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import numpy as np |
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import pandas as pd |
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import numpy.ma as ma |
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from scipy.optimize import curve_fit |
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import numpy.linalg as LA |
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import math |
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import struct |
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import sys |
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import diff_classifier.utils as ut |
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import diff_classifier.msd as msd |
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View Code Duplication |
def unmask_track(track): |
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""" |
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Removes empty frames from a track in an MSD pandas dataframe. |
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Parameters |
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---------- |
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track : pandas Dataframe |
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At a minimum, must contain a Frame, Track_ID, X, Y, MSDs, and |
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Gauss column. |
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Returns |
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------- |
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comp_track : pandas Dataframe |
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Similar to track, but has all masked components removed. |
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Examples |
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-------- |
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""" |
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x = ma.masked_invalid(track['X']) |
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msd = ma.masked_invalid(track['MSDs']) |
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x_mask = ma.getmask(x) |
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msd_mask = ma.getmask(msd) |
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comp_frame = ma.compressed(ma.masked_where(msd_mask, track['Frame'])) |
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comp_ID = ma.compressed(ma.masked_where(msd_mask, track['Track_ID'])) |
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comp_x = ma.compressed(ma.masked_where(x_mask, track['X'])) |
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comp_y = ma.compressed(ma.masked_where(x_mask, track['Y'])) |
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comp_msd = ma.compressed(ma.masked_where(msd_mask, track['MSDs'])) |
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comp_gauss = ma.compressed(ma.masked_where(msd_mask, track['Gauss'])) |
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d = {'Frame': comp_frame, |
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'Track_ID': comp_ID, |
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'X': comp_x, |
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'Y': comp_y, |
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'MSDs': comp_msd, |
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'Gauss': comp_gauss |
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} |
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comp_track = pd.DataFrame(data=d) |
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return comp_track |
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View Code Duplication |
def alpha_calc(track): |
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""" |
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Calculates the parameter alpha by fitting track MSD data to a function. |
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Parameters |
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---------- |
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track : pandas DataFrame |
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At a minimum, must contain a Frames and a MSDs column. The function |
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msd_calc can be used to generate the correctly formatted pd dataframe. |
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Returns |
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------- |
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a : numpy.float64 |
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The anomalous exponent derived by fitting MSD values to the function, |
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<r**2(n)> = 4*D*(n*delt)**a |
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D : numpy.float64 |
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The fitted diffusion coefficient derived by fitting MSD values to the |
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function above. |
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Examples |
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-------- |
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>>> frames = 5 |
