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* gsl-ref: (gsl-ref).                   GNU Scientific Library - Reference
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   This file documents the GNU Scientific Library.

   Copyright (C) 1996, 1997, 1998, 1999 The GSL Project.

   Permission is granted to make and distribute verbatim copies of this
manual provided the copyright notice and this permission notice are
preserved on all copies.

   Permission is granted to copy and distribute modified versions of
this manual under the conditions for verbatim copying, provided that
the entire resulting derived work is distributed under the terms of a
permission notice identical to this one.

   Permission is granted to copy and distribute translations of this
manual into another language, under the above conditions for modified
versions, except that this permission notice may be stated in a
translation approved by the Foundation.


File: gsl-ref.info,  Node: Concept Index,  Next: Function Index,  Prev: Copying,  Up: Top

Concept Index
*************

* Menu:

* 2D histograms:                         Two dimensional histograms.
* 2D random direction vector:            The Spherical Distribution (2D & 3D).
* 3D random direction vector:            The Spherical Distribution (2D & 3D).
* 3j symbols:                            Coupling Coefficients.
* 6j symbols:                            Coupling Coefficients.
* 9j symbols:                            Coupling Coefficients.
* acceleration of series:                Series Acceleration.
* Airy functions:                        Airy Functions.
* Ai(x):                                 Airy Functions.
* aliasing of arrays:                    Aliasing of arrays.
* alternative optimized functions:       Alternative optimized functions.
* ANSI C, use of:                        Using the library.
* argument of complex number:            Properties of complex numbers.
* arithmetic exceptions:                 Setting up your IEEE environment.
* autoconf, using with GSL:              Inline functions.
* Bernoulli trial, random numbers:       The Bernoulli Distribution.
* Bessel functions:                      Bessel Functions.
* Beta distribution random numbers:      The Beta Distribution.
* bias, IEEE format:                     Representation of floating point numbers.
* binning data:                          Histograms.
* Binomial random numbers:               The Binomial Distribution.
* bisection algorithm for finding roots: Root Bracketing Algorithms.
* Bi(x):                                 Airy Functions.
* BLAS:                                  BLAS Support.
* blocks:                                Vectors and Matrices.
* breakpoints:                           Using gdb.
* brent's method for finding minima:     Minimization Algorithms.
* brent's method for finding roots:      Root Bracketing Algorithms.
* Broyden algorithm for multidimensional roots: Algorithms without Derivatives.
* BSD random number generator:           Unix random number generators.
* BSD random number generator, rand:     Unix random number generators.
* Cauchy random numbers:                 The Cauchy Distribution.
* C++, compatibility:                    Compatibility with C++.
* C extensions, compatible use of:       Using the library.
* Chebyshev polynomials:                 Chebyshev Polynomials.
* Checkergcc:                            Accessing vector elements.
* checking permutation for validity:     Permutation properties.
* Chi-squared random numbers:            The Chi-squared Distribution.
* Cholesky decomposition:                Cholesky Decomposition.
* Clausen functions:                     Clausen Functions.
* Clenshaw-Curtis quadrature:            Numerical Integration.
* CMRG, combined multiple recursive random number generator: Random number generator algorithms.
* combinatorial optimization:            Simulated Annealing.
* combinatorial searches:                Simulated Annealing.
* comparison functions, definition:      Sorting objects.
* compatibility:                         Using the library.
* compiling programs, include paths:     Compiling and Linking.
* compiling programs, library paths:     Compiling and Linking.
* complex arithmetic:                    Complex arithmetic operators.
* complex numbers:                       Complex Numbers.
* confluent hypergeometric function:     Laguerre Functions.
* confluent hypergeometric functions:    Hypergeometric Functions.
* conical functions:                     Legendre Functions and Spherical Harmonics.
* conjugate of complex number:           Complex arithmetic operators.
* constants, mathematical -- defined as macros: Mathematical Constants.
