| Index Entry | | Section |
|---|
|
| $ | | |
|---|
| $, shell prompt: | | Conventions used in this manual |
|
| 2 | | |
|---|
| 2D histograms: | | Two dimensional histograms |
| 2D random direction vector: | | Spherical Vector Distributions |
|
| 3 | | |
|---|
| 3-j symbols: | | Coupling Coefficients |
| 3D random direction vector: | | Spherical Vector Distributions |
|
| 6 | | |
|---|
| 6-j symbols: | | Coupling Coefficients |
|
| 9 | | |
|---|
| 9-j symbols: | | Coupling Coefficients |
|
| A | | |
|---|
| 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: | | 1D 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 | | |
|---|
| B-spline wavelets: | | DWT Initialization |
| Bader and Deuflhard, Bulirsch-Stoer method.: | | Stepping Functions |
| balancing matrices: | | Balancing |
| Basic Linear Algebra Subroutines (BLAS): | | BLAS Support |
| Basic Linear Algebra Subroutines (BLAS): | | GSL CBLAS Library |
| 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: | | Working with the Greville abscissae |
| basis splines, initializing: | | Initializing the B-splines solver |
| basis splines, Marsden-Schoenberg points: | | Working with the Greville abscissae |
| 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: | | Nonlinear Least-Squares Covariance Matrix |
| 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 |
| bicubic interpolation: | | 2D Interpolation Types |
| bidiagonalization of real matrices: | | Bidiagonalization |
| bilinear interpolation: | | 2D Interpolation Types |
| 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 |
| Bivariate Gaussian distribution: | | The Multivariate Gaussian Distribution |
| BLAS: | | BLAS Support |
| BLAS, Low-level C interface: | | GSL CBLAS Library |
| BLAS, sparse: | | Sparse BLAS Support |
| 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 | | |
|---|
| 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 |
| Cholesky decomposition, modified: | | Modified Cholesky Decomposition |
| Cholesky decomposition, pivoted: | | Pivoted 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 with a constant term |
| covariance matrix, linear fits: | | Fitting Overview |
| covariance matrix, nonlinear fits: | | Nonlinear Least-Squares Covariance Matrix |
| 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: | | 1D Interpolation Types |
| cumulative distribution functions (CDFs): | | Random Number Distributions |
| Cylindrical Bessel Functions: | | Regular Cylindrical Bessel Functions |
|
| D | | |
|---|
| 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: | | General Discrete Distributions |
| Discrete random numbers: | | General Discrete Distributions |
| 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 |
| Dogleg algorithm: | | Nonlinear Least-Squares TRS Dogleg |
| Dogleg algorithm, double: | | Nonlinear Least-Squares TRS Double Dogleg |
| dollar sign $, shell prompt: | | Conventions used in this manual |
| DOT, Level-1 BLAS: | | Level 1 GSL BLAS Interface |
| double Dogleg algorithm: | | Nonlinear Least-Squares TRS Double Dogleg |
| 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 | | |
|---|
| 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 |
| 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 | | |
|---|
| F-distribution: | | The F-distribution |
| factorial: | | Factorials |
| 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 regression |
| 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 software, explanation of: | | GSL is Free Software |
| frexp: | | Elementary Functions |
| functions, numerical differentiation: | | Numerical Differentiation |
| fundamental constants: | | Fundamental Constants |
|
| G | | |
|---|
| 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 distribution, bivariate: | | The Multivariate 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 Geometric Distribution |
| Geometric random variates: | | The Hypergeometric 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: | | Givens Rotations |
| Givens Rotation, BLAS: | | Level 1 GSL BLAS Interface |
| Givens Rotation, Modified, BLAS: | | Level 1 GSL BLAS Interface |
| gmres: | | Sparse Iterative Solvers Types |
| 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 |
|
| H | | |
|---|
| 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 | | |
|---|
| I(x), Bessel Functions: | | Regular Modified Cylindrical Bessel Functions |