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>>> d = {'Frame': np.linspace(1, frames, frames), |
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'X': np.linspace(1, frames, frames)+5, |
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'Y': np.linspace(1, frames, frames)+3} |
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>>> df = pd.DataFrame(data=d) |
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>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
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>>> alpha_calc(df) |
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(2.0000000000000004, 0.4999999999999999) |
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>>> frames = 10 |
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>>> d = {'Frame': np.linspace(1, frames, frames), |
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'X': np.sin(np.linspace(1, frames, frames)+3), |
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'Y': np.cos(np.linspace(1, frames, frames)+3)} |
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>>> df = pd.DataFrame(data=d) |
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>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
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>>> alpha_calc(df) |
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(0.023690002018364065, 0.5144436515510022) |
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""" |
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# assert type(track) == pd.core.frame.DataFrame, "track must be a pandas dataframe." |
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# assert type(track['MSDs']) == pd.core.series.Series, "track must contain MSDs column." |
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# assert type(track['Frame']) == pd.core.series.Series, "track must contain Frame column." |
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# assert track.shape[0] > 0, "track must not be empty." |
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y = track['MSDs'] |
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x = track['Frame'] |
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def msd_alpha(x, a, D): |
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return 4*D*(x**a) |
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try: |
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popt, pcov = curve_fit(msd_alpha, x, y) |
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a = popt[0] |
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D = popt[1] |
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except RuntimeError: |
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print('Optimal parameters not found. Print NaN instead.') |
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a = np.nan |
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D = np.nan |
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return a, D |
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View Code Duplication |
def gyration_tensor(track): |
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""" |
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Calculates the eigenvalues and eigenvectors of the gyration tensor of the |
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input trajectory. |
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Parameters |
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---------- |
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track : pandas DataFrame |
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At a minimum, must contain an X and Y column. The function |
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msd_calc can be used to generate the correctly formatted pd dataframe. |
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Returns |
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------- |
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l1 : numpy.float64 |
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Dominant eigenvalue of the gyration tensor. |
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l2 : numpy.float64 |
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Secondary eigenvalue of the gyration tensor. |
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v1 : 2 x 1 numpy.ndarray of numpy.float64 objects |
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Dominant eigenvector of the gyration tensor. |
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v2 : 2 x 1 numpy.ndarray of numpy.float64 objects |
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Secondary eigenvector of the gyration tensor. |
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Examples |
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-------- |
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>>> frames = 5 |
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>>> d = {'Frame': np.linspace(1, frames, frames), |
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'X': np.linspace(1, frames, frames)+5, |
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'Y': np.linspace(1, frames, frames)+3} |
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>>> df = pd.DataFrame(data=d) |
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>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
