real numerical_deriv(int nx,real x[],real y[],real fity[],real combined[],real dy[],
real tendInt,int nsmooth)
{
FILE *tmpfp;
int i,nbegin,i0,i1;
real fac,fx,fy,integralSmth;
nbegin = calc_nbegin(nx,x,tendInt);
if (nsmooth == 0) {
for(i=0; (i<nbegin); i++)
combined[i]=y[i];
fac = y[nbegin]/fity[nbegin];
printf("scaling fitted curve by %g\n",fac);
for(i=nbegin; (i<nx); i++)
combined[i]=fity[i]*fac;
}
else {
i0 = max(0,nbegin);
i1 = min(nx-1,nbegin+nsmooth);
printf("Making smooth transition from %d thru %d\n",i0,i1);
for(i=0; (i<i0); i++)
combined[i]=y[i];
for(i=i0; (i<=i1); i++) {
fx = (i1-i)/(real)(i1-i0);
fy = (i-i0)/(real)(i1-i0);
if (debug)
fprintf(debug,"x: %g factors for smoothing: %10g %10g\n",x[i],fx,fy);
combined[i] = fx*y[i] + fy*fity[i];
}
for(i=i1+1; (i<nx); i++)
combined[i]=fity[i];
}
tmpfp = ffopen("integral_smth.xvg","w");
integralSmth=print_and_integrate(tmpfp,nx,x[1]-x[0],combined,NULL,1);
printf("SMOOTH integral = %10.5e\n",integralSmth);
dy[0] = (combined[1]-combined[0])/(x[1]-x[0]);
for(i=1; (i<nx-1); i++) {
dy[i] = (combined[i+1]-combined[i-1])/(x[i+1]-x[i-1]);
}
dy[nx-1] = (combined[nx-1]-combined[nx-2])/(x[nx-1]-x[nx-2]);
for(i=0; (i<nx); i++)
dy[i] *= -1;
return integralSmth;
}
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;
}
