This is gsl-ref.info, produced by makeinfo version 4.0 from
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INFO-DIR-SECTION Scientific software
START-INFO-DIR-ENTRY
* gsl-ref: (gsl-ref).                   GNU Scientific Library - Reference
END-INFO-DIR-ENTRY

   This file documents the GNU Scientific Library.

   Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001 The GSL Team.

   Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.1 or
any later version published by the Free Software Foundation; with no
Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.  A
copy of the license is included in the section entitled "GNU Free
Documentation License".


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Tag Table:
(Indirect)
Node: Top720
Node: Introduction2237
Node: Routines available in GSL2875
Node: GSL is Free Software4444
Node: Obtaining GSL6568
Node: An Example Program7697
Node: No Warranty8437
Node: Further Information8878
Node: Using the library9407
Node: ANSI C Compliance9946
Node: Compiling and Linking11008
Node: Shared Libraries13211
Node: Autoconf macros13778
Node: Inline functions16069
Node: Long double17393
Node: Portability functions18786
Node: Alternative optimized functions20243
Node: Support for different numeric types21694
Node: Compatibility with C++24756
Node: Aliasing of arrays25071
Node: Code Reuse25812
Node: Error Handling26447
Node: Error Reporting27151
Node: Error Handlers30938
Node: Using GSL error reporting in your own functions35116
Node: Mathematical Functions37027
Node: Mathematical Constants37734
Node: Infinities and Not-a-number38857
Node: Elementary Functions39911
Node: Small integer powers41601
Node: Testing the Sign of Numbers43177
Node: Testing for Odd and Even Numbers43599
Node: Maximum and Minimum functions44145
Node: Complex Numbers46154
Node: Complex numbers47508
Node: Properties of complex numbers49299
Node: Complex arithmetic operators50274
Node: Elementary Complex Functions52997
Node: Complex Trigonometric Functions54801
Node: Inverse Complex Trigonometric Functions56008
Node: Complex Hyperbolic Functions58594
Node: Inverse Complex Hyperbolic Functions59876
Node: Complex Number References and Further Reading61700
Node: Roots of Polynomials63089
Node: Polynomial evaluation63830
Node: Quadratic equations64261
Node: Cubic equations66010
Node: General polynomial equations67364
Node: Roots of Polynomials Examples69244
Node: Roots of Polynomials References and Further Reading70668
Node: Special Functions71437
Node: Special Function Usage73391
Node: The gsl_sf_result struct74570
Node: Special Function Modes75829
Node: Airy Functions and Derivatives76761
Node: Airy Functions77452
Node: Derivatives of Airy Functions78792
Node: Zeros of Airy Functions80131
Node: Zeros of Derivatives of Airy Functions80834
Node: Bessel Functions81577
Node: Regular Cylindrical Bessel Functions82764
Node: Irregular Cylindrical Bessel Functions84070
Node: Regular Modified Cylindrical Bessel Functions85508
Node: Irregular Modified Cylindrical Bessel Functions88311
Node: Regular Spherical Bessel Functions91255
Node: Irregular Spherical Bessel Functions93446
Node: Regular Modified Spherical Bessel Functions95113
Node: Irregular Modified Spherical Bessel Functions97099
Node: Regular Bessel Function - Fractional Order99145
Node: Irregular Bessel Functions - Fractional Order100129
Node: Regular Modified Bessel Functions - Fractional Order100696
Node: Irregular Modified Bessel Functions - Fractional Order101603
Node: Zeros of Regular Bessel Functions102818
Node: Clausen Functions103828
Node: Coulomb Functions104425
Node: Normalized Hydrogenic Bound States104851
Node: Coulomb Wave Functions105857
Node: Coulomb Wave Function Normalization Constant109242
Node: Coupling Coefficients109984
Node: 3-j Symbols110702
Node: 6-j Symbols111292
Node: 9-j Symbols111902
Node: Dawson Function112594
Node: Debye Functions113153
Node: Dilogarithm114433
Node: Real Argument114721
Node: Complex Argument115274
Node: Elementary Operations115728
Node: Elliptic Integrals116543
Node: Definition of Legendre Forms117009
Node: Definition of Carlson Forms117847
