def caltrackmsd(self, m_to_p=0.0645, fps=2, plot=True):
try:
import trackpy as tp
except ImportError:
print('... install trackpy')
exit
if len(self._tdata) == 0:
print('... add track data')
exit
em = tp.emsd(self._tdata, m_to_p, fps)
a = tp.utils.fit_powerlaw(em, plot=False)
tnumber = np.unique(self._tdata['particle'].values).max()+1
if plot:
fig = plt.figure(figsize=(6,4))
x = pd.Series(em.index.values, index=em.index, dtype=np.float64)
fits = x.apply(lambda x: a['A']*x**a['n'])
plt.plot(em.index, em, 'o', label='exp. %i tracks' % tnumber)
plt.plot(x, fits, label='y=%.4f x^{%.4f}'% (a['A'], a['n']))
ax = plt.gca()
ax.set_xscale('log')
ax.set_yscale('log')
ax.set(ylabel=r'$\langle \Delta r^2 \rangle$ [$\mu$m$^2$]', xlabel='lag time $t$')
plt.legend(loc='best')
plt.tight_layout()
fname = self._cwd.split('/')[-1]+'_trace_msd.pdf'
plt.savefig(fname, dpi=300)
plt.show()
return a
def test_zero_emsd(self):
N = 10
actual = tp.emsd(self.dead_still, 1, 1)
expected = Series(np.zeros(N)).iloc[1:].astype('float64')
expected.index.name = 'lagt'
expected.name = 'msd'
assert_series_equal(actual, expected)
def test_zero_emsd(self):
N = 10
actual = tp.emsd(self.dead_still, 1, 1)
expected = Series(np.zeros(N)).iloc[1:].astype('float64')
expected.index.name = 'lagt'
expected.name = 'msd'
assert_series_equal(actual, expected)
def compute_emsd(traj, DT, omit_time=0, printing=False, DS=0.025):
'''traj is a pandas.DataFrame instance with columns "frame", "particle", "x" and "y" containing the results of unwrapped trajectories.
returns a pandas.DataFrane instance containing the ensemble mean squared displacement.'''
#remove the first and last 150ms of each input trajectory by default
n_rows_omit = int(omit_time / DT)
indices_of_head = traj.groupby('particle').head(n_rows_omit).index
indices_of_tail = traj.groupby('particle').tail(n_rows_omit).index
drop_id_lst = list(indices_of_head.values)
drop_id_lst.extend(list(indices_of_tail.values))
traj.drop(index=drop_id_lst, inplace=True)
#truncate max lag to the min lifetime
len_lst = traj.groupby('particle').x.count().values
if len(len_lst) == 0:
return None
max_lag = np.min(len_lst) #frames
#compute ensemble MSD
emsd = trackpy.emsd(
traj=traj,
mpp=DS,
fps=1 / DT,
max_lagtime=max_lag,
detail=False,
pos_columns=None,
)
if printing:
print(f'max_lag was {DT*max_lag} ms')
return emsd
def test_zero_emsd(self):
N = 10
actual = tp.emsd(self.dead_still, 1, 1)
expected = Series(np.zeros(N, dtype=np.float),
index=np.arange(N, dtype=np.float)).iloc[1:]
expected.index.name = 'lagt'
expected.name = 'msd'
assert_series_equal(actual, expected)
def test_zero_emsd(self):
N = 10
actual = tp.emsd(self.dead_still, 1, 1)
expected = Series(np.zeros(N, dtype=np.float),
index=np.arange(N, dtype=np.float)).iloc[1:]
expected.index.name = 'lagt'
expected.name = 'msd'
assert_series_equal(actual, expected)
def _compute_general_msd(trajectory, space_scale, fps, max_lagtime=100):
# Calculate the MSD
msd = tp.emsd(trajectory, space_scale, fps, max_lagtime=max_lagtime)
# Format into a 2-D numpy array
msd = np.array([msd.index, msd.to_numpy()])
return msd.T
def test_zero_emsd(self):
N = 10
actual = tp.emsd(self.dead_still, 1, 1)
expected = Series(np.zeros(N, dtype=np.float),
index=np.arange(N, dtype=np.float)).iloc[1:]
expected.index.name = 'lagt'
expected.name = 'msd'
# HACK: Float64Index imprecision ruins index equality.
# Test them separately. If that works, make them exactly the same.
assert_almost_equal(actual.index.values, expected.index.values)
actual.index = expected.index
assert_series_equal(actual, expected)
def test_zero_emsd(self):
N = 10
actual = tp.emsd(self.dead_still, 1, 1)
expected = Series(np.zeros(N, dtype=np.float),
index=np.arange(N, dtype=np.float)).iloc[1:]
expected.index.name = 'lagt'
expected.name = 'msd'
