mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2025-10-30 20:40:28 -04:00
94 lines
3.8 KiB
Plaintext
94 lines
3.8 KiB
Plaintext
|
[section:main_intro About the Math Toolkit]
|
||
|
|
|
||
|
|
This library is divided into three interconnected parts:
|
||
|
|
|
||
|
|
[h4 Statistical Distributions]
|
||
|
|
|
||
|
|
Provides a reasonably comprehensive set of
|
||
|
|
[link dist statistical distributions],
|
||
|
|
upon which higher level statistical tests can be built.
|
||
|
|
|
||
|
|
The initial focus is on the central
|
||
|
|
[@http://en.wikipedia.org/wiki/Univariate univariate ]
|
||
|
|
[@http://mathworld.wolfram.com/StatisticalDistribution.html distributions].
|
||
|
|
Both [@http://mathworld.wolfram.com/ContinuousDistribution.html continuous]
|
||
|
|
(like [link math_toolkit.dist_ref.dists.normal_dist normal]
|
||
|
|
& [link math_toolkit.dist_ref.dists.f_dist Fisher])
|
||
|
|
and [@http://mathworld.wolfram.com/DiscreteDistribution.html discrete]
|
||
|
|
(like [link math_toolkit.dist_ref.dists.binomial_dist binomial]
|
||
|
|
& [link math_toolkit.dist_ref.dists.poisson_dist Poisson])
|
||
|
|
distributions are provided.
|
||
|
|
|
||
|
|
A [link math_toolkit.stat_tut comprehensive tutorial is provided],
|
||
|
|
along with a series of
|
||
|
|
[link math_toolkit.stat_tut.weg worked examples] illustrating
|
||
|
|
how the library is used to conduct statistical tests.
|
||
|
|
|
||
|
|
[h4 Mathematical Special Functions]
|
||
|
|
|
||
|
|
Provides a small number of high quality
|
||
|
|
[link special special functions],
|
||
|
|
initially these were concentrated on functions used in statistical applications
|
||
|
|
along with those in the [tr1].
|
||
|
|
|
||
|
|
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.
|
||
|
|
|
||
|
|
All the implementations
|
||
|
|
are fully generic and support the use of arbitrary "real-number" types,
|
||
|
|
including __multiprecision,
|
||
|
|
although they are optimised for use with types with known-about
|
||
|
|
[@http://en.wikipedia.org/wiki/Significand significand (or mantissa)]
|
||
|
|
sizes: typically `float`, `double` or `long double`.
|
||
|
|
|
||
|
|
[h4 Implementation Toolkit]
|
||
|
|
|
||
|
|
The section [link math_toolkit.internals_overview Internal tools]
|
||
|
|
provides many of the tools required to implement
|
||
|
|
mathematical special functions: hopefully the presence of
|
||
|
|
these will encourage other authors to contribute more special
|
||
|
|
function implementations in the future.
|
||
|
|
|
||
|
|
Some tools are now considered well-tried and their signatures stable and unlikely to change.
|
||
|
|
|
||
|
|
There is a fairly comprehensive set of root finding both
|
||
|
|
__root_finding_without_derivatives
|
||
|
|
and __root_finding_with_derivatives with derivative support,
|
||
|
|
and function minimization using __brent_minima.
|
||
|
|
|
||
|
|
Other [link math_toolkit.internals_overview Internal tools]
|
||
|
|
are currently still considered experimental: they are "exposed implementation details"
|
||
|
|
whose interfaces and\/or implementations may change without notice.
|
||
|
|
|
||
|
|
There are helpers for the
|
||
|
|
[link math_toolkit.internals.series_evaluation evaluation of infinite series],
|
||
|
|
[link math_toolkit.internals.cf continued
|
||
|
|
fractions] and [link math_toolkit.roots.rational
|
||
|
|
rational approximations].
|
||
|
|
A [link math_toolkit.internals.minimax Remez algorithm implementation]
|
||
|
|
allows for the locating of minimax rational
|
||
|
|
approximations.
|
||
|
|
|
||
|
|
There are also (experimental) classes for the
|
||
|
|
[link math_toolkit.roots.polynomials manipulation of polynomials], for
|
||
|
|
[link math_toolkit.internals.error_test
|
||
|
|
testing a special function against tabulated test data], and for
|
||
|
|
the [link math_toolkit.internals.test_data
|
||
|
|
rapid generation of test data] and/or data for output to an
|
||
|
|
external graphing application.
|
||
|
|
|
||
|
|
[endsect] [/section:intro Introduction]
|
||
|
|
|
||
|
|
[/
|
||
|
|
Copyright 2006, 2012, 2015 John Maddock and Paul A. Bristow.
|
||
|
|
Distributed under the Boost Software License, Version 1.0.
|
||
|
|
(See accompanying file LICENSE_1_0.txt or copy at
|
||
|
|
http://www.boost.org/LICENSE_1_0.txt).
|
||
|
|
]
|