|  | 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 | 
| 
 |