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142 lines
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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<title>About the Math Toolkit</title>
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<link rel="stylesheet" href="../math.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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<link rel="home" href="../index.html" title="Math Toolkit 2.5.1">
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<link rel="up" href="../overview.html" title="Chapter 1. Overview">
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<link rel="prev" href="../overview.html" title="Chapter 1. Overview">
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<link rel="next" href="navigation.html" title="Navigation">
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</head>
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
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<td align="center"><a href="../../../../../index.html">Home</a></td>
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<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
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<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
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<td align="center"><a href="../../../../../more/index.htm">More</a></td>
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</tr></table>
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<hr>
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<div class="spirit-nav">
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<a accesskey="p" href="../overview.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../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>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="math_toolkit.main_intro"></a><a class="link" href="main_intro.html" title="About the Math Toolkit">About the Math Toolkit</a>
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</h2></div></div></div>
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<p>
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This library is divided into three interconnected parts:
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</p>
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<h5>
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<a name="math_toolkit.main_intro.h0"></a>
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<span class="phrase"><a name="math_toolkit.main_intro.statistical_distributions"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.statistical_distributions">Statistical
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Distributions</a>
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</h5>
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<p>
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Provides a reasonably comprehensive set of <a class="link" href="../dist.html" title="Chapter 5. Statistical Distributions and Functions">statistical
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distributions</a>, upon which higher level statistical tests can be built.
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</p>
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<p>
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The initial focus is on the central <a href="http://en.wikipedia.org/wiki/Univariate" target="_top">univariate
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</a> <a href="http://mathworld.wolfram.com/StatisticalDistribution.html" target="_top">distributions</a>.
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Both <a href="http://mathworld.wolfram.com/ContinuousDistribution.html" target="_top">continuous</a>
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(like <a class="link" href="dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">normal</a>
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& <a class="link" href="dist_ref/dists/f_dist.html" title="F Distribution">Fisher</a>) and
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<a href="http://mathworld.wolfram.com/DiscreteDistribution.html" target="_top">discrete</a>
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(like <a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">binomial</a>
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& <a class="link" href="dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson</a>)
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distributions are provided.
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</p>
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<p>
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A <a class="link" href="stat_tut.html" title="Statistical Distributions Tutorial">comprehensive tutorial is provided</a>,
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along with a series of <a class="link" href="stat_tut/weg.html" title="Worked Examples">worked examples</a>
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illustrating how the library is used to conduct statistical tests.
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</p>
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<h5>
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<a name="math_toolkit.main_intro.h1"></a>
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<span class="phrase"><a name="math_toolkit.main_intro.mathematical_special_functions"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.mathematical_special_functions">Mathematical
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Special Functions</a>
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</h5>
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<p>
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Provides a small number of high quality <a class="link" href="../special.html" title="Chapter 6. Special Functions">special functions</a>,
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initially these were concentrated on functions used in statistical applications
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along with those in the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Technical
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Report on C++ Library Extensions</a>.
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</p>
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<p>
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The function families currently implemented are the gamma, beta & erf functions
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along with the incomplete gamma and beta functions (four variants of each)
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and all the possible inverses of these, plus digamma, various factorial functions,
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Bessel functions, elliptic integrals, sinus cardinals (along with their hyperbolic
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variants), inverse hyperbolic functions, Legrendre/Laguerre/Hermite polynomials
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and various special power and logarithmic functions.
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</p>
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<p>
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All the implementations are fully generic and support the use of arbitrary
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"real-number" types, including <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>,
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although they are optimised for use with types with known-about <a href="http://en.wikipedia.org/wiki/Significand" target="_top">significand
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(or mantissa)</a> sizes: typically <code class="computeroutput"><span class="keyword">float</span></code>,
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<code class="computeroutput"><span class="keyword">double</span></code> or <code class="computeroutput"><span class="keyword">long</span>
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<span class="keyword">double</span></code>.
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</p>
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<h5>
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<a name="math_toolkit.main_intro.h2"></a>
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<span class="phrase"><a name="math_toolkit.main_intro.implementation_toolkit"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.implementation_toolkit">Implementation
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Toolkit</a>
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</h5>
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<p>
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The section <a class="link" href="internals_overview.html" title="Overview">Internal tools</a>
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provides many of the tools required to implement mathematical special functions:
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hopefully the presence of these will encourage other authors to contribute
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more special function implementations in the future.
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</p>
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<p>
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Some tools are now considered well-tried and their signatures stable and unlikely
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to change.
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</p>
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<p>
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There is a fairly comprehensive set of root finding both <a class="link" href="roots/roots_noderiv.html" title="Root Finding Without Derivatives">root-finding
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without derivatives</a> and <a class="link" href="roots/roots_deriv.html" title="Root Finding With Derivatives: Newton-Raphson, Halley & Schröder">root-finding
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with derivatives</a> with derivative support, and function minimization
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using <a class="link" href="roots/brent_minima.html" title="Locating Function Minima using Brent's algorithm">Brent's method</a>.
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</p>
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<p>
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Other <a class="link" href="internals_overview.html" title="Overview">Internal tools</a>
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are currently still considered experimental: they are "exposed implementation
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details" whose interfaces and/or implementations may change without notice.
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</p>
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<p>
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There are helpers for the <a class="link" href="internals/series_evaluation.html" title="Series Evaluation">evaluation
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of infinite series</a>, <a class="link" href="internals/cf.html" title="Continued Fraction Evaluation">continued
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fractions</a> and <a class="link" href="roots/rational.html" title="Polynomial and Rational Function Evaluation">rational approximations</a>.
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A <a class="link" href="internals/minimax.html" title="Minimax Approximations and the Remez Algorithm">Remez algorithm implementation</a>
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allows for the locating of minimax rational approximations.
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</p>
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<p>
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There are also (experimental) classes for the <a class="link" href="roots/polynomials.html" title="Polynomials">manipulation
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of polynomials</a>, for <a class="link" href="internals/error_test.html" title="Relative Error and Testing">testing
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a special function against tabulated test data</a>, and for the <a class="link" href="internals/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">rapid
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generation of test data</a> and/or data for output to an external graphing
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application.
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</p>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
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Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
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Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
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Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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>)
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</p>
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</div></td>
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</tr></table>
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<hr>
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<div class="spirit-nav">
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<a accesskey="p" href="../overview.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../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>
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</div>
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</body>
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</html>
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