# [Numpy-discussion] distance_matrix: how to speed up?

Matthieu Brucher matthieu.brucher@gmail....
Wed May 21 07:43:25 CDT 2008

```Hi,

Bill Baxter proposed a version of this problem some months ago on this ML. I
use it regularly and it is fast enough for me.

Matthieu

2008/5/21 Emanuele Olivetti <emanuele@relativita.com>:

> Dear all,
>
> I need to speed up this function (a little example follows):
> ------
> import numpy as N
> def distance_matrix(data1,data2,weights):
>    rows = data1.shape[0]
>    columns = data2.shape[0]
>    dm = N.zeros((rows,columns))
>    for i in range(rows):
>        for j in range(columns):
>            dm[i,j] = ((data1[i,:]-data2[j,:])**2*weights).sum()
>            pass
>        pass
>    return dm
>
> size1 = 4
> size2 = 3
> dimensions = 2
> data1 = N.random.rand(size1,dimensions)
> data2 = N.random.rand(size2,dimensions)
> weights = N.random.rand(dimensions)
> dm = distance_matrix(data1,data2,weights)
> print dm
> ------------------
> The distance_matrix function computes the weighted (squared) euclidean
> distances between each pair of vectors from two sets (data1, data2).
> The previous naive algorithm is extremely slow for my standard use,
> i.e., when size1 and size2 are in the order of 1000 or more. It can be
> improved using N.subtract.outer:
>
> def distance_matrix_faster(data1,data2,weights):
>    rows = data1.shape[0]
>    columns = data2.shape[0]
>    dm = N.zeros((rows,columns))
>    for i in range(data1.shape[1]):
>        dm += N.subtract.outer(data1[:,i],data2[:,i])**2*weights[i]
>        pass
>    return dm
>
> This algorithm becomes slow when dimensions (i.e., data1.shape[1]) is
> big (i.e., >1000), due to the Python loop. In order to speed it up, I guess
> that N.subtract.outer could be used on the full matrices instead of one
> column at a time. But then there is a memory issue: 'outer' allocates
> too much memory since it stores all possible combinations along all
> dimensions. This is clearly unnecessary.
>
> Is there a NumPy way to avoid all Python loops and without wasting
> too much memory? As a comparison I coded the same algorithm in
> C through weave (inline): it is _much_ faster and requires just
> the memory to store the result. But I'd prefer not using C or weave
> if possible.
>
> Thanks in advance for any help,
>
>
> Emanuele
>
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--
French PhD student
Website : http://matthieu-brucher.developpez.com/
Blogs : http://matt.eifelle.com and http://blog.developpez.com/?blog=92