Broadcasting a function over two vectors to get a 2d numpy array

Question

I want to broadcast a function f over a vectors so that the result is a matrix P where P[i,j] = f(v[i], v[j]). I know that I can do it simply:

P = zeros( (v.shape[0], v.shape[0]) )
for i in range(P.shape[0]):
    for j in range(P.shape[0]):
        P[i, j] = f(v[i,:], v[j,:])

or more hacky:

from scipy.spatial.distance import cdist
P = cdist(v, v, metric=f)

But I am looking for the fastest and neatest way to do it. This seems like a function of broadcasting that numpy should have built-in. Any suggestions?

If it works, cdist looks like a pretty clean way of doing this. In the case of a callable metric, cdist does exactly what your code is doing. — hpaulj
– hpaulj, Commented Sep 19, 2014 at 0:42
f1 = functools.partial(cdist, metric=f) would hide the cdist usage. — hpaulj
– hpaulj, Commented Sep 19, 2014 at 3:18
@Gioelelm I am almost sure you can avoid the loops perhaps redesigning a bit your code... where do you use P[i, j]... do you need all the distance matrix or only to find the closest points for some reason... in that case, check scipy.spatial.distance.cKDTree().. — Saullo G. P. Castro
– Saullo G. P. Castro, Commented Sep 19, 2014 at 16:22

itai · Accepted Answer · 2014-09-19 00:30:40Z

1

I believe what you search for is numpy.vectorize. Use it like so:

def f(x, y):
    return x + y
v = numpy.array([1,2,3])
# vectorize the function
vf = numpy.vectorize(f)
# "transposing" the vector by producing a view with another shape
vt = v.reshape((v.shape[0], 1)
# calculate over all combinations using broadcast
vf(v, vt)

Output:
array([[ 2.,  3.,  4.],
       [ 3.,  4.,  5.],
       [ 4.,  5.,  6.]])

edited Sep 19, 2014 at 0:30

answered Sep 18, 2014 at 23:44

itai

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5 Comments

hpaulj Over a year ago

vectorize doesn't speed it up. It just wraps the loop(s), while giving access to broadcasting machinery.

itai Over a year ago

Maybe I'm wrong but believe thats exactly what he wants. Speedy numpy-level loops while being memory efficient via broadcasting.

hpaulj Over a year ago

But I don't see where broadcasting is used in his sample code.

Gioelelm Over a year ago

@itai Yes that is what I wanted, this is for sure faster than my loop

itai Over a year ago

@hpaulj you probably got it yourself but for posterity - v is broadcasted "vertically" (shape (3,1) to (3,3)) and vt is broadcasted "horizontally" (shape (1,3) to (3,3)).

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