In [1]:

    

%pylab inline


    

    




Populating the interactive namespace from numpy and matplotlib

In [1]:

    

from numpy import random


    

In [3]:

    

random.poisson?


    

In [5]:

    

s = random.poisson(1,1000)


    

In [6]:

    

s.view()


    

    
Out[6]:





array([0, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1,
       0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 0, 4, 0, 0, 0, 2, 1, 2, 3, 0, 1, 3,
       1, 2, 3, 0, 1, 1, 1, 1, 1, 0, 1, 3, 2, 1, 0, 2, 0, 1, 1, 1, 2, 1, 3,
       0, 1, 1, 0, 0, 1, 1, 0, 3, 1, 1, 0, 2, 1, 2, 1, 2, 0, 1, 1, 0, 0, 0,
       1, 1, 0, 2, 2, 0, 2, 0, 2, 1, 1, 0, 0, 0, 2, 3, 1, 2, 0, 2, 1, 0, 2,
       1, 1, 2, 2, 2, 1, 0, 2, 1, 1, 2, 0, 0, 1, 1, 0, 2, 0, 1, 0, 0, 1, 0,
       1, 0, 2, 0, 1, 2, 0, 1, 1, 1, 1, 1, 1, 2, 0, 2, 1, 0, 1, 1, 3, 3, 3,
       2, 1, 0, 0, 3, 0, 0, 1, 2, 0, 0, 0, 1, 0, 1, 0, 0, 2, 1, 1, 0, 0, 1,
       0, 3, 1, 3, 2, 2, 2, 0, 0, 4, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 2, 4, 0,
       0, 1, 1, 2, 2, 1, 0, 1, 0, 0, 0, 1, 3, 0, 0, 0, 0, 1, 1, 0, 2, 1, 1,
       0, 1, 0, 0, 1, 0, 0, 3, 2, 2, 0, 0, 2, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1,
       3, 2, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 1, 2,
       1, 0, 2, 0, 2, 0, 0, 1, 1, 1, 1, 0, 0, 2, 2, 1, 0, 1, 3, 1, 0, 3, 2,
       1, 1, 0, 0, 1, 2, 3, 0, 0, 0, 0, 4, 2, 1, 3, 1, 1, 5, 0, 0, 1, 0, 0,
       1, 0, 2, 2, 1, 0, 1, 2, 2, 0, 0, 1, 1, 2, 2, 1, 0, 3, 0, 0, 0, 1, 1,
       1, 1, 1, 1, 2, 2, 1, 1, 1, 0, 2, 4, 1, 1, 0, 1, 2, 0, 0, 2, 1, 0, 0,
       1, 0, 1, 1, 2, 3, 2, 0, 2, 1, 1, 1, 2, 1, 2, 2, 3, 2, 4, 0, 0, 2, 1,
       1, 1, 1, 0, 0, 2, 1, 0, 0, 0, 2, 2, 0, 1, 0, 1, 0, 2, 0, 3, 4, 2, 1,
       1, 0, 0, 2, 4, 3, 1, 0, 0, 1, 1, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0,
       0, 0, 0, 0, 1, 1, 2, 0, 4, 0, 3, 2, 1, 1, 0, 2, 2, 0, 1, 0, 0, 1, 0,
       1, 2, 1, 1, 1, 2, 3, 2, 1, 2, 0, 3, 2, 1, 2, 3, 1, 2, 0, 0, 2, 0, 2,
       1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 0, 2, 2, 2, 1, 1, 2, 2, 0, 1, 1, 1, 0,
       1, 0, 2, 1, 1, 0, 0, 0, 0, 2, 2, 1, 2, 1, 2, 1, 4, 1, 0, 0, 1, 0, 1,
       1, 0, 0, 2, 1, 1, 0, 0, 2, 2, 0, 0, 0, 1, 2, 1, 1, 1, 0, 2, 3, 1, 0,
       0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 2, 1, 2, 3, 0, 0, 1, 0, 1, 1, 0, 0, 1,
       1, 2, 1, 0, 0, 1, 3, 1, 1, 2, 4, 1, 1, 0, 0, 1, 3, 1, 1, 3, 1, 1, 1,
       3, 1, 3, 1, 0, 1, 1, 2, 1, 0, 2, 1, 0, 3, 0, 1, 1, 0, 0, 2, 1, 0, 1,
       1, 0, 1, 2, 1, 1, 1, 1, 2, 3, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0,
       1, 1, 0, 2, 2, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 2, 1, 3, 3, 0, 0, 0,
       1, 1, 0, 0, 1, 1, 0, 2, 1, 3, 3, 1, 2, 1, 1, 1, 0, 0, 0, 0, 2, 0, 4,
       0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 1, 0, 0, 2, 2, 2, 1, 0, 2, 0, 0, 1,
       0, 0, 1, 2, 1, 2, 2, 0, 0, 3, 2, 0, 2, 0, 0, 0, 2, 2, 1, 1, 0, 2, 1,
       1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 2, 1, 0, 2, 1, 1,
       1, 3, 1, 1, 5, 1, 2, 1, 1, 3, 1, 1, 2, 0, 1, 2, 1, 0, 0, 1, 0, 6, 1,
       0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 1, 2, 0, 1, 0, 0, 1, 0, 2, 1, 0, 1, 2,
       0, 3, 0, 3, 0, 4, 1, 2, 0, 2, 1, 2, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0,
       0, 0, 2, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 1, 3, 3, 3, 2, 1, 1, 2,
       0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 2, 1, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1,
       0, 0, 1, 0, 0, 3, 1, 1, 1, 1, 1, 4, 1, 0, 0, 1, 0, 3, 1, 1, 0, 2, 0,
       1, 3, 0, 1, 0, 2, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0,
       2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 1,
       1, 0, 2, 0, 3, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2,
       2, 0, 1, 5, 1, 0, 1, 1, 2, 0, 0, 1, 2, 0, 0, 0, 1, 1, 0, 2, 0, 0, 3,
       0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 2])

In [18]:

    

plot(s)


    

    
Out[18]:





[<matplotlib.lines.Line2D at 0x106ab7ad0>]






    

In [23]:

    

hist(s,50)
show()


    

In [24]:

    

s.mean()


    

    
Out[24]:





0.99199999999999999

In [25]:

    

s.std()


    

    
Out[25]:





0.99996799948797799

In [19]:

    

#Calculate Auto-correlation function based on fft
#only support 1D
#for cross correlation, in optimisation
#input data suggest to be numpy.ndarray(1d) or pandas.core.series.Series
def acf_fft(data):
    """ Series or 1darray ---> Series 
        Calculate the auto correlation function of input data
    """
    data_mean = data.mean()
    
    #Step 1: calculate fft for data
    fft_data = fft.fft(data)
    
    #Step 2: Calculate the pow spectrom,
    S_f = fft_data.__mul__(fft_data.conj())
                           
    #Step 3: calculate auto correlation function, result as g(\tau)
    acf = ifft(S_f)/fft_data[0]/data_mean - 1;
    
    #Clean up, return half of data
    acf = acf.real[0:int(len(acf)/2)]
    return acf


    

In [26]:

    

plot(acf_fft(s),'o')


    

    
Out[26]:





[<matplotlib.lines.Line2D at 0x106ca6190>]






    

In [7]:

    

import os


    

In [8]:

    

os?


    

In [ ]: