Concept Index

2

• 2D histograms
• 2D random direction vector
• 3

• 3-j symbols
• 3D random direction vector

• 6-j symbols

• 9-j symbols
• a

• acceleration of series
• acosh
• Adaptive step-size control, differential equations
• Ai(x)
• Airy functions
• Akima splines
• aliasing of arrays
• alternative optimized functions
• AMAX, Level-1 BLAS
• angular reduction
• ANSI C, use of
• Apell symbol, see Pochammer symbol
• approximate comparison of floating point numbers
• arctangent integral
• argument of complex number
• arithmetic exceptions
• asinh
• astronomical constants
• ASUM, Level-1 BLAS
• atanh
• atomic physics, constants
• autoconf, using with GSL
• AXPY, Level-1 BLAS
• b

• Bader and Deuflhard, Bulirsch-Stoer method.
• Basic Linear Algebra Subroutines (BLAS), Basic Linear Algebra Subroutines (BLAS)
• Bernoulli trial, random variates
• Bessel functions
• Bessel Functions, Fractional Order
• best-fit parameters, covariance
• Beta distribution
• Beta function
• Beta function, incomplete normalized
• BFGS conjugate gradient algorithm, minimization
• Bi(x)
• bias, IEEE format
• bidiagonalization of real matrices
• binning data
• Binomial random variates
• bisection algorithm for finding roots
• Bivariate Gaussian distribution
• BLAS
• BLAS, Low-level C interface
• blocks
• breakpoints
• brent's method for finding minima
• brent's method for finding roots
• Broyden algorithm for multidimensional roots
• BSD random number generator
• BSD random number generator, rand
• bug-gsl mailing list
• bugs, how to report
• Bulirsch-Stoer method
• c

• C extensions, compatible use of
• C++, compatibility
• Carlson forms of Elliptic integrals
• Cash-Karp, Runge-Kutta method
• Cauchy distribution
• Cauchy principal value, by numerical quadrature
• CBLAS
• CBLAS, Low-level interface
• CDFs, cumulative distribution functions
• Chebyshev series
• Checkergcc
• checking combination for validity
• checking permutation for validity
• Chi(x)
• Chi-squared distribution
• Cholesky decomposition
• Ci(x)
• Clausen functions
• CMRG, combined multiple recursive random number generator
• code reuse in applications
• combinations
• combinatorial factor C(m,n)
• combinatorial optimization
• combinatorial searches
• comparison functions, definition
• compatibility
• compiling programs, include paths
• compiling programs, library paths
• complementary incomplete Gamma function
• complete Fermi-Dirac integrals
• complex arithmetic
• complex cosine function, special functions
• Complex Gamma function
• complex hermitian matrix, eigensystem
• complex log sine function, special functions
• complex numbers
• complex sinc function, special functions
• complex sine function, special functions
• confluent hypergeometric function
• confluent hypergeometric functions
• conical functions
• conjugate of complex number
• constants, fundamental
• constants, mathematical -- defined as macros
• constants, physical
• constants, prefixes
• contacting the GSL developers
• convergence, accelerating a series
• conversion of units
• cooling schedule
• COPY, Level-1 BLAS
• cosine function, special functions
• cosine of complex number
• cost function
• Coulomb wave functions
• coupling coefficients
• covariance matrix, from linear regression
• covariance of best-fit parameters
• covariance, of two datasets
• CRAY random number generator, RANF
• cubic equation, solving
• cubic splines
• cumulative distribution functions (CDFs)
• Cylindrical Bessel Functions
• d

• Dawson function
• debugging numerical programs
• Debye functions
• denormalized form, IEEE format
• derivatives, calculating numerically
• determinant of a matrix, by LU decomposition
• Deuflhard and Bader, Bulirsch-Stoer method.
• DFTs, see FFT
• differential equations, initial value problems
• differentiation of functions, numeric
• digamma function
• dilogarithm
• direction vector, random 2D
• direction vector, random 3D
• direction vector, random N-dimensional
• Dirichlet distribution
• Discrete Fourier Transforms, see FFT
• discrete Hankel transforms
• Discrete Newton algorithm for multidimensional roots
• Discrete random numbers, Discrete random numbers, Discrete random numbers, Discrete random numbers
• Discrete random numbers, preprocessing
• divided differences, polynomials
• division by zero, IEEE exceptions
• DOT, Level-1 BLAS
• double factorial
• double precision, IEEE format
• e