# HACK: Float64Index imprecision ruins index equality.
# Test them separately. If that works, make them exactly the same.
assert_almost_equal(actual.index.values, expected.index.values)
actual.index = expected.index
assert_series_equal(actual, expected)
def test_linear_emsd(self):
A = 1
EARLY = 7 # only early lag times have good stats
actual = tp.emsd(self.many_walks, 1, 1, max_lagtime=EARLY)
a = np.arange(EARLY + 1, dtype='float64')
expected = Series(2 * A * a, index=a).iloc[1:]
expected.name = 'msd'
expected.index.name = 'lagt'
# HACK: Float64Index imprecision ruins index equality.
# Test them separately. If that works, make them exactly the same.
assert_almost_equal(actual.index.values, expected.index.values)
actual.index = expected.index
assert_series_equal(np.round(actual), expected)
def test_linear_emsd(self):
A = 1
EARLY = 7 # only early lag times have good stats
actual = tp.emsd(self.many_walks, 1, 1, max_lagtime=EARLY)
a = np.arange(EARLY, dtype='float64')
expected = Series(2*A*a, index=a).iloc[1:]
expected.name = 'msd'
expected.index.name = 'lag time [s]'
# HACK: Float64Index imprecision ruins index equality.
# Test them separately. If that works, make them exactly the same.
assert_almost_equal(actual.index.values, expected.index.values)
actual.index = expected.index
assert_series_equal(np.round(actual), expected)
def test_linear_emsd_gaps(self):
A = 1
EARLY = 4 # only early lag times have good stats
gapped_walks = self.many_walks.reset_index(drop=True)
to_drop = np.random.choice(gapped_walks.index,
int(len(gapped_walks) * 0.1), replace=False)
gapped_walks = gapped_walks.drop(to_drop, axis=0)
actual = tp.emsd(gapped_walks, 1, 1, max_lagtime=EARLY)
a = np.arange(EARLY+1, dtype='float64')
expected = Series(2*A*a, index=a).iloc[1:]
expected.name = 'msd'
expected.index.name = 'lagt'
# HACK: Float64Index imprecision ruins index equality.
# Test them separately. If that works, make them exactly the same.
assert_almost_equal(actual.index.values, expected.index.values)
actual.index = expected.index
assert_series_equal(np.round(actual), expected)
def nd2msd(nd_fh,
params_locate_start={'diameter':11,'minmass_percentile':92},
params_msd={'mpp':0.0645,'fps':0.2, 'max_lagtime':100},
get_coords=True,out_fh=None):
frames=nd2frames(nd_fh)
t_cor=frames2coords_cor(frames,params_locate_start=params_locate_start,params_msd=params_msd,out_fh=out_fh)
# debug
imsd=tp.imsd(t_cor,statistic='msd',**params_msd)
emsd=tp.emsd(t_cor,**params_msd)
emsd=pd.DataFrame(emsd)
emsd.index.name='lag time [s]'
# print emsd
import statsmodels.tsa.stattools as st
acf=pd.DataFrame(columns=emsd.columns)
for c in emsd:
acf[c]=st.acf(emsd.loc[:,c],nlags=len(emsd))
acf.index=emsd.index
if not out_fh is None:
figure=plt.figure()
ax=plt.subplot(111)
acf.plot(ax=ax)
plt.savefig('%s.acf.pdf' % out_fh,format='pdf')
# plt.clf()
if not out_fh is None:
imsd.to_csv(out_fh+".imsd")
emsd.to_csv(out_fh+".emsd")
acf.to_csv(out_fh+".acf")
dpkl={}
dpkl['imsd']=imsd
dpkl['emsd']=emsd
dpkl['acf']=acf
# dpkl['t']=t
# dpkl['t_flt']=t_flt
# dpkl['f_batch']=f_batch
dpkl['t_cor']=t_cor
to_pkl(dpkl,out_fh+".pkl")
if get_coords:
t_cor.to_csv(out_fh+".coords")
return imsd,emsd
def nd2msd(nd_fh):
# print nd_fh
frames=pims.ND2_Reader(nd_fh)
logging.info('number of frames = %d' % len(np.shape(frames)))
if len(np.shape(frames))==4:
frames = average_z(frames)
threshold=np.percentile(frames,75)
f_batch = tp.batch(frames,diameter=11,threshold=threshold)
t = tp.link_df(f_batch, search_range=11, memory=3)
t_flt = tp.filter_stubs(t, 3*int(len(frames)/4))
try:
d = tp.compute_drift(t_flt)
t_cor = tp.subtract_drift(t_flt, d)
except:
t_cor=t_flt
logging.info("drift correction excepted")
# plt.figure()
# tp.plot_traj(t_flt)
# plt.figure()
# d.plot()
imsd=tp.imsd(t_cor,0.1,0.2, max_lagtime=100, statistic='msd')
emsd=tp.emsd(t_cor,0.1,0.2, max_lagtime=100)
return imsd,emsd
def analyze(self, plot_gif=False):
self.drifts = []
self.v_drift_mag = []
self.D_constants = []
self.D_constants2 = []
self.msd_slope = []
self.msd_intercept = []
self.mu_hats = []
self.ed = []
self.em = []
self.frames = []
self.dataframes = []
for i, path in enumerate(self.SXM_PATH):
frames = SXMReader(path)
self.frames.append(frames)
self.NM_PER_PIXEL = frames.meters_per_pixel * 1e9
molecule_size, min_mass, max_mass, separation, min_size, max_ecc, adaptive_stop, search_range, _ = self.PARAMS[
i]
f = tp.batch(frames,
molecule_size,
minmass=min_mass,
separation=separation)
t = tp.link(f,
search_range=search_range,
adaptive_stop=adaptive_stop)
t1 = t[((t['mass'] > min_mass) & (t['size'] > min_size)
& (t['ecc'] < max_ecc)) & (t['mass'] < max_mass)]
t2 = tp.filter_stubs(t, 3)
