How to efficiently create multidimensional arrays?

Question

assuming I have any function such as

f(x, y, z) = xyz

what's the fastest way of calculating every value for f given three linear input arrays x, y, and z?

Of course I can do something along the lines of,

import numpy as np

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

for xi, xx in enumerate(x):
    for yi, yy in enumerate(y):
        for zi, zz in enumerate(z):
            f(xi, yi, zz) = xx*yy*zz

but this is probably not the best way to do it, especially if the input arrays become larger. Is there a better way of doing it, such as with a list comprehension (but multidimensional) or any other way? Help is appreciated.

Doing x * y * z will give me a resulting array of shape (11, ) instead of every combination of x, y, z, which will be an array of shape (11, 11, 11) for the above case. — user14893379
– user14893379, Commented Jun 12, 2021 at 17:16
f(xi, yi, zz) = xx*yy*zz doesn't work, does it? Python doesn't allow you to assign to a function call! — hpaulj
– hpaulj, Commented Jun 13, 2021 at 2:28
How about x[:,None,None] * y[None,:,None]*z[None,None,:]? This uses broadcasting - it's a key concept when working with numpy arrays. — hpaulj
– hpaulj, Commented Jun 13, 2021 at 2:30

patagonicus · Accepted Answer · 2021-06-12 17:09:48Z

2

First create the grid mesh array (x,y,z) as 3-tuples using meshgrid then you can apply the function in sequence:

import numpy as np
x = y = z = np.linspace(-1.0,1.0,11)
grid_coordinates = np.array(np.meshgrid(x,y,z)).reshape(-1,3)
f = lambda x,y,z : x*y*z
f_values = [ f(x,y,z) for x,y,z in grid_coordinates ]

A unit test for the f_values,

f_values[10] == grid_coordinates[10][0]*grid_coordinates[10][1]*grid_coordinates[10][2]

answered Jun 12, 2021 at 17:09

patagonicus

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5 Comments

user14893379 Over a year ago

Thank you very much, I was not familiar with how meshgrids worked but this seems to be the way to do it. Going from the documentation for anybody else reading this question, 'meshgrid is very useful to evaluate functions on a grid.'.

hpaulj Over a year ago

Why not just multiply the 3 arrays produced by meshgrid, without further reshaping and manipulating? You are doing as much python iteration as the OP this way!

patagonicus Over a year ago

@hpaulj In this simple function, that would work but if we have nonlinear function, we would need to iterate over.

hpaulj Over a year ago

If we have to iterate, feeding scalar values to a function, there's little point to using numpy. Python iteration on list is faster.

patagonicus Over a year ago

Yes we used list comprehension from plain python above [ f(x,y,z) for x,y,z in grid_coordinates]. Sure, if function can be vectorised the better, as I said earlier.

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