#using python to do least squares with svd

import numpy as np
import numpy.linalg as la


data = [[0,0],
        [1,2],
        [2,6],
        [3,12],
        [4,20],
        [5,30],
        [6,42],
        [7,56]
         ]


avals = [[1,i,i**2] for i,j in data]
bvals = [ j for i,j in data]

A = np.array(avals)
b = np.array(bvals)
b = b.reshape(len(b),1)


U,s,V = la.svd(A)

print A
print b
print
print
print U
print s
print V

print "Condition = ", s[0]/s[len(s)-1]

x=np.dot(np.transpose(U),b)
x=x[0:len(s)]
for i in range(len(s)):
   if s[i] >1e-10:
     x[i,0]=x[i,0]/s[i]
   else:
     print "+ any amount", V[i]
x=np.dot(np.transpose(V[0:len(s)]),x)
print x