• e, defined as a macro
• E1(x), E2(x), Ei(x)
• eigenvalues and eigenvectors
• elementary functions
• elementary operations
• elliptic functions (Jacobi)
• elliptic integrals
• energy function
• energy, units of
• erf(x)
• erfc(x)
• error codes
• error function
• Error handlers
• error handling
• error handling macros
• Errors
• estimated standard deviation
• estimated variance
• euclidean distance function, hypot
• Euler's constant, defined as a macro
• evaluation of polynomials
• evaluation of polynomials, in divided difference form
• exceptions, IEEE arithmetic
• exchanging permutation elements
• exp
• expm1
• exponent, IEEE format
• Exponential distribution
• exponential function
• exponential integrals
• Exponential power distribution
• exponential, difference from 1 computed accurately
• exponentiation of complex number
• f

• F-distribution
• factorial
• factorization of matrices
• false position algorithm for finding roots
• Fast Fourier Transforms, see FFT
• FDL, GNU Free Documentation License
• Fehlberg method, differential equations
• Fermi-Dirac function
• FFT
• FFT mathematical definition
• FFT of complex data, mixed-radix algorithm
• FFT of complex data, radix-2 algorithm
• FFT of real data
• FFT of real data, mixed-radix algorithm
• FFT of real data, radix-2 algorithm
• FFT, complex data
• finding minima
• finding roots
• finding zeros
• fits, multi-parameter linear
• fitting
• fitting, using Chebyshev polynomials
• Fj(x), Fermi-Dirac integral
• Fj(x,b), incomplete Fermi-Dirac integral
• flat distribution
• Fletcher-Reeves conjugate gradient algorithm, minimization
• floating point numbers, approximate comparison
• force and energy, units of
• Fortran range checking, equivalent in gcc
• Four-tap Generalized Feedback Shift Register
• Fourier integrals, numerical
• Fourier Transforms, see FFT
• Fractional Order Bessel Functions
• free documentation
• free software, explanation of
• frexp
• functions, numerical differentiation
• fundamental constants
• g

• Gamma distribution
• gamma function
• Gaussian distribution
• Gaussian distribution, bivariate
• Gaussian Tail distribution
• gcc extensions, range-checking
• gcc warning options
• gdb
• Gear method, differential equations
• Gegenbauer functions
• GEMM, Level-3 BLAS
• GEMV, Level-2 BLAS
• general polynomial equations, solving
• Geometric random variates, Geometric random variates
• GER, Level-2 BLAS
• GERC, Level-2 BLAS
• GERU, Level-2 BLAS
• Givens Rotation, BLAS
• Givens Rotation, Modified, BLAS
• golden section algorithm for finding minima
• gsl-announce mailing list
• gsl_sf_result
• gsl_sf_result_e10
• Gumbel distribution (Type 1)
• Gumbel distribution (Type 2)
• h

• Hankel transforms, discrete
• HAVE_INLINE
• hazard function, normal distribution
• HBOOK
• heapsort
• HEMM, Level-3 BLAS
• HEMV, Level-2 BLAS
• HER, Level-2 BLAS
• HER2, Level-2 BLAS
• HER2K, Level-3 BLAS
• HERK, Level-3 BLAS
• hermitian matrix, complex, eigensystem
• histogram statistics
• histogram, from ntuple
• histograms
• histograms, random sampling from
• householder linear solver
• Householder matrix
• Householder transformation
• HYBRID algorithm, unscaled without derivatives
• HYBRID algorithms for nonlinear systems
• HYBRIDJ algorithm
• HYBRIDS algorithm, scaled without derivatives
• HYBRIDSJ algorithm
• hydrogen atom
• hyperbolic cosine, inverse
• hyperbolic functions, complex numbers
• hyperbolic integrals
• hyperbolic sine, inverse
• hyperbolic space
• hyperbolic tangent, inverse
• hypergeometric functions
• hypot
• hypot function, special functions
• i

