "Std. Dev.", "Fit", "Combined", "Derivative" };
static int fix = 0, bFour = 0, bX = 1, nsmooth = 3;
static real tendInt = 5.0, tbegin = 5.0, tend = 500.0;
static real A = 0.5, tau1 = 10.0, tau2 = 1.0, eps0 = 80, epsRF = 78.5, tail = 500.0;
real lambda;
t_pargs pa[] = {
{ "-fft", FALSE, etBOOL, {&bFour},
"use fast fourier transform for correlation function" },
{ "-x1", FALSE, etBOOL, {&bX},
"use first column as [IT]x[it]-axis rather than first data set" },
{ "-eint", FALSE, etREAL, {&tendInt},
"Time to end the integration of the data and start to use the fit"},
{ "-bfit", FALSE, etREAL, {&tbegin},
"Begin time of fit" },
{ "-efit", FALSE, etREAL, {&tend},
"End time of fit" },
{ "-tail", FALSE, etREAL, {&tail},
"Length of function including data and tail from fit" },
{ "-A", FALSE, etREAL, {&A},
"Start value for fit parameter A" },
{ "-tau1", FALSE, etREAL, {&tau1},
"Start value for fit parameter [GRK]tau[grk]1" },
{ "-tau2", FALSE, etREAL, {&tau2},
"Start value for fit parameter [GRK]tau[grk]2" },
{ "-eps0", FALSE, etREAL, {&eps0},
"[GRK]epsilon[grk]0 of your liquid" },
{ "-epsRF", FALSE, etREAL, {&epsRF},
"[GRK]epsilon[grk] of the reaction field used in your simulation. A value of 0 means infinity." },
{ "-fix", FALSE, etINT, {&fix},
"Fix parameters at their start values, A (2), tau1 (1), or tau2 (4)" },
{ "-ffn", FALSE, etENUM, {s_ffn},
"Fit function" },
{ "-nsmooth", FALSE, etINT, {&nsmooth},
"Number of points for smoothing" }
};
if (!parse_common_args(&argc, argv, PCA_CAN_TIME | PCA_CAN_VIEW | PCA_BE_NICE,
NFILE, fnm, asize(pa), pa, asize(desc), desc, 0, NULL, &oenv))
{
return 0;
}
please_cite(stdout, "Spoel98a");
printf("WARNING: non-polarizable models can never yield an infinite\n"
"dielectric constant that is different from 1. This is incorrect\n"
"in the reference given above (Spoel98a).\n\n");
nx = read_xvg(opt2fn("-f", NFILE, fnm), &yd, &ny);
dt = yd[0][1] - yd[0][0];
nxtail = min(tail/dt, nx);
printf("Read data set containing %d colums and %d rows\n", ny, nx);
printf("Assuming (from data) that timestep is %g, nxtail = %d\n",
dt, nxtail);
snew(y, 6);
for (i = 0; (i < ny); i++)
{
snew(y[i], max(nx, nxtail));
}
for (i = 0; (i < nx); i++)
{
y[0][i] = yd[0][i];
for (j = 1; (j < ny); j++)
{
y[j][i] = yd[j][i];
}
}
if (nxtail > nx)
{
for (i = nx; (i < nxtail); i++)
{
y[0][i] = dt*i+y[0][0];
for (j = 1; (j < ny); j++)
{
y[j][i] = 0.0;
}
}
nx = nxtail;
}
/* We have read a file WITHOUT standard deviations, so we make our own... */
if (ny == 2)
{
printf("Creating standard deviation numbers ...\n");
srenew(y, 3);
snew(y[2], nx);
fac = 1.0/((real)nx);
for (i = 0; (i < nx); i++)
{
y[2][i] = fac;
}
}
eFitFn = sffn2effn(s_ffn);
nfitparm = nfp_ffn[eFitFn];
snew(fitparms, 4);
fitparms[0] = tau1;
if (nfitparm > 1)
{
fitparms[1] = A;
}
if (nfitparm > 2)
{
fitparms[2] = tau2;
}
snew(y[3], nx);
snew(y[4], nx);
snew(y[5], nx);
integral = print_and_integrate(NULL, calc_nbegin(nx, y[0], tbegin),
dt, y[1], NULL, 1);
integral += do_lmfit(nx, y[1], y[2], dt, y[0], tbegin, tend,
oenv, TRUE, eFitFn, fitparms, fix);
for (i = 0; i < nx; i++)
{
y[3][i] = fit_function(eFitFn, fitparms, y[0][i]);
}
if (epsRF == 0)
{
/* This means infinity! */
lambda = 0;
rffac = 1;
}
else
{
lambda = (eps0 - 1.0)/(2*epsRF - 1.0);
rffac = (2*epsRF+eps0)/(2*epsRF+1);
}
printf("DATA INTEGRAL: %5.1f, tauD(old) = %5.1f ps, "
"tau_slope = %5.1f, tau_slope,D = %5.1f ps\n",
