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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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