File:Mplwp airybi asymptotic.svg

#!/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_airybi_asymptotic.svg'
fig = mplwp.fig_standard(mpl)

xlim = -10,3; fig.gca().set_xlim(xlim)
ylim = -0.5,3; fig.gca().set_ylim(ylim)
mplwp.mark_axeszero(fig.gca())

import mpmath
x = np.linspace(xlim[0], xlim[1], 10001)

y1 = [mpmath.airybi(xx) for xx in x]
plt.plot(x, y1, label='Bi', zorder=1)

def airybi_asymptotic(x):
    if x == 0.: return float('inf')
    elif x > 0: return exp(x**1.5 / 1.5) / (sqrt(pi) * x**0.25)
    else: return cos((-x)**1.5 / 1.5 + pi/4) / (sqrt(pi) * (-x)**0.25)
y2 = [airybi_asymptotic(xx) for xx in x]
plt.plot(x, y2, label='approximation', zorder=0)

plt.legend(loc='upper left').get_frame().set_alpha(0.9)

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