#!/usr/bin/python
# -*- coding: utf8 -*-

import matplotlib.pyplot as plt
import matplotlib as mpl
import numpy as np
from math import *

code_website = 'http://commons.wikimedia.org/wiki/User:Geek3/mplwp'
try:
    import mplwp
except ImportError, er:
    print 'ImportError:', er
    print 'You need to download mplwp.py from', code_website
    exit(1)

name = 'mplwp_hermitefunction04.svg'
fig = mplwp.fig_standard(mpl)

xlim = -5,5; fig.gca().set_xlim(xlim)
ylim = -1,1; fig.gca().set_ylim(ylim)
mplwp.mark_axeszero(fig.gca())

from numpy.polynomial.hermite import Hermite

for j in range(5):
    a = (2**j * factorial(j) * sqrt(pi)) ** -0.5
    H = Hermite([0] * j + [1])
    f = lambda x: a * exp(-x**2 / 2.0) * H(x)
    x = np.linspace(xlim[0], xlim[1], 5001)
    y = [f(xx) for xx in x]
    plt.plot(x, y, label=unichr(968) + mplwp.unicode_sub(j), zorder=-j)

mpl.rc('legend', borderaxespad=0.8)
plt.legend(loc='lower right').get_frame().set_alpha(0.9)

plt.savefig(name)
mplwp.postprocess(name)