In [19]:

    

import numpy as np
import scipy.linalg as lg


    

In [20]:

    

b=np.ones((3,3))
np.fill_diagonal(b,3)


    

In [21]:

    

a=np.arange(9).reshape(3,3)


    

In [22]:

    

a=(a+a.T)*0.5


    

In [24]:

    

a,b,lg.eigh(a,b)


    

    
Out[24]:





(array([[ 0.,  2.,  4.],
       [ 2.,  4.,  6.],
       [ 4.,  6.,  8.]]),
 array([[ 3.,  1.,  1.],
       [ 1.,  3.,  1.],
       [ 1.,  1.,  3.]]),
 (array([ -7.59591794e-01,   1.00128781e-15,   3.15959179e+00]),
  array([[ 0.56260959,  0.28867513, -0.01170986],
       [ 0.11367022, -0.57735027, -0.23183129],
       [-0.33526915,  0.28867513, -0.45195273]])))

In [25]:

    

c,d=lg.eigh(a,b)


    

In [26]:

    

d


    

    
Out[26]:





array([[ 0.56260959,  0.28867513, -0.01170986],
       [ 0.11367022, -0.57735027, -0.23183129],
       [-0.33526915,  0.28867513, -0.45195273]])

In [35]:

    

d[:,0]/lg.norm(d[:,0])


    

    
Out[35]:





array([ 0.84638277,  0.17100405, -0.50437468])

In [36]:

    

d[:,1]/lg.norm(d[:,1])


    

    
Out[36]:





array([ 0.40824829, -0.81649658,  0.40824829])

In [37]:

    

d[:,2]/lg.norm(d[:,2])


    

    
Out[37]:





array([-0.02304732, -0.45628997, -0.88953262])

In [ ]: