def trackmsd(track, dt0, dtau):
""" trackmsd(track, dt0, dtau)
finds the track msd, as function of tau,
averaged over t0, for one track (worldline)
"""
trackdots = data[trackids==track]
if dt0 == dtau == 1:
if verbose: print "Using correlation"
xy = np.column_stack([trackdots['x'], trackdots['y']])
return corr.msd(xy, ret_taus=True)
trackbegin, trackend = trackdots['f'][[0,-1]]
tracklen = trackend - trackbegin + 1
if verbose:
print "tracklen =",tracklen
print "\t from %d to %d"%(trackbegin, trackend)
if isinstance(dtau, float):
taus = helpy.farange(dt0, tracklen, dtau)
elif isinstance(dtau, int):
taus = xrange(dtau, tracklen, dtau)
tmsd = []
for tau in taus: # for tau in T, by factor dtau
#print "tau =", tau
avg = t0avg(trackdots, tracklen, tau)
#print "avg =", avg
if avg > 0 and not np.isnan(avg):
tmsd.append([tau,avg[0]])
if verbose:
print "\t...actually", len(tmsd)
return tmsd
def trackmsd(track, dt0, dtau):
""" finds the mean squared displacement as a function of tau,
averaged over t0, for one track (particle)
parameters
----------
track : a single integer giving the track id to be calculated
dt0 : spacing stepsize for values of t0, gives the number of starting
points averaged over in `t0avg`
dtau : spacing stepsize for values of tau, gives the spacing of the
points in time at which the msd is evaluated
For dt0, dtau: Small values will take longer to calculate without
adding to the statistics. Large values calculate faster but give
worse statistics. For the special case dt0 = dtau = 1, a
correlation is used for a signicant speedup
returns
-------
a list of tuples (tau, msd(tau)) the value of tau and the mean squared
displacement for a single track at that value of tau
"""
trackdots = data[trackids==track]
if dt0 == dtau == 1:
if verbose: print "Using correlation"
xy = np.column_stack([trackdots['x'], trackdots['y']])
return corr.msd(xy, ret_taus=True)
trackbegin, trackend = trackdots['f'][[0,-1]]
tracklen = trackend - trackbegin + 1
if verbose:
print "tracklen =",tracklen
print "\t from %d to %d"%(trackbegin, trackend)
if isinstance(dtau, float):
taus = helpy.farange(dt0, tracklen, dtau)
elif isinstance(dtau, int):
taus = xrange(dtau, tracklen, dtau)
tmsd = []
for tau in taus: # for tau in T, by factor dtau
#print "tau =", tau
avg = t0avg(trackdots, tracklen, tau)
#print "avg =", avg
if avg > 0 and not np.isnan(avg):
tmsd.append([tau,avg[0]])
if verbose:
print "\t...actually", len(tmsd)
return tmsd
def trackmsd(trackset, dt0, dtau):
""" finds the mean squared displacement as a function of tau,
averaged over t0, for one track (particle)
parameters
----------
trackset : a subset of the data for a given track
dt0 : spacing stepsize for values of t0, gives the number of starting
points averaged over in `t0avg`
dtau : spacing stepsize for values of tau, gives the spacing of the
points in time at which the msd is evaluated
For dt0, dtau: Small values will take longer to calculate without
adding to the statistics. Large values calculate faster but give
worse statistics. For the special case dt0 = dtau = 1, a
correlation is used for a signicant speedup
returns
-------
a list of tuples (tau, msd(tau)) the value of tau and the mean squared
displacement for a single track at that value of tau
"""
if dt0 == dtau == 1:
xy = helpy.consecutive_fields_view(trackset, 'xy')
return corr.msd(xy, ret_taus=True)
trackbegin, trackend = trackset['f'][[0,-1]]
tracklen = trackend - trackbegin + 1
if verbose:
print "length {} from {} to {}".format(tracklen, trackbegin, trackend)
if isinstance(dtau, float):
taus = helpy.farange(dt0, tracklen, dtau)
elif isinstance(dtau, int):
taus = xrange(dtau, tracklen, dtau)
tmsd = []
for tau in taus:
avg = t0avg(trackset, tracklen, tau)
if avg > 0 and not np.isnan(avg):
tmsd.append([tau,avg[0]])
if verbose:
print "\t...actually", len(tmsd)
return tmsd
def trackmsd(track, dt0, dtau, data, trackids, odata, omask, mod_2pi=False):
