# [Numpy-discussion] Optimize evaluation of function on matrix

Florian Lindner mailinglists at xgm.de
Fri Mar 31 08:26:15 EDT 2017

```Hey,

Am 27.03.2017 um 16:09 schrieb Sebastian Berg:
> On Mon, 2017-03-27 at 13:06 +0200, Florian Lindner wrote:
>> Hey,
>>
>> I've timed the two versions, one basisfunction being a function:
>>
>> 1 loop, best of 3: 17.3 s per loop
>>
>> the other one, basisfunction being a list of functions:
>>
>> 1 loop, best of 3: 33.5 s per loop
>>
>>> To be honest, I am a bit surprised that its a problem, since "basis
>>> function" sounds a bit like you have to do this once and then use
>>> the
>>> result many times.
>>
>> It's part of a radial basis function interpolation algorithm. Yes, in
>> practice the matrix is filled only once and reused
>> a couple of times, but in my case, which is exploration of parameters
>> for the algorithm, I call eval_BF many times.
>>
>>> You can get rid of the `row` loop though in case row if an
>>> individual
>>> row is a pretty small array.
>>
>> Would you elaborate on that? Do you mean that the inner col loop
>> produces an array which is then assigned to the row.
>> But I think it stell need to row loop there.
>
> Well, I like to not serve the result, but if you exchange the loops:
>
> A = np.empty((len(meshA), len(meshB)))
> for j, col in enumerate(meshB):
>     for i, row in enumerate(meshA):
>         A[i, j] = self.basisfunction[j](row - col)
>
> Then you can see that there is broadcasting magic similar (do not want
> to use too many brain cells now) to:
>
> A = np.empty((len(meshA), len(meshB)))
> for j, col in enumerate(meshB):
>     # possibly insert np.newaxis/None or a reshape in [??]
>     A[:, j] = self.basisfunction[j](meshA[??] - col)

I have it like that now:

A = np.empty((len(meshA), len(meshB)))
for j, col in enumerate(meshB):
A[:,j] = self.basisfunction[j](meshA - col)

which has improved my speeds by a factor of 36.

Thanks!
Florian

>
> - Sebastian
>
>>
>> Best,
>> Florian
>>
>> Am 25.03.2017 um 22:31 schrieb Sebastian Berg:
>>> On Sat, 2017-03-25 at 18:46 +0100, Florian Lindner wrote:
>>>> Hello,
>>>>
>>>> I have this function:
>>>>
>>>> def eval_BF(self, meshA, meshB):
>>>>         """ Evaluates single BF or list of BFs on the meshes. """
>>>>         if type(self.basisfunction) is list:
>>>>             A = np.empty((len(meshA), len(meshB)))
>>>>             for i, row in enumerate(meshA):
>>>>                 for j, col in enumerate(meshB):
>>>>                     A[i, j] = self.basisfunction[j](row - col)
>>>>         else:
>>>>             mgrid = np.meshgrid(meshB, meshA)
>>>>             A = self.basisfunction( np.abs(mgrid[0] - mgrid[1]) )
>>>>         return A
>>>>
>>>>
>>>> meshA and meshB are 1-dimensional numpy arrays.
>>>> self.basisfunction is
>>>> e.g.
>>>>
>>>>     """ Gaussian Basis Function """
>>>>
>>>>
>>>> or a list of partial instantations of such functions (from
>>>> functools.partial).
>>>>
>>>> How can I optimize eval_BF? Esp. in the case of basisfunction
>>>> being a
>>>> list.
>>>>
>>>
>>> Are you sure you need to optimize it? If they have a couple of
>>> hundred
>>> elements or so for each row, the math is probably the problem and
>>> most
>>> of that might be the `exp`.
>>> You can get rid of the `row` loop though in case row if an
>>> individual
>>> row is a pretty small array.
>>>
>>> To be honest, I am a bit surprised that its a problem, since "basis
>>> function" sounds a bit like you have to do this once and then use
>>> the
>>> result many times.
>>>
>>> - Sebastian
>>>
>>>
>>>> Thanks!
>>>> Florian
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>>>>
>>>>
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