| [section:intro About the Math Toolkit] |
| |
| This library is divided into three interconnected parts: |
| |
| [h4 Statistical Distributions] |
| |
| Provides a reasonably comprehensive set of |
| [link math_toolkit.dist statistical distributions], |
| upon which higher level statistical tests can be built. |
| |
| The initial focus is on the central |
| [@http://en.wikipedia.org/wiki/Univariate univariate ] |
| [@http://mathworld.wolfram.com/StatisticalDistribution.html distributions]. |
| Both [@http://mathworld.wolfram.com/ContinuousDistribution.html continuous] |
| (like [link math_toolkit.dist.dist_ref.dists.normal_dist normal] |
| & [link math_toolkit.dist.dist_ref.dists.f_dist Fisher]) |
| and [@http://mathworld.wolfram.com/DiscreteDistribution.html discrete] |
| (like [link math_toolkit.dist.dist_ref.dists.binomial_dist binomial] |
| & [link math_toolkit.dist.dist_ref.dists.poisson_dist Poisson]) |
| distributions are provided. |
| |
| A [link math_toolkit.dist.stat_tut comprehensive tutorial is provided], |
| along with a series of |
| [link math_toolkit.dist.stat_tut.weg worked examples] illustrating |
| how the library is used to conduct statistical tests. |
| |
| [h4 Mathematical Special Functions] |
| |
| Provides a small number of high quality |
| [link math_toolkit.special special functions], |
| initially these were concentrated on functions used in statistical applications |
| along with those in the [tr1]. |
| |
| The function families currently implemented are the gamma, beta & erf functions |
| along with the incomplete gamma and beta functions (four variants |
| of each) and all the possible inverses of these, plus digamma, |
| various factorial functions, |
| Bessel functions, elliptic integrals, sinus cardinals (along with their |
| hyperbolic variants), inverse hyperbolic functions, Legrendre/Laguerre/Hermite |
| polynomials and various |
| special power and logarithmic functions. |
| |
| All the implementations |
| are fully generic and support the use of arbitrary "real-number" types, |
| although they are optimised for use with types with known-about |
| [@http://en.wikipedia.org/wiki/Significand significand (or mantissa)] |
| sizes: typically `float`, `double` or `long double`. |
| |
| [h4 Implementation Toolkit] |
| |
| Provides [link math_toolkit.toolkit many of the tools] required to implement |
| mathematical special functions: hopefully the presence of |
| these will encourage other authors to contribute more special |
| function implementations in the future. These tools are currently |
| considered experimental: they are "exposed implementation details" |
| whose interfaces and\/or implementations may change. |
| |
| There are helpers for the |
| [link math_toolkit.toolkit.internals1.series_evaluation |
| evaluation of infinite series], |
| [link math_toolkit.toolkit.internals1.cf continued |
| fractions] and [link math_toolkit.toolkit.internals1.rational |
| rational approximations]. |
| |
| There is a fairly comprehensive set of root finding and |
| [link math_toolkit.toolkit.internals1.minima function minimisation |
| algorithms]: the root finding algorithms are both |
| [link math_toolkit.toolkit.internals1.roots with] and |
| [link math_toolkit.toolkit.internals1.roots2 without] derivative support. |
| |
| A [link math_toolkit.toolkit.internals2.minimax |
| Remez algorithm implementation] allows for the locating of minimax rational |
| approximations. |
| |
| There are also (experimental) classes for the |
| [link math_toolkit.toolkit.internals2.polynomials manipulation of polynomials], for |
| [link math_toolkit.toolkit.internals2.error_test |
| testing a special function against tabulated test data], and for |
| the [link math_toolkit.toolkit.internals2.test_data |
| rapid generation of test data] and/or data for output to an |
| external graphing application. |
| |
| [endsect] [/section:intro Introduction] |
| |
| [/ |
| Copyright 2006 John Maddock and Paul A. Bristow. |
| Distributed under the Boost Software License, Version 1.0. |
| (See accompanying file LICENSE_1_0.txt or copy at |
| http://www.boost.org/LICENSE_1_0.txt). |
| ] |