* convergence, accelerating a series:    Series Acceleration.
* cooling schedule:                      Simulated Annealing algorithm.
* cosine of complex number:              Complex Trigonometric Functions.
* cost function:                         Simulated Annealing.
* Coulomb wave functions:                Coulomb Wave Functions.
* covariance, of two datasets:           Covariance.
* CRAY random number generator, RANF:    Other random number generators.
* cubic equation, solving:               Cubic equations.
* Dawson function:                       Dawson Function.
* debugging numerical programs:          Using gdb.
* Debye functions:                       Debye Functions.
* denormalized form, IEEE format:        Representation of floating point numbers.
* determinant of a matrix, by LU decomposition: LU Decomposition.
* DFTs, see FFT:                         Fast Fourier Transforms.
* digamma function:                      Psi (Digamma) Function.
* dilogarithm:                           Dilogarithm.
* direction vector, random 2D:           The Spherical Distribution (2D & 3D).
* direction vector, random 3D:           The Spherical Distribution (2D & 3D).
* direction vector, random N-dimensional: The Spherical Distribution (2D & 3D).
* Discrete Fourier Transforms, see FFT:  Fast Fourier Transforms.
* Discrete newton algorithm for multidimensional roots: Algorithms without Derivatives.
* Discrete Newton algorithm for nonlinear systems: Algorithms without Derivatives.
* Discrete random numbers:               General Discrete Distributions.
* Discrete random numbers, preprocessing: General Discrete Distributions.
* division by zero, IEEE exceptions:     Setting up your IEEE environment.
* double precision, IEEE format:         Representation of floating point numbers.
* e, defined as a macro:                 Mathematical Constants.
* elementary functions:                  Mathematical Functions.
* elementary operations:                 Elementary Operations.
* elliptic functions (Jacobi):           Elliptic Functions (Jacobi).
* elliptic integrals:                    Elliptic Integrals.
* energy function:                       Simulated Annealing.
* erfc(x):                               Error Function.
* erf(x):                                Error Function.
* error codes:                           Error reporting.
* error function:                        Error Function.
* Error handlers:                        Error handlers.
* error handling macros:                 Using GSL error reporting in your own functions.
* Errors:                                Error handling in GSL.
* estimated standard deviation:          Statistics.
* estimated variance:                    Statistics.
* euclidean distance function, hypot:    Elementary Functions.
* Euler's constant, defined as a macro:  Mathematical Constants.
* exceptions, IEEE arithmetic:           Setting up your IEEE environment.
* exchanging permutation elements:       Accessing permutation elements.
* exp:                                   Exponential Function.
* exponential function:                  Exponential Function.
* exponential integrals:                 Exponential Integrals.
* Exponential power distribution, random numbers: The Exponential Power Distribution.
* Exponential random numbers:            The Exponential Distribution.
* exponentiation of complex number:      Elementary Complex Functions.
* exponent, IEEE format:                 Representation of floating point numbers.
* factorization of matrices:             Linear Algebra.
* false position algorithm for finding roots: Root Bracketing Algorithms.
* Fast Fourier Transforms, see FFT:      Fast Fourier Transforms.
* F-distribution random numbers:         The F-distribution.
* Fermi-Dirac function:                  Fermi-Dirac Function.
* FFT:                                   Fast Fourier Transforms.
* FFT, complex data:                     Overview of complex data FFTs.
* FFT mathematical definition:           Mathematical Definitions.
* FFT of complex data, mixed-radix algorithm: Mixed-radix FFT routines for complex data.
* FFT of complex data, radix-2 algorithm: Radix-2 FFT routines for complex data.
* FFT of real data:                      Overview of real data FFTs.
* FFT of real data, mixed-radix algorithm: Mixed-radix FFT routines for real data.
* FFT of real data, radix-2 algorithm:   Radix-2 FFT routines for real data.
* finding minima:                        Minimization.
* finding roots:                         One dimensional Root-Finding.
* finding zeros:                         One dimensional Root-Finding.