# Compare the number of particles in the unfiltered and filtered data.
print('Before:', t['particle'].nunique())
print('After:', t2['particle'].nunique())
if plot_gif == True:
moviename = "{}-{}".format(min(self.fileranges[i]),
max(self.fileranges[i]))
singlemoviefolder = self.MOVIE_FOLDER + moviename + "/"
if not os.path.exists(singlemoviefolder):
os.makedirs(singlemoviefolder)
mpl.rcParams.update({'font.size': 14, 'font.weight': 'bold'})
mpl.rc('image', origin='lower')
mpl.rc('text', usetex=False)
mpl.rc('text', color='orange')
fns = []
for j, frame in enumerate(frames):
fig = plt.figure(figsize=(5, 5))
tp.plot_traj(t2[(t2['frame'] <= j)],
superimpose=frames[j],
label=True)
fn = singlemoviefolder + "Image_{}.png".format(
self.fileranges[i][j])
fig.savefig(fn)
fns.append(fn)
ax = plt.gca() # get the axis
ax.set_ylim(ax.get_ylim()[::-1]) # invert the axis
ax.xaxis.tick_top() # and move the X-Axis
ax.yaxis.set_ticks(np.arange(0, 16, 1)) # set y-ticks
ax.yaxis.tick_left() # remove right y-Ticks
plt.clf()
mpl.rc('text', color='black')
images = []
for fn in fns:
images.append(imageio.imread(fn))
imageio.mimsave(singlemoviefolder + moviename + '.gif',
images,
duration=0.5)
self._cleanup_png(singlemoviefolder)
# Compute drifts
d = tp.compute_drift(t2)
d.loc[0] = [0, 0]
t3 = t2.copy()
# Storing drifts
self.drifts.append(d)
# Method 1 of calculating D: variance of all displacements of Delta_t=1
displacements = self._calculate_displacements(t3)
self.D_constants.append(
(displacements.dx.var() + displacements.dy.var()) /
4) # r^2 = x^2 + y^2 = 2Dt + 2Dt
self.mu_hats.append(np.mean(displacements[['dx', 'dy']], axis=0))
# Method 2 of calculating D: linear fit to MSD
em = tp.emsd(t3,
frames.meters_per_pixel * 1e9,
self.DIFFUSION_TIME,
max_lagtime=len(frames),
detail=True)
self.em.append(em)
self.ed.append([em['<x>'], em['<y>']])
result = linregress(em.index[:-8] * self.DIFFUSION_TIME,
em['msd'][:-8])
self.msd_slope.append(result.slope)
self.msd_intercept.append(result.intercept)
self.D_constants2.append(result.slope / 4)
# Store dataframe for future analysis
self.dataframes.append(t3)
self.v_drift_mag = np.linalg.norm(self.mu_hats, 2, axis=1)
plt.show()
##MSD Calculation and Plot
im=tp.imsd(tm,1/5.,60) ##microns per pixel, frames per second=60
fig, ax = plt.subplots()
ax.plot(im.index, im, 'k-', alpha=0.1) # black lines, semitransparent
ax.set(ylabel=r'$\langle \Delta r^2 \rangle$ [$\mu$m$^2$]',
xlabel='lag time $t$',title='MSD')
ax.set_xscale('log')
ax.set_yscale('log')
##Total Ensemble MSD and Plot
em=tp.emsd(tm,1/5.,60)
fig, ax = plt.subplots()
ax.plot(em.index, em, 'o-')
ax.set_xscale('log')
ax.set_yscale('log')
ax.set(ylabel=r'$\langle \Delta r^2 \rangle$ [$\mu$m$^2$]', xlabel='lag time $t$', title='Ensemble MSD')
ax.set(ylim=(1e-2, 10));
##Fitting the EMSD
#plt.figure()
plt.ylabel(r'$\langle \Delta r^2 \rangle$ [$\mu$m$^2$]')
plt.title("EMSD Fit")
fps = 25 # frame per second
maxact = 11
##fig, ax = plt.subplots() # for ploting msd curve of all activites
#plt.figure('MSD for aactivities')
#plt.clf()
for act in range(8, 12): # loop for file name
print('Activity', act)
# load trajectory
traj_f = pd.read_csv(savepath_traj_f.format(act))
#==============================================================================