integral, integral*rffac, fitparms[0], fitparms[0]*rffac);
printf("tau_D from tau1 = %8.3g , eps(Infty) = %8.3f\n",
fitparms[0]*(1 + fitparms[1]*lambda),
1 + ((1 - fitparms[1])*(eps0 - 1))/(1 + fitparms[1]*lambda));
fitintegral = numerical_deriv(nx, y[0], y[1], y[3], y[4], y[5], tendInt, nsmooth);
printf("FIT INTEGRAL (tau_M): %5.1f, tau_D = %5.1f\n",
fitintegral, fitintegral*rffac);
/* Now we have the negative gradient of <Phi(0) Phi(t)> */
write_xvg(opt2fn("-d", NFILE, fnm), "Data", nx-1, 6, y, legend, oenv);
/* Do FFT and analysis */
do_four(opt2fn("-o", NFILE, fnm), opt2fn("-c", NFILE, fnm),
nx-1, y[0], y[5], eps0, epsRF, oenv);
do_view(oenv, opt2fn("-o", NFILE, fnm), "-nxy");
do_view(oenv, opt2fn("-c", NFILE, fnm), NULL);
do_view(oenv, opt2fn("-d", NFILE, fnm), "-nxy");
return 0;
}
static void do_fit(FILE *out,int n,bool bYdy,int ny,real *x0,real **val,
int npargs,t_pargs *ppa)
{
real *c1=NULL,*sig=NULL,*fitparm;
real dt=0,tendfit,tbeginfit;
int i,efitfn,nparm;
efitfn = get_acffitfn();
nparm = nfp_ffn[efitfn];
fprintf(out,"Will fit to the following function:\n");
fprintf(out,"%s\n",longs_ffn[efitfn]);
c1 = val[n];
if (bYdy) {
c1 = val[n];
sig = val[n+1];
fprintf(out,"Using two columns as y and sigma values\n");
} else {
snew(sig,ny);
}
if (opt2parg_bSet("-beginfit",npargs,ppa)) {
tbeginfit = opt2parg_real("-beginfit",npargs,ppa);
} else {
tbeginfit = x0 ? x0[0] : 0;
}
if (opt2parg_bSet("-endfit",npargs,ppa)) {
tendfit = opt2parg_real("-endfit",npargs,ppa);
} else {
tendfit = x0 ? x0[ny-1] : (ny-1)*dt;
}
snew(fitparm,nparm);
switch(efitfn) {
case effnEXP1:
fitparm[0] = 0.5;
break;
case effnEXP2:
fitparm[0] = 0.5;
fitparm[1] = c1[0];
break;
case effnEXP3:
fitparm[0] = 1.0;
fitparm[1] = 0.5*c1[0];
fitparm[2] = 10.0;
break;
case effnEXP5:
fitparm[0] = fitparm[2] = 0.5*c1[0];
fitparm[1] = 10;
fitparm[3] = 40;
fitparm[4] = 0;
break;
case effnEXP7:
fitparm[0] = fitparm[2] = fitparm[4] = 0.33*c1[0];
fitparm[1] = 1;
fitparm[3] = 10;
fitparm[5] = 100;
fitparm[6] = 0;
break;
case effnEXP9:
fitparm[0] = fitparm[2] = fitparm[4] = fitparm[6] = 0.25*c1[0];
fitparm[1] = 0.1;
fitparm[3] = 1;
fitparm[5] = 10;
fitparm[7] = 100;
fitparm[8] = 0;
break;
default:
fprintf(out,"Warning: don't know how to initialize the parameters\n");
for(i=0; (i<nparm); i++)
fitparm[i] = 1;
}
fprintf(out,"Starting parameters:\n");
for(i=0; (i<nparm); i++)
fprintf(out,"a%-2d = %12.5e\n",i+1,fitparm[i]);
if (do_lmfit(ny,c1,sig,dt,x0,tbeginfit,tendfit,
bDebugMode(),efitfn,fitparm,0)) {
for(i=0; (i<nparm); i++)
fprintf(out,"a%-2d = %12.5e\n",i+1,fitparm[i]);
}
else {
fprintf(out,"No solution was found\n");
}
}
static void process_tcaf(int nframes, real dt, int nkc, real **tc, rvec *kfac,
real rho, real wt, const char *fn_trans,
const char *fn_tca, const char *fn_tc,
const char *fn_tcf, const char *fn_cub,
const char *fn_vk, const gmx_output_env_t *oenv)
{
FILE *fp, *fp_vk, *fp_cub = NULL;
int nk, ntc;
real **tcaf, **tcafc = NULL, eta, *sig;
int i, j, k, kc;
int ncorr;
double fitparms[3];
nk = kset_c[nkc];
ntc = nk*NPK;
if (fn_trans)
{
fp = xvgropen(fn_trans, "Transverse Current", "Time (ps)", "TC (nm/ps)",
oenv);
for (i = 0; i < nframes; i++)
{
fprintf(fp, "%g", i*dt);
for (j = 0; j < ntc; j++)
{
fprintf(fp, " %g", tc[j][i]);
}
fprintf(fp, "\n");
}
xvgrclose(fp);
do_view(oenv, fn_trans, "-nxy");
}
ncorr = (nframes+1)/2;
