#SVD version to solve general matrix problem Ax=b
#with singular values smaller then 1e-10 considered zero.

import numpy as np
import numpy.linalg as la





A = np.loadtxt("matrix")
b = np.loadtxt("vector")
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)