Node: Legendre Form of Complete Elliptic Integrals118548
Node: Legendre Form of Incomplete Elliptic Integrals119414
Node: Carlson Forms121131
Node: Elliptic Functions (Jacobi)122656
Node: Error Functions123229
Node: Error Function123672
Node: Complementary Error Function124016
Node: Log Complementary Error Function124461
Node: Probability functions124897
Node: Exponential Functions125636
Node: Exponential Function126012
Node: Relative Exponential Functions127205
Node: Exponentiation With Error Estimate128854
Node: Exponential Integrals130045
Node: Exponential Integral130520
Node: Ei(x)131147
Node: Hyperbolic Integrals131577
Node: Ei_3(x)132214
Node: Trigonometric Integrals132579
Node: Arctangent Integral133160
Node: Fermi-Dirac Function133523
Node: Complete Fermi-Dirac Integrals133876
Node: Incomplete Fermi-Dirac Integrals136307
Node: Gamma Function136934
Node: Gegenbauer Functions144447
Node: Hypergeometric Functions146071
Node: Laguerre Functions150021
Node: Lambert W Functions151275
Node: Legendre Functions and Spherical Harmonics152292
Node: Legendre Polynomials152874
Node: Associated Legendre Polynomials and Spherical Harmonics154691
Node: Conical Functions157099
Node: Radial Functions for Hyperbolic Space159196
Node: Logarithm and Related Functions161354
Node: Power Function162959
Node: Psi (Digamma) Function163891
Node: Digamma Function164395
Node: Trigamma Function165204
Node: Polygamma Function165572
Node: Synchrotron Functions165940
Node: Transport Functions166691
Node: Trigonometric Functions167783
Node: Circular Trigonometric Functions168398
Node: Trigonometric Functions for Complex Arguments169385
Node: Hyperbolic Trigonometric Functions170402
Node: Conversion Functions170987
Node: Restriction Functions171754
Node: Trigonometric Functions With Error Estimates172365
Node: Zeta Functions173109
Node: Riemann Zeta Function173524
Node: Hurwitz Zeta Function174178
Node: Eta Function174660
Node: Special Functions Examples175204
Node: Special Functions References and Further Reading176885
Node: Vectors and Matrices177981
Node: Data types178739
Node: Blocks179937
Node: Block allocation180848
Node: Reading and writing blocks182240
Node: Example programs for blocks184291
Node: Vectors184922
Node: Vector allocation186787
Node: Accessing vector elements188311
Node: Initializing vector elements190426
Node: Reading and writing vectors191105
Node: Vector views193172
Node: Copying vectors200353
Node: Exchanging elements201202
Node: Vector operations201749
Node: Finding maximum and minimum elements of vectors203248
Node: Vector properties204755
Node: Example programs for vectors205103
Node: Matrices206839
Node: Matrix allocation209692
Node: Accessing matrix elements211265
Node: Initializing matrix elements212947
Node: Reading and writing matrices213728
Node: Matrix views215808
Node: Creating row and column views222927
Node: Copying matrices226076
Node: Copying rows and columns226674
Node: Exchanging rows and columns228338
Node: Matrix operations229796
Node: Finding maximum and minimum elements of matrices231412
Node: Matrix properties233099
Node: Example programs for matrices233450
Node: Vector and Matrix References and Further Reading237363
Node: Permutations237841
Node: The Permutation struct239091
Node: Permutation allocation239587
Node: Accessing permutation elements240762
Node: Permutation properties241518
Node: Permutation functions242206
Node: Applying Permutations243451
Node: Reading and writing permutations245054
Node: Permutation Examples247219
Node: Permutation References and Further Reading249661
Node: Sorting250074
Node: Sorting objects251020
Node: Sorting vectors253800
Node: Selecting the k-th smallest or largest elements256369
Node: Computing the rank259815
Node: Sorting Examples261023
Node: Sorting References and Further Reading262640
Node: BLAS Support263176
Node: GSL BLAS Interface266144
Node: Level 1 GSL BLAS Interface266624
Node: Level 2 GSL BLAS Interface273134
Node: Level 3 GSL BLAS Interface282412
Node: BLAS Examples293485
Node: BLAS References and Further Reading294936
Node: Linear Algebra296280
Node: LU Decomposition297487
