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Concept Index

2

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

  • 3D random direction vector
  • 3j symbols
  • 6

  • 6j symbols
  • 9

  • 9j symbols
  • a

  • acceleration of series
  • acosh
  • Ai(x)
  • Airy functions
  • aliasing of arrays
  • alternative optimized functions
  • ANSI C, use of
  • argument of complex number
  • arithmetic exceptions
  • asinh
  • astronomical constants
  • atanh
  • atomic physics, constants
  • autoconf, using with GSL
  • b

  • Bernoulli trial, random numbers
  • Bessel functions
  • best-fit parameters, covariance
  • Beta distribution random numbers
  • Bi(x)
  • bias, IEEE format
  • binning data
  • Binomial random numbers
  • bisection algorithm for finding roots
  • BLAS
  • 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
  • c

  • C extensions, compatible use of
  • C++, compatibility
  • Cauchy random numbers
  • Chebyshev polynomials
  • Checkergcc
  • checking permutation for validity
  • Chi-squared random numbers
  • Cholesky decomposition
  • Clausen functions
  • Clenshaw-Curtis quadrature
  • CMRG, combined multiple recursive random number generator
  • code reuse in applications
  • combinatorial optimization
  • combinatorial searches
  • comparison functions, definition
  • compatibility
  • compiling programs, include paths
  • compiling programs, library paths
  • complex arithmetic
  • complex numbers
  • confluent hypergeometric function
  • confluent hypergeometric functions
  • conical functions
  • conjugate of complex number
  • constants, fundamental
  • constants, mathematical -- defined as macros
  • constants, physical
  • convergence, accelerating a series
  • conversion of units
  • cookery units
  • cooling schedule
  • cosine of complex number
  • cost function
  • Coulomb wave functions
  • covariance of best-fit parameters
  • covariance, of two datasets
  • CRAY random number generator, RANF
  • cubic equation, solving
  • d

  • Dawson function
  • debugging numerical programs
  • Debye functions
  • denormalized form, IEEE format
  • derivatives, calculating numerically
  • determinant of a matrix, by LU decomposition
  • DFTs, see FFT
  • differentiation of functions, numeric
  • digamma function
  • dilogarithm
  • direction vector, random 2D
  • direction vector, random 3D
  • direction vector, random N-dimensional
  • Discrete Fourier Transforms, see FFT
  • Discrete newton algorithm for multidimensional roots
  • Discrete Newton algorithm for nonlinear systems
  • Discrete random numbers, Discrete random numbers, Discrete random numbers, Discrete random numbers
  • Discrete random numbers, preprocessing
  • division by zero, IEEE exceptions
  • double precision, IEEE format
  • e

  • e, defined as a macro
  • 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 macros
  • Errors
  • estimated standard deviation
  • estimated variance
  • euclidean distance function, hypot
  • Euler's constant, defined as a macro
  • exceptions, IEEE arithmetic
  • exchanging permutation elements
  • exp
  • expm1
  • exponent, IEEE format
  • exponential function
  • exponential integrals
  • Exponential power distribution, random numbers
  • Exponential random numbers
  • exponential, difference from 1 computed accurately
  • exponentiation of complex number
  • f

  • F-distribution random numbers
  • factorization of matrices
  • false position algorithm for finding roots
  • Fast Fourier Transforms, see FFT
  • 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
  • fitting
  • flat distribution random numbers
  • Fortran range checking, equivalent in gcc
  • Four-tap Generalized Feedback Shift Register
  • Fourier integrals, numerical
  • Fourier Transforms, see FFT
  • functions, numerical differentiation
  • fundamental constants
  • g

  • Gamma distribution random numbers
  • gamma function
  • Gauss-Kronrod quadrature
  • Gaussian random numbers, Gaussian random numbers
  • Gaussian Tail random numbers
  • gcc extensions, range-checking
  • gcc warning options
  • gdb
  • Gegenbauer functions
  • general polynomial equations, solving
  • Geometric random numbers, Geometric random numbers
  • GNEWTON algorithm
  • golden section algorithm for finding minima
  • gsl_sf_result
  • gsl_sf_result_e10
  • Gumbel distribution (Type 1), random numbers
  • Gumbel distribution (Type 2), random numbers
  • h

  • HAVE_INLINE
  • header files, including
  • heapsort
  • histograms
  • householder linear solver
  • HYBRID algorith, unscaled without derivates
  • HYBRID algorithms for nonlinear systems
  • HYBRIDJ algorithm
  • HYBRIDS algorithm, scaled without derivatives
  • HYBRIDSJ algorithm
  • hydrogen atom
  • hyperbolic cosine, inverse
  • hyperbolic functions, complex numbers
  • hyperbolic sine, inverse
  • hyperbolic space
  • hyperbolic tangent, inverse
  • hypergeometric functions
  • hypot
  • i

  • 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
  • indentity permutation
  • indirect sorting
  • indirect sorting, of vector elements
  • infinity, defined as a macro
  • infinity, IEEE format
  • initializing matrices
  • initializing vectors
  • inline functions
  • integer powers
  • integration, numerical (quadrature)
  • interpolation
  • inverse complex trigonometric 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
  • iterating through permutations
  • iterative refinement of solutions in linear systems
  • l