• identity permutation
• IEEE exceptions
• IEEE floating point
• IEEE format for floating point numbers
• IEEE infinity, defined as a macro
• IEEE NaN, defined as a macro
• illumination, units of
• imperial units
• importance sampling, VEGAS
• incomplete Beta function, normalized
• incomplete Fermi-Dirac integral
• incomplete Gamma function
• indirect sorting
• indirect sorting, of vector elements
• infinity, defined as a macro
• infinity, IEEE format
• initial value problems, differential equations
• initializing matrices
• initializing vectors
• inline functions
• integer powers
• integrals, exponential
• interpolation
• interpolation, using Chebyshev polynomials
• inverse complex trigonometric functions
• inverse cumulative distribution functions
• inverse hyperbolic cosine
• inverse hyperbolic functions, complex numbers
• inverse hyperbolic sine
• inverse hyperbolic tangent
• inverse of a matrix, by LU decomposition
• inverting a permutation
• Irregular Cylindrical Bessel Functions
• Irregular Modified Bessel Functions, Fractional Order
• Irregular Modified Cylindrical Bessel Functions
• Irregular Modified Spherical Bessel Functions
• Irregular Spherical Bessel Functions
• iterating through combinations
• iterating through permutations
• iterative refinement of solutions in linear systems
• j

• Jacobi elliptic functions
• l

• Laguerre functions
• Lambert function
• Landau distribution
• LAPACK, recommended for linear algebra, LAPACK, recommended for linear algebra
• Laplace distribution
• LD_LIBRARY_PATH
• ldexp
• least squares fit
• least squares fitting, nonlinear
• least-squares, covariance of best-fit parameters
• Legendre forms of elliptic integrals
• Legendre functions
• length, computed accurately using hypot
• Levenberg-Marquardt algorithms
• Levin u-transform
• Levy distribution
• Levy distribution, skew
• libraries, shared
• light, units of
• linear algebra
• linear algebra, BLAS
• linear interpolation
• linear regression
• linear systems, refinement of solutions
• linear systems, solution of
• LMDER algorithm
• log1p
• logarithm and related functions
• logarithm of Beta function
• logarithm of combinatorial factor C(m,n)
• logarithm of complex number
• logarithm of cosh function, special functions
• logarithm of double factorial
• logarithm of factorial
• logarithm of Gamma function
• logarithm of Pochhammer symbol
• logarithm of sinh function, special functions
• logarithm of the determinant of a matrix
• logarithm, computed accurately near 1
• Logarithmic random variates
• Logistic distribution
• Lognormal distribution
• long double
• low discrepancy sequences
• Low-level CBLAS
• LU decomposition
• m

• macros for mathematical constants
• magnitude of complex number
• mailing list archives
• mailing list for GSL announcements
• mailing list, bug-gsl
• mantissa, IEEE format
• mass, units of
• mathematical constants, defined as macros
• mathematical functions, elementary
• matrices, matrices
• matrices, initializing
• matrices, range-checking
• matrix determinant
• matrix factorization
• matrix inverse
• matrix square root, Cholesky decomposition
• matrix, operations
• max
• maximization, see minimization
• maximum of two numbers
• maximum value, from histogram
• mean
• mean value, from histogram
• Mill's ratio, inverse
• min
• Minimization, BFGS conjugate gradient algorithm
• Minimization, caveats
• minimization, multidimensional
• minimization, one-dimensional
• minimization, overview
• Minimization, Polak-Ribiere algorithm
• minimization, providing a function to minimize
• Minimization, simplex algorithm
• Minimization, steepest descent algorithm
• minimization, stopping parameters
• minimum finding, brent's method
• minimum finding, golden section algorithm
• minimum of two numbers
• minimum value, from histogram
• MINPACK, minimization algorithms, MINPACK, minimization algorithms
• MISCFUN
• MISER monte carlo integration
• Modified Bessel Functions, Fractional Order
• Modified Cylindrical Bessel Functions
• Modified Givens Rotation, BLAS
• Modified Newton's Method for nonlinear systems
• Modified Spherical Bessel Functions
• Monte Carlo integration
• MRG, multiple recursive random number generator
• MT19937 random number generator
• multi-parameter regression
• multidimensional root finding, Broyden algorithm
• multidimensional root finding, overview
• multidimensional root finding, providing a function to solve
• Multimin, caveats
• Multinomial distribution
• multiplication
• n

