#Open the file: in green put the name of the file
df1=pd.read_csv('/Users/JonathanPacheco/Desktop/Spots in tracks statistics.csv')


df2 = df1.set_index(['TRACK_ID'])

q = df1.iloc[1,3]-df1.iloc[0,3]

#selection of tracks by duration


ef = pd.read_csv('/Users/JonathanPacheco/Desktop/Sort.csv')

ef1 = ef.set_index(['TRACK_DURATION'])

sets = ef1.loc[4.2:, 'TRACK_ID']   # Set trajectories to analyze from time X to the end <<<<<<<<<<<<<<<<<<<<<

M = sets.values.tolist()


for j in M:

    dfk = df2.loc[j]
    dfT = dfk.iloc[:5] #clip trajectories at<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<



#Parameter input
    N = int(len(dfT))
    max_time = np.float(N*(q))
    frames = np.float(max_time/N)
    t_step = frames

    data = pd.DataFrame({'N':[N],'max_time':[max_time],'frames':[frames]})

    #print(data)

    t=np.linspace(q, max_time, N)

    #function to measure MSD (all displacement)
    def alldisplacement(dfT, t_step, coords=['POSITION_X', 'POSITION_Y']):


        tau = t.copy()
        shifts = np.divide(tau,t_step).astype(float)
        msds_sum = np.zeros(shifts.size)
        delta_inv = np.arange(N)
        delta = delta_inv[N-1::-1]




        for i, shift in enumerate(np.round(shifts,0)):
            diffs = dfT[coords] - dfT[coords].shift(-shift)
            sqdist = np.square(diffs).sum(axis=1)
            msds_sum[i] = sqdist.sum()
            msd = np.divide(msds_sum,delta)


        msds = pd.DataFrame({'msd':msd})
        return msds

    msd = alldisplacement(dfT, t_step, coords=['POSITION_X', 'POSITION_Y'])

    print(msd)


#Saving files seccion

    b = msd.to_csv('/Users/JonathanPacheco/Desktop/MSD.csv', sep=',',mode='a')

    b = msd
    a = pd.read_csv('/Users/JonathanPacheco/Desktop/MSD.csv')
    c = pd.concat ([a,b],axis=1, ignore_index=True)
    c.to_csv('/Users/JonathanPacheco/Desktop/MSD.csv', sep=',', index=False)

TRACK_ID   POSITION_X  POSITION_Y    POSITION_T
0            3       1.649       0.368       0.042
1            3       1.576       0.371       0.084
2            3       1.651       0.313       0.126
3            3       1.723       0.340       0.168
4            3       1.381       0.355       0.210
5           33       1.324       0.469       0.252
6           33       1.202       0.540       0.294
7           33       1.323       0.427       0.336
8           33       1.197       0.599       0.420
9           33       1.327       0.519       0.462
10          33       1.450       0.595       0.504
11          33       1.684       0.577       0.546
12          33       1.792       0.678       0.588
13          53       1.852       0.906       0.630
14          53       1.762       0.827       0.672
15          53       1.735       0.961       0.714
16          53       1.657       1.083       0.756
17          53       1.897       1.074       0.798
18          93       1.961       1.126       0.840
19          93       2.067       1.167       0.882
20          93       2.046       1.267       0.966
21          93       1.922       1.228       1.008
22          93       1.992       1.230       1.050
23          93       1.945       1.198       1.092
24          93       2.002       1.224       1.134
25          93       1.866       1.213       1.176
26          93       1.851       1.482       1.218

Unnamed:0 TRACK_ID  TRACK_DURATION
0             3      7652
1            33      6676
2            53      5828
3            93     20008