[Numpy-discussion] Slicing slower than matrix multiplication?

Bruce Southey bsouthey@gmail....
Fri Dec 11 10:36:54 CST 2009

On 12/11/2009 10:03 AM, Francesc Alted wrote:
> A Friday 11 December 2009 16:44:29 Dag Sverre Seljebotn escrigué:
>> Jasper van de Gronde wrote:
>>> Dag Sverre Seljebotn wrote:
>>>> Jasper van de Gronde wrote:
>>>>> I've attached a test file which shows the problem. It also tries adding
>>>>> columns instead of rows (in case the memory layout is playing tricks),
>>>>> but this seems to make no difference. This is the output I got:
>>>>>      Dot product: 5.188786
>>>>>      Add a row: 8.032767
>>>>>      Add a column: 8.070953
>>>>> Any ideas on why adding a row (or column) of a matrix is slower than
>>>>> computing a matrix product with a similarly sized matrix... (Xi has
>>>>> less columns than Xi2, but just as many rows.)
>>>> I think we need some numbers to put this into context -- how big are the
>>>> vectors/matrices? How many iterations was the loop run? If the vectors
>>>> are small and the loop is run many times, how fast the operation "ought"
>>>> to be is irrelevant as it would drown in Python overhead.
>>> Originally I had attached a Python file demonstrating the problem, but
>>> apparently this wasn't accepted by the list. In any case, the matrices
>>> and vectors weren't too big (60x20), so I tried making them bigger and
>>> indeed the "fast" version was now considerably faster.
>> 60x20 is "nothing", so a full matrix multiplication or a single
>> matrix-vector probably takes the same time (that is, the difference
>> between them in itself is likely smaller than the error you make during
>> measuring).
>> In this context, the benchmarks will be completely dominated by the
>> number of Python calls you make (each, especially taking the slice,
>> means allocating Python objects, calling a bunch of functions in C, etc.
>> etc). So it's not that strange, taking a slice isn't free, some Python
>> objects must be created etc. etc.
> Yeah, I think taking slices here is taking quite a lot of time:
> In [58]: timeit E + Xi2[P/2,:]
> 100000 loops, best of 3: 3.95 µs per loop
> In [59]: timeit E + Xi2[P/2]
> 100000 loops, best of 3: 2.17 µs per loop
> don't know why the additional ',:' in the slice is taking so much time, but my
> guess is that passing&  analyzing the second argument (slice(None,None,None))
> could be the responsible for the slowdown (but that is taking too much time).
> Mmh, perhaps it would be worth to study this more carefully so that an
> optimization could be done in NumPy.
>> I think the lesson mostly should be that with so little data,
>> benchmarking becomes a very difficult art.
> Well, I think it is not difficult, it is just that you are perhaps
> benchmarking Python/NumPy machinery instead ;-)  I'm curious whether Matlab
> can do slicing much more faster than NumPy.  Jasper?
What are using actually trying to test here?
I do not see any equivalence in the operations or output here.
-With your slices you need two dot products but ultimately you are only 
using one for your dot product.
-There are addition operations on the slices that are not present in the 
dot product.
-The final E arrays are not the same for all three operations.

Having said that, the more you can vectorize your function, the more 
efficient it will likely be especially with Atlas etc.


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