Node: QR Decomposition302322
Node: QR Decomposition with Column Pivoting307964
Node: Singular Value Decomposition312336
Node: Cholesky Decomposition315633
Node: Tridiagonal Decomposition of Real Symmetric Matrices317534
Node: Tridiagonal Decomposition of Hermitian Matrices319342
Node: Bidiagonalization321230
Node: Householder solver for linear systems323542
Node: Tridiagonal Systems324423
Node: Linear Algebra Examples325518
Node: Linear Algebra References and Further Reading327546
Node: Eigensystems329003
Node: Real Symmetric Matrices330042
Node: Complex Hermitian Matrices332258
Node: Sorting Eigenvalues and Eigenvectors334760
Node: Eigenvalue and Eigenvector Examples336079
Node: Eigenvalue and Eigenvector References338429
Node: Fast Fourier Transforms339127
Node: Mathematical Definitions340333
Node: Overview of complex data FFTs342731
Node: Radix-2 FFT routines for complex data345350
Node: Mixed-radix FFT routines for complex data349415
Node: Overview of real data FFTs358660
Node: Radix-2 FFT routines for real data361090
Node: Mixed-radix FFT routines for real data363919
Node: FFT References and Further Reading374579
Node: Numerical Integration377339
Node: Numerical Integration Introduction378881
Node: QNG non-adaptive Gauss-Kronrod integration382344
Node: QAG adaptive integration383604
Node: QAGS adaptive integration with singularities386234
Node: QAGP adaptive integration with known singular points388024
Node: QAGI adaptive integration on infinite intervals389324
Node: QAWC adaptive integration for Cauchy principal values391546
Node: QAWS adaptive integration for singular functions392709
Node: QAWO adaptive integration for oscillatory functions395938
Node: QAWF adaptive integration for Fourier integrals399692
Node: Numerical integration error codes402270
Node: Numerical integration examples403029
Node: Numerical integration References and Further Reading405055
Node: Random Number Generation405771
Node: General comments on random numbers407222
Node: The Random Number Generator Interface409170
Node: Random number generator initialization410521
Node: Sampling from a random number generator412518
Node: Auxiliary random number generator functions414993
Node: Random number environment variables417313
Node: Saving and restoring random number generator state419846
Node: Random number generator algorithms421015
Node: Unix random number generators429877
Node: Numerical Recipes generators433592
Node: Other random number generators434975
Node: Random Number Generator Performance441518
Node: Random Number References and Further Reading442809
Node: Random Number Acknowledgements444006
Node: Quasi-Random Sequences444480
Node: Quasi-random number generator initialization445504
Node: Sampling from a quasi-random number generator446408
Node: Auxiliary quasi-random number generator functions447002
Node: Saving and resorting quasi-random number generator state447934
Node: Quasi-random number generator algorithms448720
Node: Quasi-random number generator examples449486
Node: Quasi-random number references450476
Node: Random Number Distributions450989
Node: The Gaussian Distribution453253
Node: The Gaussian Tail Distribution454866
Node: The Bivariate Gaussian Distribution456479
Node: The Exponential Distribution457758
Node: The Laplace Distribution458461
Node: The Exponential Power Distribution459150
Node: The Cauchy Distribution460103
Node: The Rayleigh Distribution460936
Node: The Rayleigh Tail Distribution461662
Node: The Landau Distribution462518
Node: The Levy alpha-Stable Distributions463456
Node: The Levy skew alpha-Stable Distribution464499
Node: The Gamma Distribution466096
Node: The Flat (Uniform) Distribution466806
Node: The Lognormal Distribution467510
Node: The Chi-squared Distribution468309
Node: The F-distribution469285
Node: The t-distribution470416
Node: The Beta Distribution471396
Node: The Logistic Distribution472096
Node: The Pareto Distribution472797
Node: The Spherical Distribution (2D & 3D)473500
Node: The Weibull Distribution476309
Node: The Type-1 Gumbel Distribution477040
Node: The Type-2 Gumbel Distribution477807
Node: General Discrete Distributions478572