""" trackmsd(track, dt0, dtau, data, trackids, odata, omask)
finds the track msd, as function of tau, averaged over t0, for one track (worldline)
"""
tmask = (trackids==track) & omask
trackdots = data[tmask]
if mod_2pi:
trackodata = odata[tmask]['orient']
else:
from orientation import track_orient
trackodata = track_orient(odata, track, trackids, omask)
if dt0 == dtau == 1:
if verbose: print "Using correlation"
from correlation import msd as corrmsd
return corrmsd(trackodata, ret_taus=True)
trackbegin, trackend = trackdots['f'][[0,-1]]
tracklen = trackend - trackbegin + 1
if verbose:
print "tracklen =",tracklen
print "\t from %d to %d"%(trackbegin, trackend)
if isinstance(dtau, float):
taus = helpy.farange(dt0, tracklen, dtau)
elif isinstance(dtau, int):
taus = xrange(dtau, tracklen, dtau)
tmsd = []
for tau in taus: # for tau in T, by factor dtau
#print "tau =", tau
avg = t0avg(trackdots, tracklen, tau, trackodata, dt0, mod_2pi=mod_2pi)
#print "avg =", avg
if avg > 0 and not np.isnan(avg):
tmsd.append([tau,avg[0]])
if verbose:
print "\t...actually", len(tmsd)
return tmsd
def trackmsd(track, dt0, dtau, data, trackids, odata, omask, mod_2pi=False):
""" trackmsd(track, dt0, dtau, data, trackids, odata, omask)
finds the track msd, as function of tau, averaged over t0, for one track (worldline)
"""
tmask = (trackids == track) & omask
trackdots = data[tmask]
if mod_2pi:
trackodata = odata[tmask]['orient']
else:
from orientation import track_orient
trackodata = track_orient(odata, track, trackids, omask)
if dt0 == dtau == 1:
if verbose: print "Using correlation"
from correlation import msd as corrmsd
return corrmsd(trackodata, ret_taus=True)
trackbegin, trackend = trackdots['f'][[0, -1]]
tracklen = trackend - trackbegin + 1
if verbose:
print "tracklen =", tracklen
print "\t from %d to %d" % (trackbegin, trackend)
if isinstance(dtau, float):
taus = helpy.farange(dt0, tracklen, dtau)
elif isinstance(dtau, int):
taus = xrange(dtau, tracklen, dtau)
tmsd = []
for tau in taus: # for tau in T, by factor dtau
#print "tau =", tau
avg = t0avg(trackdots, tracklen, tau, trackodata, dt0, mod_2pi=mod_2pi)
#print "avg =", avg
if avg > 0 and not np.isnan(avg):
tmsd.append([tau, avg[0]])
if verbose:
print "\t...actually", len(tmsd)
return tmsd
def plot_msd(msds, msdids, dtau, dt0, nframes, tnormalize=False, prefix='',
show_tracks=True, figsize=(8,6), plfunc=plt.semilogx, meancol='',
title=None, xlim=None, ylim=None, fignum=None, errorbars=False,
lw=1, singletracks=None, fps=1, S=1, ang=False, sys_size=0,
kill_flats=0, kill_jumps=1e9, show_legend=False, save='', show=True):
""" Plots the MS(A)Ds """
A = 1 if ang else S**2
if verbose:
print "using dtau = {}, dt0 = {}".format(dtau, dt0)
print "using S = {} pixels, thus A = {} px^2".format(S, A)
try:
dtau = np.asscalar(dtau)
except AttributeError:
pass
if isinstance(dtau, (float, np.float)):
taus = helpy.farange(dt0, nframes+1, dtau)
elif isinstance(dtau, (int, np.int)):
taus = np.arange(dtau, nframes+1, dtau, dtype=float)
fig = plt.figure(fignum, figsize)
# Get the mean of msds
msd = mean_msd(msds, taus, msdids,
kill_flats=kill_flats, kill_jumps=kill_jumps, show_tracks=show_tracks,
singletracks=singletracks, tnormalize=tnormalize, errorbars=errorbars,
fps=fps, A=A)
if errorbars: msd, msd_err = msd
#print "Coefficient of diffusion ~", msd[np.searchsorted(taus, fps)]/A
#print "Diffusion timescale ~", taus[np.searchsorted(msd, A)]/fps
taus = taus[:len(msd)]
taus /= fps
msd /= A
if errorbars: msd_err /= A
if tnormalize:
plfunc(taus, msd/taus**tnormalize, meancol,
label="Mean Sq {}Disp/Time{}".format(
"Angular " if ang else "",
"^{}".format(tnormalize) if tnormalize != 1 else ''))
plfunc(taus, msd[0]*taus**(1-tnormalize)/dtau,
'k-', label="ref slope = 1", lw=2)
plfunc(taus, (twopi**2 if ang else 1)/(taus)**tnormalize,
'k--', lw=2, label=r"$(2\pi)^2$" if ang else
("One particle area" if S>1 else "One Pixel"))