if (ncorr > static_cast<int>(5*wt/dt+0.5))
{
ncorr = static_cast<int>(5*wt/dt+0.5)+1;
}
snew(tcaf, nk);
for (k = 0; k < nk; k++)
{
snew(tcaf[k], ncorr);
}
if (fn_cub)
{
snew(tcafc, nkc);
for (k = 0; k < nkc; k++)
{
snew(tcafc[k], ncorr);
}
}
snew(sig, ncorr);
for (i = 0; i < ncorr; i++)
{
sig[i] = std::exp(0.5*i*dt/wt);
}
low_do_autocorr(fn_tca, oenv, "Transverse Current Autocorrelation Functions",
nframes, ntc, ncorr, tc, dt, eacNormal,
1, FALSE, FALSE, FALSE, 0, 0, 0);
do_view(oenv, fn_tca, "-nxy");
fp = xvgropen(fn_tc, "Transverse Current Autocorrelation Functions",
"Time (ps)", "TCAF", oenv);
for (i = 0; i < ncorr; i++)
{
kc = 0;
fprintf(fp, "%g", i*dt);
for (k = 0; k < nk; k++)
{
for (j = 0; j < NPK; j++)
{
tcaf[k][i] += tc[NPK*k+j][i];
}
if (fn_cub)
{
for (j = 0; j < NPK; j++)
{
tcafc[kc][i] += tc[NPK*k+j][i];
}
}
if (i == 0)
{
fprintf(fp, " %g", 1.0);
}
else
{
tcaf[k][i] /= tcaf[k][0];
fprintf(fp, " %g", tcaf[k][i]);
}
if (k+1 == kset_c[kc+1])
{
kc++;
}
}
fprintf(fp, "\n");
}
xvgrclose(fp);
do_view(oenv, fn_tc, "-nxy");
if (fn_cub)
{
fp_cub = xvgropen(fn_cub, "TCAFs and fits", "Time (ps)", "TCAF", oenv);
for (kc = 0; kc < nkc; kc++)
{
fprintf(fp_cub, "%g %g\n", 0.0, 1.0);
for (i = 1; i < ncorr; i++)
{
tcafc[kc][i] /= tcafc[kc][0];
fprintf(fp_cub, "%g %g\n", i*dt, tcafc[kc][i]);
}
fprintf(fp_cub, "%s\n", output_env_get_print_xvgr_codes(oenv) ? "&" : "");
tcafc[kc][0] = 1.0;
}
}
fp_vk = xvgropen(fn_vk, "Fits", "k (nm\\S-1\\N)",
"\\8h\\4 (10\\S-3\\N kg m\\S-1\\N s\\S-1\\N)", oenv);
if (output_env_get_print_xvgr_codes(oenv))
{
fprintf(fp_vk, "@ s0 symbol 2\n");
fprintf(fp_vk, "@ s0 symbol color 1\n");
fprintf(fp_vk, "@ s0 linestyle 0\n");
if (fn_cub)
{
fprintf(fp_vk, "@ s1 symbol 3\n");
fprintf(fp_vk, "@ s1 symbol color 2\n");
}
}
fp = xvgropen(fn_tcf, "TCAF Fits", "Time (ps)", "", oenv);
for (k = 0; k < nk; k++)
{
tcaf[k][0] = 1.0;
fitparms[0] = 1;
fitparms[1] = 1;
do_lmfit(ncorr, tcaf[k], sig, dt, 0, 0, ncorr*dt,
oenv, bDebugMode(), effnVAC, fitparms, 0, NULL);
eta = 1000*fitparms[1]*rho/
(4*fitparms[0]*PICO*norm2(kfac[k])/(NANO*NANO));
fprintf(stdout, "k %6.3f tau %6.3f eta %8.5f 10^-3 kg/(m s)\n",
norm(kfac[k]), fitparms[0], eta);
fprintf(fp_vk, "%6.3f %g\n", norm(kfac[k]), eta);
for (i = 0; i < ncorr; i++)
{
fprintf(fp, "%g %g\n", i*dt, fit_function(effnVAC, fitparms, i*dt));
}
fprintf(fp, "%s\n", output_env_get_print_xvgr_codes(oenv) ? "&" : "");
}
xvgrclose(fp);
do_view(oenv, fn_tcf, "-nxy");
if (fn_cub)
{
fprintf(stdout, "Averaged over k-vectors:\n");
fprintf(fp_vk, "%s\n", output_env_get_print_xvgr_codes(oenv) ? "&" : "");
for (k = 0; k < nkc; k++)
{
tcafc[k][0] = 1.0;
fitparms[0] = 1;
fitparms[1] = 1;
do_lmfit(ncorr, tcafc[k], sig, dt, 0, 0, ncorr*dt,
oenv, bDebugMode(), effnVAC, fitparms, 0, NULL);
eta = 1000*fitparms[1]*rho/
(4*fitparms[0]*PICO*norm2(kfac[kset_c[k]])/(NANO*NANO));
fprintf(stdout,
"k %6.3f tau %6.3f Omega %6.3f eta %8.5f 10^-3 kg/(m s)\n",
norm(kfac[kset_c[k]]), fitparms[0], fitparms[1], eta);
fprintf(fp_vk, "%6.3f %g\n", norm(kfac[kset_c[k]]), eta);
for (i = 0; i < ncorr; i++)
{
fprintf(fp_cub, "%g %g\n", i*dt, fit_function(effnVAC, fitparms, i*dt));
}
fprintf(fp_cub, "%s\n", output_env_get_print_xvgr_codes(oenv) ? "&" : "");
}
fprintf(fp_vk, "%s\n", output_env_get_print_xvgr_codes(oenv) ? "&" : "");
xvgrclose(fp_cub);
do_view(oenv, fn_cub, "-nxy");
}
xvgrclose(fp_vk);
do_view(oenv, fn_vk, "-nxy");