* flat distribution random numbers:      The Flat (Uniform) Distribution.
* Fortran range checking, equivalent in gcc: Accessing vector elements.
* Fourier integrals, numerical:          QAWF adaptive integration for Fourier integrals.
* Fourier Transforms, see FFT:           Fast Fourier Transforms.
* Four-tap Generalized Feedback Shift Register: Random number generator algorithms.
* Gamma distribution random numbers:     The Gamma Distribution.
* gamma function:                        Gamma Function.
* Gaussian random numbers <1>:           The Bivariate Gaussian Distribution.
* Gaussian random numbers:               The Gaussian Distribution.
* Gaussian Tail random numbers:          The Gaussian Tail Distribution.
* Gauss-Kronrod quadrature:              Numerical Integration.
* gcc extensions, range-checking:        Accessing vector elements.
* gcc warning options:                   GCC warning options for numerical programs.
* gdb:                                   Using gdb.
* Gegenbauer functions:                  Gegenbauer Functions.
* general polynomial equations, solving: General polynomial equations.
* Geometric random numbers <1>:          The Hypergeometric Distribution.
* Geometric random numbers:              The Geometric Distribution.
* GNEWTON algorithm:                     Algorithms using Derivatives.
* golden section algorithm for finding minima: Minimization Algorithms.
* gsl_sf_result:                         The gsl_sf_result struct.
* gsl_sf_result_e10:                     The gsl_sf_result struct.
* Gumbel distribution (Type 1), random numbers: The Type-1 Gumbel Distribution.
* Gumbel distribution (Type 2), random numbers: The Type-2 Gumbel Distribution.
* HAVE_INLINE:                           Inline functions.
* header files, including:               Compiling and Linking.
* heapsort:                              Sorting.
* histograms:                            Histograms.
* householder linear solver:             Householder solver for linear systems.
* HYBRID algorithms for nonlinear systems: Algorithms using Derivatives.
* HYBRID algorith, unscaled without derivates: Algorithms without Derivatives.
* HYBRIDJ algorithm:                     Algorithms using Derivatives.
* HYBRIDS algorithm, scaled without derivatives: Algorithms without Derivatives.
* HYBRIDSJ algorithm:                    Algorithms using Derivatives.
* hydrogen atom:                         Coulomb Wave Functions.
* hyperbolic functions, complex numbers: Complex Hyperbolic Functions.
* hyperbolic space:                      Legendre Functions and Spherical Harmonics.
* hypergeometric functions:              Hypergeometric Functions.
* hypot:                                 Elementary Functions.
* IEEE exceptions:                       Setting up your IEEE environment.
* IEEE floating point:                   IEEE floating-point arithmetic.
* IEEE format for floating point numbers: Representation of floating point numbers.
* including GSL header files:            Compiling and Linking.
* indentity permutation:                 Permutation allocation.
* indirect sorting:                      Sorting objects.
* indirect sorting, of vector elements:  Sorting vectors.
* infinity, IEEE format:                 Representation of floating point numbers.
* initializing matrices:                 Initializing matrix elements.
* initializing vectors:                  Initializing vector elements.
* inline functions:                      Inline functions.
* integer powers:                        Power Function.
* integration, numerical (quadrature):   Numerical Integration.
* interpolation:                         Interpolation.
* inverse complex trigonometric functions: Inverse Complex Trigonometric Functions.
* inverse hyperbolic functions, complex numbers: Inverse Complex Hyperbolic Functions.
* inverse of a matrix, by LU decomposition: LU Decomposition.
* inverting a permutation:               Permutation functions.
* iterative refinement of solutions in linear systems: LU Decomposition.
* Laguerre functions:                    Laguerre Functions.
* LAPACK, recommended for linear algebra: Linear Algebra.
* Laplace distribution random numbers:   The Laplace Distribution.
* leading dimension, matrices:           The matrix struct.
* Legendre functions:                    Legendre Functions and Spherical Harmonics.
