Multiple Element Indexing in multi-dimensional array

Question

I have a 3d Numpy array and would like to take the mean over one axis considering certain elements from the other two dimensions.

This is an example code depicting my problem:

import numpy as np
myarray = np.random.random((5,10,30))
yy = [1,2,3,4]
xx = [20,21,22,23,24,25,26,27,28,29]
mymean = [ np.mean(myarray[t,yy,xx]) for t in np.arange(5) ]

However, this results in:

ValueError: shape mismatch: objects cannot be broadcast to a single shape

Why does an indexing like e.g. myarray[:,[1,2,3,4],[1,2,3,4]] work, but not my code above?

Answer 1

This is how you fancy-index over more than one dimension:

>>> np.mean(myarray[np.arange(5)[:, None, None], np.array(yy)[:, None], xx],
            axis=(-1, -2))
array([ 0.49482768,  0.53013301,  0.4485054 ,  0.49516017,  0.47034123])

When you use fancy indexing, i.e. a list or array as an index, over more than one dimension, numpy broadcasts those arrays to a common shape, and uses them to index the array. You need to add those extra dimensions of length 1 at the end of the first indexing arrays, for the broadcast to work properly. Here are the rules of the game.