[Numpy-discussion] Howto vectorise a dot product ?
David Warde-Farley
dwf at cs.toronto.edu
Tue Jun 9 16:27:51 EDT 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
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