}
static void estimate_error(char *eefile,int nb_min,int resol,int n,int nset,
double *av,double *sig,real **val,real dt,
bool bFitAc,bool bSingleExpFit,bool bAllowNegLTCorr)
{
FILE *fp;
int bs,prev_bs,nbs,nb;
real spacing,nbr;
int s,i,j;
double blav,var;
char **leg;
real *tbs,*ybs,rtmp,dens,*fitsig,twooe,tau1_est,tau_sig;
real fitparm[4];
real ee,a,tau1,tau2;
if (n < 4)
{
fprintf(stdout,"The number of points is smaller than 4, can not make an error estimate\n");
return;
}
fp = xvgropen(eefile,"Error estimates",
"Block size (time)","Error estimate");
if (bPrintXvgrCodes())
{
fprintf(fp,
"@ subtitle \"using block averaging, total time %g (%d points)\"\n",
(n-1)*dt,n);
}
snew(leg,2*nset);
xvgr_legend(fp,2*nset,leg);
sfree(leg);
spacing = pow(2,1.0/resol);
snew(tbs,n);
snew(ybs,n);
snew(fitsig,n);
for(s=0; s<nset; s++)
{
nbs = 0;
prev_bs = 0;
nbr = nb_min;
while (nbr <= n)
{
bs = n/(int)nbr;
if (bs != prev_bs)
{
nb = n/bs;
var = 0;
for(i=0; i<nb; i++)
{
blav=0;
for (j=0; j<bs; j++)
{
blav += val[s][bs*i+j];
}
var += sqr(av[s] - blav/bs);
}
tbs[nbs] = bs*dt;
if (sig[s] == 0)
{
ybs[nbs] = 0;
}
else
{
ybs[nbs] = var/(nb*(nb-1.0))*(n*dt)/(sig[s]*sig[s]);
}
nbs++;
}
nbr *= spacing;
nb = (int)(nbr+0.5);
prev_bs = bs;
}
if (sig[s] == 0)
{
ee = 0;
a = 1;
tau1 = 0;
tau2 = 0;
}
else
{
for(i=0; i<nbs/2; i++)
{
rtmp = tbs[i];
tbs[i] = tbs[nbs-1-i];
tbs[nbs-1-i] = rtmp;
rtmp = ybs[i];
ybs[i] = ybs[nbs-1-i];
ybs[nbs-1-i] = rtmp;
}
/* The initial slope of the normalized ybs^2 is 1.
* For a single exponential autocorrelation: ybs(tau1) = 2/e tau1
* From this we take our initial guess for tau1.
*/
twooe = 2/exp(1);
i = -1;
do
{
i++;
tau1_est = tbs[i];
} while (i < nbs - 1 &&
(ybs[i] > ybs[i+1] || ybs[i] > twooe*tau1_est));
if (ybs[0] > ybs[1])
{
fprintf(stdout,"Data set %d has strange time correlations:\n"
"the std. error using single points is larger than that of blocks of 2 points\n"
"The error estimate might be inaccurate, check the fit\n",
s+1);
/* Use the total time as tau for the fitting weights */
tau_sig = (n - 1)*dt;
}
else
{
tau_sig = tau1_est;
}
if (debug)
{
fprintf(debug,"set %d tau1 estimate %f\n",s+1,tau1_est);
}
/* Generate more or less appropriate sigma's,
* also taking the density of points into account.
*/
for(i=0; i<nbs; i++)
{
if (i == 0)
{
dens = tbs[1]/tbs[0] - 1;
}
else if (i == nbs-1)
{
dens = tbs[nbs-1]/tbs[nbs-2] - 1;
}
else
{
dens = 0.5*(tbs[i+1]/tbs[i-1] - 1);
}
fitsig[i] = sqrt((tau_sig + tbs[i])/dens);
}
if (!bSingleExpFit)
{
fitparm[0] = tau1_est;
fitparm[1] = 0.95;
/* We set the initial guess for tau2
* to halfway between tau1_est and the total time (on log scale).
*/
fitparm[2] = sqrt(tau1_est*(n-1)*dt);
do_lmfit(nbs,ybs,fitsig,0,tbs,0,dt*n,bDebugMode(),effnERREST,fitparm,0);
fitparm[3] = 1-fitparm[1];
}
if (bSingleExpFit || fitparm[0]<0 || fitparm[2]<0 || fitparm[1]<0
|| (fitparm[1]>1 && !bAllowNegLTCorr) || fitparm[2]>(n-1)*dt)
{
if (!bSingleExpFit)
{
if (fitparm[2] > (n-1)*dt)
{
fprintf(stdout,
"Warning: tau2 is longer than the length of the data (%g)\n"
" the statistics might be bad\n",
(n-1)*dt);
}
else
{
fprintf(stdout,"a fitted parameter is negative\n");
}
fprintf(stdout,"invalid fit: e.e. %g a %g tau1 %g tau2 %g\n",
sig[s]*anal_ee_inf(fitparm,n*dt),
fitparm[1],fitparm[0],fitparm[2]);
/* Do a fit with tau2 fixed at the total time.
* One could also choose any other large value for tau2.
