[SciPy-Dev] Regarding taking up project ideas and GSoC 2015

Wed Mar 11 14:14:11 EDT 2015

Hi everyone,

I have created a Wiki <https://github.com/maniteja123/GSoC/wiki/> page
and draft
proposal
<https://github.com/maniteja123/GSoC/wiki/Proposal:-add-finite-difference-numerical-derivatives-as-%60%60scipy.diff%60%60>
regarding
some approaches for API implementation for scipy.diff package after
discussing with Christoph Deil. I would really appreciate some feedback and
suggestions to incorporate more sound and concrete ideas into the proposal.
I also wanted to ask if it would be better to start a wiki page regarding
this on scipy repository. I thought it would be better to do so once the
proposal is more concrete.

Thanks again for reading along my proposal and waiting in anticipation for
your suggestions.

Cheers,
Maniteja
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On Mon, Mar 9, 2015 at 12:23 PM, Ralf Gommers <ralf.gommers at gmail.com>
wrote:

> Hi Maniteja,
>
>
> On Fri, Mar 6, 2015 at 1:12 PM, Maniteja Nandana <
> maniteja.modesty067 at gmail.com> wrote:
>
>> Hello everyone,
>>
>> I am writing this mail to enquire about implementing numerical
>> differentiation package in scipy.
>>
>> There have been discussions before (Issue #2035
>> <https://github.com/scipy/scipy/issues/2035>) and some PRs (PR #2835
>> <https://github.com/scipy/scipy/pull/2835>) to include tools to compute
>> derivatives in scipy.
>>
>> According to the comments made in them, as far as I can understand, I see
>> that there are some ways to do derivatives on the computer with varying
>>  generality and accuracy ( by Alex Griffing
>> <https://github.com/scipy/scipy/issues/2035#issuecomment-23628615> ) :
>>
>>    1. 1st order derivatives of special functions
>>    2. derivatives of univariate functions
>>    3. symbolic differentiation
>>    4. numerical derivatives - finite differences
>>    5. automatic or algorithmic differentiation
>>
>> Clearly, as suggested in the thread, the 1st option is already done in
>> functions like *jv* and *jvp* in *scipy.special. *
>>
>> I think everyone agreed that symbolic derivatives is out of scope of
>> scipy.
>>
>
> Definitely, symbolic anything is out of scipy for scipy:)
>
>
>> Though I would like to hear more about the univariate functions.
>>
>> Coming to finite differences, the modules described there, *statsmodels *and
>> *numdifftools, *they vary in aspects of speed and accuracy, in terms of
>> approaches followed as mentioned in Joseph Perktold comment
>> <https://github.com/scipy/scipy/pull/2835#issuecomment-52372036>
>>
>>    - *Statsmodels *used complex step derivatives, which are for first
>>    order derivatives and have only truncation error, no roundoff error
>>    since there is no subtraction.
>>    - *Numdifftools *uses adaptive step-size to calculate finite
>>    differences, but will suffer from dilemma to choose small step-size to
>>    reduce truncation error but at the same time avoid subtractive cancellation
>>    at too small values
>>
>> I have read the papers used by both the implementations:
>>  *Statsmodels *Statistical applications of the complex-step method of
>> numerical differentiation, Ridout, M.S.
>> <https://drive.google.com/file/d/0BwUeCS0FJLRucXdCc1JOTEY0cGc/view?usp=sharing>
>>  *Numdifftools *The pdf attached in the github repository DERIVEST.pdf
>> <https://drive.google.com/file/d/0BwUeCS0FJLRuYW1MNlp2enJCaHM/view?usp=sharing>
>>
>> Just pointing out in this platform, I think there is an error in equation
>> 13 in DERIVEST, It should be
>>
>> f'-0() = 2f'-delta/2() - f'-delta(),  instead of f'-0() = 2f'-delta() -
>> f'-delta/2()
>>
>> as also correctly mentioned in the matlab code that followed the equation
>>
>
> You may want to let the author know, he'll probably appreciate it.
>
>
>> As much as my understanding from the discussions goes, the statsmodels
>> implementation uses elegant broadcasting. Though I get the idea seeing the
>> code, I would really appreciate some examples that clearly explain this.
>>
>> Also the complex-step method is only for first order derivatives and that
>> function is analytic, so that Cauchy-Riemann equations are valid. So, is it
>> possible to differentiate any function with this ?
>>
>> Also as I was discussing with Christoph Deil, the API implementation
>> issue of whether to use classes, as in numdifftools or as functions, as in
>> statsmodels came to the fore. Though I am not an expert in it, I would love
>> to hear some suggestions on it.
>>
>
> It will be important to settle on a clean API. There's no general
> preference for classes or functions in Scipy, the pros/cons have to be
> looked at in detail for this functionality. The scope of the scipy.diff
> project is quite large, so starting a document (as I think you've already
> discussed with Christoph?) outlining the API that can be reviewed will be a
> lot more efficient than trying to do it by email alone.
>
>
>> Though at this point AD seems ahead of time, it is powerful in forward
>> and reverse methods, moreover complex-step is somewhat similar to it. The
>> packages *ad *and *algopy *use AD. Also, there were concerns with
>> interfacing these methods with C/ Fortran functions. It would also be
>> great if there could be suggestions regarding whether to implement these
>> methods.
>>
>
> It's been around for a while so not sure about "ahead of its time", but
> yes it can be powerful. It's a large topic though, should be out of scope
> for this GSoC project. Good finite difference methods will be challenging
> enough:) That doesn't mean that AD is out of scope for Scipy necessarily,
> but that's for another time to discuss.
>
> At the same time, it would be really helpful if any new methods or
>> packages to be looked into could be suggested.
>>
>
> I think what's in numdifftools and statsmodels is a good base to build on.
> What could be very useful in addition though is an indepent reference
> implementation of the methods you're working on. This could be
> Matlab/R/Julia functions or some package written by the author of a paper
> you're using. I don't have concrete suggestions now - you have a large
> collection of papers - but you could already check the papers you're using.
>
> Cheers,
> Ralf
>
>
>> Waiting in anticipation for your feedback and response. Happy to learn :)
>> Thanks for reading along my lengthy mail. Please do correct if I did some
>> mistake.
>>
>> I have attached the documents I have related to these issues, most
>> importantly *The Complex-Step Derivative Approximation by **JOAQUIM R.
>> R. A. MARTINS*
>>
>> *Numerical differentiation
>> <https://drive.google.com/folderview?id=0BwUeCS0FJLRufnJaVko3MGpJX0Nud3R0dHgyc2JBYUgxVkhBTkNvbkhFQWZucmhWSzlaVVk&usp=sharing>*
>>
>> Cheers,
>> Maniteja.
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>>
>
>
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