libs/math/doc/html/math_toolkit/main_intro.html

   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 V1.79.1">
   7 <link rel="home" href="../index.html" title="Math Toolkit 2.11.0">
   8 <link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
   9 <link rel="prev" href="../overview.html" title="Chapter&#160;1.&#160;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 several 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.floating_point_utilities"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.floating_point_utilities">Floating
  35       Point Utilities</a>
  36     </h5>
  37 <p>
  38       Utility functions for dealing with floating-point arithmetic, includes functions
  39       for floating point classification (<code class="computeroutput"><span class="identifier">fpclassify</span></code>,
  40       <code class="computeroutput"><span class="identifier">isnan</span></code>, <code class="computeroutput"><span class="identifier">isinf</span></code>
  41       etc), sign manipulation, rounding, comparison, and computing the distance between
  42       floating point numbers.
  43     </p>
  44 <h5>
  45 <a name="math_toolkit.main_intro.h1"></a>
  46       <span class="phrase"><a name="math_toolkit.main_intro.specific_width_floating_point_ty"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.specific_width_floating_point_ty">Specific
  47       Width Floating-Point Types</a>
  48     </h5>
  49 <p>
  50       A set of <code class="computeroutput"><span class="keyword">typedef</span></code>s similar to those
  51       provided by <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">cstdint</span><span class="special">&gt;</span></code> but for floating-point types.
  52     </p>
  53 <h5>
  54 <a name="math_toolkit.main_intro.h2"></a>
  55       <span class="phrase"><a name="math_toolkit.main_intro.mathematical_constants"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.mathematical_constants">Mathematical
  56       Constants</a>
  57     </h5>
  58 <p>
  59       A wide range of high-precision constants ranging from various multiples of
  60       &#960;, fractions, through to Euler's constant etc.
  61     </p>
  62 <p>
  63       These are of course usable from template code, or as non-templates with a simplified
  64       interface if that is more appropriate.
  65     </p>
  66 <h5>
  67 <a name="math_toolkit.main_intro.h3"></a>
  68       <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
  69       Distributions</a>
  70     </h5>
  71 <p>
  72       Provides a reasonably comprehensive set of <a class="link" href="../dist.html" title="Chapter&#160;5.&#160;Statistical Distributions and Functions">statistical
  73       distributions</a>, upon which higher level statistical tests can be built.
  74     </p>
  75 <p>
  76       The initial focus is on the central <a href="http://en.wikipedia.org/wiki/Univariate" target="_top">univariate
  77       </a> <a href="http://mathworld.wolfram.com/StatisticalDistribution.html" target="_top">distributions</a>.
  78       Both <a href="http://mathworld.wolfram.com/ContinuousDistribution.html" target="_top">continuous</a>
  79       (like <a class="link" href="dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">normal</a>
  80       &amp; <a class="link" href="dist_ref/dists/f_dist.html" title="F Distribution">Fisher</a>) and
  81       <a href="http://mathworld.wolfram.com/DiscreteDistribution.html" target="_top">discrete</a>
  82       (like <a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">binomial</a>
  83       &amp; <a class="link" href="dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson</a>)
  84       distributions are provided.
  85     </p>
  86 <p>
  87       A <a class="link" href="stat_tut.html" title="Statistical Distributions Tutorial">comprehensive tutorial is provided</a>,
  88       along with a series of <a class="link" href="stat_tut/weg.html" title="Worked Examples">worked examples</a>
  89       illustrating how the library is used to conduct statistical tests.
  90     </p>
  91 <h5>
  92 <a name="math_toolkit.main_intro.h4"></a>
  93       <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
  94       Special Functions</a>
  95     </h5>
  96 <p>
  97       Provides a small number of high quality <a class="link" href="../special.html" title="Chapter&#160;8.&#160;Special Functions">special functions</a>,
  98       initially these were concentrated on functions used in statistical applications
  99       along with those in the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Technical
 100       Report on C++ Library Extensions</a>.
 101     </p>
 102 <p>
 103       The function families currently implemented are the gamma, beta &amp; erf functions
 104       along with the incomplete gamma and beta functions (four variants of each)
 105       and all the possible inverses of these, plus digamma, various factorial functions,
 106       Bessel functions, elliptic integrals, sinus cardinals (along with their hyperbolic
 107       variants), inverse hyperbolic functions, Legrendre/Laguerre/Hermite polynomials
 108       and various special power and logarithmic functions.