# ## Mean Squared Displacement of Individal Probes
# im = tp.imsd(traj_f, mpp, fps, max_lagtime=100, statistic='msd') # microns per pixel = 100/285., frames per second = 24
#
# fig, ax = plt.subplots()
# ax.plot(im.index, im[18], 'k-', alpha=0.1) # black lines, semitransparent
# ax.set(ylabel=r'$\langle \Delta r^2 \rangle$ [$\mu$m$^2$]', xlabel='lag time $t$')
# ax.set_xscale('log')
# ax.set_yscale('log')
#==============================================================================
## Ensemble MSD
em = tp.emsd(traj_f, mpp, fps, max_lagtime=1600,
detail=True) #detail=True to see also <x>,<y>,<x^2>,<y^2>
# save MSD
em.to_csv(savepath_MSD.format(act), index=False)
tp.plot_traj(t1)
d = tp.compute_drift(t1)
d.plot()
plt.show()
plt.savefig("1.pdf")
tm = tp.subtract_drift(t1.copy(),d)
ax = tp.plot_traj(tm)
plt.show()
plt.savefig("2.pdf")
em = tp.emsd(tm, 0.00000119029/1, 30) # microns per pixel = 100/285., frames per second = 24
fig, ax = plt.subplots()
ax.plot(em.index, em, 'o')
ax.set_xscale('log')
ax.set_yscale('log')
ax.set(ylabel=r'$\langle \Delta r^2 \rangle$ [$\mu$m$^2$]',
xlabel='lag time $t$')
ax.set(ylim=(1e-2, 100));
plt.savefig("3.pdf")
plt.figure()
plt.ylabel(r'$\langle \Delta r^2 \rangle$ [$\mu$m$^2$]')
plt.xlabel('lag time $t$');
atre = tp.utils.fit_powerlaw(em) # performs linear best fit in log space, plots]
plt.savefig("4.pdf")
def main():
for case_idx, case in enumerate(cases.values()):
res_path = gen_path + case[1]
frames = pims.ImageSequence(gen_path + case[0], as_grey=True)
# Stores the unfiltered annotated image of a frame to local file path
if plots["Annotate_unfiltered"]:
k = tp.locate(frames[0],
11,
invert=[case_idx in [0, 1]],
minmass=200)
fig = plt.figure("Annotated_unfiltered_image_" + case[2])
ax1 = fig.add_subplot()
a = ["k", "w"][case_idx in [2, 3]]
tp.annotate(k, frames[0], color=a, ax=ax1)
#ax1.set_title("Annotated unfiltered image case: "+ case[2])
#ax1.set_xlabel("x[px]", fontsize=size)
#ax1.set_ylabel("y[px]", fontsize=size)
ax1.tick_params(axis="both",
which="both",
top=False,
bottom=False,
labelbottom=False,
right=False,
left=False,
labelleft=False)
fig.savefig(res_path + "Annotated_unfiltered_image_" + case[2] +
".png",
bbox_inches="tight",
pad_inches=0)
plt.close(fig)
# If True: Tracks all frames and stores .csv to locally, else: imports such .csv file from local
if plots["Generate_batch"]:
f = tp.batch(frames[:225],
11,
minmass=100,
invert=[case_idx in [0, 1]])
f.to_csv(res_path + "batch_" + case[2] + ".csv")
if not plots["Generate_batch"]:
f = pd.read_csv(res_path + "batch_" + case[2] + ".csv")
# Linking and filtering
t = tp.link_df(f, 5, memory=3)
t1 = tp.filter_stubs(t, 50)
# Plots the size vs mass profile and saves to local file path
if plots["Size_vs_mass"]:
fig = plt.figure("Size_vs_mass_" + case[2])
ax1 = fig.add_subplot()
tp.mass_size(
t1.groupby('particle').mean(),
ax=ax1) # convenience function -- just plots size vs. mass
#ax1.set_title("Size vs mass case: " + case[2])
ax1.set_xlabel("mass", fontsize=size)
ax1.set_ylabel("Gyration radius [px]", fontsize=size)
ax1.spines['top'].set_visible(False)
ax1.spines['right'].set_visible(False)
ax1.tick_params(axis="both", which="major", labelsize=size)
ax1.tick_params(axis="both", which="minor", labelsize=size)
fig.savefig(res_path + "Size_vs_mass_" + case[2] + ".png",
bbox_inches="tight",
pad_inches=0)
plt.close(fig)
if plots["Annotate_filtered"]:
if case_idx in [0, 1]: # Set BF condition
condition = lambda x: (
(x['mass'].mean() > 250) & (x['size'].mean() < 3.0) &
(x['ecc'].mean() < 0.1))
elif case_idx in [2, 3]: # Set DF condition
condition = lambda x: (
(x['mass'].mean() > 100) & (x['size'].mean() < 5.0) &
