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Routines for evaluating Special functions |
Bessel Functions of various types |
 |
Regular cylindrical functions |
Bessel J functions of various orders |
MathMore,
GSL,
Cernlib,
TMath |
 |
Irregular cylindrical functions |
Bessel Y functions of various orders |
MathMore,
GSL,
Cernlib,
TMath |
 |
Regular modified cylindrical |
Bessel I functions of various orders |
MathMore,
GSL,
Cernlib,
TMath |
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Irregular modified cylindrical |
Bessel K functions of various orders |
MathMore,
GSL,
Cernlib, TMath
|
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Regular spherical functions |
Bessel j functions of various orders |
MathMore,
GSL,
Cernlib |
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Irregular spherical functions |
Bessel y functions of various orders |
MathMore,
GSL,
Cernlib
|
|
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Clausen function |
Clausen integral function |
GSL,
Cernlib |
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Coulomb Wave Function |
Wave functions for bound states and scattering solutions |
GSL,
Cernlib |
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Dawson's integral function |
Dawson integral |
GSL,
Cernlib |
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Dilogarithm function |
Dilogarithms for real and complex arguments |
GSL,
Cernlib |
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Complete Elliptic integrals |
Legendre form of the various types of complete Elliptic integrals |
MathMore,
GSL,
Cernlib
|
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Uncomplete Elliptic integrals |
Carlson and Legendre form of uncomplete Elliptic integrals |
MathMore,
GSL,
Cernlib (
2 )
|
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Error functions |
Error function (ERFC) and complementary |
MathCore,
GSL,
Cernlib, TMath |
 |
Exponential integrals |
Various type of exponential integrals |
MathMore,
GSL,
Cernlib |
 |
Hyperbolic integrals |
Sinh and Cosh integrals |
GSL
|
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Trigonometric integrals |
Sin and Cos integrals |
GSL,
Cernlib
|
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Arctangent integral |
Computation of Arctangent integral |
GSL,
Cernlib
|
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Fermi Dirac function |
Complete and incomplete Fermi-Dirac functions |
GSL,
Cernlib |
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Gamma function |
Gamma and related functions
|
MathCore,
GSL,
Cernlib(
2,
3), TMath |
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Hypergeometric functions |
Confluent and Gauss hypergeometric function |
MathMore,
GSL |
 |
Laguerre functions |
Laguerre polynomials of various orders |
MathMore,
GSL |
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Legendre functions |
Legendre polynomials, functions and spherical harmonics |
MathMore,
GSL,
Cernlib |
 |
PSI function |
Digamma and polygamma functions |
GSL,
Cernlib |
 |
Zeta functions (Riemann) |
Riemann Zeta function |
MathMore,
GSL,
Cernlib |
 |
Struve functions |
Struve funcitons of order Zero and One |
Cernlib, TMath |
|
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Algorithms for evaluating and solving polynomials |
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Polynomial evaluation |
Evaluate polynommial of degree n |
GSL
|
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Quadratic equations |
Find roots (real and complex) of quadratic equation |
GSL
|
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Cubic equation |
Find roots (real and complex) of cubic equation |
GSL,
Cernlib |
 |
Quartic equations |
Find roots (real and complex) of quartic equation |
Cernlib,
GSL (t.b.r) |
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General Polynomial equations |
Numerical method fot finding roots of higher order polynomial |
GSL,
Cernlib |
|
Numerical Integration |
Algorithms for performing numerical integration
of a function in one dimension |
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Non-adaptive Gauss-Kronrod |
Simple integration method for smooth functions. |
GSL |
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Adaptive Gauss integration |
Gauss-Kronrod adaptive integration agorithms for general functions and
for special cases (singularities, infinite intervals, etc..) |
GSL,
Cernlib |
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Adaptive integration for integrands with weight functions |
Algorithms based on the Clenshaw-Curtis rule vor various cases |
GSL,
Cernlib |
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Multidimensional integration |
Monte Carlo algorithms for multi dimensional integrations |
GSL,
Cern (
2) |
|
Numerical differentiation
|
Numerical algorithms for calculating derivatives of functions |
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Numerical derivatives |
Compute numerical derivatives by finite differencing |
GSL, Cernlib |
|
Linear Algebra |
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Vector and Matrices operations (BLAS) |
Vector operation (BLAS Level 1), Matrix vector operation (BLAS Level
