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94 lines
3.8 KiB
Plaintext
94 lines
3.8 KiB
Plaintext
[section:main_intro About the Math Toolkit]
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This library is divided into three interconnected parts:
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[h4 Statistical Distributions]
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Provides a reasonably comprehensive set of
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[link dist statistical distributions],
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upon which higher level statistical tests can be built.
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The initial focus is on the central
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[@http://en.wikipedia.org/wiki/Univariate univariate ]
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[@http://mathworld.wolfram.com/StatisticalDistribution.html distributions].
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Both [@http://mathworld.wolfram.com/ContinuousDistribution.html continuous]
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(like [link math_toolkit.dist_ref.dists.normal_dist normal]
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& [link math_toolkit.dist_ref.dists.f_dist Fisher])
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and [@http://mathworld.wolfram.com/DiscreteDistribution.html discrete]
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(like [link math_toolkit.dist_ref.dists.binomial_dist binomial]
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& [link math_toolkit.dist_ref.dists.poisson_dist Poisson])
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distributions are provided.
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A [link math_toolkit.stat_tut comprehensive tutorial is provided],
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along with a series of
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[link math_toolkit.stat_tut.weg worked examples] illustrating
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how the library is used to conduct statistical tests.
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[h4 Mathematical Special Functions]
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Provides a small number of high quality
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[link special special functions],
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initially these were concentrated on functions used in statistical applications
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along with those in the [tr1].
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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
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of each) and all the possible inverses of these, plus digamma,
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various factorial functions,
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Bessel functions, elliptic integrals, sinus cardinals (along with their
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hyperbolic variants), inverse hyperbolic functions, Legrendre/Laguerre/Hermite
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polynomials and various
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special power and logarithmic functions.
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All the implementations
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are fully generic and support the use of arbitrary "real-number" types,
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including __multiprecision,
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although they are optimised for use with types with known-about
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[@http://en.wikipedia.org/wiki/Significand significand (or mantissa)]
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sizes: typically `float`, `double` or `long double`.
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[h4 Implementation Toolkit]
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The section [link math_toolkit.internals_overview Internal tools]
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provides many of the tools required to implement
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mathematical special functions: hopefully the presence of
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these will encourage other authors to contribute more special
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function implementations in the future.
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Some tools are now considered well-tried and their signatures stable and unlikely to change.
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There is a fairly comprehensive set of root finding both
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__root_finding_without_derivatives
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and __root_finding_with_derivatives with derivative support,
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and function minimization using __brent_minima.
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Other [link math_toolkit.internals_overview Internal tools]
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are currently still considered experimental: they are "exposed implementation details"
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whose interfaces and\/or implementations may change without notice.
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There are helpers for the
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[link math_toolkit.internals.series_evaluation evaluation of infinite series],
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[link math_toolkit.internals.cf continued
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fractions] and [link math_toolkit.roots.rational
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rational approximations].
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A [link math_toolkit.internals.minimax Remez algorithm implementation]
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allows for the locating of minimax rational
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approximations.
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There are also (experimental) classes for the
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[link math_toolkit.roots.polynomials manipulation of polynomials], for
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[link math_toolkit.internals.error_test
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testing a special function against tabulated test data], and for
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the [link math_toolkit.internals.test_data
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rapid generation of test data] and/or data for output to an
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external graphing application.
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[endsect] [/section:intro Introduction]
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[/
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Copyright 2006, 2012, 2015 John Maddock and Paul A. Bristow.
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt).
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]
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