 109     </p>
 110 <p>
 111       All the implementations are fully generic and support the use of arbitrary
 112       "real-number" types, including <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>,
 113       although they are optimised for use with types with known-about <a href="http://en.wikipedia.org/wiki/Significand" target="_top">significand
 114       (or mantissa)</a> sizes: typically <code class="computeroutput"><span class="keyword">float</span></code>,
 115       <code class="computeroutput"><span class="keyword">double</span></code> or <code class="computeroutput"><span class="keyword">long</span>
 116       <span class="keyword">double</span></code>.
 117     </p>
 118 <p>
 119       These functions also provide the basis of support for the TR1 special functions.
 120     </p>
 121 <h5>
 122 <a name="math_toolkit.main_intro.h5"></a>
 123       <span class="phrase"><a name="math_toolkit.main_intro.root_finding_and_function_minimi"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.root_finding_and_function_minimi">Root Finding
 124       and Function Minimisation</a>
 125     </h5>
 126 <p>
 127       A comprehensive set of root finding algorithms over the real-line, both with
 128       and without derivative support.
 129     </p>
 130 <p>
 131       Also function minimisation via Brent's Method.
 132     </p>
 133 <h5>
 134 <a name="math_toolkit.main_intro.h6"></a>
 135       <span class="phrase"><a name="math_toolkit.main_intro.polynomials_and_rational_functio"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.polynomials_and_rational_functio">Polynomials
 136       and Rational Functions</a>
 137     </h5>
 138 <p>
 139       Tools for manipulating polynomials and for efficient evaluation of rationals
 140       or polynomials.
 141     </p>
 142 <h5>
 143 <a name="math_toolkit.main_intro.h7"></a>
 144       <span class="phrase"><a name="math_toolkit.main_intro.interpolation"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.interpolation">Interpolation</a>
 145     </h5>
 146 <p>
 147       Function interpolation via Barycentric or cubic B_spline approximations. Smoothing.
 148     </p>
 149 <h5>
 150 <a name="math_toolkit.main_intro.h8"></a>
 151       <span class="phrase"><a name="math_toolkit.main_intro.numerical_integration_quadrature"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.numerical_integration_quadrature">Numerical
 152       Integration (Quadrature) and Differentiation</a>
 153     </h5>
 154 <p>
 155       A reasonably comprehensive set of routines for integration (trapezoidal, Gauss-Legendre,
 156       Gauss-Kronrod and double-exponential) and differentiation. (See also automatic
 157       differentiation).
 158     </p>
 159 <p>
 160       The integration routines are all usable for functions returning complex results
 161       - and as a result for contour integrals as well.
 162     </p>
 163 <h5>
 164 <a name="math_toolkit.main_intro.h9"></a>
 165       <span class="phrase"><a name="math_toolkit.main_intro.quaternions_and_octonions"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.quaternions_and_octonions">Quaternions
 166       and Octonions</a>
 167     </h5>
 168 <p>
 169       Quaternions and Octonians as class templates similar to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span></code>.
 170     </p>
 171 <h5>
 172 <a name="math_toolkit.main_intro.h10"></a>
 173       <span class="phrase"><a name="math_toolkit.main_intro.automatic_differentiation"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.automatic_differentiation">Automatic
 174       Differentiation</a>
 175     </h5>
 176 <p>
 177       Autodiff is a header-only C++ library that facilitates the automaticdifferentiation
 178       (forward mode) of mathematical functions of single and multiple variables.
 179     </p>
 180 </div>
 181 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 182 <td align="left"></td>
 183 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
 184       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
 185       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
 186       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
 187       Daryle Walker and Xiaogang Zhang<p>
 188         Distributed under the Boost Software License, Version 1.0. (See accompanying
 189         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>)
 190       </p>
 191 </div></td>
 192 </tr></table>
 193 <hr>
 194 <div class="spirit-nav">
 195 <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>
 196 </div>
 197 </body>
 198 </html>