How to plot 3D function as 2D colormap in python?

Question

Are there any python libraries that will let me plot z = f(x,y) where z is represented as the color in a densely rasterized image (as opposed to the color of a bunch of scat

Answer 1

To expand my comment above, here are some possible ways of computing a function on a grid

boffi@debian:~/Documents/tmp$ cat grid.py 
import numpy as np

def z(x,y):
  return np.sin(np.sqrt(x*x+y*y))

x = np.linspace(-1,1,11)
y = np.linspace(-2,2,21)

# naive

Z0 = np.zeros((len(y), len(x)))
for i, X in enumerate(x):
    for j, Y in enumerate(y):
        Z0[j,i] = z(X,Y)

# trampoline on a double list comprehension,
# it is possibly faster, sure it uses more memory

Z1 = np.array([[z(X,Y) for X in x] for Y in y])

# numpy has meshgrid, 
# meshgrid uses twice memory as the result matrix but
# if used _correctly_ it's FAST

X, Y = np.meshgrid(x, y)

# numpy can avoid you explicit looping,
# but if you are so inclined...

Z2 = np.zeros((len(y), len(x)))
for r in range(len(y)):
    for c in range(len(x)):
        Z2[r, c] = z(X[r, c], Y[r, c])

# numpy has ufuncs, and
# t h i s   i s   t h e   w a y   t o   g o

Z3 = z(X, Y)

# numpy has broadcasting (it's slower than Z = z(X, Y), less memory)

Z4 = z(x, y[:,None])

# note that x is still a _row_ of numbers, indexed by _columns_,
# while y[:,None] is now a _column_ of numbers, indexed by _rows_,
# so that Z4[row,column] <-- z(x[column], y[row])

# a bit of testing

# in previous answers, Z2 (i.e., explicit loops)
# is the preferred method --- here we show that the other four
# possible methods give you exactly the same result

print np.all(Z2==Z0)
print np.all(Z2==Z1)
print np.all(Z2==Z3)
print np.all(Z2==Z4)
boffi@debian:~/Documents/tmp$ python2 grid.py 
True
True
True
True
boffi@debian:~/Documents/tmp$