import numpy as np
import matplotlib.pyplot as plt
g = [lambda t: t**3,
     lambda t: t**2,
     lambda t: t**1,
     lambda t: 1.0]
def approximate(x,y,basis):
    N = len(y)
    m = len(basis)
    #A*x = b
    A = np.matrix(np.zeros((m,m)))
    b = np.matrix(np.zeros((m,1)))
    for j in xrange(0,m):
        for i,xi in enumerate(x):
            b[j] += basis[j](xi)*y[i]
            for k in xrange(0,m):
                A[j,k] += basis[j](xi)*basis[k](xi)
    try:
        return np.linalg.inv(A)*b
    except Exception,ex:
        return np.linalg.pinv(A)*b
        
x = [1,2,3,4,7]
y = [5,3,2,5,9]
p = approximate(x,y,g)
p = np.array(p.flatten())[0]
def ap_s(basis,param,x):
    return sum(b(x)*p for (b,p) in zip(basis,param))
    
a = plt.subplot(111)

a.plot(x,y)
xx = np.linspace(min(x),max(x),100)
a.plot(xx,ap_s(g,p,xx))
plt.show()

except Exception as ex