Concept Index

• $, 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
• Adams method: Stepping 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 Mathieu Functions: Angular Mathieu Functions
• angular reduction: Restriction Functions
• ANSI C, use of: Using the library
• Apell symbol, see Pochhammer 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
• balancing matrices: Balancing
• Basic Linear Algebra Subroutines (BLAS): GSL CBLAS Library
• Basic Linear Algebra Subroutines (BLAS): BLAS Support
• basis splines, B-splines: Basis Splines
• basis splines, derivatives: Evaluation of B-spline basis function derivatives
• basis splines, evaluation: Evaluation of B-spline basis functions
• basis splines, examples: Example programs for B-splines
• basis splines, Greville abscissae: Obtaining Greville abscissae for B-spline basis functions
• basis splines, initializing: Initializing the B-splines solver
• basis splines, overview: Overview of B-splines
• BDF method: Stepping Functions
• 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 algorithm, minimization: Multimin Algorithms with Derivatives
• 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++
• C99, inline keyword: Inline functions
• 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
• ce(q,x), Mathieu function: Angular Mathieu Functions
• Chebyshev series: Chebyshev Approximations
• checking combination for validity: Combination properties
• checking multiset for validity: Multiset 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 with Derivatives
• 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
• correlation, of two datasets: Correlation
• 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
• cquad, doubly-adaptive integration: CQUAD doubly-adaptive integration
• 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
• DAXPY, Level-1 BLAS: Level 1 GSL BLAS Interface
• 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
• discontinuities, in ODE systems: Evolution
• 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 codes, reserved: 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
• Eta Function: Eta Function
• 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, C++: Compatibility with C++
• exceptions, floating point: Handling floating point exceptions
• 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
• extern inline: Inline 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
• 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 with Derivatives
• floating point exceptions: Handling floating point exceptions
• floating point numbers, approximate comparison: Approximate Comparison of Floating Point Numbers
• floating point registers: Examining floating point registers
• 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
• 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
• generalized eigensystems: Real Generalized Nonsymmetric Eigensystems
• generalized hermitian definite eigensystems: Complex Generalized Hermitian-Definite Eigensystems
• generalized symmetric eigensystems: Real Generalized Symmetric-Definite Eigensystems
• Geometric random variates: 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_C99_INLINE: Inline functions
• GSL_RNG_SEED: Random number generator initialization
• 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
• Hessenberg decomposition: Hessenberg Decomposition of Real Matrices
• Hessenberg triangular decomposition: Hessenberg-Triangular Decomposition of Real 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
• Hurwitz Zeta Function: Hurwitz Zeta Function
• 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
• i(x), Bessel Functions: Regular Modified Spherical Bessel Functions
• I(x), Bessel Functions: Regular Modified Cylindrical Bessel 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
• Implicit Euler method: Stepping Functions
• Implicit Runge-Kutta method: Stepping Functions
• 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 multisets: Multiset functions
• iterating through permutations: Permutation functions
• iterative refinement of solutions in linear systems: LU Decomposition
• j(x), Bessel Functions: Regular Spherical Bessel Functions
• J(x), Bessel Functions: Regular Cylindrical Bessel Functions
• Jacobi elliptic functions: Elliptic Functions (Jacobi)
• Jacobi orthogonalization: Singular Value Decomposition
• Jacobian matrix, fitting: Overview of Nonlinear Least-Squares Fitting
• Jacobian matrix, ODEs: Defining the ODE System
• Jacobian matrix, root finding: Overview of Multidimensional Root Finding
• k(x), Bessel Functions: Irregular Modified Spherical Bessel Functions
• K(x), Bessel Functions: Irregular Modified Cylindrical Bessel Functions
• knots, basis splines: Constructing the knots vector
• kurtosis: Higher moments (skewness and kurtosis)
• Laguerre functions: Laguerre Functions
• Lambert function: Lambert W Functions
• Landau distribution: The Landau Distribution
• LAPACK: Eigenvalue and Eigenvector References
• 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
• Legendre polynomials: 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
• Mathieu Function Characteristic Values: Mathieu Function Characteristic Values
• Mathieu functions: Mathieu Functions
• matrices: 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
• Mills' ratio, inverse: Probability functions
• min: Statistics
• minimization, BFGS algorithm: Multimin Algorithms with Derivatives
• minimization, caveats: Minimization Caveats
• minimization, conjugate gradient algorithm: Multimin Algorithms with Derivatives
• minimization, multidimensional: Multidimensional Minimization
• minimization, one-dimensional: One dimensional Minimization
• minimization, overview: Minimization Overview
• minimization, Polak-Ribiere algorithm: Multimin Algorithms with Derivatives
• minimization, providing a function to minimize: Providing the function to minimize
• minimization, simplex algorithm: Multimin Algorithms without Derivatives
• minimization, steepest descent algorithm: Multimin Algorithms with Derivatives
• 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: 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 integration: Monte Carlo Integration
• 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
• multisets: Multisets
• multistep methods, ODEs: Stepping Functions
• 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 without Derivatives
• 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
• nonsymmetric matrix, real, eigensystem: Real Nonsymmetric Matrices
• Nordsieck form: Stepping Functions
• 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
• ordering, matrix elements: Matrices
• 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 with Derivatives
• polar form of complex numbers: Representation of 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
• predictor-corrector method, ODEs: Stepping Functions
• 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
• QAG quadrature algorithm: QAG adaptive integration
• QAGI quadrature algorithm: QAGI adaptive integration on infinite intervals
• QAGP quadrature algorithm: QAGP adaptive integration with known singular points
• QAGS quadrature algorithm: QAGS adaptive integration with singularities
• QAWC quadrature algorithm: QAWC adaptive integration for Cauchy principal values
• QAWF quadrature algorithm: QAWF adaptive integration for Fourier integrals
• QAWO quadrature algorithm: QAWO adaptive integration for oscillatory functions
• QAWS quadrature algorithm: QAWS adaptive integration for singular functions
• QNG quadrature algorithm: QNG non-adaptive Gauss-Kronrod integration
• 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
• Radial Mathieu Functions: Radial Mathieu Functions
• 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 nonsymmetric matrix, eigensystem: Real Nonsymmetric Matrices
• 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: Representation of complex numbers
• resampling from histograms: Resampling from histograms
• residual, in nonlinear systems of equations: Search Stopping Parameters for Minimization Algorithms
• residual, in nonlinear systems of equations: Search Stopping Parameters for the multidimensional solver
• reversing a permutation: Permutation functions
• Riemann Zeta Function: Riemann Zeta Function
• 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: 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
• safeguarded step-length algorithm: Minimization Algorithms
• sampling from histograms: The histogram probability distribution struct
• sampling from histograms: Resampling from histograms
• SAXPY, Level-1 BLAS: Level 1 GSL BLAS Interface
• SCAL, Level-1 BLAS: Level 1 GSL BLAS Interface
• schedule, cooling: Simulated Annealing algorithm
• se(q,x), Mathieu function: Angular Mathieu Functions
• 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 without Derivatives
• 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
• skewness: Higher moments (skewness and kurtosis)
• 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
• splines, basis: Basis Splines
• 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 with Derivatives
• 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 multiset for validity: Multiset 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: 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: 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
• y(x), Bessel Functions: Irregular Spherical Bessel Functions
• Y(x), Bessel Functions: Irregular Cylindrical Bessel Functions
• 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
• Ziggurat method: The Gaussian Distribution