ceph/src/boost/libs/math/doc/overview/overview.qbk

   1 [section:main_intro About the Math Toolkit]
   2
   3 This library is divided into three interconnected parts:
   4
   5 [h4 Statistical Distributions]
   6
   7 Provides a reasonably comprehensive set of
   8 [link dist statistical distributions],
   9 upon which higher level statistical tests can be built.
  10
  11 The initial focus is on the central
  12 [@http://en.wikipedia.org/wiki/Univariate univariate ]
  13 [@http://mathworld.wolfram.com/StatisticalDistribution.html distributions].
  14 Both [@http://mathworld.wolfram.com/ContinuousDistribution.html continuous]
  15 (like [link math_toolkit.dist_ref.dists.normal_dist normal]
  16 & [link math_toolkit.dist_ref.dists.f_dist Fisher])
  17 and [@http://mathworld.wolfram.com/DiscreteDistribution.html discrete]
  18 (like [link math_toolkit.dist_ref.dists.binomial_dist binomial]
  19 & [link math_toolkit.dist_ref.dists.poisson_dist Poisson])
  20 distributions are provided.
  21
  22 A [link math_toolkit.stat_tut comprehensive tutorial is provided],
  23 along with a series of
  24 [link math_toolkit.stat_tut.weg worked examples] illustrating
  25 how the library is used to conduct statistical tests.
  26
  27 [h4 Mathematical Special Functions]
  28
  29 Provides a small number of high quality
  30 [link special special functions],
  31 initially these were concentrated on functions used in statistical applications
  32 along with those in the [tr1].
  33
  34 The function families currently implemented are the gamma, beta & erf functions
  35 along with the incomplete gamma and beta functions (four variants
  36 of each) and all the possible inverses of these, plus digamma,
  37 various factorial functions,
  38 Bessel functions, elliptic integrals, sinus cardinals (along with their
  39 hyperbolic variants), inverse hyperbolic functions, Legrendre/Laguerre/Hermite
  40 polynomials and various
  41 special power and logarithmic functions.
  42
  43 All the implementations
  44 are fully generic and support the use of arbitrary "real-number" types,
  45 including __multiprecision,
  46 although they are optimised for use with types with known-about
  47 [@http://en.wikipedia.org/wiki/Significand significand (or mantissa)]
  48 sizes: typically `float`, `double` or `long double`.
  49
  50 [h4 Implementation Toolkit]
  51
  52 The section [link math_toolkit.internals_overview Internal tools]
  53 provides many of the tools required to implement
  54 mathematical special functions: hopefully the presence of
  55 these will encourage other authors to contribute more special
  56 function implementations in the future.
  57
  58 Some tools are now considered well-tried and their signatures stable and unlikely to change.
  59
  60 There is a fairly comprehensive set of root finding both
  61 __root_finding_without_derivatives
  62 and __root_finding_with_derivatives with derivative support,
  63 and function minimization using __brent_minima.
  64
  65 Other [link math_toolkit.internals_overview Internal tools]
  66 are currently still considered experimental: they are "exposed implementation details"
  67 whose interfaces and\/or implementations may change without notice.
  68
  69 There are helpers for the
  70 [link math_toolkit.internals.series_evaluation evaluation of infinite series],
  71 [link math_toolkit.internals.cf continued
  72 fractions] and [link math_toolkit.roots.rational
  73 rational approximations].
  74 A [link math_toolkit.internals.minimax Remez algorithm implementation]
  75 allows for the locating of minimax rational
  76 approximations.
  77
  78 There are also (experimental) classes for the
  79 [link math_toolkit.roots.polynomials manipulation of polynomials], for
  80 [link math_toolkit.internals.error_test
  81 testing a special function against tabulated test data], and for
  82 the [link math_toolkit.internals.test_data
  83 rapid generation of test data] and/or data for output to an
  84 external graphing application.
  85
  86 [endsect] [/section:intro Introduction]
  87
  88 [/
  89   Copyright 2006, 2012, 2015 John Maddock and Paul A. Bristow.
  90   Distributed under the Boost Software License, Version 1.0.
  91   (See accompanying file LICENSE_1_0.txt or copy at
  92   http://www.boost.org/LICENSE_1_0.txt).
  93 ]