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199 lines
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<html>
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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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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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<link rel="home" href="../index.html" title="Math Toolkit 2.11.0">
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<link rel="up" href="../overview.html" title="Chapter 1. Overview">
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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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<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 several 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.floating_point_utilities"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.floating_point_utilities">Floating
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Point Utilities</a>
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</h5>
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<p>
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Utility functions for dealing with floating-point arithmetic, includes functions
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for floating point classification (<code class="computeroutput"><span class="identifier">fpclassify</span></code>,
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<code class="computeroutput"><span class="identifier">isnan</span></code>, <code class="computeroutput"><span class="identifier">isinf</span></code>
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etc), sign manipulation, rounding, comparison, and computing the distance between
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floating point numbers.
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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.specific_width_floating_point_ty"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.specific_width_floating_point_ty">Specific
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Width Floating-Point Types</a>
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</h5>
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<p>
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A set of <code class="computeroutput"><span class="keyword">typedef</span></code>s similar to those
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provided by <code class="computeroutput"><span class="special"><</span><span class="identifier">cstdint</span><span class="special">></span></code> but for floating-point types.
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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.mathematical_constants"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.mathematical_constants">Mathematical
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Constants</a>
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</h5>
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<p>
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A wide range of high-precision constants ranging from various multiples of
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π, fractions, through to Euler's constant etc.
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</p>
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<p>
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These are of course usable from template code, or as non-templates with a simplified
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interface if that is more appropriate.
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</p>
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<h5>
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<a name="math_toolkit.main_intro.h3"></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.h4"></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 8. 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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<p>
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These functions also provide the basis of support for the TR1 special functions.
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</p>
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<h5>
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<a name="math_toolkit.main_intro.h5"></a>
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<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
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and Function Minimisation</a>
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</h5>
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<p>
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A comprehensive set of root finding algorithms over the real-line, both with
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and without derivative support.
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</p>
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<p>
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Also function minimisation via Brent's Method.
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</p>
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<h5>
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<a name="math_toolkit.main_intro.h6"></a>
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<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
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and Rational Functions</a>
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</h5>
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<p>
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Tools for manipulating polynomials and for efficient evaluation of rationals
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or polynomials.
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</p>
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<h5>
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<a name="math_toolkit.main_intro.h7"></a>
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<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>
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</h5>
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<p>
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Function interpolation via Barycentric or cubic B_spline approximations. Smoothing.
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</p>
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<h5>
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<a name="math_toolkit.main_intro.h8"></a>
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<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
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Integration (Quadrature) and Differentiation</a>
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</h5>
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<p>
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A reasonably comprehensive set of routines for integration (trapezoidal, Gauss-Legendre,
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Gauss-Kronrod and double-exponential) and differentiation. (See also automatic
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differentiation).
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</p>
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<p>
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The integration routines are all usable for functions returning complex results
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- and as a result for contour integrals as well.
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</p>
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<h5>
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<a name="math_toolkit.main_intro.h9"></a>
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<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
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and Octonions</a>
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</h5>
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<p>
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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>.
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</p>
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<h5>
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<a name="math_toolkit.main_intro.h10"></a>
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<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
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Differentiation</a>
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</h5>
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<p>
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Autodiff is a header-only C++ library that facilitates the automaticdifferentiation
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(forward mode) of mathematical functions of single and multiple variables.
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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 © 2006-2019 Nikhar
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Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
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Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
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Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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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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