GNU Scientific Library

• Introduction
  • Routines available in GSL
  • GSL is Free Software
  • Obtaining GSL
  • No Warranty
  • Reporting Bugs
  • Further Information
  • Conventions used in this manual
• Using the Library
  • An Example Program
  • Compiling and Linking
  • Shared Libraries
  • ANSI C Compliance
  • Inline functions
  • Long double
  • Portability functions
  • Alternative optimized functions
  • Support for different numeric types
  • Compatibility with C++
  • Aliasing of arrays
  • Thread-safety
  • Deprecated Functions
  • Code Reuse
• Error Handling
  • Error Reporting
  • Error Codes
  • Error Handlers
  • Using GSL error reporting in your own functions
  • Examples
• Mathematical Functions
  • Mathematical Constants
  • Infinities and Not-a-number
  • Elementary Functions
  • Small integer powers
  • Testing the Sign of Numbers
  • Testing for Odd and Even Numbers
  • Maximum and Minimum functions
  • Approximate Comparison of Floating Point Numbers
• Complex Numbers
  • Representation of complex numbers
  • Complex number macros
  • Assigning complex numbers
  • Properties of complex numbers
  • Complex arithmetic operators
  • Elementary Complex Functions
  • Complex Trigonometric Functions
  • Inverse Complex Trigonometric Functions
  • Complex Hyperbolic Functions
  • Inverse Complex Hyperbolic Functions
  • References and Further Reading
• Polynomials
  • Polynomial Evaluation
  • Divided Difference Representation of Polynomials
  • Quadratic Equations
  • Cubic Equations
  • General Polynomial Equations
  • Examples
  • References and Further Reading
• Special Functions
  • Usage
  • The gsl_sf_result struct
  • Modes
  • Airy Functions and Derivatives
  • Bessel Functions
  • Clausen Functions
  • Coulomb Functions
  • Coupling Coefficients
  • Dawson Function
  • Debye Functions
  • Dilogarithm
  • Elementary Operations
  • Elliptic Integrals
  • Elliptic Functions (Jacobi)
  • Error Functions
  • Exponential Functions
  • Exponential Integrals
  • Fermi-Dirac Function
  • Gamma and Beta Functions
  • Gegenbauer Functions
  • Hermite Polynomials and Functions
  • Hypergeometric Functions
  • Laguerre Functions
  • Lambert W Functions
  • Legendre Functions and Spherical Harmonics
  • Logarithm and Related Functions
  • Mathieu Functions
  • Power Function
  • Psi (Digamma) Function
  • Synchrotron Functions
  • Transport Functions
  • Trigonometric Functions
  • Zeta Functions
  • Examples
  • References and Further Reading
• Vectors and Matrices
  • Data types
  • Blocks
  • Vectors
  • Matrices
• Permutations
  • The Permutation struct
  • Permutation allocation
  • Accessing permutation elements
  • Permutation properties
  • Permutation functions
  • Applying Permutations
  • Reading and writing permutations
  • Permutations in cyclic form
  • Examples
  • References and Further Reading
• Combinations
  • The Combination struct
  • Combination allocation
  • Accessing combination elements
  • Combination properties
  • Combination functions
  • Reading and writing combinations
  • Examples
  • References and Further Reading
• Multisets
  • The Multiset struct
  • Multiset allocation
  • Accessing multiset elements
  • Multiset properties
  • Multiset functions
  • Reading and writing multisets
  • Examples
• Sorting
  • Sorting objects
  • Sorting vectors
  • Selecting the k smallest or largest elements
  • Computing the rank
  • Examples
  • References and Further Reading
• BLAS Support
  • GSL BLAS Interface
  • Examples
  • References and Further Reading
• Linear Algebra
  • LU Decomposition
  • QR Decomposition
  • QR Decomposition with Column Pivoting
  • LQ Decomposition
  • QL Decomposition
  • Complete Orthogonal Decomposition
  • Singular Value Decomposition
  • Cholesky Decomposition
  • Pivoted Cholesky Decomposition
  • Modified Cholesky Decomposition
  • LDLT Decomposition
