How do I apply some function to a python meshgrid?

matplotlib, numpy, python

Solution

I'd use `numpy.vectorize` to "vectorize" your function. Note that despite the name, `vectorize` is not intended to make your code run faster -- Just simplify it a bit.

Here's some examples:

>>> import numpy as np
>>> @np.vectorize
... def foo(a, b):
...    return a + b
... 
>>> foo([1,3,5], [2,4,6])
array([ 3,  7, 11])
>>> foo(np.arange(9).reshape(3,3), np.arange(9).reshape(3,3))
array([[ 0,  2,  4],
       [ 6,  8, 10],
       [12, 14, 16]])

With your code, it should be enough to decorate `func` with `np.vectorize` and then you can probably just call it as `func(X, Y)` -- No `ravel`ing or `reshape`ing necessary:

import numpy as np
import collections as c

# some arbitrary lookup table
a = c.defaultdict(int)
a[1] = 2
a[2] = 3
a[3] = 2
a[4] = 3

@np.vectorize
def func(x,y):
    # some arbitrary function
    return a[x] + a[y]

X,Y = np.mgrid[1:3, 1:4]
X = X.T
Y = Y.T

Z = func(X, Y)

Problem

Say I want to calculate a value for every point on a grid. I would define some function `func` that takes two values `x` and `y` as parameters and returns a third value. In the example below, calculating this value requires a look-up in an external dictionary. I would then generate a grid of points and evaluate `func` on each of them to get my desired result. The code below does precisely this, but in a somewhat roundabout way. First I reshape both the X and Y coordinate matrices into one-dimensional arrays, calculate all the values, and then reshape the result back into a matrix. My questions is, can this be done in a more elegant manner? ``` import collections as c # some arbitrary lookup table a = c.defaultdict(int) a[1] = 2 a[2] = 3 a[3] = 2 a[4] = 3 def func(x,y): # some arbitrary function return a[x] + a[y] X,Y = np.mgrid[1:3, 1:4] X = X.T Y = Y.T Z = np.array([func(x,y) for (x,y) in zip(X.ravel(), Y.ravel())]).reshape(X.shape) print Z ``` The purpose of this code is to generate a set of values that I can use with `pcolor` in matplotlib to create a heatmap-type plot.

Original source