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_element method. 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.pyshould 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.
