#ipython -pylab

import numpy as np
import pylab

n = 10;
t = np.linspace(0,1,n)
#y = np.array([1.1, 2.1, 3.2, 4.1, 6.4])
y = np.sin(np.pi*t) + 1.0*(np.random.random(n)-0.5)
pylab.plot(t,y,'x')

n = len(t)
t1 = sum(t)
t2 = sum(t**2)
t3 = sum(t**3)
t4 = sum(t**4)
A = np.array([[n,t1,t2],[t1,t2,t3],[t2,t3,t4]]) #slide 35, Ch 5.

y0 = sum(y)
y1 = sum(y*t)
y2 = sum(y*t**2)
b = np.array([y0,y1,y2])

p = np.linalg.solve(A, b)
x = np.linspace(0,1,101);
f = p[2]*x**2 + p[1]*x + p[0]
pylab.plot(x,f)

pylab.show()