1[section:main_intro About the Math Toolkit] 2 3This library is divided into several interconnected parts: 4 5[h4 Floating Point Utilities] 6 7Utility functions for dealing with floating-point arithmetic, includes functions 8for floating point classification (`fpclassify`, `isnan`, `isinf` etc), sign manipulation, 9rounding, comparison, and computing the distance between floating point numbers. 10 11[h4 Specific Width Floating-Point Types] 12 13A set of `typedef`s similar to those provided by `<cstdint>` but for floating-point types. 14 15[h4 Mathematical Constants] 16 17A wide range of high-precision constants ranging from various multiples of [pi], fractions, through to Euler's constant etc. 18 19These are of course usable from template code, or as non-templates with a simplified interface if that is more appropriate. 20 21[h4 Statistical Distributions] 22 23Provides a reasonably comprehensive set of 24[link dist statistical distributions], 25upon which higher level statistical tests can be built. 26 27The initial focus is on the central 28[@http://en.wikipedia.org/wiki/Univariate univariate ] 29[@http://mathworld.wolfram.com/StatisticalDistribution.html distributions]. 30Both [@http://mathworld.wolfram.com/ContinuousDistribution.html continuous] 31(like [link math_toolkit.dist_ref.dists.normal_dist normal] 32& [link math_toolkit.dist_ref.dists.f_dist Fisher]) 33and [@http://mathworld.wolfram.com/DiscreteDistribution.html discrete] 34(like [link math_toolkit.dist_ref.dists.binomial_dist binomial] 35& [link math_toolkit.dist_ref.dists.poisson_dist Poisson]) 36distributions are provided. 37 38A [link math_toolkit.stat_tut comprehensive tutorial is provided], 39along with a series of 40[link math_toolkit.stat_tut.weg worked examples] illustrating 41how the library is used to conduct statistical tests. 42 43[h4 Mathematical Special Functions] 44 45Provides a small number of high quality 46[link special special functions], 47initially these were concentrated on functions used in statistical applications 48along with those in the [tr1]. 49 50The function families currently implemented are the gamma, beta & erf functions 51along with the incomplete gamma and beta functions (four variants 52of each) and all the possible inverses of these, plus digamma, 53various factorial functions, 54Bessel functions, elliptic integrals, sinus cardinals (along with their 55hyperbolic variants), inverse hyperbolic functions, Legendre/Laguerre/Hermite 56polynomials and various 57special power and logarithmic functions. 58 59All the implementations 60are fully generic and support the use of arbitrary "real-number" types, 61including __multiprecision, 62although they are optimised for use with types with known-about 63[@http://en.wikipedia.org/wiki/Significand significand (or mantissa)] 64sizes: typically `float`, `double` or `long double`. 65 66These functions also provide the basis of support for the TR1 special functions. 67 68[h4 Root Finding and Function Minimisation] 69 70A comprehensive set of root finding algorithms over the real-line, both with and without derivative support. 71 72Also function minimisation via Brent's Method. 73 74[h4 Polynomials and Rational Functions] 75 76Tools for manipulating polynomials and for efficient evaluation of rationals or polynomials. 77 78[h4 Interpolation] 79 80Function interpolation via Barycentric or cubic B_spline approximations. Smoothing. 81 82[h4 Numerical Integration (Quadrature) and Differentiation] 83 84A reasonably comprehensive set of routines for integration (trapezoidal, Gauss-Legendre, Gauss-Kronrod and double-exponential) 85and differentiation. (See also automatic differentiation). 86 87The integration routines are all usable for functions returning complex results - and as a result for contour integrals as well. 88 89[h4 Quaternions and Octonions] 90 91Quaternions and Octonians as class templates similar to `std::complex`. 92 93[h4 Automatic Differentiation] 94 95Autodiff is a header-only C++ library that facilitates the automaticdifferentiation (forward mode) 96of mathematical functions of single and multiple variables. 97 98[endsect] [/section:main_intro About the Math Toolkit] 99 100 101[/ 102 Copyright 2006, 2012, 2015 John Maddock and Paul A. Bristow. 103 Distributed under the Boost Software License, Version 1.0. 104 (See accompanying file LICENSE_1_0.txt or copy at 105 http://www.boost.org/LICENSE_1_0.txt). 106] 107