User:Ozzy: Difference between revisions

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== O: Only out of interest ==
== O: Only out of interest ==
* Did you ever hear about Octave before?  
* Did you ever hear about Octave before?  
''Yes I did.''
''Yes I did. I started using it on my second year of studies where it was a recommended tool for signal processing on my university''
** If so, when and where? How far have you been involved already?
** If so, when and where? How far have you been involved already?
''I am using Octave in daily basis for my research work and I actually prefer it over Matlab due to relaxed syntax, easy access to additional packages and lower price ;)''
''I am using Octave in daily basis for my research work and I actually prefer it over Matlab due to relaxed syntax, easy access to additional packages and lower price ;)''
* What was the first question concerning Octave you could not find an answer to rather quickly?
* What was the first question concerning Octave you could not find an answer to rather quickly?
''Unfortunately there was a lot of them and they mostly include poorly documented packages''
''Unfortunately there was a lot of them and they mostly relate to poorly documented packages''


== P: Prerequisites ==
== P: Prerequisites ==
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== Y: Your task ==
== Y: Your task ==
* Did you select a task from our list of proposals and ideas?
* Did you select a task from our list of proposals and ideas?
** If yes, what task did you choose? Please describe what part of it you especially want to focus on if you can already provide this information. ''Please also wiki-link the page for your elaborated proposal here.''
** If yes, what task did you choose? Please describe what part of it you especially want to focus on if you can already provide this information. ''Please also wiki-link the page for your elaborated proposal here.''
** If you apply for a task you have added yourself instead, please describe this task, its scope and people you already talked to concerning it. What field of tasks did you miss on the list?
** If you apply for a task you have added yourself instead, please describe this task, its scope and people you already talked to concerning it. What field of tasks did you miss on the list?


I would like to work on solving the problem described [[Summer_of_Code_Project_Ideas#Symbolic_package|here]]. Because the recent discussion on the octave-maintainers mailing list suggests it would be better to prepare a general method for liking Octave to Python and than apply this to this specific issue I would follow this way.


As already mentioned in the discussion there already exist a library intended for this purpose, namely Pytave. The library was intended to be used to calling Octave code from Python code, but as suggested its code base can potentially serve for two-way communication, especially because it already contains all the required conversions between Python and Octave types.


I would like to implement a general algorithm for maximum entropy reconstruction. This is an algorithm for estimating distributions which has applications in various inverse and/or ill-posed problems. It is used for deblurring/deconvolution of images, power spectrum estimation, smoothing, measurement data processing in biology, physics and more.
My project would consist of three main parts:
 
* Cleaning up the Pytave library. This would include extracting the conversion functions between octave types and Python types (numpy arrays + primitive types), possibly leaving out legacy Python numeric types. This part would have to also include some C interface for both Octave and Python functions with proper exception mapping.
The algorithm would find its place in one of the existing packages (where ''optim'' or ''signal'' sound appropriate) or as a separate package. I plan to prepare two versions of the general algorithm, (temporal name {{codeline|maxent}})
* Writing an Octave module which would allow to call Python functions from Octave. This part would be realized as oct-files linking to the code prepared in the previous step (probably as a part of Pytave). This part would also have to include some Python session management. As a stand alone package it could be become a useful thing by itself.
* a version for problems defined by matrix. The function's declaration should be something like this
* Substituting present way of communication between Octave and Python in Symbolic Package. Since now everything is said to be done on strings, substituting current pipe approach to the one resulting from the previous step shouldn't cause much too trouble.
{{Code|Matrix problem declaration|<syntaxhighlight lang="octave" style="font-size:13px">function [x,info,...]=maxent(y,D,sigma,alpha=0.95, model=1, optset)
 
</syntaxhighlight>}}
 
 
where {{codeline|y} is the data vector, and {{codeline|D}} is the transformation matrix. {{codeline|sigma}} should be a vector or scalar which describes standard deviation of values of {{codeline|y}}. The optional parameter {{codeline|alpha}} and {{codeline|model}} describe confidence and a priori distribution of {{codeline|x}} (defaults to flat) respectively. The last parameter {{codeline|optset}} would allow to pass additional parameters to function, similar to the ones in {{codeline|optim}} package.
 
The returned value {{codeline|x}} is such that
 
<math> y \approx Dx</math>
 
where each of the coordinates of {{codeline|y}} lies within {{codeline|alpha}} confidence interval (normal distributed error assumed). Out of all possible {{codeline|x}} the one with the highest entropy is chosen. {{codeline|info}} describes the convergence of the algorithm. The other returned parameters will describe final gradients, Hessians and Lagrange's coefficient.
 
* another version would be defined for a non-linear function. The declaration would very similar
{{Code|Functional problem declaration|<syntaxhighlight lang="octave" style="font-size:13px">function [x,info,...]=maxent(y,fun,sigma,alpha=0.95, model=1, optset)
 
 
</syntaxhighlight>}}
 
All the parameters have the similar meaning here, and the new parameter {{codeline|fun}} is the handle to a function which accepts vector argument, which describes the problem to be inverted. This time the returned value should obey
 
<math> y \approx f(x)</math>
 
It is convenient to have this version of the algorithm for problem where obtaining the transformation matrix is difficult to compute or affects performance (think fft). The algorithm is expected to give good results for linear functions. For not-too-complicated non-linear cases the chances are still there.
 
Additional  work will be put to provide some wrapper functions to allow the user quickly use MEM in their problem. This includes function for 1D and image deconvolutions, time series components analysis, power spectral estimation and other applications I will be able to find in Matlab or other computational software.
 
Another sub-task is to analyze the speed and numerical precision of the implemented algorithms.
 
* Please provide a rough estimated timeline for your work on the task. ''This should include the GSoC midterms and personal commitments like exams or vacation ("non-coding time"). Optionally include two or three milestones you expect.''
 
** Start of GSoC
***''development of the algorithm in matrix version with future extension in mind''
** Midterm evaluation
***''upgrading the matrix algorithm to accept function handle argument''
***''stability tests''
***''identification of the remaining issues''
***''adding wrappers for easy use''


** Final evaluation
Timeline (brief):
* Getting involved -- two weeks
* Cleaning Pytave -- four weeks
* Octave module for Python -- two weeks
* Symbolics -- two weeks
(since in June-August period there are 13 weeks there still is some reserve for holidays and possible delays)


[[Category: Summer of Code]]
[[Category: Summer of Code]]
Ozzy
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