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<title>About the Math Toolkit</title>
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<div class="section math_toolkit_main_overview_intro">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.main_overview.intro"></a><a class="link" href="intro.html" title="About the Math Toolkit">About the Math Toolkit</a>
</h3></div></div></div>
<p>
This library is divided into three interconnected parts:
</p>
<h5>
<a name="math_toolkit.main_overview.intro.h0"></a>
<span><a name="math_toolkit.main_overview.intro.statistical_distributions"></a></span><a class="link" href="intro.html#math_toolkit.main_overview.intro.statistical_distributions">Statistical
Distributions</a>
</h5>
<p>
Provides a reasonably comprehensive set of <a class="link" href="../dist.html" title="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/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">normal</a>
& <a class="link" href="../dist/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/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">binomial</a>
& <a class="link" href="../dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson</a>)
distributions are provided.
</p>
<p>
A <a class="link" href="../dist/stat_tut.html" title="Statistical Distributions Tutorial">comprehensive tutorial is provided</a>,
along with a series of <a class="link" href="../dist/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_overview.intro.h1"></a>
<span><a name="math_toolkit.main_overview.intro.mathematical_special_functions"></a></span><a class="link" href="intro.html#math_toolkit.main_overview.intro.mathematical_special_functions">Mathematical
Special Functions</a>
</h5>
<p>
Provides a small number of high quality <a class="link" href="../special.html" title="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, 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_overview.intro.h2"></a>
<span><a name="math_toolkit.main_overview.intro.implementation_toolkit"></a></span><a class="link" href="intro.html#math_toolkit.main_overview.intro.implementation_toolkit">Implementation
Toolkit</a>
</h5>
<p>
Provides <a class="link" href="../toolkit.html" title="Tools and Internal Details">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="../toolkit/internals1/series_evaluation.html" title="Series Evaluation">evaluation
of infinite series</a>, <a class="link" href="../toolkit/internals1/cf.html" title="Continued Fraction Evaluation">continued
fractions</a> and <a class="link" href="../toolkit/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="../toolkit/internals1/minima.html" title="Locating Function Minima: Brent's algorithm">function
minimisation algorithms</a>: the root finding algorithms are both <a class="link" href="../toolkit/internals1/roots.html" title="Root Finding With Derivatives: Newton-Raphson, Halley & Schroeder">with</a> and <a class="link" href="../toolkit/internals1/roots2.html" title="Root Finding Without Derivatives: Bisection, Bracket and TOMS748">without</a>
derivative support.
</p>
<p>
A <a class="link" href="../toolkit/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="../toolkit/internals2/polynomials.html" title="Polynomials">manipulation
of polynomials</a>, for <a class="link" href="../toolkit/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="../toolkit/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>
</div>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<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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