在python中绘制2D积分函数

Question

Here is my first steps within the NumPy world. As a matter of fact the target is plotting below 2-D function as a 3-D mesh:

N = \frac{n}{2\sigma\sqrt{\pi}}\exp^{-\frac{n^{2}x^{2}}{4\sigma^{2}}}

That could been done as a piece a cake in Matlab with below snippet:

[x,n] = meshgrid(0:0.1:20, 1:1:100);

mu = 0;
sigma = sqrt(2)./n;

f = normcdf(x,mu,sigma);
mesh(x,n,f);

But the bloody result is ugly enough to drive me trying Python capabilities to generate scientific plots.

I searched something and found that the primary steps to hit above mark in Pyhton might be acquired by below snippet:

from matplotlib.patches import Polygon
import numpy as np
from scipy.integrate import quad
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

sigma = 1

def integrand(x,n):
    return (n/(2*sigma*np.sqrt(np.pi)))*np.exp(-(n**2*x**2)/(4*sigma**2))

t = np.linespace(0, 20, 0.01)
n = np.linespace(1, 100, 1)

lower_bound = -100000000000000000000 #-inf
upper_bound = t

tt, nn = np.meshgrid(t,n)

real_integral = quad(integrand(tt,nn), lower_bound, upper_bound)

Axes3D.plot_trisurf(real_integral, tt,nn)

Edit: With due attention to more investigations on Greg's advices, above code is the most updated snippet.

Here is the generated exception:

RuntimeError: infinity comparisons don't work for you

It is seemingly referring to the quad call...

Would you please helping me to handle this integrating-plotting problem?!...

Best

Answer 1

Just a few hints to get you in the right direction. numpy.meshgrid can do the same as MatLABs function: http://docs.scipy.org/doc/numpy/reference/generated/numpy.meshgrid.html

When you have x and n you can do math just like in matlab:

sigma = numpy.sqrt(2)/n

(in python multiplication/division is default index by index - no dot needed)

scipy has a lot more advanced functions, see for example How to calculate cumulative normal distribution in Python for a 1D case.

For plotting you can use matplotlibs pcolormesh:

import matplotlib.pyplot as plt
plt.pcolormesh(x,n,real_integral)

Hope this helps until someone can give you a more detailed answer.