# [Numpy-discussion] Howto vectorise a dot product ?

David Warde-Farley dwf@cs.toronto....
Tue Jun 9 15:27:51 CDT 2009

```On 9-Jun-09, at 2:56 PM, bruno Piguet wrote:
> Phi is now of size(n) and V (n, 3).
> (I really whish to have this shape, for direct correspondance to
> file).
>
> The corresponding function looks like :
>
> def rotat_vect(phi, V):
>    s = np.sin(phi)
>    c = np.cos(phi)
>    M = np.zeros((len(phi), 3, 3))
>    M[:, 2, 2] = M[:, 1, 1] = c
>    M[:, 1, 2] = -s
>    M[:, 2, 1] = s
>    M[:, 0, 0] = np.ones (len(phi))
>    return np.dot(M, V)

Well, if you make V have a singleton dimension on the end you can then
do it, but you will get one more axis than you care about.

The help for dot() says this:

For 2-D arrays it is equivalent to matrix multiplication, and for
1-D
arrays to inner product of vectors (without complex conjugation).
For
N dimensions it is a sum product over the last axis of `a` and
the second-to-last of `b`::

dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])

So changing your code to this:

return np.dot(M, V[:,:,np.newaxis])[arange(len(phi)), :,
arange(len(phi)), :]

will do what you want, but it will also do a lot of useless
multiplication in computing that product. I'm not sure of any better
way, and am kind of curious myself (since I often have to take
products of one or several vectors with several matrices).

David
```