• N-dimensional random direction vector
• NaN, defined as a macro
• nautical units
• Negative Binomial distribution, random variates
• Nelder-Mead simplex algorithm for minimization
• Newton algorithm, discrete
• Newton algorithm, globally convergent
• Newton's Method algorithm for finding roots
• Newton's Method for systems of nonlinear equations
• Niederreiter sequence
• NIST Statistical Reference Datasets
• non-linear equation, solutions of
• non-linear functions, minimization
• non-normalized incomplete Gamma function
• nonlinear fitting, stopping parameters
• nonlinear least squares fitting
• nonlinear least-squares fitting, overview
• nonlinear systems of equations, solution of
• normalized form, IEEE format
• normalized incomplete Beta function
• Not-a-number, defined as a macro
• NRM2, Level-1 BLAS
• ntuples
• nuclear physics, constants
• numerical constants, defined as macros
• numerical derivatives
• o

• obtaining GSL
• ODEs, initial value problems
• optimization -- combinatorial
• optimization, see minimization
• optimized functions, alternatives
• ordinary differential equations, initial value problem
• oscillatory functions, numerical integration of
• overflow, IEEE exceptions
• p

• Pareto distribution
• PAW
• permutations
• physical constants
• physical dimension, matrices
• pi, defined as a macro
• plain monte carlo
• Pochhammer symbol
• Poisson random numbers
• Polak-Ribiere algorithm, minimization
• polar form of complex numbers
• polar to rectangular conversion
• polygamma functions
• polynomial evaluation
• polynomial interpolation
• polynomials, roots of
• power function
• power of complex number
• power, units of
• precision, IEEE arithmetic
• prefixes
• pressure, units of
• Prince-Dormand, Runge-Kutta method
• printers units
• probability distribution, from histogram
• probability distributions, from histograms
• projection of ntuples
• psi function
• q

• QR decomposition
• QR decomposition with column pivoting
• quantile functions
• quasi-random sequences
• r

• R250 shift-register random number generator
• Racah coefficients
• Radix-2 FFT for real data
• rand48 random number generator
• random number distributions
• random number generators
• random sampling from histograms
• RANDU random number generator
• RANF random number generator
• range
• range-checking for matrices
• range-checking for vectors
• RANLUX random number generator
• RANLXD random number generator
• RANLXS random number generator
• RANMAR random number generator, RANMAR random number generator
• Rayleigh distribution
• Rayleigh Tail distribution
• real symmetric matrix, eigensystem
• Reciprocal Gamma function
• rectangular to polar conversion
• recursive stratified sampling, MISER
• reduction of angular variables
• refinement of solutions in linear systems
• regression, least squares
• Regular Bessel Functions, Fractional Order
• Regular Bessel Functions, Zeros of
• Regular Cylindrical Bessel Functions
• Regular Modified Bessel Functions - Fractional Order
• Regular Modified Cylindrical Bessel Functions
• Regular Modified Spherical Bessel Functions
• Regular Spherical Bessel Functions
• Regulated Gamma function
• relative Pochhammer symbol
• reporting bugs in GSL
• representations of complex numbers
• resampling from histograms
• residual, in nonlinear systems of equations, residual, in nonlinear systems of equations
• reversing a permutation
• RK2, Runge-Kutta Method
• RK4, Runge-Kutta Method
• RKF45, Runge-Kutta-Fehlberg method
• root finding
• root finding, bisection algorithm
• root finding, brent's method
• root finding, caveats
• root finding, false position algorithm
• root finding, initial guess
• root finding, Newton's Method algorithm
• root finding, overview
• root finding, providing a function to solve
• root finding, search bounds
• root finding, Secant Method algorithm
• root finding, Steffenson's Method
• root finding, stopping parameters, root finding, stopping parameters
• roots
• ROTG, Level-1 BLAS
• rounding mode
• Runge-Kutta Cash-Karp method
• Runge-Kutta methods, ordinary differential equations
• Runge-Kutta Prince-Dormand method
• s