*/
fitparm[0] = tau1_est;
fitparm[1] = 0.95;
fitparm[2] = (n-1)*dt;
fprintf(stderr,"Will fix tau2 at the total time: %g\n",fitparm[2]);
do_lmfit(nbs,ybs,fitsig,0,tbs,0,dt*n,bDebugMode(),effnERREST,fitparm,4);
fitparm[3] = 1-fitparm[1];
}
if (bSingleExpFit || fitparm[0]<0 || fitparm[1]<0
|| (fitparm[1]>1 && !bAllowNegLTCorr))
{
if (!bSingleExpFit) {
fprintf(stdout,"a fitted parameter is negative\n");
fprintf(stdout,"invalid fit: e.e. %g a %g tau1 %g tau2 %g\n",
sig[s]*anal_ee_inf(fitparm,n*dt),
fitparm[1],fitparm[0],fitparm[2]);
}
/* Do a single exponential fit */
fprintf(stderr,"Will use a single exponential fit for set %d\n",s+1);
fitparm[0] = tau1_est;
fitparm[1] = 1.0;
fitparm[2] = 0.0;
do_lmfit(nbs,ybs,fitsig,0,tbs,0,dt*n,bDebugMode(),effnERREST,fitparm,6);
fitparm[3] = 1-fitparm[1];
}
}
ee = sig[s]*anal_ee_inf(fitparm,n*dt);
a = fitparm[1];
tau1 = fitparm[0];
tau2 = fitparm[2];
}
fprintf(stdout,"Set %3d: err.est. %g a %g tau1 %g tau2 %g\n",
s+1,ee,a,tau1,tau2);
fprintf(fp,"@ legend string %d \"av %f\"\n",2*s,av[s]);
fprintf(fp,"@ legend string %d \"ee %6g\"\n",
2*s+1,sig[s]*anal_ee_inf(fitparm,n*dt));
for(i=0; i<nbs; i++)
{
fprintf(fp,"%g %g %g\n",tbs[i],sig[s]*sqrt(ybs[i]/(n*dt)),
sig[s]*sqrt(fit_function(effnERREST,fitparm,tbs[i])/(n*dt)));
}
if (bFitAc)
{
int fitlen;
real *ac,acint,ac_fit[4];
snew(ac,n);
for(i=0; i<n; i++) {
ac[i] = val[s][i] - av[s];
if (i > 0)
fitsig[i] = sqrt(i);
else
fitsig[i] = 1;
}
low_do_autocorr(NULL,NULL,n,1,-1,&ac,
dt,eacNormal,1,FALSE,TRUE,
FALSE,0,0,effnNONE,0);
fitlen = n/nb_min;
/* Integrate ACF only up to fitlen/2 to avoid integrating noise */
acint = 0.5*ac[0];
for(i=1; i<=fitlen/2; i++)
{
acint += ac[i];
}
acint *= dt;
/* Generate more or less appropriate sigma's */
for(i=0; i<=fitlen; i++)
{
fitsig[i] = sqrt(acint + dt*i);
}
ac_fit[0] = 0.5*acint;
ac_fit[1] = 0.95;
ac_fit[2] = 10*acint;
do_lmfit(n/nb_min,ac,fitsig,dt,0,0,fitlen*dt,
bDebugMode(),effnEXP3,ac_fit,0);
ac_fit[3] = 1 - ac_fit[1];
fprintf(stdout,"Set %3d: ac erest %g a %g tau1 %g tau2 %g\n",
s+1,sig[s]*anal_ee_inf(ac_fit,n*dt),
ac_fit[1],ac_fit[0],ac_fit[2]);
fprintf(fp,"&\n");
for(i=0; i<nbs; i++)
{
fprintf(fp,"%g %g\n",tbs[i],
sig[s]*sqrt(fit_function(effnERREST,ac_fit,tbs[i]))/(n*dt));
}
sfree(ac);
}
if (s < nset-1)
{
fprintf(fp,"&\n");
}
}
sfree(fitsig);
sfree(ybs);
sfree(tbs);
fclose(fp);
}
real fit_acf(int ncorr, int fitfn, const gmx_output_env_t *oenv, gmx_bool bVerbose,
real tbeginfit, real tendfit, real dt, real c1[], real *fit)
{
double fitparm[3];
double tStart, tail_corr, sum, sumtot = 0, c_start, ct_estimate;
real *sig;
int i, j, jmax, nf_int;
gmx_bool bPrint;
bPrint = bVerbose || bDebugMode();
if (bPrint)
{
printf("COR:\n");
}
if (tendfit <= 0)
{
tendfit = ncorr*dt;
}
nf_int = std::min(ncorr, (int)(tendfit/dt));
sum = print_and_integrate(debug, nf_int, dt, c1, NULL, 1);
if (bPrint)
{
printf("COR: Correlation time (plain integral from %6.3f to %6.3f ps) = %8.5f ps\n",
0.0, dt*nf_int, sum);
printf("COR: Relaxation times are computed as fit to an exponential:\n");
printf("COR: %s\n", effnDescription(fitfn));
printf("COR: Fit to correlation function from %6.3f ps to %6.3f ps, results in a\n", tbeginfit, std::min(ncorr*dt, tendfit));
}
tStart = 0;
if (bPrint)
{
printf("COR:%11s%11s%11s%11s%11s%11s%11s\n",
"Fit from", "Integral", "Tail Value", "Sum (ps)", " a1 (ps)",
(effnNparams(fitfn) >= 2) ? " a2 ()" : "",
(effnNparams(fitfn) >= 3) ? " a3 (ps)" : "");
}
snew(sig, ncorr);
if (tbeginfit > 0)
{
jmax = 3;
}
else
{
jmax = 1;
}
for (j = 0; ((j < jmax) && (tStart < tendfit) && (tStart < ncorr*dt)); j++)
{
/* Estimate the correlation time for better fitting */
