# This source code is public domain

import numpy, pylab
import matplotlib.pyplot as plt

x = [208, 152, 113, 227, 137, 238, 178, 104, 191, 130]
y = [21.6, 15.5, 10.4, 31.0, 13.0, 32.4, 19.0, 10.4, 19.0, 11.8]
N = 2
A = numpy.zeros((N,N))
for i in range(N):
    for j in range(N):
        A[i,j]=sum(xi**(i+j) for xi in x)
b = numpy.zeros((N))
for i in range(N):
    b[i]=sum(xi**(i)*yi for xi,yi in zip(x,y))
c = numpy.linalg.solve(A, b)
#print numpy.std(numpy.asarray(y)-numpy.sum([c[i]*numpy.asarray(x)**i for i in range(len(c))],axis=0))
xneu = numpy.linspace(100, 250, num=2)
yneu = numpy.sum([c[i]*xneu**i for i in range(len(c))],axis=0)

fig = plt.figure(figsize=(4.2, 3.2))
y1 = plt.plot(x,y,'o')
y2 = plt.plot(xneu,yneu,'r-')
plt.xlabel(u'x (L\u00e4nge in m)')
plt.ylabel(u'y (Breite in m)')
leg = plt.legend(('Messpunkte','Modellfunktion'),frameon=True,loc='lower right')
plt.grid(True, alpha=0.7)
plt.tight_layout()
#plt.savefig('MDKQ2.svg')