Awesome! Ping me if you need someone to help with code review. -- Benjamin Jones benjaminfjo...@gmail.com
On Tue, May 28, 2013 at 11:48 AM, Eviatar <eviatarb...@gmail.com> wrote: > Hello, > > I am grateful to have been selected as one of the Google Summer of Code > students for this summer. I will be working on a benchmark framework for > testing functions over different domains, making symbolic the special > functions that are not yet, and implementing generalized hypergeometric > functions. Here are some more details from my application: > > 1. Symbolic wrappers >> A pending patch, ticket >> #4102<http://trac.sagemath.org/sage_trac/ticket/4102>, >> will make the Bessel functions symbolic. I will similarly update the rest >> of the special functions. This will involve defining methods for evaluation >> and wrapping third-party libraries for handling simplification, >> integration, etc. >> > > > From the open-source software listed at the > DLMF<http://dlmf.nist.gov/software/>, >> Sage ships with Cephes (although it is not used for anything at the >> moment), GSL, MPFR, Maxima, PARI/GP, SLATEC (through Maxima), and mpmath. >> All these except Cephes and SLATEC have existing interfaces, facilitating >> the wrapping of functionality. >> The Bessel functions will be made symbolic by #4102, and the Airy >> functions by the pending >> #12455<http://trac.sagemath.org/sage_trac/ticket/12455>. >> hypergeometric_U, spherical_bessel_J, spherical_bessel_Y, >> spherical_hankel1, spherical_hankel2, spherical_harmonic, elliptic_J, >> jacobi, inverse_jacobi, elliptic_e, elliptic_ec, elliptic_eu, elliptic_f, >> elliptic_kc, and elliptic_pi remain to be done. >> > > > 2. Benchmark framework >> The benchmark framework is important for determining which backend is >> appropriate for numeric evaluation of functions on different domains. Due >> to implementation details, different algorithms will be suited to different >> regions of the function's domain; for example, hypergeometric_U(-4, 10, >> 100) is faster with PARI, but hypergeometric_U(-40, -40, 10) is faster >> with SciPy. Picking the domains will require looking at the algorithm >> implementation. A benchmark framework will allow Sage to more intelligently >> decide between the backends depending on input, and also to detect and >> track regressions. A sufficiently versatile implementation could also be >> extended to other types of functions in the future. >> > > > I would begin by building on the benchmark system in tests/benchmark.py. >> I would create a subclass of Benchmark designed for numerical functions; >> it would accept arguments of domains on which to test functions, and >> generate random test values using the underlying rings' >> random_elementmethod. For example, benchmark_function(gamma, >> domains=[[1, 10], [50, 60]], ring=ZZ, systems=['maxima', 'sympy']) would >> benchmark the gamma function on the integer domains [1, 10] and [50,60] >> using Maxima and SymPy (this is only an example to illustrate the proposed >> functionality; gamma does not currently have the option to be evaluated >> with different backends). benchmark_function(gamma, domains=[[-10 - >> 10*I, 10 - 5*I]], ring=CC) would benchmark gamma on the region of the >> complex plane bounded by the two points -10 - 10i and 10 - 5i. The current >> output format of the Benchmark class in benchmark.py should be changed >> to be machine-readable. >> > > > After the benchmark framework is completed, I would determine appropriate >> domains on which to test each of the special functions, and create a >> benchmark suite. Using the results of these benchmarks, I will modify the >> functions that have multiple backends to use the optimal one for a given >> domain > > > > 3. Hypergeometric functions >> #2516 <http://trac.sagemath.org/sage_trac/ticket/2516> is going to >> implement generalized hypergeometric functions. These are a class of >> holonomic functions, solutions to linear differential equations with >> polynomial coefficients. Holonomic power series are closed under sum, >> Cauchy product, and Hadamard product, so these operations could be >> implemented. Useful references include >> 1<http://www.risc.jku.at/research/combinat/software/GeneratingFunctions/pub/mallinger96.pdf> >> and >> 2<http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.187.6502&rep=rep1&type=pdf> >> . > > > My mentors for this project are Flavia Stan and Burcin Erocal. > > Now is the Community Bonding period; since I am already acquainted with > Sage and the community I can get to work :) I will be at Sage Days 48 in > Seattle. > > If anyone has any comments, suggestions, or additional ideas please let me > know. > > Thank you, > Eviatar Bach > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel?hl=en. > For more options, visit https://groups.google.com/groups/opt_out. > > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. 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