GSoC 2019 Project Idea : Project in Numerical Methods

[shrivast...@gmail.com]

Certain modules in the SymPy code base like the Quadrature module pertain to Numerical methods. 

I would be vibrantly interested in extending such already existing modules or make new ones. 

If any mentor is interested in taking this forward and discussing on the extension/addition of modules relating to Numerical methods, I would love to discuss a plan of action and start working on my proposal.

Regards --
Avi Shrivastava

[Antoine Falaize]

+1

I currently develop the PyPHS package, that makes an intensive use of sympy to derive symbolically numerical methods for the simulation of a class of finite dimensional dynamical systems (namely, the port-Hamiltonian systems). Then, the actual simulation code is generated for a variety of langage (python, C++ and FAUST).

And I plan to go a step further by implementing spatial discretization to deal with infinite dimensional systems as well.

I would love to participate in any way to this project!

Best regards;

Antoine Falaize (afalaize)

[shrivast...@gmail.com]

Antoine, 

Yes I would love to work on this project with you. But we need to first see how much work can be done in this area (the mentioned project) and then we could divide the work too. Also, we could extend this to a bigger project and then start working on it. 

A mentor would be highly appreciated to guide us through this.

[Aaron Meurer]

Can you give an example of the sort of thing the code from this would look like?

Aaron Meurer

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[shrivast...@gmail.com]

Dear Aaron,

An extension of the quadrature module could include :-

1. for implementing the computation of multi - dimensional integrals :-

   

    a. Monte Carlo methods

    b. Sparse Grids

    c. Bayesian Quadrature

2. for implementing the computation of one - dimensional integrals :-

    a. Clenshaw Curtis Quadrature

    b. Gauss Kronrod Quadrature

    c. Tanh-Sinh Quadrature

    d. Romberg's method

These are a few of the methods that can be in included in the quadrature module (for computation of one - dimensional and multi - dimensional integrals) thereby making it a lot better.

Would love your (or any mentor's) insights in this, so that this can be taken progressively ahead.

Please do let me know about what you think of implementing these methods.

Regards --
Avi Shrivastava

[Aaron Meurer]

Purely numerical algorithms are out of scope for SymPy. See
https://github.com/sympy/sympy/wiki/GSoC-2019-Ideas#non-ideas.

However, the symbolic ideas mentioned by Antoine are interesting and
could be in scope for SymPy so long as they are not too domain
specific.

Aarn Meurer

> To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/29a6942b-b073-4b8e-ad2b-537acb17445c%40googlegroups.com.

[shrivast...@gmail.com]

I would love to go forward, together with Antoine to make this a viable project idea (the symbolic ideas mentioned by Antoine before like implementing spatial discretization to deal with infinite dimensional systems) and work on it (but not too domain specific, as Aaron pointed out), if he has no issues with it.

Aaron, would you (or any other mentor) be willing to guide us through this (making this into a well defined GSoC project idea and planning a line of action)?

Antoine, I would love to hear from you too, on how you want this idea to go ahead, and/or if you have any issues with us working on this together.

Regards --
Avi Shrivastava