c_start = -1;
ct_estimate = 0;
for (i = 0; (i < ncorr) && (dt*i < tStart || c1[i] > 0); i++)
{
if (c_start < 0)
{
if (dt*i >= tStart)
{
c_start = c1[i];
ct_estimate = 0.5*c1[i];
}
}
else
{
ct_estimate += c1[i];
}
}
if (c_start > 0)
{
ct_estimate *= dt/c_start;
}
else
{
/* The data is strange, so we need to choose somehting */
ct_estimate = tendfit;
}
if (debug)
{
fprintf(debug, "tStart %g ct_estimate: %g\n", tStart, ct_estimate);
}
if (fitfn == effnEXPEXP)
{
fitparm[0] = 0.002*ncorr*dt;
fitparm[1] = 0.95;
fitparm[2] = 0.2*ncorr*dt;
}
else
{
/* Good initial guess, this increases the probability of convergence */
fitparm[0] = ct_estimate;
fitparm[1] = 1.0;
fitparm[2] = 1.0;
}
/* Generate more or less appropriate sigma's */
for (i = 0; i < ncorr; i++)
{
sig[i] = sqrt(ct_estimate+dt*i);
}
nf_int = std::min(ncorr, (int)((tStart+1e-4)/dt));
sum = print_and_integrate(debug, nf_int, dt, c1, NULL, 1);
tail_corr = do_lmfit(ncorr, c1, sig, dt, NULL, tStart, tendfit, oenv,
bDebugMode(), fitfn, fitparm, 0, NULL);
sumtot = sum+tail_corr;
if (fit && ((jmax == 1) || (j == 1)))
{
double mfp[3];
for (i = 0; (i < 3); i++)
{
mfp[i] = fitparm[i];
}
for (i = 0; (i < ncorr); i++)
{
fit[i] = lmcurves[fitfn](i*dt, mfp);
}
}
if (bPrint)
{
printf("COR:%11.4e%11.4e%11.4e%11.4e", tStart, sum, tail_corr, sumtot);
for (i = 0; (i < effnNparams(fitfn)); i++)
{
printf(" %11.4e", fitparm[i]);
}
printf("\n");
}
tStart += tbeginfit;
}
sfree(sig);
return sumtot;
}
static void do_fit(FILE *out, int n, gmx_bool bYdy,
int ny, real *x0, real **val,
int npargs, t_pargs *ppa, const gmx_output_env_t *oenv,
const char *fn_fitted)
{
real *c1 = NULL, *sig = NULL;
double *fitparm;
real tendfit, tbeginfit;
int i, efitfn, nparm;
efitfn = get_acffitfn();
nparm = effnNparams(efitfn);
fprintf(out, "Will fit to the following function:\n");
fprintf(out, "%s\n", effnDescription(efitfn));
c1 = val[n];
if (bYdy)
{
c1 = val[n];
sig = val[n+1];
fprintf(out, "Using two columns as y and sigma values\n");
}
else
{
snew(sig, ny);
}
if (opt2parg_bSet("-beginfit", npargs, ppa))
{
tbeginfit = opt2parg_real("-beginfit", npargs, ppa);
}
else
{
tbeginfit = x0[0];
}
if (opt2parg_bSet("-endfit", npargs, ppa))
{
tendfit = opt2parg_real("-endfit", npargs, ppa);
}
else
{
tendfit = x0[ny-1];
}
snew(fitparm, nparm);
switch (efitfn)
{
case effnEXP1:
fitparm[0] = 0.5;
break;
case effnEXP2:
fitparm[0] = 0.5;
fitparm[1] = c1[0];
break;
case effnEXPEXP:
fitparm[0] = 1.0;
fitparm[1] = 0.5*c1[0];
fitparm[2] = 10.0;
break;
case effnEXP5:
fitparm[0] = fitparm[2] = 0.5*c1[0];
fitparm[1] = 10;
fitparm[3] = 40;
fitparm[4] = 0;
break;
case effnEXP7:
fitparm[0] = fitparm[2] = fitparm[4] = 0.33*c1[0];
fitparm[1] = 1;
fitparm[3] = 10;
fitparm[5] = 100;
fitparm[6] = 0;
break;
case effnEXP9:
fitparm[0] = fitparm[2] = fitparm[4] = fitparm[6] = 0.25*c1[0];
fitparm[1] = 0.1;
fitparm[3] = 1;
fitparm[5] = 10;
fitparm[7] = 100;
fitparm[8] = 0;
break;
default:
fprintf(out, "Warning: don't know how to initialize the parameters\n");
for (i = 0; (i < nparm); i++)
{
fitparm[i] = 1;
}
}
fprintf(out, "Starting parameters:\n");
for (i = 0; (i < nparm); i++)
{
fprintf(out, "a%-2d = %12.5e\n", i+1, fitparm[i]);
}
if (do_lmfit(ny, c1, sig, 0, x0, tbeginfit, tendfit,
oenv, bDebugMode(), efitfn, fitparm, 0,
fn_fitted) > 0)
{
for (i = 0; (i < nparm); i++)
{
fprintf(out, "a%-2d = %12.5e\n", i+1, fitparm[i]);
}
}
else
{
fprintf(out, "No solution was found\n");
}
}
static void interfaces_txy (real ****Densmap, int xslices, int yslices, int zslices,
int tblocks, real binwidth, int method,
real dens1, real dens2, t_interf ****intf1,
