In [1]:
import string
import copy
import scipy
import Tkinter, tkFileDialog
import numpy as np
import pandas as pd
from scipy.spatial.distance import cdist
import matplotlib.pyplot as plt
import os
import sys
import datetime
import matplotlib.units
import re
import glob
from numba import jit,int32
import time
sys.path.append(os.path.abspath("C:\Users\Scherer Lab E\Documents\GitHub\Python_Data_Analysis"))
import common_functions
%matplotlib inline
Other Data Set¶
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from IPython.display import Image
os.chdir("C:\Users\Scherer Lab E\Documents\IPython Notebooks\SPIFF Manuscript\Data")
Image(filename="06191317_example_image.png")
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In [3]:
#os.chdir("C:\Users\Scherer Lab E\Documents\IPython Notebooks\Dynamical Phase Transition\Data\SPIFF")
Image(filename="06191317_particle_closeup.png")
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Import the Raghu Data for Mov_06191306 for different windows¶
Used windows with diameter 3, 5, 7, 9, 11, 13, 15, and 17 pixels.
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os.chdir("C:\Users\Scherer Lab E\Downloads\TrackingGUI_and_associated_files_20July2014 My Version")
file_list = glob.glob('Mov_06191306-centroid*')
file_list = file_list[4:] + file_list[:4]
raghu_list = []
for traj_data in file_list:
if len(traj_data) == 38:
dia_size = int(traj_data[-5])
elif len(traj_data) == 39:
dia_size = int(traj_data[-6:-4])
data = common_functions.import_matlab_gui(traj_data)
df_raghu = common_functions.matlab_gui_to_data_frame(data)
#df_mos = df_mos.rename(columns={'x': 'x pos', 'y': 'y pos', 'Trajectory': 'track id', 'Frame': 'frame'})
raghu_list.append([df_raghu, dia_size])
Re-Link Particles with Trackpy¶
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import trackpy as tp
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'''Link the image data for each window'''
tracked_data = []
for frame, window in raghu_list:
tracked = tp.link_df(frame, 10, memory=1, pos_columns=['x pos', 'y pos'])
tracked_data.append([tracked, window])
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'''Checkpoint after linking'''
os.chdir("C:\Users\Scherer Lab E\Documents\IPython Notebooks\SPIFF Manuscript\Data")
import cPickle
pik = open('Ana_16042801_linked_positions.pkl', 'w')
cPickle.dump(tracked_data, pik)
pik.close()
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import cPickle
pik = open('Ana_16042801_linked_positions.pkl', 'r')
tracked_data = cPickle.load(pik)
pik.close()
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def disp_calc_en(grp, tau):
if len(grp) < tau:
return pd.Series([np.nan])
#print grp[['x pos', 'y pos']],grp.shift(tau, axis=0)[['x pos', 'y pos']]
disp = ((grp[['x pos', 'y pos']] - grp.shift(tau, axis=0)[['x pos', 'y pos']])**2).sum(skipna=False,axis=1)
#if grp.name > 5000:
#print grp.name
return disp
def calc_en_msd(df, percent=0.3):
en_msd = []
pivot = pd.pivot_table(df, values=['x pos','y pos'], index='frame', columns='track id')
for tau in range(int(max(df['frame'])*percent)):
del_xy = (pivot - pivot.shift(tau+1, axis=0))**2
en_msd.append((del_xy['x pos'] + del_xy['y pos']).stack().mean())
return en_msd
Calculated the ensemble averaged MSD on the first 3rd of the data.
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'''Calculate the ensemble MSD for each window'''
en_msd = []
for tracks, window in tracked_data:
temp_track = tracks.drop('track id', axis=1)
temp_track = temp_track.rename(columns={'x': 'x pos', 'y': 'y pos', 'particle': 'track id' })
en_msd.append([calc_en_msd(temp_track),window])
print 'done with window '+str(window)
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'''Checkpoint after calculating ensemble MSD'''
import cPickle
pik = open('Ana_16042801_ensemble_msd.pkl', 'w')
cPickle.dump(en_msd, pik)
pik.close()
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for num, entry in enumerate(tracked_data):
df, window = entry
plt.figure(figsize=[10,4])
plt.subplot(121)
plt.hist2d(df['x pos']%1, df['y pos']%1, bins=50)
plt.axis('equal')
cbar = plt.colorbar()
cbar.set_label('counts')
plt.minorticks_on()
plt.title('SPIFF for window='+str(window))
len_msd = len(en_msd[num][0])+1
ax2 = plt.subplot(122)
plt.plot(range(1,len_msd), en_msd[num][0], '-ob')
pwr_law = lambda x, param: param*x
fit_params = scipy.optimize.curve_fit(pwr_law, np.arange(1,len_msd), en_msd[num][0])