(x['ecc'].mean() < 0.1))
t2 = tp.filter(
t1, condition
) # a wrapper for pandas' filter that works around a bug in v 0.12
fig = plt.figure("Annotated_filtered_image_" + case[2])
ax1 = fig.add_subplot()
k = ["k", "w"][case_idx in [2, 3]]
tp.annotate(t2[t2['frame'] == 0], frames[0], color=k, ax=ax1)
#ax1.set_title("Annotated filtered image case: " + case[2])
#ax1.set_xlabel("x[px]", fontsize=size)
#ax1.set_ylabel("y[px]", fontsize=size)
ax1.tick_params(axis="both",
which="both",
top=False,
bottom=False,
labelbottom=False,
right=False,
left=False,
labelleft=False)
fig.savefig(res_path + "Annotated_filtered_image_" + case[2] +
".png",
bbox_inches="tight",
pad_inches=0)
plt.close(fig)
if plots["Gyration_radius_filtered"]:
size_dis_t1 = [i * ratio_μm_px for i in t1['size']]
plt.figure("Gyration_radius_filtered_" + case[2])
plt.hist(size_dis_t1, bins=300, color="k", alpha=0.5)
#plt.title("Gyration radius filtered case: "+ case[2])
plt.ylabel("Events", fontsize=size)
plt.xlabel("Gyration radius [μm]", fontsize=size)
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)
plt.tick_params(axis="both", which="major", labelsize=size)
plt.tick_params(axis="both", which="minor", labelsize=size)
plt.savefig(res_path + "Gyration_radius_filtered" + case[2] +
".png",
bbox_inches="tight",
pad_inches=0)
plt.close("all")
if plots["Gyration_radius_unfiltered"]:
size_dis_t = [i * ratio_μm_px for i in t['size']]
plt.figure("Gyration_radius_unfiltered_" + case[2])
plt.hist(size_dis_t, bins=300, color="k", alpha=0.5)
#plt.title("Gyration radius unfiltered case: " + case[2])
plt.ylabel("Events", fontsize=size)
plt.xlabel("Gyration radius [μm]", fontsize=size)
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)
plt.tick_params(axis="both", which="major", labelsize=size)
plt.tick_params(axis="both", which="minor", labelsize=size)
plt.savefig(res_path + "Gyration_radius_unfiltered" + case[2] +
".png",
bbox_inches="tight",
pad_inches=0)
plt.close("all")
d = tp.compute_drift(t1)
tm = tp.subtract_drift(t1, d)
if plots["Trajectory_drift"]:
fig = plt.figure("Trajectory_drift_subtracted_" + case[2])
ax1 = fig.add_subplot()
ax1.tick_params(axis="both", which="major", labelsize=size)
ax1.tick_params(axis="both", which="minor", labelsize=size)
ax1.spines['top'].set_visible(False)
ax1.spines['right'].set_visible(False)
tp.plot_traj(tm, ax=ax1)
#ax1.set_title("Trajectory with drift subtracted case: " + case[2])
plt.savefig(res_path + "Trajectory_drift_subtracted_" + case[2] +
".png",
bbox_inches="tight",
pad_inches=0)
plt.close(fig)
if plots["Variance_all_parts"]:
im = tp.imsd(
tm, ratio_μm_px, fps, max_lagtime=225
) # microns per pixel = 100/285., frames per second = 24
plt.figure("Variance_for_all_particles_" + case[2])
#plt.title("Variance for all particles case: " + case[2])
plt.plot(im.index, im, 'k-',
alpha=0.1) # black lines, semitransparent
plt.ylabel(r'$\langle \Delta r^2 \rangle$ [$\mu$m$^2$]',
fontsize=size),
plt.xlabel('time $t$', fontsize=size)
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)
plt.xscale('log')
plt.yscale('log')
plt.savefig(res_path + "Variance_for_all_particles_" + case[2] +
".png",
bbox_inches="tight",
pad_inches=0)
if plots["Variance_linear"] or plots["Variance_power_fit"] or plots[
"Return_A_and_D"]:
em = tp.emsd(tm, ratio_μm_px, fps, max_lagtime=225)
if plots["Variance_linear"]:
plt.figure("Variance_linear_fit_" + case[2])
#plt.title("Variance linear fit case: " + case[2])