t_interf ****intf2, const gmx_output_env_t *oenv)
{
/*Returns two pointers to 3D arrays of t_interf structs containing (position,thickness) of the interface(s)*/
FILE *xvg;
real *zDensavg; /* zDensavg[z]*/
int i, j, k, n;
int xysize;
int ndx1, ndx2, *zperm;
real densmid;
real splitpoint, startpoint, endpoint;
real *sigma1, *sigma2;
double beginfit1[4];
double beginfit2[4];
double *fit1 = NULL, *fit2 = NULL;
const double *avgfit1;
const double *avgfit2;
const real onehalf = 1.00/2.00;
t_interf ***int1 = NULL, ***int2 = NULL; /*Interface matrices [t][x,y] - last index in row-major order*/
/*Create int1(t,xy) and int2(t,xy) arrays with correct number of interf_t elements*/
xysize = xslices*yslices;
snew(int1, tblocks);
snew(int2, tblocks);
for (i = 0; i < tblocks; i++)
{
snew(int1[i], xysize);
snew(int2[i], xysize);
for (j = 0; j < xysize; j++)
{
snew(int1[i][j], 1);
snew(int2[i][j], 1);
init_interf(int1[i][j]);
init_interf(int2[i][j]);
}
}
if (method == methBISECT)
{
densmid = onehalf*(dens1+dens2);
snew(zperm, zslices);
for (n = 0; n < tblocks; n++)
{
for (i = 0; i < xslices; i++)
{
for (j = 0; j < yslices; j++)
{
rangeArray(zperm, zslices); /*reset permutation array to identity*/
/*Binsearch returns slice-nr where the order param is <= setpoint sgmid*/
ndx1 = start_binsearch(Densmap[n][i][j], zperm, 0, zslices/2-1, densmid, 1);
ndx2 = start_binsearch(Densmap[n][i][j], zperm, zslices/2, zslices-1, densmid, -1);
/* Linear interpolation (for use later if time allows)
* rho_1s= Densmap[n][i][j][zperm[ndx1]]
* rho_1e =Densmap[n][i][j][zperm[ndx1+1]] - in worst case might be far off
* rho_2s =Densmap[n][i][j][zperm[ndx2+1]]
* rho_2e =Densmap[n][i][j][zperm[ndx2]]
* For 1st interface we have:
densl= Densmap[n][i][j][zperm[ndx1]];
densr= Densmap[n][i][j][zperm[ndx1+1]];
alpha=(densmid-densl)/(densr-densl);
deltandx=zperm[ndx1+1]-zperm[ndx1];
if(debug){
printf("Alpha, Deltandx %f %i\n", alpha,deltandx);
}
if(abs(alpha)>1.0 || abs(deltandx)>3){
pos=zperm[ndx1];
spread=-1;
}
else {
pos=zperm[ndx1]+alpha*deltandx;
spread=binwidth*deltandx;
}
* For the 2nd interface can use the same formulation, since alpha should become negative ie:
* alpha=(densmid-Densmap[n][i][j][zperm[ndx2]])/(Densmap[n][i][j][zperm[nxd2+1]]-Densmap[n][i][j][zperm[ndx2]]);
* deltandx=zperm[ndx2+1]-zperm[ndx2];
* pos=zperm[ndx2]+alpha*deltandx; */
/*After filtering we use the direct approach */
int1[n][j+(i*yslices)]->Z = (zperm[ndx1]+onehalf)*binwidth;
int1[n][j+(i*yslices)]->t = binwidth;
int2[n][j+(i*yslices)]->Z = (zperm[ndx2]+onehalf)*binwidth;
int2[n][j+(i*yslices)]->t = binwidth;
}
}
}
}
if (method == methFUNCFIT)
{
/*Assume a box divided in 2 along midpoint of z for starters*/
startpoint = 0.0;
endpoint = binwidth*zslices;
splitpoint = (startpoint+endpoint)/2.0;
/*Initial fit proposals*/
beginfit1[0] = dens1;
beginfit1[1] = dens2;
beginfit1[2] = (splitpoint/2);
beginfit1[3] = 0.5;
beginfit2[0] = dens2;
beginfit2[1] = dens1;
beginfit2[2] = (3*splitpoint/2);
beginfit2[3] = 0.5;
snew(zDensavg, zslices);
snew(sigma1, zslices);
snew(sigma2, zslices);
for (k = 0; k < zslices; k++)
{
sigma1[k] = sigma2[k] = 1;
}
/*Calculate average density along z - avoid smoothing by using coarse-grained-mesh*/
for (k = 0; k < zslices; k++)
{
for (n = 0; n < tblocks; n++)
{
for (i = 0; i < xslices; i++)
{
for (j = 0; j < yslices; j++)
{
zDensavg[k] += (Densmap[n][i][j][k]/(xslices*yslices*tblocks));
}
}
}
}
if (debug)
{
xvg = xvgropen("DensprofileonZ.xvg", "Averaged Densityprofile on Z", "z[nm]", "Density[kg/m^3]", oenv);
for (k = 0; k < zslices; k++)
{
fprintf(xvg, "%4f.3 %8f.4\n", k*binwidth, zDensavg[k]);
}
