[SciPy-Dev] Differentiate function

[Jonathan Stickel]

Robert,

I think, conceptually, something like this could be of interest in 
SciPy, but the devil is in the details. There are a lot of ways to 
implement finite differences; the code you shared provides the 
forward/backward finite differences with optional shift in the x 
positions. These are first-order accurate. Your interpolation of forward 
differences effectively results in the second-order accurate 
central-difference method.

Evaluation of the endpoints is a bit more tricky; your approaches are 
simple but lack rigor (I am not sure of the accuracy). I know of 
formulas for second-order accurate endpoint finite differences for 
equally spaced x, but I am not sure about unequally spaced data (I am 
sure they exist but I haven't looked them up).

So, should this functionality exist in SciPy, what methods should be 
implemented and made available? I think many of us (including myself) 
have implemented our own methods that are satisfactory for our 
particular needs, and no one has submitted general utility 
finite-differences functions that provides multiple methods with 
appropriate mathematical rigor. Such a function should also provide 
higher-order derivatives (at least second, but maybe up to fourth; or 
perhaps nth-order methods using a series formula).

Also, the name should not be "diff" to avoid confusion with numpy.diff.

Regards,
Jonathan



On 11/6/16 23:53 , Robert Rehammar wrote:
> Dear Pierre,
>
> Thank you for your reply. I am note fully aware of the difference
> between numpy and scipy and also not a developer, but it seems to me
> this function could fit in scipy where you often will want to
> differentiate w.r.t. a particular variable. I am aware of diff, but it
> is really a much more basic function. In many areas of science and
> engineering is the sampling points of crucial importance, and having a
> function giving you the appropriate sampling points can be very
> important for accuracy.
>
> I have been missing this function several times my self, and hence the
> reason why I submitted it here. Anyway, if there is no interest, I will
> of course not peruse the matter further.
>
> Best,
>
> Robert
>
>
> On 2016-11-05 22:53, Pierre de Buyl wrote:
>> Dear Robert,
>>
>> On Thu, Nov 03, 2016 at 08:37:07PM +0100, Robert Rehammar wrote:
>>> Dear all,
>>>
>>> I implemented a simple function to differentiate an array which seems
>>> other
>>> people might like to have. It looks like:
>>> def diff(f, x, retval = 'same'):
>>> (...)
>>>
>>> What do you think about adding it to scipy?
>> I am not a SciPy developer myself but I thought that I would point out
>> NumPy's
>> diff function. It does not go as far as your routine in terms of
>> options but
>> goes most of the way. It applies the differentiation to order 'n' as
>> an option
>> that is similar to the recursive application. Given this existing
>> routine, the
>> incentive to add another one might be low.
>>
>> Regards,
>>
>> Pierre
>>
>> _______________________________________________
>> SciPy-Dev mailing list
>> SciPy-Dev at scipy.org
>> https://mail.scipy.org/mailman/listinfo/scipy-dev
>
> _______________________________________________
> SciPy-Dev mailing list
> SciPy-Dev at scipy.org
> https://mail.scipy.org/mailman/listinfo/scipy-dev