How do I apply some function to a python meshgrid?

Question

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.

codereview.stackoverflow.com is probably a better place for this — Joran Beasley
– Joran Beasley, Commented Nov 26, 2013 at 21:43
I believe that X.reshape(X.size) is the same as X.ravel() — mgilson
– mgilson, Commented Nov 26, 2013 at 21:43

user · Accepted Answer · 2019-07-13 17:11:34Z

41

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 raveling or reshapeing 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)

edited Jul 13, 2019 at 17:11

user

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answered Nov 26, 2013 at 21:51

mgilson

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2 Comments

Evgeni Sergeev Over a year ago

We can also apply vectorize as a function directly. For example, vectorising the built-in chr(..) function: np.vectorize(chr)(np.arange(97, 107)) gives array(['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'], dtype='|S1').

mgilson Over a year ago

That's true -- But you're just unraveling the decorator syntactic sugar. The downside is that you'll be creating a new function each time that line is executed which is a somewhat expensive operation. With the decorator syntax, usually the line is only executed once (at import time) so it's not as big of a concern.

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