  • Laguerre functions
  • LAPACK, recommended for linear algebra
  • Laplace distribution random numbers
  • leading dimension, matrices
  • least squares fit
  • least squares fitting, nonlinear
  • least-squares, covariance of best-fit parameters
  • Legendre functions
  • length, computed accurately using hypot
  • Levenberg-Marquardt algorithms
  • Levin u-transform
  • Levy distribution, random numbers, Levy distribution, random numbers
  • libraries, linking with
  • light, units of
  • linear algebra
  • linear systems, refinement of solutions
  • linear systems, solution of
  • linking with GSL libraries
  • LMDER algorithm
  • log1p
  • logarithm
  • logarithm of complex number
  • logarithm of the determinant of a matrix
  • logarithm, computed accurately near 1
  • Logarithmic random numbers
  • Logistic random numbers
  • Lognormal random numbers
  • long double
  • LU decomposition
  • m

  • macros for mathematical constants
  • magnitude of complex number
  • 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
  • mean
  • min
  • Minimization, caveats
  • minimization, one-dimensional
  • minimization, overview
  • minimization, providing a function to minimize
  • minimization, stopping parameters
  • minimum finding, brent's method
  • minimum finding, golden section algorithm
  • minimum of two numbers
  • MINPACK, minimization algorithms, MINPACK, minimization algorithms
  • MISER monte carlo integration
  • Mixed-radix FFT, complex data
  • Mixed-radix FFT, real data
  • Modified Clenshaw-Curtis quadrature
  • Modified Newton's Method for nonlinear systems
  • Monte Carlo integration
  • MRG, multiple recursive random number generator
  • MT19937 random number generator
  • multidimensional root finding, Broyden algorithm
  • multidimensional root finding, overview
  • multidimensional root finding, providing a function to solve
  • multiplication
  • n

  • N-dimensional random direction vector
  • NaN, defined as a macro
  • nautical units
  • Negative Binomial distribution, random numbers
  • Newton algorithm, discrete
  • Newton's Method algorithm for finding roots
  • Newton's Method for systems of nonlinear equations
  • non-linear equation, solutions of
  • non-linear functions, minimisation
  • nonlinear least squares fitting
  • nonlinear least-squares fitting, overview
  • nonlinear systems of equations, solution of
  • normalized form, IEEE format
  • Not-a-number, defined as a macro
  • ntuples
  • nuclear physics, constants
  • numerical constants, defined as macros
  • numerical derivatives
  • numerical integration (quadrature)
  • Numerical recipes, random number generators
  • o

  • optimization -- combinatorial
  • optimization, see minimization
  • optimized functions, alternatives
  • overflow, IEEE exceptions
  • p

  • Pareto random numbers
  • permutations
  • physical constants
  • physical dimension, matrices
  • pi, defined as a macro
  • plain monte carlo
  • Poisson random numbers
  • polar form of complex numbers
  • polygamma functions
  • polynomial manipulation
  • polynomials, roots of
  • power function
  • power of complex number
  • power, units of
  • precision, IEEE arithmetic
  • pressure, units of
  • printers units
  • probability distributions, from histograms
  • psi function
  • q

  • QR decomposition
  • QR decomposition with column pivoting
  • QUADPACK
  • quadratic equation, solving
  • quadrature
  • 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 number generators, Numerical recipes
  • 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 random numbers
  • Rayleigh Tail random numbers
  • recursive stratified sampling, MISER
  • refinement of solutions in linear systems
  • regression, least squares
  • representations of complex numbers
  • resampling from histograms
  • residual, in nonlinear systems of equations, residual, in nonlinear systems of equations
  • reversing a permutation
  • 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, root finding, stopping parameters
  • roots
  • rounding mode
  • s

  • sampling from histograms
  • schedule - cooling
  • Secant Method algorithm for finding roots
  • series, acceleration
  • shift-register random number generator
  • sign bit, IEEE format
  • sign of the determinant of a matrix
  • simulated annealing
  • sin of complex number
  • single precision, IEEE format
  • singular value decomposition
  • 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 vector elements
  • source code, reuse in applications
  • Special Functions
  • spherical harmonics
  • spherical random numbers, 2D
  • spherical random numbers, 3D
  • spherical random numbers, N-dimensional
  • spline
  • square root of a matrix, Cholesky decomposition
  • square root of complex number
  • standard deviation
  • standards conformance, ANSI C
  • statistics
  • Steffenson's Method for finding roots
  • stride, of vector index
  • summation, acceleration
  • SVD
  • swapping permutation elements
  • Synchrotron functions
  • systems of equations, nonlinear
  • t

  • t-distribution random numbers
  • t-test
  • tangent of complex number
  • Tausworthe random number generator
  • testing permutation for validity
  • thermal energy, units of
  • time units
  • trailing dimension, matrices
  • Transport functions
  • Traveling Salesman Problem
  • tridiagonal systems
  • Trigonometric functions
  • trigonometric functions of complex numbers
  • TSP
  • TT800 random number generator
  • two dimensional histograms
  • two-sided exponential random numbers
  • Type 1 Gumbel distribution, random numbers
  • Type 2 Gumbel distribution, random numbers
  • u

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

  • variance
  • 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

  • warning options
  • Weibull distribution random numbers
  • weight, units of
  • Wigner coefficients
  • z

  • zero finding
  • zero, IEEE format
  • Zeta functions

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