plt.plot(em.index, em, 'ko', alpha=0.5)
plt.ylabel(r'$\langle \Delta r^2 \rangle$ [$\mu$m$^2$]',
fontsize=size),
plt.xlabel('time $t$ [s]', fontsize=size)
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)
plt.tick_params(axis="both", which="major", labelsize=size)
plt.tick_params(axis="both", which="minor", labelsize=size)
plt.xscale('log')
plt.yscale('log')
plt.ylim(1e-2, 50)
plt.savefig(res_path + "Variance_linear_fit_" + case[2] + ".png",
bbox_inches="tight",
pad_inches=0)
if plots["Variance_power_fit"]:
fig = plt.figure("Variance_power_fit_" + case[2])
ax1 = fig.add_subplot()
tp.utils.fit_powerlaw(em, ax=ax1, color="k", alpha=0.5)
#ax1.set_title("Variance power fitted case: " + case[2])
ax1.set_ylabel(r'$\langle \Delta r^2 \rangle$ [$\mu$m$^2$]',
fontsize=size)
ax1.set_xlabel('time $t$ [s]', fontsize=size)
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)
ax1.tick_params(axis="both", which="major", labelsize=size)
ax1.tick_params(axis="both", which="minor", labelsize=size)
fig.savefig(res_path + "Variance_power_fit_" + case[2] + ".png",
bbox_inches="tight",
pad_inches=0)
plt.close(fig)
if plots["Hydrodynamic_radius_filtered"]:
im = tp.imsd(tm, ratio_μm_px, fps, max_lagtime=225)
r_h = []
count = 0
im = im.rename_axis("ID").values
for index in range(1, len(im[0])):
if isinstance(im[40][index], float) and isinstance(
im[8][index], float):
D = (im[40][index] - im[8][index]) / (4 * (40 - 8) /
fps) * 10**(-12)
if isinstance(D, float):
r_h += [abs(10**6 * (k_b * T) / (6 * np.pi * μ * D))]
if 0 < abs(10**6 * (k_b * T) /
(6 * np.pi * μ * D)) < 6:
count += 1
print("In interval: ", count, "Total: ", len(r_h), "Ratio: ",
count / len(r_h))
plt.figure("Hydrodynamic_radius_filtered_" + case[2])
plt.hist(r_h,
bins=int(count / 3),
color="k",
alpha=0.5,
range=(0, 6))
#plt.title("Hydrodynamic radius filtered case: "+ case[2])
plt.ylabel("Trajectories", fontsize=size)
plt.xlabel("Hydrodynamic radius [μm]", fontsize=size)
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)
plt.tick_params(axis="both", which="major", labelsize=size)
plt.tick_params(axis="both", which="minor", labelsize=size)
plt.savefig(res_path + "Hydrodynamic_radius_filtered" + case[2] +
".png",
bbox_inches="tight",
pad_inches=0)
plt.close("all")
if plots["Return_A_and_D"]:
A = tp.utils.fit_powerlaw(em, ax=ax1, color="k",
alpha=0.5)["A"] * 10**(-12)
print(tp.utils.fit_powerlaw(em, ax=ax1, color="k", alpha=0.5))
print("For case ", case[2], " A=", A, ", and D=", A / 4, ".")
max_lagtime = 500 nop = 500 # settings end # reference line x = [0.01,1,10,100,1000] y = x dxb = 0 dyb = 0 datapath = '/Users/Zhengyang/Documents/20160715/a1l' filename = os.path.join(datapath,'trajectory.dat') traj = pd.read_csv(filename,delimiter=',') #remove drift msd = tp.emsd(traj,mpp,fps,max_lagtime,detail=True) p1 = np.polyfit(msd['lagt'],msd['<x>'],1) p2 = np.polyfit(msd['lagt'],msd['<y>'],1) trajr = traj trajr['x'] = traj['x']-p1[0]*traj['frame']/fps trajr['y'] = traj['y']-p2[0]*traj['frame']/fps # mean squared displacement msd = tp.emsd(trajr,mpp,fps,max_lagtime,detail=True) plt.ion() plt.figure(1) plt.loglog(msd['lagt'],msd['msd'],linestyle='None',marker='o',mec='r',mfc='w') plt.loglog(x,y,linestyle='solid') plt.draw()
def plot_tracks_MSD(N, a, logmu, Tf, ax_lim, MSD_show, refresh, log_scale):
'''Function plotting random tracks of particles and their associated mean square displacements,
depending on several physical parameters and plotting options.
