Table of Contents

Overview

About the Math Toolkit

Navigation

Directory and File Structure

Namespaces

Calculation of the Type of the Result

Error Handling

Compilers

Configuration Macros

Policies

Thread Safety

Performance

If and How to Build a Boost.Math Library, and its Examples and Tests

History and What's New

C99 and C++ TR1 C-style Functions

Frequently Asked Questions FAQ

Contact Info and Support

Statistical Distributions and Functions

Statistical Distributions Tutorial

Overview of Distributions

Headers and Namespaces

Distributions are Objects

Generic operations common to all distributions are non-member functions

Complements are supported too - and when to use them

Parameters can be calculated

Summary

Worked Examples

Distribution Construction Example

Student's t Distribution Examples

Chi Squared Distribution Examples

F Distribution Examples

Binomial Distribution Examples

Geometric Distribution Examples

Negative Binomial Distribution Examples

Normal Distribution Examples

Inverse Chi-Squared Distribution Bayes Example

Non Central Chi Squared Example

Error Handling Example

Find Location and Scale Examples

Comparison with C, R, FORTRAN-style Free Functions

Using the Distributions from Within C#

Random Variates and Distribution Parameters

Discrete Probability Distributions

Statistical Distributions Reference

Non-Member Properties

Distributions

Bernoulli Distribution

Beta Distribution

Binomial Distribution

Cauchy-Lorentz Distribution

Chi Squared Distribution

Exponential Distribution

Extreme Value Distribution

F Distribution

Gamma (and Erlang) Distribution

Geometric Distribution

Hypergeometric Distribution

Inverse Chi Squared Distribution

Inverse Gamma Distribution

Inverse Gaussian (or Inverse Normal) Distribution

Laplace Distribution

Logistic Distribution

Log Normal Distribution

Negative Binomial Distribution

Noncentral Beta Distribution

Noncentral Chi-Squared Distribution

Noncentral F Distribution

Noncentral T Distribution

Normal (Gaussian) Distribution

Pareto Distribution

Poisson Distribution

Rayleigh Distribution

Students t Distribution

Triangular Distribution

Uniform Distribution

Weibull Distribution

Distribution Algorithms

Extras/Future Directions

Special Functions

Gamma Functions

Gamma

Log Gamma

Digamma

Ratios of Gamma Functions

Incomplete Gamma Functions

Incomplete Gamma Function Inverses

Derivative of the Incomplete Gamma Function

Factorials and Binomial Coefficients

Factorial

Double Factorial

Rising Factorial

Falling Factorial

Binomial Coefficients

Beta Functions

Beta

Incomplete Beta Functions

The Incomplete Beta Function Inverses

Derivative of the Incomplete Beta Function

Error Functions

Error Functions

Error Function Inverses

Polynomials

Legendre (and Associated) Polynomials

Laguerre (and Associated) Polynomials

Hermite Polynomials

Spherical Harmonics

Bessel Functions

Bessel Function Overview

Bessel Functions of the First and Second Kinds

Modified Bessel Functions of the First and Second Kinds

Spherical Bessel Functions of the First and Second Kinds

Elliptic Integrals

Elliptic Integral Overview

Elliptic Integrals - Carlson Form

Elliptic Integrals of the First Kind - Legendre Form

Elliptic Integrals of the Second Kind - Legendre Form

Elliptic Integrals of the Third Kind - Legendre Form

Zeta Functions

Riemann Zeta Function

Exponential Integrals

Exponential Integral En

Exponential Integral Ei

Logs, Powers, Roots and Exponentials

log1p

expm1

cbrt

sqrt1pm1

powm1

hypot

Compile Time Power of a Runtime Base

Sinus Cardinal and Hyperbolic Sinus Cardinal Functions

Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview

sinc_pi

sinhc_pi

Inverse Hyperbolic Functions

Inverse Hyperbolic Functions Overview

acosh

asinh

atanh

Floating Point Utilities

Rounding Truncation and Integer Conversion

Rounding Functions

Truncation Functions

Integer and Fractional Part Splitting (modf)

Floating-Point Classification: Infinities and NaNs

Sign Manipulation Functions

Facets for Floating-Point Infinities and NaNs

Introduction

Reference

Examples

Portability

Design Rationale

Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values

Finding the Next Representable Value in a Specific Direction (nextafter)

Finding the Next Greater Representable Value (float_next)

Finding the Next Smaller Representable Value (float_prior)

Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance

Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance

TR1 and C99 external "C" Functions

C99 and TR1 C Functions Overview

C99 C Functions

TR1 C Functions Quick Reference

Tools, Constants and Internal Details

Overview

Utilities - Constants & Tools

Numeric Constants

Series Evaluation

Continued Fraction Evaluation

Polynomial and Rational Function Evaluation

Root Finding With Derivatives: Newton-Raphson, Halley & Schroeder

Root Finding Without Derivatives: Bisection, Bracket and TOMS748

Locating Function Minima: Brent's algorithm

Tuples

Testing and Development

Polynomials

Minimax Approximations and the Remez Algorithm

Relative Error and Testing

Graphing, Profiling, and Generating Test Data for Special Functions

Use with User-Defined Floating-Point Types

Using With NTL - a High-Precision Floating-Point Library

Using With MPFR / GMP - a High-Precision Floating-Point Library

e_float Support

Conceptual Requirements for Real Number Types

Conceptual Requirements for Distribution Types

Conceptual Archetypes for Reals and Distributions

Policies

Policy Overview

Policy Tutorial

So Just What is a Policy Anyway?

Policies Have Sensible Defaults

So How are Policies Used Anyway?

Changing the Policy Defaults

Setting Policies for Distributions on an Ad Hoc Basis

Changing the Policy on an Ad Hoc Basis for the Special Functions

Setting Policies at Namespace or Translation Unit Scope

Calling User Defined Error Handlers

Understanding Quantiles of Discrete Distributions

Policy Reference

Error Handling Policies

Internal Floating-point Promotion Policies

Mathematically Undefined Function Policies

Discrete Quantile Policies

Precision Policies

Iteration Limits Policies

Using Macros to Change the Policy Defaults

Setting Polices at Namespace Scope

Policy Class Reference

Performance

Performance Overview

Interpreting these Results

Getting the Best Performance from this Library

Comparing Compilers

Performance Tuning Macros

Comparisons to Other Open Source Libraries

The Performance Test Application

Backgrounders

Additional Implementation Notes

Relative Error

The Lanczos Approximation

The Remez Method

References

Library Status

History and What's New

Known Issues, and TODO List

Credits and Acknowledgements

Function Index

Class Index

Typedef Index

Macro Index

Index