Changes between Version 1 and Version 2 of SoC2014

Timestamp:

Jan 12, 2014, 8:24:11 PM (9 years ago)

Author:

christopher_kormanyos

Comment:

--

SoC2014

@@ -22 +22 @@
 
 Projects from previous years can be found [wiki:SoCPrevious here]. There are still a number of interesting projects found in these pages.
+
+=== Boost.Math Generalized Hypergeometric Functions === 
+
+Boost.Math [http://www.boost.org/doc/libs/1_55_0/libs/math/doc/html/index.html]
+is a large well-established Boost library, but new mathematical functions can always be added.  
+
+Generalized hypergeometric functions are convergent power series
+that have rational coefficients.
+
+[http://en.wikipedia.org/wiki/Generalized_hypergeometric_function]
+
+Hypergeometric functions are remarkably versatile because many of
+the well-known functions and special functions of pure and applied
+mathematics are special cases of hypergeometric functions.
+These include various mathematical constants,
+elementary transcendental functions, Bessel functions,
+the incomplete gamma function, confluent hypergemetric functions,
+generalized Legendre functions, and (infinitely) many more.
+
+Even though the theory of hypergeometric functions is well-established,
+there are, nonetheless, very few programs or libraries that offer
+calculations of these fascinating and versatile functions.
+
+In this project, we will implement fast, accurate calculations of
+certain generalized hypergeometric functions and establish convergent
+parameter ranges for these. We will write them with generic templates,
+as is customary and suitable for Boost.Math.
+
+Our work will make use of many numerical methods for special functions,
+including expansions in Chebyshev polynomials, rational approximations,
+Pade approximations, Taylor series, asymptotic series, and others.
+
+The main goals of the project include:
+
+* Investigate calculation methods for hypergeometric_0f1, 1f0, 1f1, 1f2, 2f1.
+* Evaluate regions of parameter convergence for these.
+* Ensure that calculations are fast and accurate computation for all built-in types and multiple-precision types.
+* Optional: Add support generalized Legendre functions of type-I to Boost.Math.
+* Optional: Replace certain internal calculations within Boost.Math with hypergemetric functions.
+
+This project requires strong interest in and dedication to serious mathematical programming
+and knowledge of C++, especially using templates which Boost.Math makes much
+use of to support not only built-in float, double and long double but also multiple precision types.
+You will need to have experience of using Boost libraries, including Boost.Test, and
+a rudimentary or working knowledge of GIT will be useful.
+
+A preliminary investigation for this project can be found here:
+[https://github.com/boostorg/multiprecision/blob/develop/example/hypergeometric_luke_algorithms.cpp]
+In this file, we are investigating Chebyshev expansions for multiple-precision calculations
+of hypergeometric functions.
+
+If this code leaves you terrified, then this project is not for you.
+But if it only frightens you a little bit and piques your interest
+(and you have a passion for numerical programming), then this project
+is right for you.
+
+If you would like to demonstrate your skills, use the file in the
+link above such that hypergeometric_0f1 is used for multiple-precision
+calculations of cylindrical Bessel functions (i.e., cyl_bessel_j).
+Use Boost's cpp_dec_float_50 type, for example. Discuss the relation between
+hypergeometric_0f1 and cyl_bessel_j, investigate convergence properties,
+and take a peek at run-time characteristics.
+You can use any platform, Linux, Mac or Microsoft with your IDE of choice,
+perhaps Visual Studio, Eclipse, Code Blocks, or NetBeans.
+
+This project will by mentored by Christopher Kormanyos, and
+supported by Paul Bristow and John Maddock mathematical and algorithmic expertise,
+administration, Boost infrastructure.
+