plt.plot(np.arange(1,len_msd), pwr_law(np.arange(1,len_msd), fit_params[0][0]), 'g')
plt.loglog()
ax2.text(0.5, 0.2, str(fit_params[0][0])+'t', transform=ax2.transAxes)
plt.title('MSD and Power Law for window='+str(window))
print 'Average particles per frame = '+str(df.groupby('frame').apply(len).mean())
plt.show()
SPIFF Correction¶
Do the SPIFF correction on the Raghu Data
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def spiff_correction(df, x_key='x', y_key='y'):
df_copy = df.copy()
spiff = df_copy[[x_key, y_key]] % 1
spiff['spiff_x_corr'] = spiff[x_key].rank()/len(spiff)
spiff['spiff_y_corr'] = spiff[y_key].rank()/len(spiff)
df_copy[x_key] = np.floor(df_copy[x_key]) + spiff.spiff_x_corr
df_copy[y_key] = np.floor(df_copy[y_key]) + spiff.spiff_y_corr
return df_copy
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corr_tracked_data = []
for tracks, window in tracked_data:
tracks_temp = spiff_correction(tracks, x_key='x pos', y_key='y pos')
corr_tracked_data.append([tracks_temp, window])
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'''Calculate the ensemble MSD for each window (for only first third of tau)'''
corr_en_msd = []
for tracks, window in corr_tracked_data:
temp_track = tracks.drop('track id', axis=1)
temp_track = temp_track.rename(columns={'x': 'x pos', 'y': 'y pos', 'particle': 'track id' })
corr_en_msd.append([calc_en_msd(temp_track),window])
print 'done with window '+str(window)
MSD of Corrected SPIFF¶
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for num, entry in enumerate(corr_tracked_data):
df, window = entry
plt.figure(figsize=[10,4])
plt.subplot(121)
plt.hist2d(df['x pos']%1, df['y pos']%1, bins=50)
plt.axis('equal')
cbar = plt.colorbar()
cbar.set_label('counts')
plt.minorticks_on()
plt.title('SPIFF for window='+str(window))
plt.ylabel('Meta Pixel Y')
plt.xlabel('Meta Pixel X')
len_msd = len(corr_en_msd[num][0])+1
ax2 = plt.subplot(122)
plt.plot(range(1,len_msd), corr_en_msd[num][0], '-ob')
pwr_law = lambda x, param: param*x
fit_params = scipy.optimize.curve_fit(pwr_law, np.arange(1,len_msd)[-200:], corr_en_msd[num][0][-200:])
plt.plot(np.arange(1,len_msd), pwr_law(np.arange(1,len_msd), fit_params[0][0]), 'g')
plt.loglog()
ax2.text(0.5, 0.2, str(fit_params[0][0])+'t', transform=ax2.transAxes)
plt.title('MSD and Power Law for window='+str(window))
plt.ylabel('MSD (Pixels$^2$)')
plt.xlabel('Lag Time (Frames)')
plt.tight_layout()
print 'Average particles per frame = '+str(df.groupby('frame').apply(len).mean())
plt.show()
Summary of SPIFF Correction and MSD¶
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for num, entry in enumerate(corr_tracked_data):
df, window = tracked_data[num]
plt.figure(figsize=[8,6])
plt.subplot(221)
plt.hist2d(df['x pos']%1, df['y pos']%1, bins=50)
plt.axis('equal')
cbar = plt.colorbar()
cbar.set_label('counts')
plt.minorticks_on()
plt.title('SPIFF for window='+str(window))
plt.ylabel('Meta Pixel Y')
plt.xlabel('Meta Pixel X')
len_msd = len(en_msd[num][0])+1
ax2 = plt.subplot(222)
plt.plot(range(1,len_msd), en_msd[num][0], '-ob')
pwr_law = lambda x, param: param*x
fit_params = scipy.optimize.curve_fit(pwr_law, np.arange(1,len_msd)[-200:], en_msd[num][0][-200:])
plt.plot(np.arange(1,len_msd), pwr_law(np.arange(1,len_msd), fit_params[0][0]), 'g')
plt.loglog()
ax2.text(0.5, 0.2, str(fit_params[0][0])+'t', transform=ax2.transAxes)
plt.title('MSD and Power Law for window='+str(window))
plt.ylabel('MSD (Pixels$^2$)')
plt.xlabel('Lag Time (Frames)')
plt.tight_layout()
df, window = entry
plt.subplot(223)
plt.hist2d(df['x pos']%1, df['y pos']%1, bins=50)
plt.axis('equal')
cbar = plt.colorbar()
cbar.set_label('counts')
plt.minorticks_on()
plt.title('Corrected SPIFF for window='+str(window))
plt.ylabel('Meta Pixel Y')
plt.xlabel('Meta Pixel X')
len_msd = len(corr_en_msd[num][0])+1
ax4 = plt.subplot(224)
plt.plot(range(1,len_msd), corr_en_msd[num][0], '-ob')
pwr_law = lambda x, param: param*x
fit_params = scipy.optimize.curve_fit(pwr_law, np.arange(1,len_msd)[-200:], corr_en_msd[num][0][-200:])
plt.plot(np.arange(1,len_msd), pwr_law(np.arange(1,len_msd), fit_params[0][0]), 'g')
plt.loglog()
ax4.text(0.5, 0.2, str(fit_params[0][0])+'t', transform=ax4.transAxes)
plt.title('Corrected MSD and Power Law for window='+str(window))
plt.ylabel('MSD (Pixels$^2$)')
plt.xlabel('Lag Time (Frames)')
plt.tight_layout()
print 'Average particles per frame = '+str(df.groupby('frame').apply(len).mean())
plt.show()
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