In [1]:

    

import numpy as np
import pandas as pd


    

In [2]:

    

import pyaf.TS.Signal_Transformation as transf


    

In [3]:

    

%matplotlib inline


    

In [4]:

    

series = pd.Series(range(1, 12))


    

In [5]:

    

def tr1(x):
    if(x >= 0):
        return np.log(1 + x);
    return -np.log(1 - x);


    

In [6]:

    

df = pd.DataFrame()
N = 1000
df['t'] = range(N)
df['gauss'] = np.random.randn(N)
df['sig'] = np.exp(np.random.randn(N))
df['tr_sig'] = df['sig'].apply(tr1);


    

In [7]:

    

df.plot('t', ['sig'], figsize=(32,8))
df.plot('t', ['tr_sig'], figsize=(32,8))


    

    
Out[7]:





<matplotlib.axes._subplots.AxesSubplot at 0x7f8333130908>






    













    

In [8]:

    

df.describe()


    

    
Out[8]:






  

    

      

      
t
      
gauss
      
sig
      
tr_sig
    
  
  

    

      
count
      
1000.000000
      
1000.000000
      
1000.000000
      
1000.000000
    
    

      
mean
      
499.500000
      
0.016132
      
1.702997
      
0.820173
    
    

      
std
      
288.819436
      
0.982243
      
2.217595
      
0.530541
    
    

      
min
      
0.000000
      
-3.586764
      
0.023493
      
0.023222
    
    

      
25%
      
249.750000
      
-0.633596
      
0.528404
      
0.424224
    
    

      
50%
      
499.500000
      
0.043997
      
1.037966
      
0.711952
    
    

      
75%
      
749.250000
      
0.632666
      
2.066961
      
1.120687
    
    

      
max
      
999.000000
      
3.126885
      
22.786594
      
3.169122
    
  

In [9]:

    

transf.cSignalTransform_Differencing().apply(series)


    

    
Out[9]:





0     NaN
1     1.0
2     1.0
3     1.0
4     1.0
5     1.0
6     1.0
7     1.0
8     1.0
9     1.0
10    1.0
dtype: float64

In [10]:

    

tr1 = transf.cSignalTransform_RelativeDifferencing();
tr1.fit(series)
s1 = tr1.apply(series)
s2 = tr1.invert(s1)
print(s1.head())
print(s2.head())


    

    




0    0.000000
1    0.100000
2    0.090909
3    0.083333
4    0.076923
dtype: float64
0    1.0
1    2.0
2    3.0
3    4.0
4    5.0
dtype: float64

In [11]:

    

s2 - series


    

    
Out[11]:





0     0.0
1     0.0
2     0.0
3     0.0
4     0.0
5     0.0
6     0.0
7     0.0
8     0.0
9     0.0
10    0.0
dtype: float64

In [12]:

    

def invert2(df):
        r = df;
        df_orig = 0.0 * df;
        df_orig.iloc[0] = (tr1.mFirstValue - tr1.mMinValue) / tr1.mDelta

        for i in range(1,df.shape[0]):
            previous_value = df_orig.iloc[i - 1] 
            df_orig.iloc[i] = previous_value + r.iloc[i]  * (previous_value + 1)

        df_orig = df_orig * tr1.mDelta + tr1.mMinValue;
        
        return df_orig;


    

In [13]:

    

s3 = invert2(s1)


    

In [14]:

    

s3


    

    
Out[14]:





0     0.0
1     0.9
2     1.8
3     2.7
4     3.6
5     4.5
6     5.4
7     6.3
8     7.2
9     8.1
10    9.0
dtype: float64

In [15]:

    

def invert3(df):
    r = df;
    df_orig = 0.0 * df;
    df_orig.iloc[0] = (tr1.mFirstValue - tr1.mMinValue) / tr1.mDelta

    for i in range(1,df.shape[0]):
        previous_value = df_orig.iloc[i - 1] 
        df_orig.iloc[i] = previous_value + r.iloc[i]  * (previous_value + 1)

    df_orig = df_orig * tr1.mDelta + tr1.mMinValue;
        
    return df_orig;


    

In [16]:

    

invert3(s1)


    

    
Out[16]:





0     0.0
1     0.9
2     1.8
3     2.7
4     3.6
5     4.5
6     5.4
7     6.3
8     7.2
9     8.1
10    9.0
dtype: float64

In [ ]: