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1 | <html> |
| 2 | <head> | |
| 3 | <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> | |
| 4 | <title>About the Math Toolkit</title> | |
| 5 | <link rel="stylesheet" href="../math.css" type="text/css"> | |
| 6 | <meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> | |
| 7 | <link rel="home" href="../index.html" title="Math Toolkit 2.5.1"> | |
| 8 | <link rel="up" href="../overview.html" title="Chapter 1. Overview"> | |
| 9 | <link rel="prev" href="../overview.html" title="Chapter 1. Overview"> | |
| 10 | <link rel="next" href="navigation.html" title="Navigation"> | |
| 11 | </head> | |
| 12 | <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> | |
| 13 | <table cellpadding="2" width="100%"><tr> | |
| 14 | <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> | |
| 15 | <td align="center"><a href="../../../../../index.html">Home</a></td> | |
| 16 | <td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> | |
| 17 | <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> | |
| 18 | <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> | |
| 19 | <td align="center"><a href="../../../../../more/index.htm">More</a></td> | |
| 20 | </tr></table> | |
| 21 | <hr> | |
| 22 | <div class="spirit-nav"> | |
| 23 | <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> | |
| 24 | </div> | |
| 25 | <div class="section"> | |
| 26 | <div class="titlepage"><div><div><h2 class="title" style="clear: both"> | |
| 27 | <a name="math_toolkit.main_intro"></a><a class="link" href="main_intro.html" title="About the Math Toolkit">About the Math Toolkit</a> | |
| 28 | </h2></div></div></div> | |
| 29 | <p> | |
| 30 | This library is divided into three interconnected parts: | |
| 31 | </p> | |
| 32 | <h5> | |
| 33 | <a name="math_toolkit.main_intro.h0"></a> | |
| 34 | <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 | |
| 35 | Distributions</a> | |
| 36 | </h5> | |
| 37 | <p> | |
| 38 | Provides a reasonably comprehensive set of <a class="link" href="../dist.html" title="Chapter 5. Statistical Distributions and Functions">statistical | |
| 39 | distributions</a>, upon which higher level statistical tests can be built. | |
| 40 | </p> | |
| 41 | <p> | |
| 42 | The initial focus is on the central <a href="http://en.wikipedia.org/wiki/Univariate" target="_top">univariate | |
| 43 | </a> <a href="http://mathworld.wolfram.com/StatisticalDistribution.html" target="_top">distributions</a>. | |
| 44 | Both <a href="http://mathworld.wolfram.com/ContinuousDistribution.html" target="_top">continuous</a> | |
| 45 | (like <a class="link" href="dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">normal</a> | |
| 46 | & <a class="link" href="dist_ref/dists/f_dist.html" title="F Distribution">Fisher</a>) and | |
| 47 | <a href="http://mathworld.wolfram.com/DiscreteDistribution.html" target="_top">discrete</a> | |
| 48 | (like <a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">binomial</a> | |
| 49 | & <a class="link" href="dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson</a>) | |
| 50 | distributions are provided. | |
| 51 | </p> | |
| 52 | <p> | |
| 53 | A <a class="link" href="stat_tut.html" title="Statistical Distributions Tutorial">comprehensive tutorial is provided</a>, | |
| 54 | along with a series of <a class="link" href="stat_tut/weg.html" title="Worked Examples">worked examples</a> | |
| 55 | illustrating how the library is used to conduct statistical tests. | |
| 56 | </p> | |
| 57 | <h5> | |
| 58 | <a name="math_toolkit.main_intro.h1"></a> | |
| 59 | <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 | |
| 60 | Special Functions</a> | |
| 61 | </h5> | |
| 62 | <p> | |
| 63 | Provides a small number of high quality <a class="link" href="../special.html" title="Chapter 6. Special Functions">special functions</a>, | |
| 64 | initially these were concentrated on functions used in statistical applications | |
| 65 | along with those in the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Technical | |
| 66 | Report on C++ Library Extensions</a>. | |
| 67 | </p> | |
| 68 | <p> | |
| 69 | The function families currently implemented are the gamma, beta & erf functions | |
| 70 | along with the incomplete gamma and beta functions (four variants of each) | |
| 71 | and all the possible inverses of these, plus digamma, various factorial functions, | |
