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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 three interconnected parts:
</p>
<h5>
<a name="math_toolkit.main_intro.h0"></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.h1"></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 6. 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="http://www.boost.org/doc/libs/1_53_0_beta1/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>
<h5>
<a name="math_toolkit.main_intro.h2"></a>
<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
Toolkit</a>
</h5>
<p>
Provides <a class="link" href="../toolkit.html" title="Chapter 12. Internals (Series, Rationals and Continued Fractions, Root Finding, Function Minimization, Testing and Development Tools)">many of the tools</a> required to implement
mathematical special functions: hopefully the presence of these will encourage
other authors to contribute more special function implementations in the future.
These tools are currently considered experimental: they are "exposed implementation
details" whose interfaces and/or implementations may change.
</p>
<p>
There are helpers for the <a class="link" href="internals1/series_evaluation.html" title="Series Evaluation">evaluation
of infinite series</a>, <a class="link" href="internals1/cf.html" title="Continued Fraction Evaluation">continued
fractions</a> and <a class="link" href="internals1/rational.html" title="Polynomial and Rational Function Evaluation">rational
approximations</a>.
</p>
<p>
There is a fairly comprehensive set of root finding and <a class="link" href="internals1/minima.html" title="Locating Function Minima: Brent's algorithm">function
minimisation algorithms</a>: the root finding algorithms are both <a class="link" href="internals1/roots.html" title="Root Finding With Derivatives: Newton-Raphson, Halley & Schroeder">with</a> and <a class="link" href="internals1/roots2.html" title="Root Finding Without Derivatives: Bisection, Bracket and TOMS748">without</a>
derivative support.
</p>
<p>
A <a class="link" href="internals2/minimax.html" title="Minimax Approximations and the Remez Algorithm">Remez algorithm implementation</a>
allows for the locating of minimax rational approximations.
</p>
<p>
There are also (experimental) classes for the <a class="link" href="internals2/polynomials.html" title="Polynomials">manipulation
of polynomials</a>, for <a class="link" href="internals2/error_test.html" title="Relative Error and Testing">testing
a special function against tabulated test data</a>, and for the <a class="link" href="internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">rapid
generation of test data</a> and/or data for output to an external graphing
application.
</p>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta,
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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