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>>> gyration_tensor(df) |
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(4.0, |
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4.4408920985006262e-16, |
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array([ 0.70710678, -0.70710678]), |
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array([ 0.70710678, 0.70710678])) |
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>>> frames = 10 |
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>>> d = {'Frame': np.linspace(1, frames, frames), |
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'X': np.sin(np.linspace(1, frames, frames)+3), |
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'Y': np.cos(np.linspace(1, frames, frames)+3)} |
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>>> df = pd.DataFrame(data=d) |
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>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
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>>> gyration_tensor(df) |
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(0.53232560128104522, |
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0.42766829138901619, |
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array([ 0.6020119 , -0.79848711]), |
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array([-0.79848711, -0.6020119 ])) |
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""" |
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df = track |
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assert type(df) == pd.core.frame.DataFrame, "track must be a pandas dataframe." |
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assert type(df['X']) == pd.core.series.Series, "track must contain X column." |
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assert type(df['Y']) == pd.core.series.Series, "track must contain Y column." |
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assert df.shape[0] > 0, "track must not be empty." |
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Ta = np.sum((df['X'] - np.mean(df['X']))**2)/df['X'].shape[0] |
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Tb = np.sum((df['Y'] - np.mean(df['Y']))**2)/df['Y'].shape[0] |
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Tab = np.sum((df['X'] - np.mean(df['X']))*(df['Y'] - np.mean(df['Y'])))/df['X'].shape[0] |
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w, v = LA.eig(np.array([[Ta, Tab], [Tab, Tb]])) |
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dom = np.argmax(np.abs(w)) |
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rec = np.argmin(np.abs(w)) |
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l1 = w[dom] |
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l2 = w[rec] |
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v1 = v[dom] |
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v2 = v[rec] |
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return l1, l2, v1, v2 |
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View Code Duplication |
def kurtosis(track): |
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""" |
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Calculates the kurtosis of input track. |
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Parameters |
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---------- |
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track : pandas DataFrame |
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At a minimum, must contain an X and Y column. The function |
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msd_calc can be used to generate the correctly formatted pd dataframe. |
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Returns |
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------- |
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kurt : numpy.float64 |
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Kurtosis of the input track. Calculation based on projected 2D positions |
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on the dominant eigenvector of the radius of gyration tensor. |
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Examples |
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-------- |
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>>> frames = 5 |
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>>> d = {'Frame': np.linspace(1, frames, frames), |
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'X': np.linspace(1, frames, frames)+5, |
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'Y': np.linspace(1, frames, frames)+3} |
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>>> df = pd.DataFrame(data=d) |
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>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
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>>> kurtosis(df) |
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2.5147928994082829 |
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>>> frames = 10 |
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>>> d = {'Frame': np.linspace(1, frames, frames), |
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'X': np.sin(np.linspace(1, frames, frames)+3), |
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'Y': np.cos(np.linspace(1, frames, frames)+3)} |
