#This source code is public domain
import numpy, pylab
from matplotlib.font_manager import FontProperties
import matplotlib.pyplot as plt

x=[1,2,3,4,5,6,7]
y=[2.0,2.5,2.5,3.4,3.7,6.6,3]

for N in range(1,8):
    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)
    xr=numpy.asarray(x)
    yr=numpy.sum([c[i]*xr**i for i in range(len(c))],axis=0)
    residuen=[]
    for i in range(len(x)): residuen+=[[xr[i],xr[i]],[y[i],yr[i]],'g-']
    xneu=numpy.linspace(0, 8, num=100)
    yneu=numpy.sum([c[i]*xneu**i for i in range(len(c))],axis=0)
    plt.clf()
    fig = plt.figure(figsize=(4.5, 3.5))
    fig.subplotpars.bottom=0.13
    y0=plt.plot(*residuen[:-3])
    plt.setp(y0, color='#80d080', linewidth=1.5)
    y0=plt.plot(*residuen[-3:])
    plt.setp(y0, color='#80d080', linewidth=1.5)
    y2=plt.plot(xneu,yneu,'r-')
    y1=plt.plot(x,y,'o')
    plt.xlabel('x')
    plt.ylabel('y')
    font = FontProperties()
    font.set_size('medium')
    leg = plt.legend([y1,y2,y0],['Messpunkte','Modellfunktion','Residuen'],frameon=True,loc='lower right',labelspacing=0.3,prop=font)
    plt.grid(True)
    plt.axis([0, 8, 0, 8])
    plt.text(1,7, "Polynomgrad "+str(N-1),bbox=dict(boxstyle="square,pad=0.5",color='white',ec='black',fill=True))
    #plt.show()
    plt.savefig('MDKQ_anim%i.png'%N)