2) and matrix-matrix operations (BLAS Level 3) |
GSL, CBLAS, CLHEP
matrix |
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Linear Algebra problems |
Functions for solving systems of linear equations |
GSL, LAPACK,
Cernlib,
Others ?? |
Random
Number generation |
Various random number generators |
 |
Random number generators
|
various generators of uniform distributed random numbers, either
as integers or double precision floating point numbers |
GSL,
CLHEP,
TRandom
|
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Quasi-Random Sequences |
Sequences of numbers covering progressively a d-dimensional space |
GSL |
|
Random
Number Distributions and Probability Distributions |
GSL provides
generation of random numbers according to a certain pdf, functions
to calculate the pdf and the corresponding
comulative
distributions P and Q and inverse. Generation of random distribution
is also provided in CLHEP and
ROOT
|
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Gaussian distributions |
One and 2 variable gaussian random numbers, pdf and comulative distributions |
MathCore,
GSL,
Cernlib (2),
TMath |
 |
Exponential distribution |
One dim exponential random numbers, pdf and comulative distributions |
MathCore,
GSL
|
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Cauchy distribution |
Cauchy (Lorentz) random numbers, pdf and comulative distributions |
MathCore,
GSL |
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Landau distribution |
Landau random numbers, pdf and comulative distributions |
MathCore,
GSL,
Cernlib, TMath
|
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Gamma distribution |
Gamma random numbers, pdf and comulative distributions |
MathCore,
GSL,
Cernlib (
2),
TMath |
 |
Flat distribution |
Flat random numbers, pdf and comulative distributions |
MathCore,
GSL
|
 |
Lognormal distribution |
Lognormal random numbers, pdf and comulative distributions |
MathCore,
GSL |
 |
Chi2-squared distribution |
Chi2 random numbers, pdf and comulative distributions |
MathCore,
GSL,
Cernlib (
2,
3 ), TMath |
 |
F distribution |
F random numbers, pdf and comulative distributions |
MathCore,
GSL |
 |
Student t-distribution |
Student-t random numbers, pdf and comulative distributions |
MathCore,
GSL,
Cernlib
|
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Poisson distribution |
Poisson random numbers, pdf and comulative distributions |
MathCore,
GSL,
Cernlib,
TMath |
 |
Binomial distribution |
Binomial random numbers, pdf and comulative distributions |
MathCore,
GSL,
Cernlib,
TMath
|
 |
Multinomial distribution |
Multinomial random numbers, pdf and comulative distributions |
GSL,
Cernlib
|
 |
Breit Wigner distribution |
Breit Wigner distributed random numbers |
MathCore,
CLHEP,
TMath
|
 |
Kolgomorov distribution |
Only Kolgomorov distribution |
Cernlib,
TMath
|
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Vavilov distribution |
Vavilov pdf and its inverse |
Cernlib (
2)
|
|
Minimization |
Algorithms for finding the minimum (or maximum) of a function in one or more dimensions |
 |
One dim. minimization |
minimization algorithms for one dimensional functions |
GSL, Cernlib |
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Multidimensional minimization |
various algorithms for unconstrained minimization including the calculation
of the covariance matrix of best fit parameters |
Minuit, GSL |
|
Root Finding |
Algorithms for finding the root of a function in one or more dimensions |
 |
One dimensional root finders |
Algorithms to find root of a function in one dimension |
GSL,
Cernlib |
 |
Multidimensional root finders |
Algorithms to find n-roots of a set of n functions, to solve a system
of non linear equations |
GSL, Cernlib |
|
Interpolation
|
various types of algorithms for performing interpolation |
 |
Polynomial interpolation |
simple method recommended for small number of points |
GSL
Cernlib |
 |
Cubic spline interpolation |
Cubic spline with natural and periodic boundary conditions |
GSL
Cernlib
|
 |
Akima spline interpolation |
Method based on the non-rounded corner algorithm of Wodicka |
GSL |
|
Function Approximations
|
routines for computing approximations to functions |
 |
Chebyshev Approximations |
routines for create and calculate Chebyshev series with derivatives and
integrals |
GSL,
Cernlib (
2)
|
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Trigonometric series |
summation of trigonometric series |
Cernlib |
 |
Series acceleration |
method to accelerate convergence of series using Levin u-transform |
GSL |
|
Fast Fourier Transform
|
routines for computing discrete Fast Fourier Transforms (FFT) |
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Complex data FFT |
compute FFT (and its inverse) for complex data sequences |
GSL,
Cernlib (
2)
|
 |
Real data FFT |
compute FFT (and its inverse) for real data sequences |
GSL,
Cernlib (
2)
|
|
Differential Equations
|
Algorithms for solving n-dimensional first-order systems of differential equations
|
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Range-Kutta algorithms |
various types of Range-Kutta solving methods |
GSL,
Cernlib (
2)
|
 |
Burlirsch-Stoer method |
Implicit Bulirsch-Stoer method. Requires Jacobian |
GSL,
Cernlib
|
|