* length, computed accurately using hypot: Elementary Functions.
* Levin u-transform:                     Series Acceleration.
* Levy distribution, random numbers:     The Symmetric Levy Distribution.
* libraries, linking with:               Compiling and Linking.
* linear algebra:                        Linear Algebra.
* linear systems, refinement of solutions: LU Decomposition.
* linear systems, solution of:           LU Decomposition.
* linking with GSL libraries:            Compiling and Linking.
* log1p:                                 Elementary Functions.
* logarithm:                             Logarithm and Related Functions.
* logarithm, computed accurately:        Elementary Functions.
* Logarithmic random numbers:            The Logarithmic Distribution.
* logarithm of complex number:           Elementary Complex Functions.
* logarithm of the determinant of a matrix: LU Decomposition.
* Logistic random numbers:               The Logistic Distribution.
* Lognormal random numbers <1>:          The Pareto Distribution.
* Lognormal random numbers:              The Lognormal Distribution.
* long double:                           Long double.
* LU decomposition:                      LU Decomposition.
* macros for mathematical constants:     Mathematical Constants.
* magnitude of complex number:           Properties of complex numbers.
* mantissa, IEEE format:                 Representation of floating point numbers.
* mathematical constants, defined as macros: Mathematical Constants.
* mathematical functions, elementary:    Mathematical Functions.
* matrices <1>:                          The matrix struct.
* matrices:                              Vectors and Matrices.
* matrices, initializing:                Initializing matrix elements.
* matrices, range-checking:              Accessing matrix elements.
* matrix determinant:                    LU Decomposition.
* matrix factorization:                  Linear Algebra.
* matrix inverse:                        LU Decomposition.
* matrix, operations:                    BLAS Support.
* matrix square root, Cholesky decomposition: Cholesky Decomposition.
* max:                                   Statistics.
* maximization, see minimization:        Minimization.
* maximum of two numbers:                Maximum and Minimum functions.
* mean:                                  Statistics.
* min:                                   Statistics.
* Minimization, caveats:                 Minimization Caveats.
* minimization, one-dimensional:         Minimization.
* minimization, overview:                Minimization Overview.
* minimization, providing a function to minimize: Providing the function to minimize.
* minimization, stopping parameters:     Minimization Stopping Parameters.
* minimum finding, brent's method:       Minimization Algorithms.
* minimum finding, golden section algorithm: Minimization Algorithms.
* minimum of two numbers:                Maximum and Minimum functions.
* MINPACK, minimization algorithms:      Algorithms using Derivatives.
* Mixed-radix FFT, complex data:         Mixed-radix FFT routines for complex data.
* Mixed-radix FFT, real data:            Mixed-radix FFT routines for real data.
* Modified Clenshaw-Curtis quadrature:   Numerical Integration.
* Modified Newton's Method for nonlinear systems: Algorithms using Derivatives.
* Monte Carlo integrators:               Monte Carlo Integration.
* MRG, multiple recursive random number generator: Random number generator algorithms.
* MT19937 random number generator:       Random number generator algorithms.
* multidimensional root finding, Broyden algorithm: Algorithms without Derivatives.
* multidimensional root finding, overview: Overview of Multidimensional Root Finding.
* multidimensional root finding, providing a function to solve: Providing the multidimensional system of equations to solve.
* multiplication:                        Elementary Operations.
* N-dimensional random direction vector: The Spherical Distribution (2D & 3D).
* Negative Binomial distribution, random numbers: The Negative Binomial Distribution.
* Newton algorithm, discrete:            Algorithms without Derivatives.
* Newton's Method algorithm for finding roots: Root Finding Algorithms using Derivatives.
* Newton's Method for systems of nonlinear equations: Algorithms using Derivatives.
* non-linear equation, solutions of:     One dimensional Root-Finding.
* non-linear functions, minimisation:    Minimization.
* nonlinear systems of equations, solution of: Multidimensional Root-Finding.
