# that is, if f.min() > fmin for a track, then it still aligns at zero
rncorrs = helpy.pad_uneven([
rn[np.searchsorted(f, fmin):np.searchsorted(f, fmax)]
for f, rn in rncorrs if f.min() <= fmin ],
np.nan)
tcorr = np.arange(fmin, fmax)/fps
meancorr = np.nanmean(rncorrs, 0)
added = np.sum(np.isfinite(rncorrs), 0)
errcorr = np.nanstd(rncorrs, 0)/np.sqrt(added - 1)
sigma = errcorr + errcorr.std() # add something small to prevent 0
if args.verbose:
print "Merged rn corrs"
# Fit to capped exponential growth
fitform = lambda s, v_D, D=D_R:\
0.5*np.sign(s)*v_D*(1 - corr.exp_decay(np.abs(s), 1/D))
fitstr = r'$\frac{v_0}{2D_R}(1 - e^{-D_R|s|})\operatorname{sign}(s)$'
# p0 = [v_0/D_R, D_R]
p0 = [1]
if not args.nn or args.fitdr:
p0 += [D_R]
print "============="
print "Fits to <rn>:"
try:
popt, pcov = curve_fit(fitform, tcorr, meancorr, p0=p0, sigma=sigma)
except RuntimeError as e:
try:
p0[0] = -1 # If dots are backwards, has trouble fitting with v0>0
popt, pcov = curve_fit(fitform, tcorr, meancorr, p0=p0, sigma=sigma)
except RuntimeError as e:
sincorrs = [ corr.autocorr(np.sin(otrackset), cumulant=False, norm=False)
for otrackset in otracksets.values() ]
# Gather all the track correlations and average them
allcorr = coscorrs + sincorrs
allcorr = helpy.pad_uneven(allcorr, np.nan)
tcorr = np.arange(allcorr.shape[1])/fps
meancorr = np.nanmean(allcorr, 0)
errcorr = np.nanstd(allcorr, 0)/sqrt(len(allcorr))
if verbose:
print "Merged nn corrs"
# Fit to exponential decay
tmax = 50
fmax = np.searchsorted(tcorr, tmax)
fitform = lambda *args, **kwargs: 0.5*corr.exp_decay(*args, **kwargs)
popt, pcov = curve_fit(fitform, tcorr[:fmax], meancorr[:fmax],
p0=[1], sigma=errcorr[:fmax].mean() + errcorr[:fmax])
D_R = 1/popt[0]
print 'D_R: {:.4f}'.format(D_R)
pl.figure()
plot_individual = True
if plot_individual:
pl.semilogy(tcorr, allcorr.T, 'b', alpha=.25)
pl.errorbar(tcorr, meancorr, errcorr, None, 'ok',
capthick=0, elinewidth=1, errorevery=3)
pl.plot(tcorr, fitform(tcorr, *popt), 'r',
label=r"$\frac{1}{2}e^{-D_R t}$" + '\n' +\
"$D_R$: {:.4f}, $1/D_R$: {:.3f}".format(D_R, 1/D_R))
pl.xlim(0, tmax)