  • Tridiagonal Decomposition of Real Symmetric Matrices
  • Tridiagonal Decomposition of Hermitian Matrices
  • Hessenberg Decomposition of Real Matrices
  • Hessenberg-Triangular Decomposition of Real Matrices
  • Bidiagonalization
  • Givens Rotations
  • Householder Transformations
  • Householder solver for linear systems
  • Tridiagonal Systems
  • Triangular Systems
  • Banded Systems
  • Balancing
  • Examples
  • References and Further Reading
• Eigensystems
  • Real Symmetric Matrices
  • Complex Hermitian Matrices
  • Real Nonsymmetric Matrices
  • Real Generalized Symmetric-Definite Eigensystems
  • Complex Generalized Hermitian-Definite Eigensystems
  • Real Generalized Nonsymmetric Eigensystems
  • Sorting Eigenvalues and Eigenvectors
  • Examples
  • References and Further Reading
• Fast Fourier Transforms (FFTs)
  • Mathematical Definitions
  • Overview of complex data FFTs
  • Radix-2 FFT routines for complex data
  • Mixed-radix FFT routines for complex data
  • Overview of real data FFTs
  • Radix-2 FFT routines for real data
  • Mixed-radix FFT routines for real data
  • References and Further Reading
• Numerical Integration
  • Introduction
  • QNG non-adaptive Gauss-Kronrod integration
  • QAG adaptive integration
  • QAGS adaptive integration with singularities
  • QAGP adaptive integration with known singular points
  • QAGI adaptive integration on infinite intervals
  • QAWC adaptive integration for Cauchy principal values
  • QAWS adaptive integration for singular functions
  • QAWO adaptive integration for oscillatory functions
  • QAWF adaptive integration for Fourier integrals
  • CQUAD doubly-adaptive integration
  • Romberg integration
  • Gauss-Legendre integration
  • Fixed point quadratures
  • Integrating on the unit sphere
  • Error codes
  • Examples
  • References and Further Reading
• Random Number Generation
  • General comments on random numbers
  • The Random Number Generator Interface
  • Random number generator initialization
  • Sampling from a random number generator
  • Auxiliary random number generator functions
  • Random number environment variables
  • Copying random number generator state
  • Reading and writing random number generator state
  • Random number generator algorithms
  • Unix random number generators
  • Other random number generators
  • Performance
  • Examples
  • References and Further Reading
  • Acknowledgements
• Quasi-Random Sequences
  • Quasi-random number generator initialization
  • Sampling from a quasi-random number generator
  • Auxiliary quasi-random number generator functions
  • Saving and restoring quasi-random number generator state
  • Quasi-random number generator algorithms
  • Examples
  • References
• Random Number Distributions
  • Introduction
  • The Gaussian Distribution
  • The Gaussian Tail Distribution
  • The Bivariate Gaussian Distribution
  • The Multivariate Gaussian Distribution
  • The Exponential Distribution
  • The Laplace Distribution
  • The Exponential Power Distribution
  • The Cauchy Distribution
  • The Rayleigh Distribution
  • The Rayleigh Tail Distribution
  • The Landau Distribution
  • The Levy alpha-Stable Distributions
  • The Levy skew alpha-Stable Distribution
  • The Gamma Distribution
  • The Flat (Uniform) Distribution
  • The Lognormal Distribution
  • The Chi-squared Distribution
  • The F-distribution
  • The t-distribution
  • The Beta Distribution
  • The Logistic Distribution
  • The Pareto Distribution
  • Spherical Vector Distributions
  • The Weibull Distribution
  • The Type-1 Gumbel Distribution
  • The Type-2 Gumbel Distribution
  • The Dirichlet Distribution
  • General Discrete Distributions
  • The Poisson Distribution
  • The Bernoulli Distribution
  • The Binomial Distribution
  • The Multinomial Distribution
  • The Negative Binomial Distribution
  • The Pascal Distribution