Node: The Poisson Distribution482422
Node: The Bernoulli Distribution483137
Node: The Binomial Distribution483863
Node: The Negative Binomial Distribution484731
Node: The Pascal Distribution485732
Node: The Geometric Distribution486555
Node: The Hypergeometric Distribution487359
Node: The Logarithmic Distribution488324
Node: Shuffling and Sampling489100
Node: Random Number Distribution Examples491939
Node: Random Number Distribution References and Further Reading494338
Node: Statistics495541
Node: Mean and standard deviation and variance496808
Node: Absolute deviation499853
Node: Higher moments (skewness and kurtosis)501137
Node: Autocorrelation503264
Node: Covariance504067
Node: Weighted Samples504886
Node: Maximum and Minimum values510097
Node: Median and Percentiles512533
Node: Example statistical programs514943
Node: Statistics References and Further Reading517677
Node: Histograms518861
Node: The histogram struct520615
Node: Histogram allocation522415
Node: Copying Histograms525396
Node: Updating and accessing histogram elements526060
Node: Searching histogram ranges529309
Node: Histogram Statistics530300
Node: Histogram Operations531974
Node: Reading and writing histograms534017
Node: Resampling from histograms537038
Node: The histogram probability distribution struct537829
Node: Example programs for histograms540856
Node: Two dimensional histograms542977
Node: The 2D histogram struct543689
Node: 2D Histogram allocation545479
Node: Copying 2D Histograms547537
Node: Updating and accessing 2D histogram elements548228
Node: Searching 2D histogram ranges551854
Node: 2D Histogram Statistics552863
Node: 2D Histogram Operations553995
Node: Reading and writing 2D histograms556145
Node: Resampling from 2D histograms559789
Node: Example programs for 2D histograms562794
Node: N-tuples564843
Node: The ntuple struct566103
Node: Creating ntuples566574
Node: Opening an existing ntuple file567231
Node: Writing ntuples567849
Node: Reading ntuples568297
Node: Closing an ntuple file568616
Node: Histogramming ntuple values568945
Node: Example ntuple programs570941
Node: Ntuple References and Further Reading574493
Node: Monte Carlo Integration574804
Node: Monte Carlo Interface576048
Node: PLAIN Monte Carlo578682
Node: MISER581109
Node: VEGAS586932
Node: Monte Carlo Examples595229
Node: Monte Carlo Integration References and Further Reading601257
Node: Simulated Annealing602009
Node: Simulated Annealing algorithm603186
Node: Simulated Annealing functions604681
Node: Examples with Simulated Annealing607072
Node: Trivial example607612
Node: Traveling Salesman Problem610058
Node: Ordinary Differential Equations613476
Node: Defining the ODE System614294
Node: Stepping Functions615672
Node: Adaptive Step-size Control619183
Node: Evolution623873
Node: ODE Example programs625928
Node: ODE References and Further Reading629399
Node: Interpolation630032
Node: Introduction to Interpolation631042
Node: Interpolation Functions631472
Node: Interpolation Types632638
Node: Index Look-up and Acceleration634079
Node: Evaluation of interpolating functions635692
Node: Higher-level interface638044
Node: Interpolation Example programs639892
Node: Interpolation References and Further Reading641629
Node: Numerical Differentiation642059
Node: Numerical Differentiation functions642639
Node: Numerical Differentiation Example644246
Node: Numerical Differentiation References645658
Node: Chebyshev Approximations646056
Node: The gsl_cheb_series struct647012
Node: Creation and Calculation of Chebyshev Series647657
Node: Chebyshev Series Evaluation648621
Node: Derivatives and Integrals649981
Node: Chebyshev Approximation examples651214
Node: Chebyshev Approximation References and Further Reading652748
Node: Series Acceleration653187
Node: Acceleration functions653957
Node: Acceleration functions without error estimation656189
Node: Example of accelerating a series658795
Node: Series Acceleration References661236
Node: Discrete Hankel Transforms662115
Node: Discrete Hankel Transform Definition662581
Node: Discrete Hankel Transform Functions664419
Node: Discrete Hankel Transform References665923
