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

Charles R Harris charlesr.harris at gmail.com
Tue Jun 9 16:46:25 EDT 2009

```On Tue, Jun 9, 2009 at 12:56 PM, bruno Piguet <bruno.piguet at gmail.com>wrote:

> Dear all,
>
>    Can someone point me to a doc on dot product vectorisation ?
>
> Here is what I try to do :
>
> I've got a rotation function which looks like :
>
> def rotat_scal(phi, V):
>     s = math.sin(phi)
>     c = math.cos(phi)
>     M = np.zeros((3, 3))
>     M[2, 2] = M[1, 1] = c
>     M[1, 2] = -s
>     M[2, 1] = s
>     M[0, 0] = 1
>     return np.dot(M, V)
>
> (where phi is a scalar, and V and array of size (3,1))
>
> Now, I want to apply it to a time series of phi and V, in a vectorised way.
> So, I tried to simply add a first dimension :
> Phi is now of size(n) and V (n, 3).
> (I really whish to have this shape, for direct correspondance to file).
>

Well, in this case you can use complex multiplication and either work with
just the x,y components or use two complex components, i.e., [x + 1j*y, z].
In the first case you can then do the rotation as V*exp(1j*phi). If you want
more general rotations, a ufunc for quaternions would do the trick.

Chuck
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