In this post we will see how to visualize a function of two variables in two ways. First, we will create an intensity image of the function and, second, we will use the 3D plotting capabilities of matplotlib to create a shaded surface plot. So, let's go with the code:

from numpy import exp,arange
from pylab import meshgrid,cm,imshow,contour,clabel,colorbar,axis,title,show

# the function that I'm going to plot
def z_func(x,y):
 return (1-(x**2+y**3))*exp(-(x**2+y**2)/2)
 
x = arange(-3.0,3.0,0.1)
y = arange(-3.0,3.0,0.1)
X,Y = meshgrid(x, y) # grid of point
Z = z_func(X, Y) # evaluation of the function on the grid

im = imshow(Z,cmap=cm.RdBu) # drawing the function
# adding the Contour lines with labels
cset = contour(Z,arange(-1,1.5,0.2),linewidths=2,cmap=cm.Set2)
clabel(cset,inline=True,fmt='%1.1f',fontsize=10)
colorbar(im) # adding the colobar on the right
# latex fashion title
title('$z=(1-x^2+y^3) e^{-(x^2+y^2)/2}$')
show()

The script would have the following output:

And now we are going to use the values stored in X,Y and Z to make a 3D plot using the mplot3d toolkit. Here's the snippet:

from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
from numpy import sin,sqrt

fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, 
                      cmap=cm.RdBu,linewidth=0, antialiased=False)

ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))

fig.colorbar(surf, shrink=0.5, aspect=5)

plt.show()

And this is the result:

Source: http://glowingpython.blogspot.com/2012/01/how-to-plot-two-variable-functions-with.html