xvgrclose(xvg);
}
/*Fit average density in z over whole trajectory to obtain tentative fit-parameters in fit1 and fit2*/
/*Fit 1st half of box*/
do_lmfit(zslices, zDensavg, sigma1, binwidth, NULL, startpoint, splitpoint, oenv, FALSE, effnERF, beginfit1, 8, NULL);
/*Fit 2nd half of box*/
do_lmfit(zslices, zDensavg, sigma2, binwidth, NULL, splitpoint, endpoint, oenv, FALSE, effnERF, beginfit2, 8, NULL);
/*Initialise the const arrays for storing the average fit parameters*/
avgfit1 = beginfit1;
avgfit2 = beginfit2;
/*Now do fit over each x y and t slice to get Zint(x,y,t) - loop is very large, we potentially should average over time directly*/
for (n = 0; n < tblocks; n++)
{
for (i = 0; i < xslices; i++)
{
for (j = 0; j < yslices; j++)
{
/*Reinitialise fit for each mesh-point*/
srenew(fit1, 4);
srenew(fit2, 4);
for (k = 0; k < 4; k++)
{
fit1[k] = avgfit1[k];
fit2[k] = avgfit2[k];
}
/*Now fit and store in structures in row-major order int[n][i][j]*/
do_lmfit(zslices, Densmap[n][i][j], sigma1, binwidth, NULL, startpoint, splitpoint, oenv, FALSE, effnERF, fit1, 0, NULL);
int1[n][j+(yslices*i)]->Z = fit1[2];
int1[n][j+(yslices*i)]->t = fit1[3];
do_lmfit(zslices, Densmap[n][i][j], sigma2, binwidth, NULL, splitpoint, endpoint, oenv, FALSE, effnERF, fit2, 0, NULL);
int2[n][j+(yslices*i)]->Z = fit2[2];
int2[n][j+(yslices*i)]->t = fit2[3];
}
}
}
}
*intf1 = int1;
*intf2 = int2;
}
real fit_acf(int ncorr,int fitfn,const output_env_t oenv,gmx_bool bVerbose,
real tbeginfit,real tendfit,real dt,real c1[],real *fit)
{
real fitparm[3];
real tStart,tail_corr,sum,sumtot=0,ct_estimate,*sig;
int i,j,jmax,nf_int;
gmx_bool bPrint;
bPrint = bVerbose || bDebugMode();
if (bPrint) printf("COR:\n");
if (tendfit <= 0)
tendfit = ncorr*dt;
nf_int = min(ncorr,(int)(tendfit/dt));
sum = print_and_integrate(debug,nf_int,dt,c1,NULL,1);
/* Estimate the correlation time for better fitting */
ct_estimate = 0.5*c1[0];
for(i=1; (i<ncorr) && (c1[i]>0); i++)
ct_estimate += c1[i];
ct_estimate *= dt/c1[0];
if (bPrint) {
printf("COR: Correlation time (plain integral from %6.3f to %6.3f ps) = %8.5f ps\n",
0.0,dt*nf_int,sum);
printf("COR: Relaxation times are computed as fit to an exponential:\n");
printf("COR: %s\n",longs_ffn[fitfn]);
printf("COR: Fit to correlation function from %6.3f ps to %6.3f ps, results in a\n",tbeginfit,min(ncorr*dt,tendfit));
}
tStart = 0;
if (bPrint)
printf("COR:%11s%11s%11s%11s%11s%11s%11s\n",
"Fit from","Integral","Tail Value","Sum (ps)"," a1 (ps)",
(nfp_ffn[fitfn]>=2) ? " a2 ()" : "",
(nfp_ffn[fitfn]>=3) ? " a3 (ps)" : "");
if (tbeginfit > 0)
jmax = 3;
else
jmax = 1;
if (fitfn == effnEXP3) {
fitparm[0] = 0.002*ncorr*dt;
fitparm[1] = 0.95;
fitparm[2] = 0.2*ncorr*dt;
} else {
/* Good initial guess, this increases the probability of convergence */
fitparm[0] = ct_estimate;
fitparm[1] = 1.0;
fitparm[2] = 1.0;
}
/* Generate more or less appropriate sigma's */
snew(sig,ncorr);
for(i=0; i<ncorr; i++)
sig[i] = sqrt(ct_estimate+dt*i);
for(j=0; ((j<jmax) && (tStart < tendfit)); j++) {
/* Use the previous fitparm as starting values for the next fit */
nf_int = min(ncorr,(int)((tStart+1e-4)/dt));
sum = print_and_integrate(debug,nf_int,dt,c1,NULL,1);
tail_corr = do_lmfit(ncorr,c1,sig,dt,NULL,tStart,tendfit,oenv,
bDebugMode(),fitfn,fitparm,0);
sumtot = sum+tail_corr;
if (fit && ((jmax == 1) || (j == 1)))
for(i=0; (i<ncorr); i++)
fit[i] = fit_function(fitfn,fitparm,i*dt);
if (bPrint) {
printf("COR:%11.4e%11.4e%11.4e%11.4e",tStart,sum,tail_corr,sumtot);
for(i=0; (i<nfp_ffn[fitfn]); i++)
printf(" %11.4e",fitparm[i]);
printf("\n");
}
tStart += tbeginfit;
}
sfree(sig);
return sumtot;
}
