[SciPy-Dev] Differentiate function

[Robert Rehammar]

This is also a good function to have, but it seems complementary to the 
function I propose since it operate on functions and mine operates on 
arrays.

Best,

Robert


On 2016-11-07 17:52, Evgeni Burovski wrote:
> Note that `approx_derivative` implements several finite-difference schemes,
>
> https://github.com/scipy/scipy/blob/master/scipy/optimize/_numdiff.py#L179
>
> For the moment, it's well hidden in scipy.optimize, but in the long
> run the idea is to offer public functionality. So far the main issue
> was the lack of bandwidth --- meaning if someone feels like working on
> it, great!
>
>
>
>
> On Mon, Nov 7, 2016 at 7:21 PM, Jonathan Stickel <jjstickel at gmail.com> wrote:
>> 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
>>>>
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