* normalized form, IEEE format:          Representation of floating point numbers.
* numerical constants, defined as macros: Mathematical Constants.
* numerical integration (quadrature):    Numerical Integration.
* Numerical recipes, random number generators: Numerical Recipes generators.
* optimization - combinatorial:          Simulated Annealing.
* optimization, see minimization:        Minimization.
* optimized functions, alternatives:     Alternative optimized functions.
* overflow, IEEE exceptions:             Setting up your IEEE environment.
* permutations:                          Permutations.
* physical dimension, matrices:          The matrix struct.
* pi, defined as a macro:                Mathematical Constants.
* Poisson random numbers:                The Poisson Distribution.
* polar form of complex numbers:         Complex numbers.
* polygamma functions:                   Psi (Digamma) Function.
* polynomial manipulation:               Polynomial Manipulation.
* polynomials, roots of:                 Roots of Polynomials.
* power function:                        Power Function.
* power of complex number:               Elementary Complex Functions.
* precision, IEEE arithmetic:            Setting up your IEEE environment.
* probability distributions, from histograms: Resampling from histograms.
* psi function:                          Psi (Digamma) Function.
* QR decomposition:                      QR Decomposition.
* QR decomposition with column pivoting: QR Decomposition with Column Pivoting.
* QUADPACK:                              Numerical Integration.
* quadratic equation, solving:           Quadratic equations.
* quadrature:                            Numerical Integration.
* R250 shift-register random number generator: Other random number generators.
* Racah coefficients:                    Coupling Coefficients.
* Radix-2 FFT, complex data:             Radix-2 FFT routines for complex data.
* Radix-2 FFT for real data:             Radix-2 FFT routines for real data.
* rand48 random number generator:        Unix random number generators.
* random number distributions:           Random Number Distributions.
* random number generators:              Random Number Generation.
* Random number generators, Numerical recipes: Numerical Recipes generators.
* RANDU random number generator:         Other random number generators.
* RANF random number generator:          Other random number generators.
* range:                                 Statistics.
* range-checking for matrices:           Accessing matrix elements.
* range-checking for vectors:            Accessing vector elements.
* RANLUX random number generator:        Random number generator algorithms.
* RANLXD random number generator:        Random number generator algorithms.
* RANLXS random number generator:        Random number generator algorithms.
* RANMAR random number generator:        Other random number generators.
* Rayleigh random numbers:               The Rayleigh Distribution.
* Rayleigh Tail random numbers:          The Rayleigh Tail Distribution.
* refinement of solutions in linear systems: LU Decomposition.
* representations of complex numbers:    Complex numbers.
* resampling from histograms:            Resampling from histograms.
* residual, in nonlinear systems of equations: Search Stopping Parameters for the multidimensional solver.
* reversing a permutation:               Permutation functions.
* root finding:                          One dimensional Root-Finding.
* root finding, bisection algorithm:     Root Bracketing Algorithms.
* root finding, brent's method:          Root Bracketing Algorithms.
* root finding, caveats:                 Root Finding Caveats.
* root finding, false position algorithm: Root Bracketing Algorithms.
* root finding, initial guess:           Search Bounds and Guesses.
* root finding, Newton's Method algorithm: Root Finding Algorithms using Derivatives.
* root finding, overview:                Root Finding Overview.
* root finding, providing a function to solve: Providing the function to solve.
* root finding, search bounds:           Search Bounds and Guesses.
* root finding, Secant Method algorithm: Root Finding Algorithms using Derivatives.
* root finding, Steffenson's Method:     Root Finding Algorithms using Derivatives.
* root finding, stopping parameters <1>: Search Stopping Parameters for the multidimensional solver.
* root finding, stopping parameters:     Search Stopping Parameters.
* roots:                                 One dimensional Root-Finding.
* rounding mode:                         Setting up your IEEE environment.
* sampling from histograms:              Resampling from histograms.
* schedule - cooling:                    Simulated Annealing algorithm.