| 72 | Bessel functions, elliptic integrals, sinus cardinals (along with their hyperbolic | |
| 73 | variants), inverse hyperbolic functions, Legrendre/Laguerre/Hermite polynomials | |
| 74 | and various special power and logarithmic functions. | |
| 75 | </p> | |
| 76 | <p> | |
| 77 | All the implementations are fully generic and support the use of arbitrary | |
| 78 | "real-number" types, including <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>, | |
| 79 | although they are optimised for use with types with known-about <a href="http://en.wikipedia.org/wiki/Significand" target="_top">significand | |
| 80 | (or mantissa)</a> sizes: typically <code class="computeroutput"><span class="keyword">float</span></code>, | |
| 81 | <code class="computeroutput"><span class="keyword">double</span></code> or <code class="computeroutput"><span class="keyword">long</span> | |
| 82 | <span class="keyword">double</span></code>. | |
| 83 | </p> | |
| 84 | <h5> | |
| 85 | <a name="math_toolkit.main_intro.h2"></a> | |
| 86 | <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 | |
| 87 | Toolkit</a> | |
| 88 | </h5> | |
| 89 | <p> | |
| 90 | The section <a class="link" href="internals_overview.html" title="Overview">Internal tools</a> | |
| 91 | provides many of the tools required to implement mathematical special functions: | |
| 92 | hopefully the presence of these will encourage other authors to contribute | |
| 93 | more special function implementations in the future. | |
| 94 | </p> | |
| 95 | <p> | |
| 96 | Some tools are now considered well-tried and their signatures stable and unlikely | |
| 97 | to change. | |
| 98 | </p> | |
| 99 | <p> | |
| 100 | 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 | |
| 101 | without derivatives</a> and <a class="link" href="roots/roots_deriv.html" title="Root Finding With Derivatives: Newton-Raphson, Halley & Schröder">root-finding | |
| 102 | with derivatives</a> with derivative support, and function minimization | |
| 103 | using <a class="link" href="roots/brent_minima.html" title="Locating Function Minima using Brent's algorithm">Brent's method</a>. | |
| 104 | </p> | |
| 105 | <p> | |
| 106 | Other <a class="link" href="internals_overview.html" title="Overview">Internal tools</a> | |
| 107 | are currently still considered experimental: they are "exposed implementation | |
| 108 | details" whose interfaces and/or implementations may change without notice. | |
| 109 | </p> | |
| 110 | <p> | |
| 111 | There are helpers for the <a class="link" href="internals/series_evaluation.html" title="Series Evaluation">evaluation | |
| 112 | of infinite series</a>, <a class="link" href="internals/cf.html" title="Continued Fraction Evaluation">continued | |
| 113 | fractions</a> and <a class="link" href="roots/rational.html" title="Polynomial and Rational Function Evaluation">rational approximations</a>. | |
| 114 | A <a class="link" href="internals/minimax.html" title="Minimax Approximations and the Remez Algorithm">Remez algorithm implementation</a> | |
| 115 | allows for the locating of minimax rational approximations. | |
| 116 | </p> | |
| 117 | <p> | |
| 118 | There are also (experimental) classes for the <a class="link" href="roots/polynomials.html" title="Polynomials">manipulation | |
| 119 | of polynomials</a>, for <a class="link" href="internals/error_test.html" title="Relative Error and Testing">testing | |
| 120 | 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 | |
| 121 | generation of test data</a> and/or data for output to an external graphing | |
| 122 | application. | |
| 123 | </p> | |
| 124 | </div> | |
| 125 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
| 126 | <td align="left"></td> | |
| 127 | <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, | |
| 128 | Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert | |
| 129 | Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, | |
| 130 | Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> | |
| 131 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
| 132 | 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>) | |
| 133 | </p> | |
| 134 | </div></td> | |
| 135 | </tr></table> | |
| 136 | <hr> | |
| 137 | <div class="spirit-nav"> | |
| 138 | <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> | |
| 139 | </div> | |
| 140 | </body> | |
| 141 | </html> |