This is gsl-ref.info, produced by makeinfo version 4.6 from gsl-ref.texi. INFO-DIR-SECTION Scientific software START-INFO-DIR-ENTRY * gsl-ref: (gsl-ref). GNU Scientific Library - Reference END-INFO-DIR-ENTRY Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006 The GSL Team. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with the Invariant Sections being "GNU General Public License" and "Free Software Needs Free Documentation", the Front-Cover text being "A GNU Manual", and with the Back-Cover Text being (a) (see below). A copy of the license is included in the section entitled "GNU Free Documentation License". (a) The Back-Cover Text is: "You have freedom to copy and modify this GNU Manual, like GNU software."  File: gsl-ref.info, Node: Concept Index, Prev: Type Index, Up: Top Concept Index ************* * Menu: * $, shell prompt: Conventions used in this manual. * 2D histograms: Two dimensional histograms. * 2D random direction vector: Spherical Vector Distributions. * 3-j symbols: Coupling Coefficients. * 3D random direction vector: Spherical Vector Distributions. * 6-j symbols: Coupling Coefficients. * 9-j symbols: Coupling Coefficients. * acceleration of series: Series Acceleration. * acosh: Elementary Functions. * Adaptive step-size control, differential equations: Adaptive Step-size Control. * Ai(x): Airy Functions and Derivatives. * Airy functions: Airy Functions and Derivatives. * Akima splines: Interpolation Types. * aliasing of arrays: Aliasing of arrays. * alternative optimized functions: Alternative optimized functions. * AMAX, Level-1 BLAS: Level 1 GSL BLAS Interface. * angular reduction: Restriction Functions. * ANSI C, use of: Using the library. * Apell symbol, see Pochammer symbol: Pochhammer Symbol. * approximate comparison of floating point numbers: Approximate Comparison of Floating Point Numbers. * arctangent integral: Arctangent Integral. * argument of complex number: Properties of complex numbers. * arithmetic exceptions: Setting up your IEEE environment. * asinh: Elementary Functions. * astronomical constants: Astronomy and Astrophysics. * ASUM, Level-1 BLAS: Level 1 GSL BLAS Interface. * atanh: Elementary Functions. * atomic physics, constants: Atomic and Nuclear Physics. * autoconf, using with GSL: Autoconf Macros. * AXPY, Level-1 BLAS: Level 1 GSL BLAS Interface. * B-spline wavelets: DWT Initialization. * Bader and Deuflhard, Bulirsch-Stoer method.: Stepping Functions. * Basic Linear Algebra Subroutines (BLAS) <1>: GSL CBLAS Library. * Basic Linear Algebra Subroutines (BLAS): BLAS Support. * Bernoulli trial, random variates: The Bernoulli Distribution. * Bessel functions: Bessel Functions. * Bessel Functions, Fractional Order: Regular Bessel Function - Fractional Order. * best-fit parameters, covariance: Computing the covariance matrix of best fit parameters. * Beta distribution: The Beta Distribution. * Beta function: Beta Functions. * Beta function, incomplete normalized: Incomplete Beta Function. * BFGS conjugate gradient algorithm, minimization: Multimin Algorithms. * Bi(x): Airy Functions and Derivatives. * bias, IEEE format: Representation of floating point numbers. * bidiagonalization of real matrices: Bidiagonalization. * binning data: Histograms. * Binomial random variates: The Binomial Distribution. * biorthogonal wavelets: DWT Initialization. * bisection algorithm for finding roots: Root Bracketing Algorithms. * Bivariate Gaussian distribution: The Bivariate Gaussian Distribution. * BLAS: BLAS Support. * BLAS, Low-level C interface: GSL CBLAS Library. * blocks: Vectors and Matrices. * bounds checking, extension to GCC: Accessing vector elements. * 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. * bug-gsl mailing list: Reporting Bugs. * bugs, how to report: Reporting Bugs. * Bulirsch-Stoer method: Stepping Functions. * C extensions, compatible use of: Using the library. * C++, compatibility: Compatibility with C++. * Carlson forms of Elliptic integrals: Definition of Carlson Forms. * Cash-Karp, Runge-Kutta method: Stepping Functions. * Cauchy distribution: The Cauchy Distribution. * Cauchy principal value, by numerical quadrature: QAWC adaptive integration for Cauchy principal values. * CBLAS: BLAS Support. * CBLAS, Low-level interface: GSL CBLAS Library. * CDFs, cumulative distribution functions: Random Number Distributions. * Chebyshev series: Chebyshev Approximations. * checking combination for validity: Combination properties. * checking permutation for validity: Permutation properties. * Chi(x): Hyperbolic Integrals. * Chi-squared distribution: The Chi-squared Distribution. * Cholesky decomposition: Cholesky Decomposition. * Ci(x): Trigonometric Integrals. * Clausen functions: Clausen Functions. * Clenshaw-Curtis quadrature: Integrands with weight functions. * CMRG, combined multiple recursive random number generator: Random number generator algorithms. * code reuse in applications: Code Reuse. * combinations: Combinations. * combinatorial factor C(m,n): Factorials. * combinatorial