GSoC 2018 Report Sidhant Nagpal: Discrete Transforms, Convolutions & Recurrences

Sidhant Nagpal edited this page Aug 14, 2018 · 1 revision

This wiki page summarises the work I have done during GSoC 2018 for SymPy. The links to PRs are in chronological order under each header. For following the progress made during GSoC, see my blog for the weekly posts.

About Me

My name is Sidhant Nagpal and I have completed my third year of Bachelor's in Computer Science from University of Delhi at Netaji Subhas Institute of Technology.

Project Synopsis

My project involved writing a new discrete module in SymPy to implement transforms & convolutions for finite sequences and add capabilities for recurrence evaluation. For further information, my proposal for the project can be referred.

I have implemented all that was planned plus a few additional things (discovering and fixing bugs). However, there is certainly room for improvement, and I will mention where the work could continue post GSoC.

Pull Requests

Major Additions

  1. sympy/sympy#14725: Add discrete module, and transforms sub-module including Fast Fourier Transform, Number Theoretic Transform, and include docstring, doctests, unit-tests.

  2. sympy/sympy#14745: Add convolution sub-module including convolution_fft, convolution_ntt and a general method convolution for identifying the type of convolution and handling the cyclic convolution case, and include docstring, doctests, unit-tests.

  3. sympy/sympy#14765: Implement Walsh Hadamard Transform and include doctests, unit-tests, docstring for the same.

  4. sympy/sympy#14783: Implement convolution_fwht and add support for keyword dyadic in the general convolution method, and include docstring, doctests, unit-tests.

  5. sympy/sympy#14816: Add a method linrec which allows evaluation of linear recurrences without obtaining closed form expressions, and include tests for the same.

  6. sympy/sympy#14853: Implement Möbius Transform using Yate's Dynamic Programming method while having subset keyword for flexibility of the implementation, and include docstring, doctests, unit-tests.

  7. sympy/sympy#14878: Implement subset convolution and include docstring, doctests, unit-tests.

  8. sympy/sympy#14928: Add covering product in convolutions sub-module and include docstring, doctests, unit-tests.

  9. sympy/sympy#14954: Add intersecting product in convolutions sub-module and include docstring, doctests, unit-tests.

Documentation and Code Refinements

  1. sympy/sympy#14969: Improve Sphinx docs for SymPy, use plural module names - convolutions and recurrences, refine the documentation for discrete module.

  2. sympy/sympy#14994: Add reStructuredText file for discrete module for inclusion in Sphinx docs, which can be referred here.

  3. sympy/sympy#15025: Refine discrete module to fix tests using floats instead of Rationals, adding warning about sequence size for fft and other improvements.

Additional Improvements

  1. sympy/sympy#14712: Add .rewrite(exp) capability for instances of Pow and fix bugs in solvers module.

  2. sympy/sympy#14907: Fix exception handling for factorial modulo and refine the signature for general convolution method.

  3. sympy/sympy-bot#18: Fix the issue of incorrect links being referred in wiki by explicitly specifying the links instead of using relative paths.

Future Work

  • Adding a user-facing public method that internally calls discrete.recurrences.linrec and possibly extending it for different types of recurrences as well.

  • Making methods fft and convolution_fft efficient for both symbolic and numeric variants, as some discussion and benchmarking has been done for it and there is some work done by Colin for implementing a ComplexFloat class in sympy/sympy#12192 which would be very helpful for the same.

Conclusion

This summer has been a great learning experience and has helped me get a good exposure of test-driven development. I plan to actively review the work that has went into this project and continue contributing to SymPy. I am grateful to my mentors, Kalevi and Aaron for reviewing my work, giving me valuable suggestions, and being readily available for discussions.

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