* Secant Method algorithm for finding roots: Root Finding Algorithms using Derivatives.
* series, acceleration:                  Series Acceleration.
* shift-register random number generator: Other random number generators.
* sign bit, IEEE format:                 Representation of floating point numbers.
* sign of the determinant of a matrix:   LU Decomposition.
* simulated annealing:                   Simulated Annealing.
* single precision, IEEE format:         Representation of floating point numbers.
* singular value decomposition:          Singular Value Decomposition.
* sin of complex number:                 Complex Trigonometric Functions.
* solution of linear system by householder transformations: Householder solver for linear systems.
* solution of linear systems, Ax=b:      Linear Algebra.
* solving a non-linear equation:         One dimensional Root-Finding.
* solving nonlinear systems of equations: Multidimensional Root-Finding.
* sorting:                               Sorting.
* sorting vector elements:               Sorting vectors.
* Special Functions:                     Special Functions.
* spherical harmonics:                   Legendre Functions and Spherical Harmonics.
* spherical random numbers, 2D:          The Spherical Distribution (2D & 3D).
* spherical random numbers, 3D:          The Spherical Distribution (2D & 3D).
* spherical random numbers, N-dimensional: The Spherical Distribution (2D & 3D).
* spline:                                Interpolation.
* square root of a matrix, Cholesky decomposition: Cholesky Decomposition.
* square root of complex number:         Elementary Complex Functions.
* standard deviation:                    Statistics.
* standards conformance, ANSI C:         Using the library.
* statistics:                            Statistics.
* Steffenson's Method for finding roots: Root Finding Algorithms using Derivatives.
* stride, of vector index:               The vector struct.
* summation, acceleration:               Series Acceleration.
* SVD:                                   Singular Value Decomposition.
* swapping permutation elements:         Accessing permutation elements.
* Synchrotron functions:                 Synchrotron Functions.
* systems of equations, nonlinear:       Multidimensional Root-Finding.
* tangent of complex number:             Complex Trigonometric Functions.
* Tausworthe random number generator:    Random number generator algorithms.
* t-distribution random numbers:         The t-distribution.
* testing permutation for validity:      Permutation properties.
* trailing dimension, matrices:          The matrix struct.
* Transport functions:                   Transport Functions.
* Traveling Salesman Problem:            Traveling Salesman Problem.
* tridiagonal systems:                   Tridiagonal Systems.
* Trigonometric functions:               Trigonometric Functions.
* trigonometric functions of complex numbers: Complex Trigonometric Functions.
* TSP:                                   Traveling Salesman Problem.
* TT800 random number generator:         Other random number generators.
* t-test:                                Statistics.
* two dimensional histograms:            Two dimensional histograms.
* two-sided exponential random numbers:  The Laplace Distribution.
* Type 1 Gumbel distribution, random numbers: The Type-1 Gumbel Distribution.
* Type 2 Gumbel distribution, random numbers: The Type-2 Gumbel Distribution.
* underflow, IEEE exceptions:            Setting up your IEEE environment.
* Unix random number generators, rand:   Unix random number generators.
* Unix random number generators, rand48: Unix random number generators.
* usage, compiling application programs: Using the library.
* u-transform for series:                Series Acceleration.
* variance:                              Statistics.
* VAX random number generator:           Other random number generators.
* vector, operations:                    BLAS Support.
* vectors <1>:                           The vector struct.
* vectors:                               Vectors and Matrices.
* vectors, initializing:                 Initializing vector elements.
* vector, sorting elements of:           Sorting vectors.
* vectors, range-checking:               Accessing vector elements.
* warning options:                       GCC warning options for numerical programs.
* Weibull distribution random numbers:   The Weibull Distribution.
* Wigner coefficients:                   Coupling Coefficients.
* zero finding:                          One dimensional Root-Finding.
* zero, IEEE format:                     Representation of floating point numbers.
* Zeta functions:                        Zeta Functions.