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>>> df = pd.DataFrame(data=d) |
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>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
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>>> kurtosis(df) |
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1.8515139698652476 |
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""" |
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df = track |
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assert type(df) == pd.core.frame.DataFrame, "track must be a pandas dataframe." |
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assert type(df['X']) == pd.core.series.Series, "track must contain X column." |
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assert type(df['Y']) == pd.core.series.Series, "track must contain Y column." |
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assert df.shape[0] > 0, "track must not be empty." |
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l1, l2, v1, v2 = gyration_tensor(df) |
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projection = df['X']*v1[0] + df['Y']*v1[1] |
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kurt = np.mean((projection - np.mean(projection))**4/(np.std(projection)**4)) |
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return kurt |
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View Code Duplication |
def asymmetry(track): |
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""" |
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Calculates the asymmetry of the trajectory. |
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Parameters |
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---------- |
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track : pandas DataFrame |
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At a minimum, must contain an X and Y column. The function |
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msd_calc can be used to generate the correctly formatted pd dataframe. |
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Returns |
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------- |
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l1 : numpy.float64 |
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Dominant eigenvalue of the gyration tensor. |
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l2 : numpy.float64 |
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Secondary eigenvalue of the gyration tensor. |
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a1 : numpy.float64 |
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asymmetry of the input track. Equal to 0 for circularly symmetric tracks, |
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and 1 for linear tracks. |
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a2 : numpy.float64 |
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alternate definition of asymmetry. Equal to 1 for circularly |
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symmetric tracks, and 0 for linear tracks. |
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a3 : numpy.float64 |
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alternate definition of asymmetry. |
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Examples |
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-------- |
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>>> frames = 10 |
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>>> d = {'Frame': np.linspace(1, frames, frames), |
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'X': np.linspace(1, frames, frames)+5, |
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'Y': np.linspace(1, frames, frames)+3} |
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>>> df = pd.DataFrame(data=d) |
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>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
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>>> asymmetry(df) |
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(16.5, 0.0, 1.0, 0.0, 0.69314718055994529) |
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>>> frames = 10 |
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>>> d = {'Frame': np.linspace(1, frames, frames), |
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'X': np.sin(np.linspace(1, frames, frames)+3), |
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'Y': np.cos(np.linspace(1, frames, frames)+3)} |
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>>> df = pd.DataFrame(data=d) |
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>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
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>>> asymmetry(df) |
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(0.53232560128104522, |
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0.42766829138901619, |
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0.046430119259539708, |
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0.80339606128247354, |
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0.0059602683290953052) |
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""" |
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assert type(track) == pd.core.frame.DataFrame, "track must be a pandas dataframe." |
