[SciPy-User] fast small matrix multiplication with cython?

[Robert Kern]

On Mon, Dec 6, 2010 at 18:11, Pauli Virtanen <pav at iki.fi> wrote:
> On Mon, 06 Dec 2010 17:34:19 -0500, Skipper Seabold wrote:
>> I'm wondering if anyone might have a look at my cython code that does
>> matrix multiplication and see where I can speed it up or offer some
>> pointers/reading.  I'm new to Cython and my knowledge of C is pretty
>> basic based on trial and (mostly) error, so I am sure the code is still
>> very naive.
>
> You'll be hard pressed to do better than Numpy's dot. In the raw data
> handling, BLAS is very likely faster than most things you can code
> manually. Moreover, the Cython routine you write must have as much
> overhead as dot() --- dealing with refcounting, allocating/dellocating
> PyArrayObjects (which is expensive) etc.

The main thing for his use case is reducing the overhead when called
from Cython. This started in a Cython-user thread where he was
directly calling the Python numpy.dot() from Cython. I suggested that
writing a Cython implementation may be better given the small
dimensions (only up to 10x10) might be better handled by writing the
matmult directly. Unfortunately, the buffer syntax adds a bunch of
overhead. Not the *same* overhead, mind, and I was hoping it would be
less, but it turns out to be more.

Getting access to the C BLAS implementations would be best. I guess
you could get descr.f.dotfunc and use that.

> If you are willing to give up wrapping each small matrix in a separate
> Numpy ndarray, then you can expect to get additional speed gains.
> (Although even in that case it could make more sense to call BLAS
> routines to do the multiplication instead, unless your matrices are small
> and of fixed size in which case the C compiler may be able to produce
> some tightly optimized code.)
>
> However, in many cases the small matrices can be just stuffed into a
> single Numpy array.

His use case (Kalman filters) prevents this.

-- 
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