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Concept Index

$

  • $, shell prompt

    • 2

  • 2D histograms
  • 2D random direction vector

    • 3

  • 3-j symbols
  • 3D random direction vector

    • 6

  • 6-j symbols

    • 9

  • 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
  • Clenshaw-Curtis quadrature
  • 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 gradient algorithm, minimization
  • conjugate of complex number
  • constant matrix
  • constants, fundamental
  • constants, mathematical -- defined as macros
  • constants, physical
  • constants, prefixes
  • contacting the GSL developers
  • conventions, used in manual
  • 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
  • diagonal, of a matrix
  • 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
  • dollar sign $, shell prompt
  • DOT, Level-1 BLAS
  • double factorial
  • double precision, IEEE format
  • downloading GSL

    • 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
  • examples, conventions used in
  • 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
  • Gauss-Kronrod quadrature
  • 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
  • GNU General Public License
  • 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
  • header files, including
  • 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
  • hypergeometric random variates
  • hypot
  • hypot function, special functions

    • i

  • identity matrix
  • 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
  • including GSL header files
  • 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
  • integration, numerical (quadrature)
  • 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
  • leading dimension, matrices
  • 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, linking with
  • libraries, shared
  • license of GSL
  • light, units of
  • linear algebra
  • linear algebra, BLAS
  • linear interpolation
  • linear regression
  • linear systems, refinement of solutions
  • linear systems, solution of
  • linking with GSL libraries
  • 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 diagonal
  • matrix factorization
  • matrix inverse
  • matrix square root, Cholesky decomposition
  • matrix subdiagonal
  • matrix superdiagonal
  • matrix, constant
  • matrix, identity
  • matrix, operations
  • matrix, zero
  • 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, conjugate gradient algorithm
  • 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
  • Mixed-radix FFT, complex data
  • Mixed-radix FFT, real data
  • Modified Bessel Functions, Fractional Order
  • Modified Clenshaw-Curtis quadrature
  • 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
  • numerical integration (quadrature)

    • 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
  • QUADPACK
  • quadratic equation, solving
  • quadrature
  • quantile functions
  • quasi-random sequences

    • r

  • R250 shift-register random number generator
  • Racah coefficients
  • radioactivity, units of
  • Radix-2 FFT for real data
  • Radix-2 FFT, complex 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
  • shell prompt
  • 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
  • slope, see numerical derivative
  • 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
  • subdiagonal, of a matrix
  • summation, acceleration
  • superdiagonal, matrix
  • 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 matrix
  • zero, IEEE format
  • Zeros of Regular Bessel Functions
  • Zeta functions

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