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assert type(track['X']) == pd.core.series.Series, "track must contain X column." |
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assert type(track['Y']) == pd.core.series.Series, "track must contain Y column." |
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assert track.shape[0] > 0, "track must not be empty." |
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l1, l2, v1, v2 = gyration_tensor(track) |
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a1 = (l1**2 - l2**2)**2/(l1**2 + l2**2)**2 |
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a2 = l2/l1 |
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a3 = -np.log(1-((l1-l2)**2)/(2*(l1+l2)**2)) |
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return l1, l2, a1, a2, a3 |
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View Code Duplication |
def minBoundingRect(df): |
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""" |
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Calculates the minimum bounding rectangle of an input trajectory. |
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Parameters |
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---------- |
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df : pandas DataFrame |
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At a minimum, must contain an X and Y column. The function |
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msd_calc can be used to generate the correctly formatted pd dataframe. |
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Returns |
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------- |
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rot_angle : numpy.float64 |
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Angle of rotation of the bounding box. |
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area : numpy.float64 |
315
|
|
|
Area of the bounding box. |
316
|
|
|
width : numpy.float64 |
317
|
|
|
Width of the bounding box. |
318
|
|
|
height : numpy.float64 |
319
|
|
|
Height of the bounding box. |
320
|
|
|
center_point : 2 x 1 numpy.ndarray of numpy.float64 objects |
321
|
|
|
Center point of the bounding box. |
322
|
|
|
corner_points : 4 x 2 numpy.ndarray of numpy.float64 objects |
323
|
|
|
Corner points of the bounding box. |
324
|
|
|
|
325
|
|
|
Examples |
326
|
|
|
-------- |
327
|
|
|
>>> frames = 10 |
328
|
|
|
>>> d = {'Frame': np.linspace(1, frames, frames), |
329
|
|
|
'X': np.linspace(1, frames, frames)+5, |
330
|
|
|
'Y': np.linspace(1, frames, frames)+3} |
331
|
|
|
>>> df = pd.DataFrame(data=d) |
332
|
|
|
>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
333
|
|
|
>>> minBoundingRect(df) |
334
|
|
|
(-2.3561944901923448, |
335
|
|
|
2.8261664256307952e-14, |
336
|
|
|
12.727922061357855, |
337
|
|
|
2.2204460492503131e-15, |
338
|
|
|
array([ 10.5, 8.5]), |
339
|
|
|
array([[ 6., 4.], |
340
|
|
|
[ 15., 13.], |
341
|
|
|
[ 15., 13.], |
342
|
|
|
[ 6., 4.]])) |
343
|
|
|
|
344
|
|
|
>>> frames = 10 |
345
|
|
|
>>> d = {'Frame': np.linspace(1, frames, frames), |
346
|
|
|
'X': np.sin(np.linspace(1, frames, frames))+3, |
347
|
|
|
'Y': np.cos(np.linspace(1, frames, frames))+3} |
348
|
|
|
>>> df = pd.DataFrame(data=d) |
349
|
|
|
>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
350
|
|
|
>>> minBoundingRect(df) |
351
|
|
|
(0.78318530717958657, |
352
|
|
|
3.6189901131223992, |
353
|
|
|
1.9949899732081091, |
354
|
|
|
1.8140392491811692, |
355
|
|
|
array([ 3.02076903, 2.97913884]), |
356
|
|
|
array([[ 4.3676025 , 3.04013439], |
357
|
|
|
[ 2.95381341, 1.63258851], |
358
|
|
|
[ 1.67393557, 2.9181433 ], |
359
|
|
|
[ 3.08772466, 4.32568917]])) |
360
|
|
|
|
361
|
|
|
Notes |
362
|
|
|
----- |
363
|
|
|
Based off of code from the following repo: |
364
|
|
|
https://github.com/dbworth/minimum-area-bounding-rectangle/blob/master/python/min_bounding_rect.py |
365
|
|
|
""" |
366
|
|
|
|
367
|
|
|
assert type(df) == pd.core.frame.DataFrame, "track must be a pandas dataframe." |
|
|
|
|
368
|
|
|
assert type(df['X']) == pd.core.series.Series, "track must contain X column." |
|
|
|
|
369
|
|
|
assert type(df['Y']) == pd.core.series.Series, "track must contain Y column." |
|
|
|
|
370
|
|
|
assert df.shape[0] > 0, "track must not be empty." |
371
|
|
|
|
372
|
|
|
df2 = np.zeros((df.shape[0]+1, 2)) |
373
|
|
|
df2[:-1, :] = df[['X', 'Y']].values |
374
|
|
|
df2[-1, :] = df[['X', 'Y']].values[0, :] |
375
|
|
|
hull_points_2d = df2 |
376
|
|
|
|
377
|
|
|
edges = np.zeros((len(hull_points_2d)-1, 2)) |
378
|
|
|
|
379
|
|
|
for i in range(len(edges)): |
|
|
|
|
380
|
|
|
edge_x = hull_points_2d[i+1, 0] - hull_points_2d[i, 0] |
381
|
|
|
edge_y = hull_points_2d[i+1, 1] - hull_points_2d[i, 1] |
382
|
|
|
edges[i] = [edge_x, edge_y] |
383
|
|
|
|
384
|
|
|
edge_angles = np.zeros((len(edges))) |
385
|
|
|
|
386
|
|
|
for i in range(len(edge_angles)): |
|
|
|
|
387
|
|
|
edge_angles[i] = math.atan2(edges[i, 1], edges[i, 0]) |
388
|
|
|
edge_angles = np.unique(edge_angles) |
389
|
|
|
|
390
|
|
|
start_area = platform_c_maxint = 2 ** (struct.Struct('i').size * 8 - 1) - 1 |
|
|
|
|
391
|
|
|
min_bbox = (0, start_area, 0, 0, 0, 0, 0, 0) |
392
|
|
|
for i in range(len(edge_angles)): |
|
|
|
|
393
|
|
|