  • The Geometric Distribution
  • The Hypergeometric Distribution
  • The Logarithmic Distribution
  • The Wishart Distribution
  • Shuffling and Sampling
  • Examples
  • References and Further Reading
• Statistics
  • Mean, Standard Deviation and Variance
  • Absolute deviation
  • Higher moments (skewness and kurtosis)
  • Autocorrelation
  • Covariance
  • Correlation
  • Weighted Samples
  • Maximum and Minimum values
  • Median and Percentiles
  • Order Statistics
  • Robust Location Estimates
  • Robust Scale Estimates
  • Examples
  • References and Further Reading
• Running Statistics
  • Initializing the Accumulator
  • Adding Data to the Accumulator
  • Current Statistics
  • Quantiles
  • Examples
  • References and Further Reading
• Moving Window Statistics
  • Introduction
  • Handling Endpoints
  • Allocation for Moving Window Statistics
  • Moving Mean
  • Moving Variance and Standard Deviation
  • Moving Minimum and Maximum
  • Moving Sum
  • Moving Median
  • Robust Scale Estimation
  • User-defined Moving Statistics
  • Accumulators
  • Examples
  • References and Further Reading
• Digital Filtering
  • Introduction
  • Handling Endpoints
  • Linear Digital Filters
  • Nonlinear Digital Filters
  • Examples
  • References and Further Reading
• Histograms
  • The histogram struct
  • Histogram allocation
  • Copying Histograms
  • Updating and accessing histogram elements
  • Searching histogram ranges
  • Histogram Statistics
  • Histogram Operations
  • Reading and writing histograms
  • Resampling from histograms
  • The histogram probability distribution struct
  • Example programs for histograms
  • Two dimensional histograms
  • The 2D histogram struct
  • 2D Histogram allocation
  • Copying 2D Histograms
  • Updating and accessing 2D histogram elements
  • Searching 2D histogram ranges
  • 2D Histogram Statistics
  • 2D Histogram Operations
  • Reading and writing 2D histograms
  • Resampling from 2D histograms
  • Example programs for 2D histograms
• N-tuples
  • The ntuple struct
  • Creating ntuples
  • Opening an existing ntuple file
  • Writing ntuples
  • Reading ntuples
  • Closing an ntuple file
  • Histogramming ntuple values
  • Examples
  • References and Further Reading
• Monte Carlo Integration
  • Interface
  • PLAIN Monte Carlo
  • MISER
  • VEGAS
  • Examples
  • References and Further Reading
• Simulated Annealing
  • Simulated Annealing algorithm
  • Simulated Annealing functions
  • Examples
  • References and Further Reading
• Ordinary Differential Equations
  • Defining the ODE System
  • Stepping Functions
  • Adaptive Step-size Control
  • Evolution
  • Driver
  • Examples
  • References and Further Reading
• Interpolation
  • Introduction to 1D Interpolation
  • 1D Interpolation Functions
  • 1D Interpolation Types
  • 1D Index Look-up and Acceleration
  • 1D Evaluation of Interpolating Functions
  • 1D Higher-level Interface
  • 1D Interpolation Example Programs
  • Introduction to 2D Interpolation
  • 2D Interpolation Functions
  • 2D Interpolation Grids
  • 2D Interpolation Types
  • 2D Evaluation of Interpolating Functions
  • 2D Higher-level Interface
  • 2D Interpolation Example programs
  • References and Further Reading
• Numerical Differentiation
  • Functions
  • Examples
  • References and Further Reading
• Chebyshev Approximations
  • Definitions
  • Creation and Calculation of Chebyshev Series
  • Auxiliary Functions
  • Chebyshev Series Evaluation
  • Derivatives and Integrals
  • Examples
  • References and Further Reading
• Series Acceleration
  • Acceleration functions
  • Acceleration functions without error estimation
  • Examples
  • References and Further Reading
• Wavelet Transforms
  • Definitions
  • Initialization
  • Transform Functions
  • Examples
  • References and Further Reading
• Discrete Hankel Transforms
  • Definitions
  • Functions
