# [Numpy-discussion] arrays of matrices

Robert Kern robert.kern@gmail....
Thu Feb 28 18:55:11 CST 2008

```On Thu, Feb 28, 2008 at 6:43 PM, Geoffrey Irving <irving@pixar.com> wrote:
>  > The magic is in In[27]. We reshape the array of vectors to be
>  > compatible with the shape of the array of matrices. When we multiply
>  > the two together, it is as if we multiplied two (n,3,3) matrices, the
>  > latter being the vectors repeated 3 times. Then we sum along the rows
>  > of each of the product matrices to get the desired dot product.
>
>  Thanks!  That'll do nicely.
>
>  For large matrices, that could be problematic due to the blowup in
>  intermediate memory, but on the other hand for large matrices a loop
>  through the toplevel index wouldn't add much cost.

If you really want to save memory and you can destroy A, then you
could do the multiplication in-place. If you really want to get fancy
and can destroy b, you can use it as storage for the summation output,
too.

In [11]: A *= b.reshape([n,1,3])

In [12]: c = A.sum(axis=-1, out=b)

In [13]: b
Out[13]:
array([[   50,   140,   230],
[ 1220,  1580,  1940],
[ 4010,  4640,  5270],
[ 8420,  9320, 10220],
[14450, 15620, 16790]])

In [14]: c is b
Out[14]: True

>  > PS: Are you perchance the Geoffrey Irving I knew at CalTech, class of '03?
>
>  However, it's spelled Caltech, not CalTech!

Yeah, yeah, yeah. The Wikis, they have taken over my finger ReFlexes.

NumPy Rudds += 1. Take that, Tim Hochberg!  :-)

--
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless
enigma that is made terrible by our own mad attempt to interpret it as
though it had an underlying truth."
-- Umberto Eco
```