R = np.array([[math.cos(edge_angles[i]), math.cos(edge_angles[i]-(math.pi/2))], |
|
|
|
|
394
|
|
|
[math.cos(edge_angles[i]+(math.pi/2)), math.cos(edge_angles[i])]]) |
|
|
|
|
395
|
|
|
|
396
|
|
|
rot_points = np.dot(R, np.transpose(hull_points_2d)) |
397
|
|
|
|
398
|
|
|
min_x = np.nanmin(rot_points[0], axis=0) |
399
|
|
|
max_x = np.nanmax(rot_points[0], axis=0) |
400
|
|
|
min_y = np.nanmin(rot_points[1], axis=0) |
401
|
|
|
max_y = np.nanmax(rot_points[1], axis=0) |
402
|
|
|
|
403
|
|
|
width = max_x - min_x |
404
|
|
|
height = max_y - min_y |
405
|
|
|
area = width*height |
406
|
|
|
|
407
|
|
|
if (area < min_bbox[1]): |
|
|
|
|
408
|
|
|
min_bbox = (edge_angles[i], area, width, height, min_x, max_x, min_y, max_y) |
409
|
|
|
|
410
|
|
|
angle = min_bbox[0] |
411
|
|
|
R = np.array([[math.cos(angle), math.cos(angle-(math.pi/2))], [math.cos(angle+(math.pi/2)), math.cos(angle)]]) |
|
|
|
|
412
|
|
|
proj_points = np.dot(R, np.transpose(hull_points_2d)) |
|
|
|
|
413
|
|
|
|
414
|
|
|
min_x = min_bbox[4] |
415
|
|
|
max_x = min_bbox[5] |
416
|
|
|
min_y = min_bbox[6] |
417
|
|
|
max_y = min_bbox[7] |
418
|
|
|
|
419
|
|
|
center_x = (min_x + max_x)/2 |
420
|
|
|
center_y = (min_y + max_y)/2 |
421
|
|
|
center_point = np.dot([center_x, center_y], R) |
422
|
|
|
|
423
|
|
|
corner_points = np.zeros((4, 2)) |
424
|
|
|
corner_points[0] = np.dot([max_x, min_y], R) |
425
|
|
|
corner_points[1] = np.dot([min_x, min_y], R) |
426
|
|
|
corner_points[2] = np.dot([min_x, max_y], R) |
427
|
|
|
corner_points[3] = np.dot([max_x, max_y], R) |
428
|
|
|
|
429
|
|
|
return (angle, min_bbox[1], min_bbox[2], min_bbox[3], center_point, corner_points) |
430
|
|
|
|
431
|
|
|
|
432
|
|
View Code Duplication |
def aspectratio(track): |
|
|
|
|
433
|
|
|
""" |
434
|
|
|
Calculates the aspect ratio of the rectangle containing the input track. |
435
|
|
|
|
436
|
|
|
Parameters |
437
|
|
|
---------- |
438
|
|
|
track : pandas DataFrame |
439
|
|
|
At a minimum, must contain an X and Y column. The function |
440
|
|
|
msd_calc can be used to generate the correctly formatted pd dataframe. |
441
|
|
|
|
442
|
|
|
Returns |
443
|
|
|
------- |
444
|
|
|
ar : numpy.float64 |
445
|
|
|
aspect ratio of the trajectory. Always >= 1. |
446
|
|
|
elong : numpy.float64 |
447
|
|
|
elongation of the trajectory. A transformation of the aspect ratio given |
448
|
|
|
by 1 - ar**-1. |
449
|
|
|
|
450
|
|
|
Examples |
451
|
|
|
-------- |
452
|
|
|
>>> frames = 10 |
453
|
|
|
>>> d = {'Frame': np.linspace(1, frames, frames), |
454
|
|
|
'X': np.linspace(1, frames, frames)+5, |
455
|
|
|
'Y': np.linspace(1, frames, frames)+3} |
456
|
|
|
>>> df = pd.DataFrame(data=d) |
457
|
|
|
>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
458
|
|
|
>>> aspectratio(df) |
459
|
|
|
(5732146505273195.0, 0.99999999999999978) |
460
|
|
|
|
461
|
|
|
>>> frames = 10 |
462
|
|
|
>>> d = {'Frame': np.linspace(1, frames, frames), |
463
|
|
|
'X': np.sin(np.linspace(1, frames, frames))+3, |
464
|
|
|
'Y': np.cos(np.linspace(1, frames, frames))+3} |
465
|
|
|
>>> df = pd.DataFrame(data=d) |
466
|
|
|
>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
467
|
|
|
>>> aspectratio(df) |
468
|
|
|
(1.0997501702946164, 0.090702573174318291) |
469
|
|
|
|
470
|
|
|
""" |
471
|
|
|
|
472
|
|
|
assert type(track) == pd.core.frame.DataFrame, "track must be a pandas dataframe." |
|
|
|
|
473
|
|
|
assert type(track['X']) == pd.core.series.Series, "track must contain X column." |
|
|
|
|
474
|
|
|
assert type(track['Y']) == pd.core.series.Series, "track must contain Y column." |
|
|
|
|
475
|
|
|
assert track.shape[0] > 0, "track must not be empty." |
476
|
|
|
|
477
|
|
|
rot_angle, area, width, height, center_point, corner_points = minBoundingRect(track) |
|
|
|
|
478
|
|
|
ar = width/height |
|
|
|
|
479
|
|
|
if ar > 1: |
480
|
|
|
counter = 1 |
|
|
|
|
481
|
|
|
else: |
482
|
|
|
ar = 1/ar |
|
|
|
|
483
|
|
|
elong = 1 - (1/ar) |
484
|
|
|
|
485
|
|
|
return ar, elong, center_point |
486
|
|
|
|
487
|
|
|
|
488
|
|
View Code Duplication |
def boundedness(track, framerate=1): |
|
|
|
|
489
|
|
|
""" |
490
|
|
|
Calculates the boundedness, fractal dimension, and trappedness of the input track. |
491
|
|
|
|
492
|
|
|
Parameters |
493
|
|
|
---------- |
494
|
|
|
track : pandas DataFrame |
495
|
|
|
At a minimum, must contain a Frames and a MSDs column. The function |
496
|
|
|
msd_calc can be used to generate the correctly formatted pd dataframe. |
497
|
|
|
framerate : framrate of the video being analyzed. Actually cancels out. So |
498
|
|
|
why did I include this. Default is 1. |
499
|
|
|
|
500
|
|
|
Returns |
501
|
|
|
------- |
502
|
|
|
B : numpy.float64 |
503
|
|
|
Boundedness of the input track. Quantifies how much a particle with |
504
|
|
|
diffusion coefficient D is restricted by a circular confinement of radius |
505
|
|
|
r when it diffuses for a time duration N*delt. Defined as B = D*N*delt/r**2. |
506
|
|
|
For this case, D is the short time diffusion coefficient (after 2 frames), |
507
|
|
|
and r is half the maximum distance between any two positions. |
508
|
|
|
Df : numpy.float64 |
509
|
|
|
The fractal path dimension defined as Df = log(N)/log(N*d*l**-1) where L |
510
|
|
|
is the total length (sum over all steplengths), N is the number of steps, |
511
|
|
|
