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| <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> |
| <a name="math_toolkit.main_overview.intro.statistical_distributions"></a><h5> |
| <a name="id894863"></a> |
| <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> |
| <a name="math_toolkit.main_overview.intro.mathematical_special_functions"></a><h5> |
| <a name="id894947"></a> |
| <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> |
| <a name="math_toolkit.main_overview.intro.implementation_toolkit"></a><h5> |
| <a name="id895014"></a> |
| <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="Internal Details and Tools (Experimental)">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">function |
| minimisation algorithms</a>: the root finding algorithms are both <a class="link" href="../toolkit/internals1/roots.html" title="Root Finding With Derivatives">with</a> and <a class="link" href="../toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">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> |
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| <td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, |
| Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and |
| Thijs van den Berg<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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