• safe comparison of floating point numbers
• sampling from histograms, sampling from histograms
• SCAL, Level-1 BLAS
• schedule - cooling
• Secant Method algorithm for finding roots
• selection function, ntuples
• series, acceleration
• shared libraries
• Shi(x)
• shift-register random number generator
• Si(x)
• sign bit, IEEE format
• sign of the determinant of a matrix
• Simplex algorithm, minimization
• simulated annealing
• sin of complex number
• sine function, special functions
• single precision, IEEE format
• singular functions, numerical integration of
• singular points, specifying positions in quadrature
• singular value decomposition
• Skew Levy distribution
• Sobol sequence
• solution of linear system by householder transformations
• solution of linear systems, Ax=b
• solving a non-linear equation
• solving nonlinear systems of equations
• sorting
• sorting eigenvalues and eigenvectors
• sorting vector elements
• source code, reuse in applications
• Special Functions
• Spherical Bessel Functions
• spherical harmonics
• spherical random variates, 2D
• spherical random variates, 3D
• spherical random variates, N-dimensional
• spline
• square root of a matrix, Cholesky decomposition
• square root of complex number
• standard deviation
• standard deviation, from histogram
• standards conformance, ANSI C
• Statistical Reference Datasets (StRD)
• statistics
• statistics, from histogram
• Steepest descent algorithm, minimization
• Steffenson's Method for finding roots
• stratified sampling in monte carlo integration
• stride, of vector index
• Student t-distribution
• summation, acceleration
• SVD
• SWAP, Level-1 BLAS
• swapping permutation elements
• SYMM, Level-3 BLAS
• symmetric matrix, real, eigensystem
• SYMV, Level-2 BLAS
• Synchrotron functions
• SYR, Level-2 BLAS
• SYR2, Level-2 BLAS
• SYR2K, Level-3 BLAS
• SYRK, Level-3 BLAS
• systems of equations, nonlinear
• t

• t-distribution
• t-test
• tangent of complex number
• Tausworthe random number generator
• Taylor coefficients, computation of
• testing combination for validity
• testing permutation for validity
• thermal energy, units of
• time units
• trailing dimension, matrices
• transformation, Householder
• transforms, Hankel
• Transport functions
• Traveling Salesman Problem
• tridiagonal decomposition, tridiagonal decomposition
• tridiagonal systems
• Trigonometric functions
• trigonometric functions of complex numbers
• trigonometric integrals
• TRMM, Level-3 BLAS
• TRMV, Level-2 BLAS
• TRSM, Level-3 BLAS
• TRSV, Level-2 BLAS
• TSP
• TT800 random number generator
• two dimensional histograms
• Two-dimensional Gaussian distribution
• Two-sided exponential distribution
• Type 1 Gumbel distribution, random variates
• Type 2 Gumbel distribution
• u

• u-transform for series
• underflow, IEEE exceptions
• uniform distribution
• units, conversion of
• units, imperial
• Unix random number generators, rand
• Unix random number generators, rand48
• usage, compiling application programs
• v

• value function, ntuples
• Van der Pol oscillator, example
• variance
• variance, from histogram
• VAX random number generator
• vector, operations
• vector, sorting elements of
• vectors, vectors
• vectors, initializing
• vectors, range-checking
• VEGAS monte carlo integration
• viscosity, units of
• volume units
• w

• W function
• warning options
• warranty (none)
• website, developer information
• Weibull distribution
• weight, units of
• weighted linear fits
• Wigner coefficients
• z

• zero finding
• zero, IEEE format
• Zeros of Regular Bessel Functions
• Zeta functions