  • References and Further Reading
• One Dimensional Root-Finding
  • Overview
  • Caveats
  • Initializing the Solver
  • Providing the function to solve
  • Search Bounds and Guesses
  • Iteration
  • Search Stopping Parameters
  • Root Bracketing Algorithms
  • Root Finding Algorithms using Derivatives
  • Examples
  • References and Further Reading
• One Dimensional Minimization
  • Overview
  • Caveats
  • Initializing the Minimizer
  • Providing the function to minimize
  • Iteration
  • Stopping Parameters
  • Minimization Algorithms
  • Examples
  • References and Further Reading
• Multidimensional Root-Finding
  • Overview
  • Initializing the Solver
  • Providing the function to solve
  • Iteration
  • Search Stopping Parameters
  • Algorithms using Derivatives
  • Algorithms without Derivatives
  • Examples
  • References and Further Reading
• Multidimensional Minimization
  • Overview
  • Caveats
  • Initializing the Multidimensional Minimizer
  • Providing a function to minimize
  • Iteration
  • Stopping Criteria
  • Algorithms with Derivatives
  • Algorithms without Derivatives
  • Examples
  • References and Further Reading
• Linear Least-Squares Fitting
  • Overview
  • Linear regression
  • Multi-parameter regression
  • Regularized regression
  • Robust linear regression
  • Large dense linear systems
  • Troubleshooting
  • Examples
  • References and Further Reading
• Nonlinear Least-Squares Fitting
  • Overview
  • Solving the Trust Region Subproblem (TRS)
  • Weighted Nonlinear Least-Squares
  • Tunable Parameters
  • Initializing the Solver
  • Providing the Function to be Minimized
  • Iteration
  • Testing for Convergence
  • High Level Driver
  • Covariance matrix of best fit parameters
  • Troubleshooting
  • Examples
  • References and Further Reading
• Basis Splines
  • Overview
  • Allocation of B-splines
  • Initializing the knots vector
  • Properties of B-splines
  • Evaluation of B-splines
  • Evaluation of B-spline derivatives
  • Evaluation of B-spline integrals
  • Least Squares Fitting with B-splines
  • Gram Matrix
  • Interpolation with B-splines
  • Hermite Interpolation with B-splines
  • Projection onto the B-spline Basis
  • Greville abscissae
  • Examples
  • References and Further Reading
• Sparse Matrices
  • Data types
  • Sparse Matrix Storage Formats
  • Overview
  • Allocation
  • Accessing Matrix Elements
  • Initializing Matrix Elements
  • Reading and Writing Matrices
  • Copying Matrices
  • Exchanging Rows and Columns
  • Matrix Operations
  • Matrix Properties
  • Finding Maximum and Minimum Elements
  • Compressed Format
  • Conversion Between Sparse and Dense Matrices
  • Examples
  • References and Further Reading
• Sparse BLAS Support
  • Sparse BLAS operations
  • References and Further Reading
• Sparse Linear Algebra
  • Overview
  • Sparse Iterative Solvers
  • Examples
  • References and Further Reading
• Physical Constants
  • Fundamental Constants
  • Astronomy and Astrophysics
  • Atomic and Nuclear Physics
  • Measurement of Time
  • Imperial Units
  • Speed and Nautical Units
  • Printers Units
  • Volume, Area and Length
  • Mass and Weight
  • Thermal Energy and Power
  • Pressure
  • Viscosity
  • Light and Illumination
  • Radioactivity
  • Force and Energy
  • Prefixes
  • Examples
  • References and Further Reading
• IEEE floating-point arithmetic
  • Representation of floating point numbers
  • Setting up your IEEE environment
  • References and Further Reading
• Debugging Numerical Programs
  • Using gdb
  • Examining floating point registers
  • Handling floating point exceptions
  • GCC warning options for numerical programs
  • References and Further Reading
• Contributors to GSL
• Autoconf Macros
• GSL CBLAS Library
  • Level 1
  • Level 2
  • Level 3
  • Examples
• GNU General Public License
• GNU Free Documentation License

• Index