In [1]:

    

import pandas as pd


    

In [2]:

    

from numpy.linalg import inv
import numpy as np
from scipy.linalg import eig

from sklearn.datasets import make_blobs
from sklearn.metrics import pairwise_distances

from diffmaps_util import *


    

In [3]:

    

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D


    

In [4]:

    

%matplotlib nbagg


    

In [6]:

    

df = pd.read_csv('annulus.csv')
df = df[['X', 'Y']]
df.head()


    

    
Out[6]:






  

    

      

      
X
      
Y
    
  
  

    

      
0
      
1.303494
      
-1.088609
    
    

      
1
      
-1.307464
      
1.993007
    
    

      
2
      
-0.032100
      
0.241350
    
    

      
3
      
-1.094944
      
-0.253496
    
    

      
4
      
0.430289
      
0.280286
    
  

In [7]:

    

X = df.as_matrix()


    

In [8]:

    

plt.scatter(X[:,0], X[:,1])
plt.show()


    

In [29]:

    

L = k(X, .1)
print 'L shape %s %s' % L.shape
D = diag(L)
print 'D shape %s %s' % D.shape

M = inv(D).dot(L)
print 'M shape %s %s' % M.shape

w, v = eig(M)
w = np.abs(w.real)
v = v.real
print 'eigenvalue shape %s' % w.shape
print 'eigenvector shape %s %s' % v.shape


    

    




L shape 1000 1000
D shape 1000 1000
M shape 1000 1000
eigenvalue shape 1000
eigenvector shape 1000 1000

In [30]:

    

w, v = sort_eigens(w, v)
print 'eigenvalue shape %s' % w.shape
print 'eigenvector shape %s %s' % v.shape


    

    




eigenvalue shape 1000
eigenvector shape 1000 1000

In [31]:

    

psi = v / v[:,0]
psi.shape


    

    
Out[31]:





(1000L, 1000L)

In [32]:

    

diffmap = (w.reshape(-1,1) * psi.T).T[:,1:]
diffmap.shape


    

    
Out[32]:





(1000L, 999L)

In [33]:

    

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
diffmap = (w.reshape(-1,1) * psi.T).T[:,1:]
diffmap.shape
ax.scatter(diffmap[:,0], diffmap[:,1], diffmap[:,2])
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
ax.set_title('T = 1')


    

    















    












    
Out[33]:





<matplotlib.text.Text at 0x1ed49be0>