<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>About the Math Toolkit</title> <link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.74.0"> <link rel="home" href="../../index.html" title="Math Toolkit"> <link rel="up" href="../main_overview.html" title="Overview"> <link rel="prev" href="../main_overview.html" title="Overview"> <link rel="next" href="navigation.html" title="Navigation"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> <td align="center"><a href="../../../../../../../index.html">Home</a></td> <td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> <td align="center"><a href="../../../../../../../more/index.htm">More</a></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="../main_overview.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="navigation.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> <div class="section" lang="en"> <div class="titlepage"><div><div><h3 class="title"> <a name="math_toolkit.main_overview.intro"></a><a class="link" href="intro.html" title="About the Math Toolkit"> About the Math Toolkit</a> </h3></div></div></div> <p> This library is divided into three interconnected parts: </p> <a name="math_toolkit.main_overview.intro.statistical_distributions"></a><h5> <a name="id905120"></a> <a class="link" href="intro.html#math_toolkit.main_overview.intro.statistical_distributions">Statistical Distributions</a> </h5> <p> Provides a reasonably comprehensive set of <a class="link" href="../dist.html" title="Statistical Distributions and Functions">statistical distributions</a>, upon which higher level statistical tests can be built. </p> <p> The initial focus is on the central <a href="http://en.wikipedia.org/wiki/Univariate" target="_top">univariate </a> <a href="http://mathworld.wolfram.com/StatisticalDistribution.html" target="_top">distributions</a>. Both <a href="http://mathworld.wolfram.com/ContinuousDistribution.html" target="_top">continuous</a> (like <a class="link" href="../dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">normal</a> & <a class="link" href="../dist/dist_ref/dists/f_dist.html" title="F Distribution">Fisher</a>) and <a href="http://mathworld.wolfram.com/DiscreteDistribution.html" target="_top">discrete</a> (like <a class="link" href="../dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">binomial</a> & <a class="link" href="../dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson</a>) distributions are provided. </p> <p> A <a class="link" href="../dist/stat_tut.html" title="Statistical Distributions Tutorial">comprehensive tutorial is provided</a>, along with a series of <a class="link" href="../dist/stat_tut/weg.html" title="Worked Examples">worked examples</a> illustrating how the library is used to conduct statistical tests. </p> <a name="math_toolkit.main_overview.intro.mathematical_special_functions"></a><h5> <a name="id905204"></a> <a class="link" href="intro.html#math_toolkit.main_overview.intro.mathematical_special_functions">Mathematical Special Functions</a> </h5> <p> Provides a small number of high quality <a class="link" href="../special.html" title="Special Functions">special functions</a>, initially these were concentrated on functions used in statistical applications along with those in the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Technical Report on C++ Library Extensions</a>. </p> <p> 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. </p> <p> 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 <a href="http://en.wikipedia.org/wiki/Significand" target="_top">significand (or mantissa)</a> sizes: typically <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code> or <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>. </p> <a name="math_toolkit.main_overview.intro.implementation_toolkit"></a><h5> <a name="id905271"></a> <a class="link" href="intro.html#math_toolkit.main_overview.intro.implementation_toolkit">Implementation Toolkit</a> </h5> <p> Provides <a class="link" href="../toolkit.html" title="Internal Details and Tools (Experimental)">many of the tools</a> 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. </p> <p> There are helpers for the <a class="link" href="../toolkit/internals1/series_evaluation.html" title="Series Evaluation">evaluation of infinite series</a>, <a class="link" href="../toolkit/internals1/cf.html" title="Continued Fraction Evaluation">continued fractions</a> and <a class="link" href="../toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">rational approximations</a>. </p> <p> There is a fairly comprehensive set of root finding and <a class="link" href="../toolkit/internals1/minima.html" title="Locating Function Minima">function minimisation algorithms</a>: the root finding algorithms are both <a class="link" href="../toolkit/internals1/roots.html" title="Root Finding With Derivatives">with</a> and <a class="link" href="../toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">without</a> derivative support. </p> <p> A <a class="link" href="../toolkit/internals2/minimax.html" title="Minimax Approximations and the Remez Algorithm">Remez algorithm implementation</a> allows for the locating of minimax rational approximations. </p> <p> There are also (experimental) classes for the <a class="link" href="../toolkit/internals2/polynomials.html" title="Polynomials">manipulation of polynomials</a>, for <a class="link" href="../toolkit/internals2/error_test.html" title="Relative Error and Testing">testing a special function against tabulated test data</a>, and for the <a class="link" href="../toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">rapid generation of test data</a> and/or data for output to an external graphing application. </p> </div> <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> </div></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="../main_overview.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="navigation.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html>