optimization: Simulated Annealing. * comparison functions, definition: Sorting objects. * compatibility: Using the library. * compiling programs, include paths: Compiling and Linking. * compiling programs, library paths: Linking programs with the library. * complementary incomplete Gamma function: Incomplete Gamma Functions. * complete Fermi-Dirac integrals: Complete Fermi-Dirac Integrals. * complex arithmetic: Complex arithmetic operators. * complex cosine function, special functions: Trigonometric Functions for Complex Arguments. * Complex Gamma function: Gamma Functions. * complex hermitian matrix, eigensystem: Complex Hermitian Matrices. * complex log sine function, special functions: Trigonometric Functions for Complex Arguments. * complex numbers: Complex Numbers. * complex sinc function, special functions: Circular Trigonometric Functions. * complex sine function, special functions: Trigonometric Functions for Complex Arguments. * confluent hypergeometric function: Laguerre Functions. * confluent hypergeometric functions: Hypergeometric Functions. * conical functions: Legendre Functions and Spherical Harmonics. * Conjugate gradient algorithm, minimization: Multimin Algorithms. * conjugate of complex number: Complex arithmetic operators. * constant matrix: Initializing matrix elements. * constants, fundamental: Fundamental Constants. * constants, mathematical--defined as macros: Mathematical Constants. * constants, physical: Physical Constants. * constants, prefixes: Prefixes. * contacting the GSL developers: Further Information. * conventions, used in manual: Conventions used in this manual. * convergence, accelerating a series: Series Acceleration. * conversion of units: Physical Constants. * cooling schedule: Simulated Annealing algorithm. * COPY, Level-1 BLAS: Level 1 GSL BLAS Interface. * cosine function, special functions: Circular Trigonometric Functions. * cosine of complex number: Complex Trigonometric Functions. * cost function: Simulated Annealing. * Coulomb wave functions: Coulomb Functions. * coupling coefficients: Coupling Coefficients. * covariance matrix, from linear regression: Linear regression. * covariance matrix, linear fits: Fitting Overview. * covariance matrix, nonlinear fits: Computing the covariance matrix of best fit parameters. * covariance, of two datasets: Covariance. * CRAY random number generator, RANF: Other random number generators. * cubic equation, solving: Cubic Equations. * cubic splines: Interpolation Types. * cumulative distribution functions (CDFs): Random Number Distributions. * Cylindrical Bessel Functions: Regular Cylindrical Bessel Functions. * Daubechies wavelets: DWT Initialization. * Dawson function: Dawson Function. * debugging numerical programs: Using gdb. * Debye functions: Debye Functions. * denormalized form, IEEE format: Representation of floating point numbers. * deprecated functions: Deprecated Functions. * derivatives, calculating numerically: Numerical Differentiation. * determinant of a matrix, by LU decomposition: LU Decomposition. * Deuflhard and Bader, Bulirsch-Stoer method.: Stepping Functions. * DFTs, see FFT: Fast Fourier Transforms. * diagonal, of a matrix: Creating row and column views. * differential equations, initial value problems: Ordinary Differential Equations. * differentiation of functions, numeric: Numerical Differentiation. * digamma function: Psi (Digamma) Function. * dilogarithm: Dilogarithm. * direction vector, random 2D: Spherical Vector Distributions. * direction vector, random 3D: Spherical Vector Distributions. * direction vector, random N-dimensional: Spherical Vector Distributions. * Dirichlet distribution: The Dirichlet Distribution. * Discrete Fourier Transforms, see FFT: Fast Fourier Transforms. * discrete Hankel transforms: Discrete Hankel Transforms. * Discrete Newton algorithm for multidimensional roots: Algorithms without Derivatives. * Discrete random numbers: General Discrete Distributions. * Discrete random numbers, preprocessing: General Discrete Distributions. * divided differences, polynomials: Divided Difference Representation of Polynomials. * division by zero, IEEE exceptions: Setting up your IEEE environment. * dollar sign $, shell prompt: Conventions used in this manual. * DOT, Level-1 BLAS: Level 1 GSL BLAS Interface. * double factorial: Factorials. * double precision, IEEE format: Representation of floating point numbers. * downloading GSL: Obtaining GSL. * DWT initialization: DWT Initialization. * DWT, mathematical definition: DWT Definitions. * DWT, one dimensional: DWT in one dimension. * DWT, see wavelet transforms: Wavelet Transforms. * DWT, two dimensional: DWT in two dimension. * e, defined as a macro: Mathematical Constants. * E1(x), E2(x), Ei(x): Exponential Integral. * eigenvalues and eigenvectors: Eigensystems. * elementary functions: Mathematical Functions. * elementary operations: Elementary Operations. * elliptic functions (Jacobi): Elliptic Functions (Jacobi). * elliptic integrals: Elliptic Integrals. * energy function: Simulated Annealing. * energy, units of: Thermal Energy and Power. * erf(x): Error Functions. * erfc(x): Error Functions. * Erlang distribution: The Gamma Distribution. * error codes: Error Codes. * error function: Error Functions. * Error handlers: Error Handlers. * error handling: Error Handling. * error handling macros: Using GSL error reporting in your own functions. * Errors: Error Handling. * estimated standard deviation: Statistics. * estimated variance: Statistics. * euclidean distance function, hypot: Elementary Functions. * Euler's constant, defined as a macro: Mathematical Constants. * evaluation of polynomials: Polynomial Evaluation. * evaluation of polynomials, in divided difference form: Divided Difference Representation of Polynomials. * examples, conventions used in: Conventions used in this manual. * exceptions, IEEE arithmetic: Setting up your IEEE environment. * exchanging permutation elements: Accessing permutation elements. * exp: Exponential Functions. * expm1: Elementary Functions. * exponent, IEEE format: Representation of floating point numbers. * Exponential distribution: The Exponential Distribution. * exponential function: Exponential Functions. * exponential integrals: Exponential Integrals. * Exponential power distribution: The Exponential Power Distribution. * exponential, difference from 1 computed accurately: Elementary Functions. * exponentiation of complex number: Elementary Complex Functions. * F-distribution: The F-distribution. * factorial: Factorials. * factorization of matrices: Linear Algebra. * false position algorithm for finding roots: Root Bracketing Algorithms. * Fast Fourier Transforms, see FFT: Fast Fourier Transforms. * FDL, GNU Free Documentation License: GNU Free Documentation License. * Fehlberg method, differential equations: Stepping Functions. * Fermi-Dirac function: Fermi-Dirac Function. * FFT: Fast Fourier Transforms. * 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. * FFT, complex data: Overview of complex data FFTs. * finding minima: One dimensional Minimization. * finding roots: One dimensional Root-Finding. * finding zeros: One dimensional Root-Finding. * fits, multi-parameter linear: Multi-parameter fitting. * fitting: Least-Squares Fitting. * fitting, using Chebyshev polynomials: Chebyshev Approximations. * Fj(x), Fermi-Dirac integral: Complete Fermi-Dirac Integrals. * Fj(x,b), incomplete Fermi-Dirac integral: Incomplete Fermi-Dirac Integrals. * flat distribution: The Flat (Uniform) Distribution. * Fletcher-Reeves conjugate gradient algorithm, minimization: Multimin Algorithms. * floating point numbers, approximate comparison: Approximate Comparison of Floating Point Numbers. * force and energy, units of: Force and Energy. * Fortran range checking, equivalent in gcc: Accessing vector elements. * Four-tap Generalized Feedback Shift Register: Random number generator algorithms. * Fourier integrals, numerical: QAWF adaptive integration for Fourier integrals. * Fourier Transforms, see FFT: Fast Fourier Transforms. * Fractional Order Bessel Functions: Regular Bessel Function - Fractional Order. * free documentation: Free Software Needs Free Documentation. * free software, explanation of: GSL is Free Software. * frexp: Elementary Functions. * functions, numerical differentiation: Numerical Differentiation. * fundamental constants: Fundamental Constants. * Gamma distribution: The Gamma Distribution. * gamma functions: Gamma Functions. * Gauss-Kronrod quadrature: Integrands without weight functions. * Gaussian distribution: The Gaussian Distribution. * Gaussian distribution, bivariate: The Bivariate Gaussian Distribution. * Gaussian Tail distribution: The Gaussian Tail Distribution. * gcc extensions, range-checking: Accessing vector elements. * gcc warning options: GCC warning options for numerical programs. * gdb: Using gdb. * Gear method, differential equations: Stepping Functions. * Gegenbauer functions: Gegenbauer Functions. * GEMM, Level-3 BLAS: Level 3 GSL BLAS Interface. * GEMV, Level-2 BLAS: Level 2 GSL BLAS Interface. * general polynomial equations, solving: General Polynomial Equations. * Geometric random variates <1>: The Hypergeometric Distribution. * Geometric random variates: The Geometric Distribution. * GER, Level-2 BLAS: Level 2 GSL BLAS Interface. * GERC, Level-2 BLAS: Level 2 GSL BLAS Interface. * GERU, Level-2 BLAS: Level 2 GSL BLAS Interface. * Givens Rotation, BLAS: Level 1 GSL BLAS Interface. * Givens Rotation, Modified, BLAS: Level 1 GSL BLAS Interface. * GNU General Public License: Introduction. * 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): The Type-1 Gumbel Distribution. * Gumbel distribution (Type 2): The Type-2 Gumbel Distribution. * Haar wavelets: DWT Initialization. * Hankel transforms, discrete: Discrete Hankel Transforms. * HAVE_INLINE: Inline functions. * hazard function, normal distribution: Probability functions. * HBOOK: Ntuple References and Further Reading. * header