| i(x), Bessel Functions: | | Regular Modified Spherical 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 | | |
|---|
| J(x), Bessel Functions: | | Regular Cylindrical Bessel Functions |
| j(x), Bessel Functions: | | Regular Spherical Bessel Functions |
| Jacobi elliptic functions: | | Elliptic Functions (Jacobi) |
| Jacobi orthogonalization: | | Singular Value Decomposition |
| Jacobian matrix, ODEs: | | Defining the ODE System |
| Jacobian matrix, root finding: | | Overview of Multidimensional Root Finding |
|
| K | | |
|---|
| K(x), Bessel Functions: | | Irregular Modified Cylindrical Bessel Functions |
| k(x), Bessel Functions: | | Irregular Modified Spherical Bessel Functions |
| knots, basis splines: | | Constructing the knots vector |
| kurtosis: | | Higher moments (skewness and kurtosis) |
|
| L | | |
|---|
| Laguerre functions: | | Laguerre Functions |
| Lambert function: | | Lambert W Functions |
| Landau distribution: | | The Landau Distribution |
| LAPACK: | | Eigenvalue and Eigenvector References |
| Laplace distribution: | | The Laplace Distribution |
| large dense linear least squares: | | Large Dense Linear Systems |
| large linear least squares, normal equations: | | Large Dense Linear Systems Normal Equations |
| large linear least squares, routines: | | Large Dense Linear Systems Routines |
| large linear least squares, steps: | | Large Dense Linear Systems Solution Steps |
| large linear least squares, TSQR: | | Large Dense Linear Systems TSQR |
| ldexp: | | Elementary Functions |
| LD_LIBRARY_PATH: | | Shared Libraries |
| leading dimension, matrices: | | Matrices |
| least squares fit: | | Least-Squares Fitting |
| least squares troubleshooting: | | Troubleshooting |
| least squares, covariance of best-fit parameters: | | Nonlinear Least-Squares Covariance Matrix |
| least squares, nonlinear: | | Nonlinear Least-Squares Fitting |
| least squares, regularized: | | Regularized regression |
| least squares, robust: | | Robust linear regression |
| 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 |
| length, computed accurately using hypot: | | Elementary Functions |
| Levenberg-Marquardt algorithm: | | Nonlinear Least-Squares TRS Levenberg-Marquardt |
| Levenberg-Marquardt algorithm, geodesic acceleration: | | Nonlinear Least-Squares TRS Levenberg-Marquardt with Geodesic Acceleration |
| 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 algebra, sparse: | | Sparse Linear Algebra |
| linear interpolation: | | 1D Interpolation Types |
| linear least squares, large: | | Large Dense Linear Systems |
| 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 |
| 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 |
|
| M | | |
|---|
| 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: | | Vectors and Matrices |
| matrices: | | Matrices |
| matrices, initializing: | | Initializing matrix elements |
| matrices, range-checking: | | Accessing matrix elements |
| matrices, sparse: | | Sparse Matrices |
| 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: | | 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 Cholesky Decomposition: | | Modified Cholesky Decomposition |
| 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 regression |
| 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 | | |
|---|
| 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, convergence: | | Nonlinear Least-Squares Testing for Convergence |
| nonlinear functions, minimization: | | One dimensional Minimization |
| nonlinear least squares: | | Nonlinear Least-Squares Fitting |
| nonlinear least squares, dogleg: | | Nonlinear Least-Squares TRS Dogleg |
| nonlinear least squares, double dogleg: | | Nonlinear Least-Squares TRS Double Dogleg |
| nonlinear least squares, levenberg-marquardt: | | Nonlinear Least-Squares TRS Levenberg-Marquardt |
| nonlinear least squares, levenberg-marquardt, geodesic acceleration: | | Nonlinear Least-Squares TRS Levenberg-Marquardt with Geodesic Acceleration |
| nonlinear least squares, overview: | | Nonlinear Least-Squares Overview |
| 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 |
|
| O | | |
|---|
| obtaining GSL: | | Obtaining GSL |
| ODEs, initial value problems: | | Ordinary Differential Equations |
| online statistics: | | Running Statistics |
| 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 |
|
| P | | |
|---|
| 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 |
| Pivoted Cholesky Decomposition: | | Pivoted Cholesky Decomposition |