Designed to be used with ipywidgets
INPUTS:
N : number of particles
a : radius of particles [um]
logmu: log of viscosity of fluid log[Pa s]
Tf: length of tracks [s]
ax_lim: limit of axis display [um]
MSD_show: boolean for showing graphs of mean square displacements (MSDs)
refresh: dummy argument for the widgets
log_scale: boolean to show MSDs in loglog scale
'''
# we have a few constants
dt = 1e-2 # timestep of simulation [s]
T = 305 # temperature, fixed [K]
k_B = 1.38e-23 # Boltzman constant [J K-1]
# we compute the diffusivity [m2/s]
D = k_B*T/(6*np.pi*10**(logmu)*a*1e-6) #
# we start all tracks from the center of the plot
pos0 = [0, 0]
# initialisation of figure
fig, (ax, ax2) = plt.subplots(1,2,figsize = (12,6)) # option to use gridspec here
# we add a bullseye pattern for guiding the viewer
angle = np.linspace( 0 , 2 * np.pi , 150 )
x = np.cos( angle )
y = np.sin( angle )
r_list = np.arange(15) # in microns
for i, r in enumerate(r_list):
ax.plot(r*x, r*y, color = 'k', linestyle = '--', alpha = 0.5)
pos = []
for i in range(N):
track = generate_diff_track(pos0, D, dt, Tf)
track = track*1e6 # convert to microns
# Now, we draw the trajectory and final position
ax.plot(track[0,:],track[1,:], color = 'k', alpha = 0.5)
ax.plot(track[0,-1],track[1,-1],marker='o', ms=6, markerfacecolor = 'm', markeredgecolor = 'k')
# we also populate a tracks panda frame (mostly empty) for use with trackpy
track_pd = np.concatenate((track, np.zeros((6,track.shape[1])),
np.arange(0,track.shape[1],1)[np.newaxis,:],
i*np.ones((1,track.shape[1]))),axis =0)
if i==0:
pos = track_pd
else:
pos = np.concatenate((pos, track_pd), axis=1)
# mark initial position
ax.plot(0,0,marker='o', ms=6, markerfacecolor = 'w', markeredgecolor = 'k')
# we also plot the scaling
ax.plot(np.sqrt(4*D*Tf)*1e6*x,np.sqrt(4*D*Tf)*1e6*y, color = 'r', linestyle = '--')
ax.text(0.0, 1.3*np.sqrt(4*D*Tf)*1e6, r"$r = \sqrt{4 D t_\mathrm{f}}$", fontsize=16, color='r',
ha="center", va="center", bbox=dict(boxstyle="square", ec=(1.0, 1.0, 1.0), fc=(1., 1., 1.),alpha = 0.7))
# polish the plot
ax.set_xlabel(r'$x$ ($\mu$m)')
ax.set_ylabel(r'$y$ ($\mu$m)')
ax.axis('equal')
ax.set_xlim(-ax_lim, ax_lim)
ax.set_ylim(-ax_lim, ax_lim)
#ax.set_axis_off()
if MSD_show:
# we finish formatting the panda frame for use with Trackpy
pos = np.transpose(pos)
df = pd.DataFrame(pos, columns=['x', 'y','mass', 'size', 'ecc', 'signal', 'raw_mass', 'ep', 'frame','particle'])
# we compute the msd of each particle, and the ensemble value
im = tp.imsd(df, mpp = 1., fps = 1/dt, max_lagtime=int(np.floor((Tf/dt)/2)))
em = tp.emsd(df, mpp = 1., fps = 1/dt, max_lagtime=int(np.floor((Tf/dt)/2)))
# we do a linear regression in log space on the whole range of times
slope, intercept, r, p, stderr = stats.linregress(np.log(em.index), np.log(em))
# we plot the individual msd with the theoretical trend and ensemble average overlaid
ax2.plot(im.index, im, 'k-', alpha=0.2)
ax2.plot(em.index, 1e12*4*D*em.index, linestyle = '--', color='r', label=r'theoretical power law $\langle \Delta r^2 \rangle = 4 D \Delta t$')
ax2.plot(em.index, em, 'o', label='ensemble average', alpha = 0.8)
ax2.plot(em.index, np.exp(intercept)*em.index**slope,linestyle = '-.', color='m', label=r'fitted power law $\langle \Delta r^2 \rangle = \alpha \Delta t^\beta$')
ax2.set(ylabel=r'$\langle \Delta r^2 \rangle$ [$\mu$m$^2$]',
xlabel='lag time $\Delta t$ [s]')
if log_scale:
ax2.set_xscale('log')
ax2.set_yscale('log')
plt.legend(loc=2, prop={'size': 12})
else:
ax2.set_axis_off()
fig.tight_layout()
if MSD_show:
print(' ================================================================================================')
print('| Theoretical Diffusivity D = {0:.2E} um2/s | Fitted power law: beta = {1:.2E} |'.format(D*1e12,slope))
print(' ================================================================================================')
else:
print(' =============================================')
print('| Theoretical Diffusivity D = {:.2E} um2/s |'.format(D*1e12))
print(' =============================================')
plt.show()
def plot_tracks_MSD_box(N, D, Tf, L, refresh, log_scale):
'''Function plotting random tracks of particles in a square box and their associated mean square displacements,
depending on several physical parameters and plotting options.