plt.ylim([0, 1.3*np.max(msd/taus**tnormalize)])
else:
plt.loglog(taus, msd, meancol, lw=lw,
label="Mean Squared {}Displacement".format('Angular '*ang))
#plt.loglog(taus, msd[0]*taus/dtau/2, meancol+'--', lw=2,
# label="slope = 1")
if errorbars:
plt.errorbar(taus, msd/taus**tnormalize,
msd_err/taus**tnormalize,
fmt=meancol, capthick=0, elinewidth=1, errorevery=errorbars)
if sys_size:
plt.axhline(sys_size, ls='--', lw=.5, c='k', label='System Size')
plt.title("Mean Sq {}Disp".format("Angular " if ang else "") if title is None else title)
plt.xlabel('Time (' + ('s)' if fps > 1 else 'frames)'), fontsize='x-large')
if ang:
plt.ylabel('Squared Angular Displacement ($rad^2$)',
fontsize='x-large')
else:
plt.ylabel('Squared Displacement ('+('particle area)' if S>1 else 'square pixels)'),
fontsize='x-large')
if xlim is not None:
plt.xlim(*xlim)
if ylim is not None:
plt.ylim(*ylim)
if show_legend: plt.legend(loc='best')
if save is True:
save = prefix + "_MS{}D.pdf".format('A' if ang else '')
if save:
print "saving to", save
plt.savefig(save)
if show: plt.show()
return [fig] + fig.get_axes() + [taus] + [msd, msd_err] if errorbars else [msd]
def plot_msd(msds, msdids, dtau, dt0, nframes, tnormalize=False, prefix='',
show_tracks=True, figsize=(8,6), plfunc=pl.semilogx, meancol='',
title=None, xlim=None, ylim=None, fignum=None, errorbars=False,
lw=1, singletracks=xrange(1000), fps=1, S=1, ang=False, sys_size=0,
kill_flats=0, kill_jumps=1e9, show_legend=False, save='', show=True):
""" Plots the MS(A)Ds """
print "using dtau = {}, dt0 = {}".format(dtau, dt0)
A = 1 if ang else S**2
print "using S = {} pixels, thus A = {} px^2".format(S, A)
try:
dtau = np.asscalar(dtau)
except AttributeError:
pass
if isinstance(dtau, (float, np.float)):
taus = helpy.farange(dt0, nframes-1, dtau)
elif isinstance(dtau, (int, np.int)):
taus = np.arange(dtau, nframes-1, dtau, dtype=float)
fig = pl.figure(fignum, figsize)
# Get the mean of msds
msd = mean_msd(msds, taus, msdids,
kill_flats=kill_flats, kill_jumps=kill_jumps, show_tracks=show_tracks,
singletracks=singletracks, tnormalize=tnormalize, errorbars=errorbars,
fps=fps, A=A)
if errorbars: msd, msd_err = msd
#print "Coefficient of diffusion ~", msd[np.searchsorted(taus, fps)]/A
#print "Diffusion timescale ~", taus[np.searchsorted(msd, A)]/fps
if tnormalize:
plfunc(taus/fps, msd/A/(taus/fps)**tnormalize, meancol,
label="Mean Sq {}Disp/Time{}".format(
"Angular " if ang else "",
"^{}".format(tnormalize) if tnormalize != 1 else ''))
plfunc(taus/fps, msd[0]/A*(taus/fps)**(1-tnormalize)/dtau,
'k-', label="ref slope = 1", lw=2)
plfunc(taus/fps, (twopi**2 if ang else 1)/(taus/fps)**tnormalize,
'k--', lw=2, label=r"$(2\pi)^2$" if ang else
("One particle area" if S>1 else "One Pixel"))
pl.ylim([0, 1.3*np.max(msd/A/(taus/fps)**tnormalize)])
else:
pl.loglog(taus/fps, msd/A, meancol, lw=lw,
label=prefix+'\ndt0=%d dtau=%d'%(dt0,dtau))
#pl.loglog(taus/fps, msd[0]/A*taus/dtau/2, meancol+'--', lw=2,
# label="slope = 1")
if errorbars:
pl.errorbar(taus/fps, msd/A/(taus/fps)**tnormalize,
msd_err/A/(taus/fps)**tnormalize,
fmt=meancol, capthick=0, elinewidth=1, errorevery=errorbars)
if sys_size:
pl.axhline(sys_size, ls='--', lw=.5, c='k', label='System Size')
pl.title("Mean Sq {}Disp".format("Angular " if ang else "") if title is None else title)
pl.xlabel('Time (' + ('s)' if fps > 1 else 'frames)'), fontsize='x-large')
if ang:
pl.ylabel('Squared Angular Displacement ($rad^2$)',
fontsize='x-large')
else:
pl.ylabel('Squared Displacement ('+('particle area)' if S>1 else 'square pixels)'),
fontsize='x-large')
if xlim is not None:
pl.xlim(*xlim)
if ylim is not None:
pl.ylim(*ylim)
if show_legend: pl.legend(loc='best')
if save is None:
save = locdir + prefix + "_MS{}D.pdf".format('A' if ang else '')
if save:
print "saving to", save
pl.savefig(save)
if show: pl.show()
return [fig] + fig.get_axes() + [taus] + [msd, msd_err] if errorbars else [msd]