import numpy as np
import scipy as sp
from sklearn import decomposition as decomp

#functions to play with

xs=np.linspace(0,1,10e3)

def sinewave(xs,**kwargs):
    nw=kwargs.setdefault('nw',100) #num waves
    return np.sin(xs*nw*2*np.pi)

def const(xs,**kwargs):
    c=kwargs.setdefault('c',0)
    cs=np.empty(len(xs));cs.fill(c)
    return cs

#put an even number of waves in a matrix

nts=np.empty((100,len(xs)))
for i in xrange(len(nts)):
    nts[i]=sinewave(xs,nw=(i+1)*2)
nts[-1]=const(xs,c=123) #throw in a const

from matplotlib.pylab import plot
%matplotlib inline
for i in xrange(3): plot(nts[i])

nc=int(len(nts)*.5) #arbitrary choice of num of components 
#pd=decomp.PCA(n_components=nc)
pd=decomp.FastICA(max_iter=int(3e3),n_components=nc)

pdc=pd.fit(nts)

#try to reconstruct...
x=np.array([+10*sinewave(xs,nw=4) #an even num of waves
            ,+7*sinewave(xs,nw=5) #an odd num
            ,const(xs,c=3)]) #a constant

#recontruct signal
recon=pd.inverse_transform(pd.transform(x))

plot(x[0]);plot(recon[0]);#even number of waves
#is sort of reconstruted

plot(x[1]);plot(recon[1]);#odd number of waves is not

plot(x[2]);plot(recon[2]);#constant is sort of 
#reconstructed