In computing

Computing

Computing is usually defined as the activity of using and improving computer hardware and software. It is the computer-specific part of information technology...

, the GNU Scientific Library (or GSL) is a software library written in the C programming language

C (programming language)

C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system....

 for numerical calculations in applied mathematics

Applied mathematics

Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...

 and science

Science

Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

. The GSL is part of the GNU Project

GNU Project

The GNU Project is a free software, mass collaboration project, announced on September 27, 1983, by Richard Stallman at MIT. It initiated GNU operating system development in January, 1984...

 and is distributed under the GNU General Public License

GNU General Public License

The GNU General Public License is the most widely used free software license, originally written by Richard Stallman for the GNU Project....

.

Software which uses GSL includes PSPP

PSPP

PSPP is a free software application for analysis of sampled data. It has a graphical user interface and conventional command line interface. It is written in C, uses GNU Scientific Library for its mathematical routines, and plotutils for generating graphs....

 and Perl Data Language

Perl Data Language

PDL is a set of array programming extensions to the Perl programming language.PDL is an extension to Perl v5, intended for scientific and other data intensive programming tasks...

.
The following example program calculates the value of the Bessel function

Bessel function

In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y of Bessel's differential equation:...

 for 5:

1. include
2. include

int main(void)
{
double x = 5.0;
double y = gsl_sf_bessel_J0(x);
printf("J0(%g) = %.18e\n", x, y);
return 0;
}

The example program has to be linked to the GSL library
upon compilation:

gcc $(gsl-config --cflags) example.c $(gsl-config --libs)

The output is shown below, and should be correct to double-precision accuracy:

J0(5) = -1.775967713143382920e-01

The software library provides facilities for:

• Basic mathematical functions
• Complex number
  Complex number
  A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
  
  s
• Polynomial
  Polynomial
  In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
  
  s
• Special functions
  Special functions
  Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications....
  
  
• Vector
  Vector space
  A vector space is a mathematical structure formed by a collection of vectors: objects that may be added together and multiplied by numbers, called scalars in this context. Scalars are often taken to be real numbers, but one may also consider vector spaces with scalar multiplication by complex...
  
  s and matrices
  Matrix (mathematics)
  In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
  
  
• Permutation
  Permutation
  In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...
  
  s
• Combination
  Combination
  In mathematics a combination is a way of selecting several things out of a larger group, where order does not matter. In smaller cases it is possible to count the number of combinations...
  
  s
• Multiset
  Multiset
  In mathematics, the notion of multiset is a generalization of the notion of set in which members are allowed to appear more than once...
  
  s
• Sorting
  Sorting
  Sorting is any process of arranging items in some sequence and/or in different sets, and accordingly, it has two common, yet distinct meanings:# ordering: arranging items of the same kind, class, nature, etc...
  
  
• BLAS
  Basic Linear Algebra Subprograms
  Basic Linear Algebra Subprograms is a de facto application programming interface standard for publishing libraries to perform basic linear algebra operations such as vector and matrix multiplication. They were first published in 1979, and are used to build larger packages such as LAPACK...
  
  
• Linear algebra
  Linear algebra
  Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
  
  
• Eigensystems
• Fast Fourier transform
  Fast Fourier transform
  A fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform and its inverse. "The FFT has been called the most important numerical algorithm of our lifetime ." There are many distinct FFT algorithms involving a wide range of mathematics, from simple...
  
  s
• Numerical integration
  Numerical integration
  In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of...
  
   (based on QUADPACK
  QUADPACK
  QUADPACK is a FORTRAN 77 library for numerical integration of one-dimensional functions. It was included in the SLATEC Common Mathematical Library and is therefore in the public domain. The individual subprograms are also available on netlib....
  
  )
• Random number generation
• Quasi-random sequences
• Random number distributions
  Probability distribution
  In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
  
  
• Statistics
  Statistics
  Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
  
  
• Histogram
  Histogram
  In statistics, a histogram is a graphical representation showing a visual impression of the distribution of data. It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson...
  
  s
• N-tuples
• Monte Carlo integration
• Simulated annealing
  Simulated annealing
  Simulated annealing is a generic probabilistic metaheuristic for the global optimization problem of locating a good approximation to the global optimum of a given function in a large search space. It is often used when the search space is discrete...
  
  
• Ordinary differential equation
  Ordinary differential equation
  In mathematics, an ordinary differential equation is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable....
  
  s
• Interpolation
  Interpolation
  In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....
  
  
• Numerical differentiation
  Numerical differentiation
  In numerical analysis, numerical differentiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.-Finite difference formulae:...
  
  
• Chebyshev approximations
• Series acceleration
  Series acceleration
  In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numerical analysis, where they are used to improve the speed of numerical integration...
  
  
• Discrete Hankel transform
  Hankel transform
  In mathematics, the Hankel transform expresses any given function f as the weighted sum of an infinite number of Bessel functions of the first kind Jν. The Bessel functions in the sum are all of the same order ν, but differ in a scaling factor k along the r-axis...
  
  
• Root-finding
  Root-finding algorithm
  A root-finding algorithm is a numerical method, or algorithm, for finding a value x such that f = 0, for a given function f. Such an x is called a root of the function f....
  
   in one and multiple dimensions
• Minimization
  Optimization (mathematics)
  In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
  
   in one and multiple dimensions
• Least-squares fitting
  Least squares
  The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in solving every...
  
  
• Nonlinear least-squares fitting
  Levenberg-Marquardt algorithm
  In mathematics and computing, the Levenberg–Marquardt algorithm provides a numerical solution to the problem of minimizing a function, generally nonlinear, over a space of parameters of the function...
  
  
• Physical constants
• IEEE floating-point arithmetic
• Discrete wavelet transform
  Discrete wavelet transform
  In numerical analysis and functional analysis, a discrete wavelet transform is any wavelet transform for which the wavelets are discretely sampled...
  
  

The GSL can be used in C++

C++

C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...

 classes, but not using pointers to member functions, because the type of pointer to member function is different from pointer to function.