from pylab import linspace,pi,exp,real,imag,axis

import matplotlib.path as mpath
import matplotlib.patches as mpatches
import matplotlib.pyplot as plt

w=exp(1j*linspace(0,2*pi,200))

Path=mpath.Path
fig = plt.figure()

for name,z in zip(['Euler','trapezoidal',  'AB2'],\
                  [ w-1,       [5j,-5+5j,-5-5j,-5j,5j],2*(w**2-w)/(3*w-1)]):
    fig.clf()
    ax=fig.add_subplot(111)

    verts=map(lambda z:(real(z),imag(z)), z)
    codes=[Path.MOVETO]+[Path.LINETO]*(len(verts)-2)+[Path.CLOSEPOLY]

    path=mpath.Path(verts,codes)
    patch=mpatches.PathPatch(path,facecolor=[1, 0.5, 0.8],edgecolor='black',alpha=1)
    ax.add_patch(patch)
    ax.plot([-3,2],[0,0],'--',color='black')
    ax.plot([0,0],[-2,2],'--',color='black')
    ax.set_xlim(-3,2)
    ax.set_ylim(-2,2)

    fig.savefig("Stability region for "+name+" method.svg")