files, including: Compiling and Linking. * heapsort: Sorting. * HEMM, Level-3 BLAS: Level 3 GSL BLAS Interface. * HEMV, Level-2 BLAS: Level 2 GSL BLAS Interface. * HER, Level-2 BLAS: Level 2 GSL BLAS Interface. * HER2, Level-2 BLAS: Level 2 GSL BLAS Interface. * HER2K, Level-3 BLAS: Level 3 GSL BLAS Interface. * HERK, Level-3 BLAS: Level 3 GSL BLAS Interface. * hermitian matrix, complex, eigensystem: Complex Hermitian Matrices. * histogram statistics: Histogram Statistics. * histogram, from ntuple: Histogramming ntuple values. * histograms: Histograms. * histograms, random sampling from: The histogram probability distribution struct. * Householder linear solver: Householder solver for linear systems. * Householder matrix: Householder Transformations. * Householder transformation: Householder Transformations. * HYBRID algorithm, unscaled without derivatives: Algorithms without Derivatives. * HYBRID algorithms for nonlinear systems: Algorithms using Derivatives. * HYBRIDJ algorithm: Algorithms using Derivatives. * HYBRIDS algorithm, scaled without derivatives: Algorithms without Derivatives. * HYBRIDSJ algorithm: Algorithms using Derivatives. * hydrogen atom: Coulomb Functions. * hyperbolic cosine, inverse: Elementary Functions. * hyperbolic functions, complex numbers: Complex Hyperbolic Functions. * hyperbolic integrals: Hyperbolic Integrals. * hyperbolic sine, inverse: Elementary Functions. * hyperbolic space: Legendre Functions and Spherical Harmonics. * hyperbolic tangent, inverse: Elementary Functions. * hypergeometric functions: Hypergeometric Functions. * hypergeometric random variates: The Hypergeometric Distribution. * hypot: Elementary Functions. * hypot function, special functions: Circular Trigonometric Functions. * identity matrix: Initializing matrix elements. * identity permutation: Permutation allocation. * 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. * IEEE infinity, defined as a macro: Infinities and Not-a-number. * IEEE NaN, defined as a macro: Infinities and Not-a-number. * illumination, units of: Light and Illumination. * imperial units: Imperial Units. * importance sampling, VEGAS: VEGAS. * including GSL header files: Compiling and Linking. * incomplete Beta function, normalized: Incomplete Beta Function. * incomplete Fermi-Dirac integral: Incomplete Fermi-Dirac Integrals. * incomplete Gamma function: Incomplete Gamma Functions. * indirect sorting: Sorting objects. * indirect sorting, of vector elements: Sorting vectors. * infinity, defined as a macro: Infinities and Not-a-number. * infinity, IEEE format: Representation of floating point numbers. * info-gsl mailing list: Obtaining GSL. * initial value problems, differential equations: Ordinary Differential Equations. * initializing matrices: Initializing matrix elements. * initializing vectors: Initializing vector elements. * inline functions: Inline functions. * integer powers: Power Function. * integrals, exponential: Exponential Integrals. * integration, numerical (quadrature): Numerical Integration. * interpolation: Interpolation. * interpolation, using Chebyshev polynomials: Chebyshev Approximations. * inverse complex trigonometric functions: Inverse Complex Trigonometric Functions. * inverse cumulative distribution functions: Random Number Distributions. * inverse hyperbolic cosine: Elementary Functions. * inverse hyperbolic functions, complex numbers: Inverse Complex Hyperbolic Functions. * inverse hyperbolic sine: Elementary Functions. * inverse hyperbolic tangent: Elementary Functions. * inverse of a matrix, by LU decomposition: LU Decomposition. * inverting a permutation: Permutation functions. * Irregular Cylindrical Bessel Functions: Irregular Cylindrical Bessel Functions. * Irregular Modified Bessel Functions, Fractional Order: Irregular Modified Bessel Functions - Fractional Order. * Irregular Modified Cylindrical Bessel Functions: Irregular Modified Cylindrical Bessel Functions. * Irregular Modified Spherical Bessel Functions: Irregular Modified Spherical Bessel Functions. * Irregular Spherical Bessel Functions: Irregular Spherical Bessel Functions. * iterating through combinations: Combination functions. * iterating through permutations: Permutation functions. * iterative refinement of solutions in linear systems: LU Decomposition. * Jacobi elliptic functions: Elliptic Functions (Jacobi). * Laguerre functions: Laguerre Functions. * Lambert function: Lambert W Functions. * Landau distribution: The Landau Distribution. * LAPACK, recommended for linear algebra <1>: Eigensystems. * LAPACK, recommended for linear algebra: Linear Algebra. * Laplace distribution: The Laplace Distribution. * LD_LIBRARY_PATH: Shared Libraries. * ldexp: Elementary Functions. * leading dimension, matrices: Matrices. * least squares fit: Least-Squares Fitting. * least squares fitting, nonlinear: Nonlinear Least-Squares Fitting. * least squares, covariance of best-fit parameters: Computing the covariance matrix of best fit parameters. * Legendre forms of