Node: One dimensional Root-Finding666317
Node: Root Finding Overview667574
Node: Root Finding Caveats669425
Node: Initializing the Solver671183
Node: Providing the function to solve673800
Node: Search Bounds and Guesses677604
Node: Root Finding Iteration678458
Node: Search Stopping Parameters680294
Node: Root Bracketing Algorithms682802
Node: Root Finding Algorithms using Derivatives686091
Node: Root Finding Examples689562
Node: Root Finding References and Further Reading696910
Node: One dimensional Minimization697537
Node: Minimization Overview698836
Node: Minimization Caveats700510
Node: Initializing the Minimizer701840
Node: Providing the function to minimize704059
Node: Minimization Iteration704530
Node: Minimization Stopping Parameters706204
Node: Minimization Algorithms707805
Node: Minimization Examples710237
Node: Minimization References and Further Reading713204
Node: Multidimensional Root-Finding713582
Node: Overview of Multidimensional Root Finding715068
Node: Initializing the Multidimensional Solver717248
Node: Providing the multidimensional system of equations to solve720413
Node: Iteration of the multidimensional solver725289
Node: Search Stopping Parameters for the multidimensional solver726892
Node: Algorithms using Derivatives728624
Node: Algorithms without Derivatives733359
Node: Example programs for Multidimensional Root finding736141
Node: References and Further Reading for Multidimensional Root Finding744865
Node: Multidimensional Minimization746094
Node: Multimin Overview747383
Node: Multimin Caveats748961
Node: Initializing the Multidimensional Minimizer749703
Node: Providing a function to minimize751858
Node: Multimin Iteration755076
Node: Multimin Stopping Criteria756612
Node: Multimin Algorithms757803
Node: Multimin Examples760566
Node: Multimin References and Further Reading763661
Node: Least-Squares Fitting764147
Node: Linear regression765078
Node: Linear fitting without a constant term767671
Node: Multi-parameter fitting770063
Node: Fitting Examples773815
Node: Fitting References and Further Reading780589
Node: Nonlinear Least-Squares Fitting781398
Node: Overview of Nonlinear Least-Squares Fitting782849
Node: Initializing the Nonlinear Least-Squares Solver783732
Node: Providing the Function to be Minimized786393
Node: Iteration of the Minimization Algorithm789032
Node: Search Stopping Parameters for Minimization Algorithms790359
Node: Minimization Algorithms using Derivatives792448
Node: Minimization Algorithms without Derivatives795684
Node: Computing the covariance matrix of best fit parameters796069
Node: Example programs for Nonlinear Least-Squares Fitting797127
Node: References and Further Reading for Nonlinear Least-Squares Fitting804043
Node: Physical Constants804766
Node: Fundamental Constants806109
Node: Astronomy and Astrophysics806953
Node: Atomic and Nuclear Physics807602
Node: Measurement of Time808827
Node: Imperial Units809243
Node: Nautical Units809660
Node: Printers Units809975
Node: Volume810260
Node: Mass and Weight810771
Node: Thermal Energy and Power811553
Node: Pressure811960
Node: Viscosity812554
Node: Light and Illumination812816
Node: Radioactivity813389
Node: Physical Constant Examples813719
Node: Physical Constant References and Further Reading815509
Node: IEEE floating-point arithmetic815865
Node: Representation of floating point numbers816448
Node: Setting up your IEEE environment820951
Node: IEEE References and Further Reading827038
Node: Debugging Numerical Programs828036
Node: Using gdb828498
Node: Examining floating point registers831854
Node: Handling floating point exceptions833142
Node: GCC warning options for numerical programs834551
Node: Debugging References838738
Node: Contributors to GSL839280
Node: Autoconf Macros840848
Node: GSL CBLAS Library841647
Node: Level 1 CBLAS Functions842143
Node: Level 2 CBLAS Functions847289
Node: Level 3 CBLAS Functions863651
Node: GSL CBLAS Examples873170
Node: GNU General Public License874766
Node: GNU Free Documentation License894045
Node: Function Index913962
Node: Variable Index1021364
Node: Type Index1022174
Node: Concept Index1023812

End Tag Table