Designed to be used with ipywidgets
INPUTS:
N : number of particles
D : diffusivity of particles [um2/s]
Tf: length of tracks [s]
L: half-width of of bounding box [um]
refresh: dummy argument for the widgets
log_scale: boolean to show MSDs in loglog scale
'''
# we have a few constants
dt = 1e-2 # timestep of simulation [s]
# we start all tracks from the center of the plot
pos0 = [0, 0]
# initialisation of figure
fig, (ax, ax2) = plt.subplots(1,2,figsize = (12,6)) # option to use gridspec here
# we add the box
ax.plot([L,L,-L,-L,L], [-L,L,L,-L,-L], color = 'c', linestyle = '-.', alpha = 1,lw=2)
pos = []
for i in range(N):
track = generate_diff_track([np.random.uniform(-L,L),np.random.uniform(-L,L)], D, dt, Tf)
track_box = reflect(track,L)
track_box = track_box*1e6 # convert to microns
# Now, we draw the trajectory and final position
ax.plot(track[0,:],track[1,:], color = 'k', alpha = 0.5)
ax.plot(track[0,-1],track[1,-1],marker='o', ms=6, markerfacecolor = 'm', markeredgecolor = 'k')
ax.plot(track[0,0],track[1,0],marker='o', ms=6, markerfacecolor = 'w', markeredgecolor = 'k')
# we also populate a tracks panda frame (mostly empty) for use with trackpy
track_pd = np.concatenate((track, np.zeros((6,track.shape[1])),
np.arange(0,track.shape[1],1)[np.newaxis,:],
i*np.ones((1,track.shape[1]))),axis =0)
if i==0:
pos = track_pd
else:
pos = np.concatenate((pos, track_pd), axis=1)
# mark initial position
#ax.plot(0,0,marker='o', ms=6, markerfacecolor = 'w', markeredgecolor = 'k')
# polish the plot
ax.set_xlabel(r'$x$ ($\mu$m)')
ax.set_ylabel(r'$y$ ($\mu$m)')
ax.axis('equal')
ax.set_xlim(-1.2*L, 1.2*L)
ax.set_ylim(-1.2*L, 1.2*L)
#ax.set_axis_off()
# we finish formatting the panda frame for use with Trackpy
pos = np.transpose(pos)
df = pd.DataFrame(pos, columns=['x', 'y','mass', 'size', 'ecc', 'signal', 'raw_mass', 'ep', 'frame','particle'])
# we compute the msd of each particle, and the ensemble value
im = tp.imsd(df, mpp = 1., fps = 1/dt, max_lagtime=int(np.floor((Tf/dt)/2)))
em = tp.emsd(df, mpp = 1., fps = 1/dt, max_lagtime=int(np.floor((Tf/dt)/2)))
# we plot the individual msd with the theoretical trend and ensemble average overlaid
ax2.plot(im.index, im, 'k-', alpha=0.2)
ax2.plot(em.index, 4*D*em.index, linestyle = '--', color='r', label=r'theoretical power law $\langle \Delta r^2 \rangle = 4 D \Delta t$')
ax2.plot(em.index, em, 'o', label='ensemble average', alpha = 0.8)
ax2.plot(em.index, 0*em.index + 4*L**2/3,linestyle = '-.', color='c', label=r'box limit $4 L^2/3$')
ax2.set(ylabel=r'$\langle \Delta r^2 \rangle$ [$\mu$m$^2$]',
xlabel='lag time $ \Delta t$ [s]')
if log_scale:
ax2.set_xscale('log')
ax2.set_yscale('log')
ax2.set_ylim(2*D*dt, 10*L**2)
else:
ax2.set_ylim(0, 3*L**2)
plt.legend(loc=2, prop={'size': 12})
fig.tight_layout()
plt.show()