elliptic integrals: Definition of Legendre Forms. * Legendre functions: Legendre Functions and Spherical Harmonics. * length, computed accurately using hypot: Elementary Functions. * Levenberg-Marquardt algorithms: Minimization Algorithms using Derivatives. * Levin u-transform: Series Acceleration. * Levy distribution: The Levy alpha-Stable Distributions. * Levy distribution, skew: The Levy skew alpha-Stable Distribution. * libraries, linking with: Linking programs with the library. * libraries, shared: Shared Libraries. * license of GSL: Introduction. * light, units of: Light and Illumination. * linear algebra: Linear Algebra. * linear algebra, BLAS: BLAS Support. * linear interpolation: Interpolation Types. * linear regression: Linear regression. * linear systems, refinement of solutions: LU Decomposition. * linear systems, solution of: LU Decomposition. * linking with GSL libraries: Linking programs with the library. * LMDER algorithm: Minimization Algorithms using Derivatives. * log1p: Elementary Functions. * logarithm and related functions: Logarithm and Related Functions. * logarithm of Beta function: Beta Functions. * logarithm of combinatorial factor C(m,n): Factorials. * logarithm of complex number: Elementary Complex Functions. * logarithm of cosh function, special functions: Hyperbolic Trigonometric Functions. * logarithm of double factorial: Factorials. * logarithm of factorial: Factorials. * logarithm of Gamma function: Gamma Functions. * logarithm of Pochhammer symbol: Pochhammer Symbol. * logarithm of sinh function, special functions: Hyperbolic Trigonometric Functions. * logarithm of the determinant of a matrix: LU Decomposition. * logarithm, computed accurately near 1: Elementary Functions. * Logarithmic random variates: The Logarithmic Distribution. * Logistic distribution: The Logistic Distribution. * Lognormal distribution: The Lognormal Distribution. * long double: Long double. * low discrepancy sequences: Quasi-Random Sequences. * Low-level CBLAS: GSL CBLAS Library. * LU decomposition: LU Decomposition. * macros for mathematical constants: Mathematical Constants. * magnitude of complex number: Properties of complex numbers. * mailing list archives: Further Information. * mailing list for GSL announcements: Obtaining GSL. * mailing list, bug-gsl: Reporting Bugs. * mantissa, IEEE format: Representation of floating point numbers. * mass, units of: Mass and Weight. * mathematical constants, defined as macros: Mathematical Constants. * mathematical functions, elementary: Mathematical Functions. * matrices <1>: Matrices. * matrices: Vectors and Matrices. * matrices, initializing: Initializing matrix elements. * matrices, range-checking: Accessing matrix elements. * matrix determinant: LU Decomposition. * matrix diagonal: Creating row and column views. * matrix factorization: Linear Algebra. * matrix inverse: LU Decomposition. * matrix square root, Cholesky decomposition: Cholesky Decomposition. * matrix subdiagonal: Creating row and column views. * matrix superdiagonal: Creating row and column views. * matrix, constant: Initializing matrix elements. * matrix, identity: Initializing matrix elements. * matrix, operations: BLAS Support. * matrix, zero: Initializing matrix elements. * max: Statistics. * maximal phase, Daubechies wavelets: DWT Initialization. * maximization, see minimization: One dimensional Minimization. * maximum of two numbers: Maximum and Minimum functions. * maximum value, from histogram: Histogram Statistics. * mean: Statistics. * mean value, from histogram: Histogram Statistics. * Mill's ratio, inverse: Probability functions. * min: Statistics. * minimization, BFGS conjugate gradient algorithm: Multimin Algorithms. * minimization, caveats: Minimization Caveats. * minimization, conjugate gradient algorithm: Multimin Algorithms. * minimization, multidimensional: Multidimensional Minimization. * minimization, one-dimensional: One dimensional Minimization. * minimization, overview: Minimization Overview. * minimization, Polak-Ribiere algorithm: Multimin Algorithms. * minimization, providing a function to minimize: Providing the function to minimize. * minimization, simplex algorithm: Multimin Algorithms. * minimization, steepest descent algorithm: Multimin Algorithms. * 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. * minimum value, from histogram: Histogram Statistics. * MINPACK, minimization algorithms <1>: Minimization Algorithms using Derivatives. * MINPACK, minimization algorithms: Algorithms using Derivatives. * MISCFUN: Special Functions References and Further Reading. * MISER monte carlo integration: MISER. * 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 Bessel Functions, Fractional Order: Regular Modified Bessel Functions - Fractional Order. * Modified Clenshaw-Curtis quadrature: Integrands with weight functions. * Modified Cylindrical Bessel Functions: Regular Modified Cylindrical Bessel Functions. * Modified Givens Rotation, BLAS: Level 1 GSL BLAS Interface. * Modified