[Numpy-discussion] vectorization vs. numpy.linalg (shape (3, 3, 777) vs shape (777, 3, 3))
Sebastian Berg
sebastian at sipsolutions.net
Sun Mar 5 09:52:55 EST 2017
On Thu, 2017-03-02 at 10:27 +0000, Nico Schlömer wrote:
> Hi everyone,
>
> When trying to speed up my code, I noticed that simply by reordering
> my data I could get more than twice as fast for the simplest
> operations:
> ```
> import numpy
> a = numpy.random.rand(50, 50, 50)
>
> %timeit a[0] + a[1]
> 1000000 loops, best of 3: 1.7 µs per loop
>
> %timeit a[:, 0] + a[:, 1]
> 100000 loops, best of 3: 4.42 µs per loop
>
> %timeit a[..., 0] + a[..., 1]
> 100000 loops, best of 3: 5.99 µs per loop
> ```
> This makes sense considering the fact that, by default, NumPy
> features C-style memory allocation: the last index runs fastest. The
> blocks that are added with `a[0] + a[1]` are contiguous in memory, so
> cache is nicely made use of. As opposed to that, the blocks that are
> added with `a[:, 0] + a[:, 1]` are not contiguous, even more so with
> `a[..., 0] + a[..., 1]`; hence the slowdown. Would that be the
> correct explanation?
>
> If yes, I'm wondering why most numpy.linalg methods, when vectorized,
> put the vector index up front. E.g., to mass-compute determinants,
> one has to do
> ```
> a = numpy.random.rand(777, 3, 3)
> numpy.linalg.det(a)
> ```
> This way, all 3x3 matrices form a memory block, so if you do `det`
> block by block, that'll be fine. However, vectorized operations (like
> `+` above) will be slower than necessary.
> Any background on this?
>
I am honestly not sure where you are going at. This order seems the
more natural order for most operations. Also numpy does not create
copies normally even for transposed data (though some functions may
internally, numpy just _defaults_ to C-order). So of course what is
faster depends on your use-case, but if you have an operation on many
3x3 arrays the way numpy does it is the more natural way. If you do
other things that are faster the other way around, you will have to
decide which operation is the more important one overall.
- Sebastian
> (I came across this when having to rearrange my data (swapaxes,
> rollaxis) from shape (3, 3, 777) (which allows for fast vectorized
> operations in the rest of the code) to (777, 3, 3) for using numpy's
> svd.)
>
> Cheers,
> Nico
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