and d is the largest distance between any two positions. |
512
|
|
|
pf : numpy.float64 |
513
|
|
|
The probability that a particle with diffusion coefficient D and traced |
514
|
|
|
for a period of time N*delt is trapped in region r0. Given by |
515
|
|
|
pt = 1 - exp(0.2048 - 0.25117*(D*N*delt/r0**2)) |
516
|
|
|
For this case, D is the short time diffusion coefficient, and r0 is half |
517
|
|
|
the maximum distance between any two positions. |
518
|
|
|
|
519
|
|
|
Examples |
520
|
|
|
-------- |
521
|
|
|
>>> frames = 10 |
522
|
|
|
>>> d = {'Frame': np.linspace(1, frames, frames), |
523
|
|
|
'X': np.linspace(1, frames, frames)+5, |
524
|
|
|
'Y': np.linspace(1, frames, frames)+3} |
525
|
|
|
>>> df = pd.DataFrame(data=d) |
526
|
|
|
>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
527
|
|
|
>>> boundedness(df) |
528
|
|
|
(1.0, 1.0000000000000002, 0.045311337970735499) |
529
|
|
|
|
530
|
|
|
>>> frames = 10 |
531
|
|
|
>>> d = {'Frame': np.linspace(1, frames, frames), |
532
|
|
|
'X': np.sin(np.linspace(1, frames, frames)+3), |
533
|
|
|
'Y': np.cos(np.linspace(1, frames, frames)+3)} |
534
|
|
|
>>> df = pd.DataFrame(data=d) |
535
|
|
|
>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
536
|
|
|
>>> boundedness(df) |
537
|
|
|
(0.96037058689895005, 2.9989749477908401, 0.03576118370932313) |
538
|
|
|
""" |
539
|
|
|
|
540
|
|
|
assert type(track) == pd.core.frame.DataFrame, "track must be a pandas dataframe." |
|
|
|
|
541
|
|
|
assert type(track['MSDs']) == pd.core.series.Series, "track must contain MSDs column." |
|
|
|
|
542
|
|
|
assert type(track['Frame']) == pd.core.series.Series, "track must contain Frame column." |
|
|
|
|
543
|
|
|
assert track.shape[0] > 0, "track must not be empty." |
544
|
|
|
|
545
|
|
|
df = track |
|
|
|
|
546
|
|
|
|
547
|
|
|
if df.shape[0] > 2: |
548
|
|
|
length = df.shape[0] |
549
|
|
|
distance = np.zeros((length, length)) |
550
|
|
|
|
551
|
|
|
for frame in range(0, length-1): |
552
|
|
|
distance[frame, 0:length-frame-1] = (np.sqrt(msd.nth_diff(df['X'], frame+1)**2 + msd.nth_diff(df['Y'], frame+1)**2).values) |
|
|
|
|
553
|
|
|
|
554
|
|
|
L = np.sum((np.sqrt(msd.nth_diff(df['X'], 1)**2 + msd.nth_diff(df['Y'], 1)**2).values)) |
|
|
|
|
555
|
|
|
r = np.max(distance)/2 |
|
|
|
|
556
|
|
|
N = df['Frame'][df['Frame'].shape[0]-1] |
|
|
|
|
557
|
|
|
f = N*framerate |
|
|
|
|
558
|
|
|
D = df['MSDs'][2]/(4*f) |
|
|
|
|
559
|
|
|
|
560
|
|
|
B = D*f/(r**2) |
|
|
|
|
561
|
|
|
Df = np.log(N)/np.log(N*2*r/L) |
|
|
|
|
562
|
|
|
pf = 1 - np.exp(0.2048 - 0.25117*(D*f/(r**2))) |
|
|
|
|
563
|
|
|
else: |
564
|
|
|
B = np.nan |
|
|
|
|
565
|
|
|
Df = np.nan |
|
|
|
|
566
|
|
|
pf = np.nan |
|
|
|
|
567
|
|
|
|
568
|
|
|
return B, Df, pf |
569
|
|
|
|
570
|
|
|
|
571
|
|
View Code Duplication |
def efficiency(track): |
|
|
|
|
572
|
|
|
""" |
573
|
|
|
Calculates the efficiency and straitness of the input track |
574
|
|
|
|
575
|
|
|
Parameters |
576
|
|
|
---------- |
577
|
|
|
track : pandas DataFrame |
578
|
|
|
At a minimum, must contain a Frames and a MSDs column. The function |
579
|
|
|
msd_calc can be used to generate the correctly formatted pd dataframe. |
580
|
|
|
|
581
|
|
|
Returns |
582
|
|
|
------- |
583
|
|
|
eff : numpy.float64 |
584
|
|
|
Efficiency of the input track. Relates the sum of squared step |
585
|
|
|
lengths. Based on Helmuth et al. (2007) and defined as: |
586
|
|
|
E = |x(N-1)-x(0)|**2/SUM(|x(i) - x(i-1)|**2 |
587
|
|
|
strait : numpy.float64 |
588
|
|
|
Relates the net displacement L to teh sum of step lengths and is |
589
|
|
|
defined as: |
590
|
|
|
S = |x(N-1)-x(0)|/SUM(|x(i) - x(i-1)| |
591
|
|
|
|
592
|
|
|
Examples |
593
|
|
|
-------- |
594
|
|
|
>>> frames = 10 |
595
|
|
|
>>> d = {'Frame': np.linspace(1, frames, frames), |
596
|
|
|
'X': np.linspace(1, frames, frames)+5, |
597
|
|
|
'Y': np.linspace(1, frames, frames)+3} |
598
|
|
|
>>> df = pd.DataFrame(data=d) |
599
|
|
|
>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
600
|
|
|
>>> ft.efficiency(df) |
601
|
|
|
(9.0, 0.9999999999999999) |
602
|
|
|
|
603
|
|
|
>>> frames = 10 |
604
|
|
|
>>> d = {'Frame': np.linspace(1, frames, frames), |
605
|
|
|
'X': np.sin(np.linspace(1, frames, frames))+3, |
606
|
|
|
'Y': np.cos(np.linspace(1, frames, frames))+3} |
607
|
|
|
>>> df = pd.DataFrame(data=d) |
608
|
|
|
>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
609
|
|
|
>>> ft.efficiency(df) |
610
|
|
|
(0.46192924086141945, 0.22655125514290225) |
611
|
|
|
""" |
612
|
|
|
|
613
|
|
|
df = track |
|
|
|
|
614
|
|
|
length = df.shape[0] |
615
|
|
|
num = (msd.nth_diff(df['X'], length-1)**2 + msd.nth_diff(df['Y'], length-1)**2)[0] |
616
|
|
|
num2 = np.sqrt(num) |
617
|
|
|
|
618
|
|
|
den = np.sum(msd.nth_diff(df['X'], 1)**2 + msd.nth_diff(df['Y'], 1)**2) |
619
|
|
|
den2 = np.sum(np.sqrt(msd.nth_diff(df['X'], 1)**2 + msd.nth_diff(df['Y'], 1)**2)) |
620
|
|
|
|
621
|
|
|
eff = num/den |
622
|
|
|
strait = num2/den2 |
623
|
|
|
return eff, strait |
624
|
|
|
|
625
|
|
|
|
626
|
|
View Code Duplication |
def msd_ratio(track, n1=3, n2=100): |
|
|
|
|
627
|
|
|
""" |
628
|
|
|
Calculates the MSD ratio of the input track at the specified frames. |
629
|
|
|
|
630
|
|
|
Parameters |
631
|
|
|
---------- |
632
|
|
|
track : pandas DataFrame |
633
|
|
|
At a minimum, must contain a Frames and a MSDs column. The function |