Newton's method for nonlinear systems: Algorithms using Derivatives. * Modified Spherical Bessel Functions: Regular Modified Spherical Bessel Functions. * Monte Carlo integration: Monte Carlo Integration. * MRG, multiple recursive random number generator: Random number generator algorithms. * MT19937 random number generator: Random number generator algorithms. * multi-parameter regression: Multi-parameter fitting. * 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. * Multimin, caveats: Multimin Caveats. * Multinomial distribution: The Multinomial Distribution. * multiplication: Elementary Operations. * N-dimensional random direction vector: Spherical Vector Distributions. * NaN, defined as a macro: Infinities and Not-a-number. * nautical units: Speed and Nautical Units. * Negative Binomial distribution, random variates: The Negative Binomial Distribution. * Nelder-Mead simplex algorithm for minimization: Multimin Algorithms. * Newton algorithm, discrete: Algorithms without Derivatives. * Newton algorithm, globally convergent: Algorithms using Derivatives. * Newton's method for finding roots: Root Finding Algorithms using Derivatives. * Newton's method for systems of nonlinear equations: Algorithms using Derivatives. * Niederreiter sequence: Quasi-Random Sequences. * NIST Statistical Reference Datasets: Fitting References and Further Reading. * non-normalized incomplete Gamma function: Incomplete Gamma Functions. * nonlinear equation, solutions of: One dimensional Root-Finding. * nonlinear fitting, stopping parameters: Search Stopping Parameters for Minimization Algorithms. * nonlinear functions, minimization: One dimensional Minimization. * nonlinear least squares fitting: Nonlinear Least-Squares Fitting. * nonlinear least squares fitting, overview: Overview of Nonlinear Least-Squares Fitting. * nonlinear systems of equations, solution of: Multidimensional Root-Finding. * normalized form, IEEE format: Representation of floating point numbers. * normalized incomplete Beta function: Incomplete Beta Function. * Not-a-number, defined as a macro: Infinities and Not-a-number. * NRM2, Level-1 BLAS: Level 1 GSL BLAS Interface. * ntuples: N-tuples. * nuclear physics, constants: Atomic and Nuclear Physics. * numerical constants, defined as macros: Mathematical Constants. * numerical derivatives: Numerical Differentiation. * numerical integration (quadrature): Numerical Integration. * obtaining GSL: Obtaining GSL. * ODEs, initial value problems: Ordinary Differential Equations. * optimization, combinatorial: Simulated Annealing. * optimization, see minimization: One dimensional Minimization. * optimized functions, alternatives: Alternative optimized functions. * ordinary differential equations, initial value problem: Ordinary Differential Equations. * oscillatory functions, numerical integration of: QAWO adaptive integration for oscillatory functions. * overflow, IEEE exceptions: Setting up your IEEE environment. * Pareto distribution: The Pareto Distribution. * PAW: Ntuple References and Further Reading. * permutations: Permutations. * physical constants: Physical Constants. * physical dimension, matrices: Matrices. * pi, defined as a macro: Mathematical Constants. * plain monte carlo: PLAIN Monte Carlo. * Pochhammer symbol: Pochhammer Symbol. * Poisson random numbers: The Poisson Distribution. * Polak-Ribiere algorithm, minimization: Multimin Algorithms. * polar form of complex numbers: Complex numbers. * polar to rectangular conversion: Conversion Functions. * polygamma functions: Psi (Digamma) Function. * polynomial evaluation: Polynomial Evaluation. * polynomial interpolation: Interpolation Types. * polynomials, roots of: Polynomials. * power function: Power Function. * power of complex number: Elementary Complex Functions. * power, units of: Thermal Energy and Power. * precision, IEEE arithmetic: Setting up your IEEE environment. * prefixes: Prefixes. * pressure, units of: Pressure. * Prince-Dormand, Runge-Kutta method: Stepping Functions. * printers units: Printers Units. * probability distribution, from histogram: The histogram probability distribution struct. * probability distributions, from histograms: Resampling from histograms. * projection of ntuples: Histogramming ntuple values. * 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. * quantile functions: Random Number Distributions. * quasi-random sequences: Quasi-Random Sequences. * R250 shift-register random number generator: Other random number generators. * Racah coefficients: Coupling Coefficients. * radioactivity, units of: Radioactivity. * Radix-2 FFT for real data: Radix-2 FFT routines for real data. * Radix-2 FFT, complex data: Radix-2 FFT routines for complex data. * rand, BSD random number generator: Unix random number generators. * rand48 random number generator: Unix random number generators. * random number distributions: Random Number Distributions. * random number generators: Random Number Generation. * random sampling from histograms: The