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- <title>About the Math Toolkit</title>
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- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="math_toolkit.main_intro"></a><a class="link" href="main_intro.html" title="About the Math Toolkit">About the Math Toolkit</a>
- </h2></div></div></div>
- <p>
- This library is divided into several interconnected parts:
- </p>
- <h5>
- <a name="math_toolkit.main_intro.h0"></a>
- <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
- Point Utilities</a>
- </h5>
- <p>
- Utility functions for dealing with floating-point arithmetic, includes functions
- for floating point classification (<code class="computeroutput"><span class="identifier">fpclassify</span></code>,
- <code class="computeroutput"><span class="identifier">isnan</span></code>, <code class="computeroutput"><span class="identifier">isinf</span></code>
- etc), sign manipulation, rounding, comparison, and computing the distance between
- floating point numbers.
- </p>
- <h5>
- <a name="math_toolkit.main_intro.h1"></a>
- <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
- Width Floating-Point Types</a>
- </h5>
- <p>
- A set of <code class="computeroutput"><span class="keyword">typedef</span></code>s similar to those
- provided by <code class="computeroutput"><span class="special"><</span><span class="identifier">cstdint</span><span class="special">></span></code> but for floating-point types.
- </p>
- <h5>
- <a name="math_toolkit.main_intro.h2"></a>
- <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
- Constants</a>
- </h5>
- <p>
- A wide range of high-precision constants ranging from various multiples of
- π, fractions, through to Euler's constant etc.
- </p>
- <p>
- These are of course usable from template code, or as non-templates with a simplified
- interface if that is more appropriate.
- </p>
- <h5>
- <a name="math_toolkit.main_intro.h3"></a>
- <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
- Distributions</a>
- </h5>
- <p>
- Provides a reasonably comprehensive set of <a class="link" href="../dist.html" title="Chapter 5. 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_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">normal</a>
- & <a class="link" href="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_ref/dists/binomial_dist.html" title="Binomial Distribution">binomial</a>
- & <a class="link" href="dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson</a>)
- distributions are provided.
- </p>
- <p>
- A <a class="link" href="stat_tut.html" title="Statistical Distributions Tutorial">comprehensive tutorial is provided</a>,
- along with a series of <a class="link" href="stat_tut/weg.html" title="Worked Examples">worked examples</a>
- illustrating how the library is used to conduct statistical tests.
- </p>
- <h5>
- <a name="math_toolkit.main_intro.h4"></a>
- <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
- Special Functions</a>
- </h5>
- <p>
- Provides a small number of high quality <a class="link" href="../special.html" title="Chapter 8. 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, including <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>,
- 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>
- <p>
- These functions also provide the basis of support for the TR1 special functions.
- </p>
- <h5>
- <a name="math_toolkit.main_intro.h5"></a>
- <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
- and Function Minimisation</a>
- </h5>
- <p>
- A comprehensive set of root finding algorithms over the real-line, both with
- and without derivative support.
- </p>
- <p>
- Also function minimisation via Brent's Method.
- </p>
- <h5>
- <a name="math_toolkit.main_intro.h6"></a>
- <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
- and Rational Functions</a>
- </h5>
- <p>
- Tools for manipulating polynomials and for efficient evaluation of rationals
- or polynomials.
- </p>
- <h5>
- <a name="math_toolkit.main_intro.h7"></a>
- <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>
- </h5>
- <p>
- Function interpolation via Barycentric or cubic B_spline approximations. Smoothing.
- </p>
- <h5>
- <a name="math_toolkit.main_intro.h8"></a>
- <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
- Integration (Quadrature) and Differentiation</a>
- </h5>
- <p>
- A reasonably comprehensive set of routines for integration (trapezoidal, Gauss-Legendre,
- Gauss-Kronrod and double-exponential) and differentiation. (See also automatic
- differentiation).
- </p>
- <p>
- The integration routines are all usable for functions returning complex results
- - and as a result for contour integrals as well.
- </p>
- <h5>
- <a name="math_toolkit.main_intro.h9"></a>
- <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
- and Octonions</a>
- </h5>
- <p>
- 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>.
- </p>
- <h5>
- <a name="math_toolkit.main_intro.h10"></a>
- <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
- Differentiation</a>
- </h5>
- <p>
- Autodiff is a header-only C++ library that facilitates the automaticdifferentiation
- (forward mode) of mathematical functions of single and multiple variables.
- </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 © 2006-2019 Nikhar
- Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
- Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
- Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
- Daryle Walker and Xiaogang Zhang<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>)
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