634
|
|
|
msd_calc can be used to generate the correctly formatted pd dataframe. |
635
|
|
|
n1 : int |
636
|
|
|
First frame at which to calculate the MSD ratio. |
637
|
|
|
n2 : int |
638
|
|
|
Last frame at which to calculate the MSD ratio. |
639
|
|
|
|
640
|
|
|
Returns |
641
|
|
|
------- |
642
|
|
|
ratio: numpy.float64 |
643
|
|
|
MSD ratio as defined by |
644
|
|
|
[MSD(n1)/MSD(n2)] - [n1/n2] |
645
|
|
|
where n1 < n2. For Brownian motion, it is 0; for restricted motion it |
646
|
|
|
is < 0. For directed motion it is > 0. |
647
|
|
|
|
648
|
|
|
Examples |
649
|
|
|
-------- |
650
|
|
|
>>> frames = 10 |
651
|
|
|
>>> d = {'Frame': np.linspace(1, frames, frames), |
652
|
|
|
'X': np.linspace(1, frames, frames)+5, |
653
|
|
|
'Y': np.linspace(1, frames, frames)+3} |
654
|
|
|
>>> df = pd.DataFrame(data=d) |
655
|
|
|
>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
656
|
|
|
>>> ft.msd_ratio(df, 1, 9) |
657
|
|
|
-0.18765432098765433 |
658
|
|
|
|
659
|
|
|
>>> frames = 10 |
660
|
|
|
>>> d = {'Frame': np.linspace(1, frames, frames), |
661
|
|
|
'X': np.sin(np.linspace(1, frames, frames))+3, |
662
|
|
|
'Y': np.cos(np.linspace(1, frames, frames))+3} |
663
|
|
|
>>> df = pd.DataFrame(data=d) |
664
|
|
|
>>> df['MSDs'], df['Gauss'] = msd_calc(df) |
665
|
|
|
>>> ft.msd_ratio(df, 1, 9) |
666
|
|
|
0.04053708075268797 |
667
|
|
|
""" |
668
|
|
|
|
669
|
|
|
df = track |
|
|
|
|
670
|
|
|
assert n1 < n2, "n1 must be less than n2" |
671
|
|
|
ratio = (df['MSDs'][n1]/df['MSDs'][n2]) - (df['Frame'][n1]/df['Frame'][n2]) |
672
|
|
|
return ratio |
673
|
|
|
|
674
|
|
|
|
675
|
|
View Code Duplication |
def calculate_features(df, framerate=1): |
|
|
|
|
676
|
|
|
""" |
677
|
|
|
Calculates multiple features from input MSD dataset and stores in pandas dataframe. |
678
|
|
|
|
679
|
|
|
Parameters |
680
|
|
|
---------- |
681
|
|
|
df : pandas dataframe |
682
|
|
|
Output from msd.all_msds2. Must have at a minimum the following columns: |
683
|
|
|
Track_ID, Frame, X, Y, and MSDs. |
684
|
|
|
framerate : int or float64 |
685
|
|
|
Framerate of the input videos from which trajectories were calculated. Required |
686
|
|
|
for accurate calculation of some features. Default is 1. Possibly not required. |
687
|
|
|
Ignore if performing all calcuations without units. |
688
|
|
|
|
689
|
|
|
Returns |
690
|
|
|
------- |
691
|
|
|
di: pandas dataframe |
692
|
|
|
Contains a row for each trajectory in df. Holds the following features of each |
693
|
|
|
trajetory: Track_ID, alpha, D_fit, kurtosis, asymmetry1, asymmetry2, asymmetry3, |
694
|
|
|
aspect ratio (AR), elongation, boundedness, fractal dimension (fractal_dim), |
695
|
|
|
trappedness, efficiency, straightness, MSD ratio, frames, X, and Y. |
696
|
|
|
|
697
|
|
|
Examples |
698
|
|
|
-------- |
699
|
|
|
See example outputs from individual feature functions. |
700
|
|
|
""" |
701
|
|
|
# Skeleton of Trajectory features metadata table. |
702
|
|
|
# Builds entry for each unique Track ID. |
703
|
|
|
holder = df.Track_ID.unique().astype(float) |
704
|
|
|
die = {'Track_ID': holder, |
705
|
|
|
'alpha': holder, |
706
|
|
|
'D_fit': holder, |
707
|
|
|
'kurtosis': holder, |
708
|
|
|
'asymmetry1': holder, |
709
|
|
|
'asymmetry2': holder, |
710
|
|
|
'asymmetry3': holder, |
711
|
|
|
'AR': holder, |
712
|
|
|
'elongation': holder, |
713
|
|
|
'boundedness': holder, |
714
|
|
|
'fractal_dim': holder, |
715
|
|
|
'trappedness': holder, |
716
|
|
|
'efficiency': holder, |
717
|
|
|
'straightness': holder, |
718
|
|
|
'MSD_ratio': holder, |
719
|
|
|
'frames': holder, |
720
|
|
|
'X': holder, |
721
|
|
|
'Y': holder} |
722
|
|
|
|
723
|
|
|
di = pd.DataFrame(data=die) |
|
|
|
|
724
|
|
|
|
725
|
|
|
trackids = df.Track_ID.unique() |
726
|
|
|
partcount = trackids.shape[0] |
727
|
|
|
|
728
|
|
|
for particle in range(0, partcount): |
729
|
|
|
single_track_masked = df.loc[df['Track_ID'] == trackids[particle]].sort_values(['Track_ID', 'Frame'], |
|
|
|
|
730
|
|
|
ascending=[1, 1]).reset_index(drop=True) |
|
|
|
|
731
|
|
|
single_track = unmask_track(single_track_masked) |
732
|
|
|
di['alpha'][particle], di['D_fit'][particle] = alpha_calc(single_track) |
733
|
|
|
di['kurtosis'][particle] = kurtosis(single_track) |
734
|
|
|
l1, l2, di['asymmetry1'][particle], di['asymmetry2'][particle], di['asymmetry3'][particle] = asymmetry(single_track) |
|
|
|
|
735
|
|
|
di['AR'][particle], di['elongation'][particle], (di['X'][particle], di['Y'][particle]) = aspectratio(single_track) |
|
|
|
|
736
|
|
|
di['boundedness'][particle], di['fractal_dim'][particle], di['trappedness'][particle] = boundedness(single_track, framerate) |
|
|
|
|
737
|
|
|
di['efficiency'][particle], di['straightness'][particle] = efficiency(single_track) |
738
|
|
|
di['frames'][particle] = single_track.shape[0] |
739
|
|
|
if single_track['Frame'][single_track.shape[0]-2] > 2: |
740
|
|
|
di['MSD_ratio'][particle] = msd_ratio(single_track, 2, single_track['Frame'][single_track.shape[0]-2]) |
|
|
|
|
741
|
|
|
else: |
742
|
|
|
di['MSD_ratio'][particle] = 0 |
743
|
|
|
|
744
|
|
|
return di |
745
|
|
|
|
The coding style of this project requires that you add a docstring to this code element. Below, you find an example for methods:
If you would like to know more about docstrings, we recommend to read PEP-257: Docstring Conventions.