histogram probability distribution struct. * 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 distribution: The Rayleigh Distribution. * Rayleigh Tail distribution: The Rayleigh Tail Distribution. * real symmetric matrix, eigensystem: Real Symmetric Matrices. * Reciprocal Gamma function: Gamma Functions. * rectangular to polar conversion: Conversion Functions. * recursive stratified sampling, MISER: MISER. * reduction of angular variables: Restriction Functions. * refinement of solutions in linear systems: LU Decomposition. * regression, least squares: Least-Squares Fitting. * Regular Bessel Functions, Fractional Order: Regular Bessel Function - Fractional Order. * Regular Bessel Functions, Zeros of: Zeros of Regular Bessel Functions. * Regular Cylindrical Bessel Functions: Regular Cylindrical Bessel Functions. * Regular Modified Bessel Functions, Fractional Order: Regular Modified Bessel Functions - Fractional Order. * Regular Modified Cylindrical Bessel Functions: Regular Modified Cylindrical Bessel Functions. * Regular Modified Spherical Bessel Functions: Regular Modified Spherical Bessel Functions. * Regular Spherical Bessel Functions: Regular Spherical Bessel Functions. * Regulated Gamma function: Gamma Functions. * relative Pochhammer symbol: Pochhammer Symbol. * reporting bugs in GSL: Reporting Bugs. * representations of complex numbers: Complex numbers. * resampling from histograms: Resampling from histograms. * residual, in nonlinear systems of equations <1>: Search Stopping Parameters for Minimization Algorithms. * residual, in nonlinear systems of equations: Search Stopping Parameters for the multidimensional solver. * reversing a permutation: Permutation functions. * RK2, Runge-Kutta method: Stepping Functions. * RK4, Runge-Kutta method: Stepping Functions. * RKF45, Runge-Kutta-Fehlberg method: Stepping 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: 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: 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. * ROTG, Level-1 BLAS: Level 1 GSL BLAS Interface. * rounding mode: Setting up your IEEE environment. * Runge-Kutta Cash-Karp method: Stepping Functions. * Runge-Kutta methods, ordinary differential equations: Stepping Functions. * Runge-Kutta Prince-Dormand method: Stepping Functions. * safe comparison of floating point numbers: Approximate Comparison of Floating Point Numbers. * sampling from histograms <1>: The histogram probability distribution struct. * sampling from histograms: Resampling from histograms. * SCAL, Level-1 BLAS: Level 1 GSL BLAS Interface. * schedule, cooling: Simulated Annealing algorithm. * secant method for finding roots: Root Finding Algorithms using Derivatives. * selection function, ntuples: Histogramming ntuple values. * series, acceleration: Series Acceleration. * shared libraries: Shared Libraries. * shell prompt: Conventions used in this manual. * Shi(x): Hyperbolic Integrals. * shift-register random number generator: Other random number generators. * Si(x): Trigonometric Integrals. * sign bit, IEEE format: Representation of floating point numbers. * sign of the determinant of a matrix: LU Decomposition. * simplex algorithm, minimization: Multimin Algorithms. * simulated annealing: Simulated Annealing. * sin, of complex number: Complex Trigonometric Functions. * sine function, special functions: Circular Trigonometric Functions. * single precision, IEEE format: Representation of floating point numbers. * singular functions, numerical integration of: QAWS adaptive integration for singular functions. * singular points, specifying positions in quadrature: QAGP adaptive integration with known singular points. * singular value decomposition: Singular Value Decomposition. * Skew Levy distribution: The Levy skew alpha-Stable Distribution. * slope, see numerical derivative: Numerical Differentiation. * Sobol sequence: Quasi-Random Sequences. * solution of linear system by Householder transformations: Householder solver for linear systems. * solution of linear systems, Ax=b: Linear Algebra. * solving a nonlinear equation: One dimensional Root-Finding. * solving nonlinear systems of equations: Multidimensional Root-Finding. * sorting: Sorting. * sorting eigenvalues and eigenvectors: Sorting Eigenvalues and Eigenvectors. * sorting vector elements: Sorting vectors. * source code, reuse in applications: Code Reuse. * special functions: Special Functions. * Spherical Bessel Functions: Regular Spherical Bessel Functions. * spherical harmonics: Legendre Functions and Spherical Harmonics. * spherical random variates, 2D: Spherical Vector Distributions. * spherical random variates, 3D: Spherical Vector Distributions. * spherical random variates, N-dimensional: Spherical Vector Distributions. * spline: Interpolation. * square root of a matrix, Cholesky decomposition: Cholesky Decomposition. * square root of complex number: Elementary Complex Functions. * standard deviation: Statistics. * standard deviation, from histogram: Histogram