| 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: | | 1D 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 |
|
| Q | | |
|---|
| 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 |
|
| R | | |
|---|
| 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 |
| 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 |
| regression, ridge: | | Regularized regression |
| regression, robust: | | Robust linear regression |
| regression, Tikhonov: | | Regularized regression |
| 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 the multidimensional solver |
| reversing a permutation: | | Permutation functions |
| ridge regression: | | Regularized regression |
| 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 |
| robust regression: | | Robust linear regression |
| 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 |
| root finding, stopping parameters: | | Search Stopping Parameters for the multidimensional solver |
| 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 |
| running statistics: | | Running Statistics |
|
| S | | |
|---|
| safe comparison of floating point numbers: | | Approximate Comparison of Floating Point Numbers |
| safeguarded step-length algorithm: | | Minimization Algorithms |
| sampling from histograms: | | Resampling from histograms |
| sampling from histograms: | | The histogram probability distribution struct |
| 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 |
| sparse BLAS: | | Sparse BLAS Support |
| sparse linear algebra: | | Sparse Linear Algebra |
| sparse linear algebra, examples: | | Sparse Linear Algebra Examples |
| sparse linear algebra, iterative solvers: | | Sparse Iterative Solvers |
| sparse linear algebra, overview: | | Overview of Sparse Linear Algebra |
| sparse linear algebra, references: | | Sparse Linear Algebra References and Further Reading |
| sparse matrices: | | Sparse Matrices |
| sparse matrices, accessing elements: | | Sparse Matrices Accessing Elements |
| sparse matrices, allocation: | | Sparse Matrices Allocation |
| sparse matrices, BLAS operations: | | Sparse BLAS operations |
| sparse matrices, compression: | | Sparse Matrices Compressed Format |
| sparse matrices, conversion: | | Sparse Matrices Conversion Between Sparse and Dense |
| sparse matrices, copying: | | Sparse Matrices Copying |
| sparse matrices, examples: | | Sparse Matrices Examples |
| sparse matrices, exchanging rows and columns: | | Sparse Matrices Exchanging Rows and Columns |
| sparse matrices, initializing elements: | | Sparse Matrices Initializing Elements |
| sparse matrices, iterative solvers: | | Sparse Iterative Solvers |
| sparse matrices, min/max elements: | | Sparse Matrices Finding Maximum and Minimum Elements |
| sparse matrices, operations: | | Sparse Matrices Operations |
| sparse matrices, overview: | | Sparse Matrices Overview |
| sparse matrices, properties: | | Sparse Matrices Properties |
| sparse matrices, reading: | | Sparse Matrices Reading and Writing |
| sparse matrices, references: | | Sparse Matrices References and Further Reading |
| sparse matrices, references: | | Sparse BLAS References and Further Reading |
| sparse matrices, writing: | | Sparse Matrices Reading and Writing |
| sparse, iterative solvers: | | Sparse Iterative Solvers |
| 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 | | |
|---|
| 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 |
| Tikhonov regression: | | Regularized regression |
| 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 |
| triangular systems: | | Triangular Systems |
| tridiagonal decomposition: | | Tridiagonal Decomposition of Real Symmetric Matrices |
| tridiagonal decomposition: | | Tridiagonal Decomposition of Hermitian 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 Gaussian distribution: | | The Multivariate 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 | | |
|---|
| 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 |
|
| V | | |
|---|
| 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 and Matrices |
| vectors: | | Vectors |
| 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 | | |
|---|
| 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 | | |
|---|
| Y(x), Bessel Functions: | | Irregular Cylindrical Bessel Functions |
| y(x), Bessel Functions: | | Irregular Spherical Bessel Functions |
|
| Z | | |
|---|
| 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 |
|