Statistics. * standards conformance, ANSI C: Using the library. * Statistical Reference Datasets (StRD): Fitting References and Further Reading. * statistics: Statistics. * statistics, from histogram: Histogram Statistics. * steepest descent algorithm, minimization: Multimin Algorithms. * Steffenson's method for finding roots: Root Finding Algorithms using Derivatives. * stratified sampling in monte carlo integration: Monte Carlo Integration. * stride, of vector index: Vectors. * Student t-distribution: The t-distribution. * subdiagonal, of a matrix: Creating row and column views. * summation, acceleration: Series Acceleration. * superdiagonal, matrix: Creating row and column views. * SVD: Singular Value Decomposition. * SWAP, Level-1 BLAS: Level 1 GSL BLAS Interface. * swapping permutation elements: Accessing permutation elements. * SYMM, Level-3 BLAS: Level 3 GSL BLAS Interface. * symmetric matrix, real, eigensystem: Real Symmetric Matrices. * SYMV, Level-2 BLAS: Level 2 GSL BLAS Interface. * synchrotron functions: Synchrotron Functions. * SYR, Level-2 BLAS: Level 2 GSL BLAS Interface. * SYR2, Level-2 BLAS: Level 2 GSL BLAS Interface. * SYR2K, Level-3 BLAS: Level 3 GSL BLAS Interface. * SYRK, Level-3 BLAS: Level 3 GSL BLAS Interface. * systems of equations, nonlinear: Multidimensional Root-Finding. * t-distribution: The t-distribution. * t-test: Statistics. * tangent of complex number: Complex Trigonometric Functions. * Tausworthe random number generator: Random number generator algorithms. * Taylor coefficients, computation of: Factorials. * testing combination for validity: Combination properties. * testing permutation for validity: Permutation properties. * thermal energy, units of: Thermal Energy and Power. * time units: Measurement of Time. * trailing dimension, matrices: Matrices. * transformation, Householder: Householder Transformations. * transforms, Hankel: Discrete Hankel Transforms. * transforms, wavelet: Wavelet Transforms. * transport functions: Transport Functions. * traveling salesman problem: Traveling Salesman Problem. * tridiagonal decomposition <1>: Tridiagonal Decomposition of Hermitian Matrices. * tridiagonal decomposition: Tridiagonal Decomposition of Real Symmetric Matrices. * tridiagonal systems: Tridiagonal Systems. * trigonometric functions: Trigonometric Functions. * trigonometric functions of complex numbers: Complex Trigonometric Functions. * trigonometric integrals: Trigonometric Integrals. * TRMM, Level-3 BLAS: Level 3 GSL BLAS Interface. * TRMV, Level-2 BLAS: Level 2 GSL BLAS Interface. * TRSM, Level-3 BLAS: Level 3 GSL BLAS Interface. * TRSV, Level-2 BLAS: Level 2 GSL BLAS Interface. * TSP: Traveling Salesman Problem. * TT800 random number generator: Other random number generators. * two dimensional Gaussian distribution: The Bivariate Gaussian Distribution. * two dimensional histograms: Two dimensional histograms. * two-sided exponential distribution: The Laplace Distribution. * Type 1 Gumbel distribution, random variates: The Type-1 Gumbel Distribution. * Type 2 Gumbel distribution: The Type-2 Gumbel Distribution. * u-transform for series: Series Acceleration. * underflow, IEEE exceptions: Setting up your IEEE environment. * uniform distribution: The Flat (Uniform) Distribution. * units, conversion of: Physical Constants. * units, imperial: Imperial Units. * Unix random number generators, rand: Unix random number generators. * Unix random number generators, rand48: Unix random number generators. * unnormalized incomplete Gamma function: Incomplete Gamma Functions. * unweighted linear fits: Least-Squares Fitting. * usage, compiling application programs: Using the library. * value function, ntuples: Histogramming ntuple values. * Van der Pol oscillator, example: ODE Example programs. * variance: Statistics. * variance, from histogram: Histogram Statistics. * variance-covariance matrix, linear fits: Fitting Overview. * VAX random number generator: Other random number generators. * vector, operations: BLAS Support. * vector, sorting elements of: Sorting vectors. * vectors <1>: Vectors. * vectors: Vectors and Matrices. * vectors, initializing: Initializing vector elements. * vectors, range-checking: Accessing vector elements. * VEGAS monte carlo integration: VEGAS. * viscosity, units of: Viscosity. * volume units: Volume Area and Length. * W function: Lambert W Functions. * warning options: GCC warning options for numerical programs. * warranty (none): No Warranty. * wavelet transforms: Wavelet Transforms. * website, developer information: Further Information. * Weibull distribution: The Weibull Distribution. * weight, units of: Mass and Weight. * weighted linear fits: Least-Squares Fitting. * Wigner coefficients: Coupling Coefficients. * zero finding: One dimensional Root-Finding. * zero matrix: Initializing matrix elements. * zero, IEEE format: Representation of floating point numbers. * Zeros of Regular Bessel Functions: Zeros of Regular Bessel Functions. * Zeta functions: Zeta Functions.