This is gsl-ref.info, produced by makeinfo version 4.0 from
gsl-ref.texi.

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".


Indirect:
gsl-ref.info-1: 720
gsl-ref.info-2: 50227
gsl-ref.info-3: 100082
gsl-ref.info-4: 149974
gsl-ref.info-5: 193125
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gsl-ref.info-8: 332211
gsl-ref.info-9: 378834
gsl-ref.info-10: 420968
gsl-ref.info-11: 470369
gsl-ref.info-12: 518814
gsl-ref.info-13: 568569
gsl-ref.info-14: 615625
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gsl-ref.info-19: 846853
gsl-ref.info-20: 893609
gsl-ref.info-21: 913526
gsl-ref.info-22: 1020928

Tag Table:
(Indirect)
Node: Top720
Node: Introduction2190
Node: Routines available in GSL2828
Node: GSL is Free Software4397
Node: Obtaining GSL6521
Node: An Example Program7650
Node: No Warranty8390
Node: Further Information8831
Node: Using the library9360
Node: ANSI C Compliance9899
Node: Compiling and Linking10961
Node: Shared Libraries13164
Node: Autoconf macros13731
Node: Inline functions16022
Node: Long double17346
Node: Portability functions18739
Node: Alternative optimized functions20196
Node: Support for different numeric types21647
Node: Compatibility with C++24709
Node: Aliasing of arrays25024
Node: Code Reuse25765
Node: Error Handling26400
Node: Error Reporting27104
Node: Error Handlers30891
Node: Using GSL error reporting in your own functions35069
Node: Mathematical Functions36980
Node: Mathematical Constants37687
Node: Infinities and Not-a-number38810
Node: Elementary Functions39864
Node: Small integer powers41554
Node: Testing the Sign of Numbers43130
Node: Testing for Odd and Even Numbers43552
Node: Maximum and Minimum functions44098
Node: Complex Numbers46107
Node: Complex numbers47461
Node: Properties of complex numbers49252
Node: Complex arithmetic operators50227
Node: Elementary Complex Functions52950
Node: Complex Trigonometric Functions54754
Node: Inverse Complex Trigonometric Functions55961
Node: Complex Hyperbolic Functions58547
Node: Inverse Complex Hyperbolic Functions59829
Node: Complex Number References and Further Reading61653
Node: Roots of Polynomials63042
Node: Polynomial evaluation63783
Node: Quadratic equations64214
Node: Cubic equations65963
Node: General polynomial equations67317
Node: Roots of Polynomials Examples69197
Node: Roots of Polynomials References and Further Reading70621
Node: Special Functions71390
Node: Special Function Usage73344
Node: The gsl_sf_result struct74523
Node: Special Function Modes75782
Node: Airy Functions and Derivatives76714
Node: Airy Functions77405
Node: Derivatives of Airy Functions78745
Node: Zeros of Airy Functions80084
Node: Zeros of Derivatives of Airy Functions80787
Node: Bessel Functions81530
Node: Regular Cylindrical Bessel Functions82717
Node: Irregular Cylindrical Bessel Functions84023
Node: Regular Modified Cylindrical Bessel Functions85461
Node: Irregular Modified Cylindrical Bessel Functions88264
Node: Regular Spherical Bessel Functions91208
Node: Irregular Spherical Bessel Functions93399
Node: Regular Modified Spherical Bessel Functions95066
Node: Irregular Modified Spherical Bessel Functions97052
Node: Regular Bessel Function - Fractional Order99098
Node: Irregular Bessel Functions - Fractional Order100082
Node: Regular Modified Bessel Functions - Fractional Order100649
Node: Irregular Modified Bessel Functions - Fractional Order101556
Node: Zeros of Regular Bessel Functions102771
Node: Clausen Functions103781
Node: Coulomb Functions104378
Node: Normalized Hydrogenic Bound States104804
Node: Coulomb Wave Functions105810
Node: Coulomb Wave Function Normalization Constant109195
Node: Coupling Coefficients109937
Node: 3-j Symbols110655
Node: 6-j Symbols111245
Node: 9-j Symbols111855
Node: Dawson Function112547
Node: Debye Functions113106
Node: Dilogarithm114386
Node: Real Argument114674
Node: Complex Argument115227
Node: Elementary Operations115681
Node: Elliptic Integrals116496
Node: Definition of Legendre Forms116962
Node: Definition of Carlson Forms117800
Node: Legendre Form of Complete Elliptic Integrals118501
Node: Legendre Form of Incomplete Elliptic Integrals119367
Node: Carlson Forms121084
Node: Elliptic Functions (Jacobi)122609
Node: Error Functions123182
Node: Error Function123625
Node: Complementary Error Function123969
Node: Log Complementary Error Function124414
Node: Probability functions124850
Node: Exponential Functions125589
Node: Exponential Function125965
Node: Relative Exponential Functions127158
Node: Exponentiation With Error Estimate128807
Node: Exponential Integrals129998
Node: Exponential Integral130473
Node: Ei(x)131100
Node: Hyperbolic Integrals131530
Node: Ei_3(x)132167
Node: Trigonometric Integrals132532
Node: Arctangent Integral133113
Node: Fermi-Dirac Function133476
Node: Complete Fermi-Dirac Integrals133829
Node: Incomplete Fermi-Dirac Integrals136260
Node: Gamma Function136887
Node: Gegenbauer Functions144400
Node: Hypergeometric Functions146024
Node: Laguerre Functions149974
Node: Lambert W Functions151228
Node: Legendre Functions and Spherical Harmonics152245
Node: Legendre Polynomials152827
Node: Associated Legendre Polynomials and Spherical Harmonics154644
Node: Conical Functions157052
Node: Radial Functions for Hyperbolic Space159149
Node: Logarithm and Related Functions161307
Node: Power Function162912
Node: Psi (Digamma) Function163844
Node: Digamma Function164348
Node: Trigamma Function165157
Node: Polygamma Function165525
Node: Synchrotron Functions165893
Node: Transport Functions166644
Node: Trigonometric Functions167736
Node: Circular Trigonometric Functions168351
Node: Trigonometric Functions for Complex Arguments169338
Node: Hyperbolic Trigonometric Functions170355
Node: Conversion Functions170940
Node: Restriction Functions171707
Node: Trigonometric Functions With Error Estimates172318
Node: Zeta Functions173062
Node: Riemann Zeta Function173477
Node: Hurwitz Zeta Function174131
Node: Eta Function174613
Node: Special Functions Examples175157
Node: Special Functions References and Further Reading176838
Node: Vectors and Matrices177934
Node: Data types178692
Node: Blocks179890
Node: Block allocation180801
Node: Reading and writing blocks182193
Node: Example programs for blocks184244
Node: Vectors184875
Node: Vector allocation186740
Node: Accessing vector elements188264
Node: Initializing vector elements190379
Node: Reading and writing vectors191058
Node: Vector views193125
Node: Copying vectors200306
Node: Exchanging elements201155
Node: Vector operations201702
Node: Finding maximum and minimum elements of vectors203201
Node: Vector properties204708
Node: Example programs for vectors205056
Node: Matrices206792
Node: Matrix allocation209645
Node: Accessing matrix elements211218
Node: Initializing matrix elements212900
Node: Reading and writing matrices213681
Node: Matrix views215761
Node: Creating row and column views222880
Node: Copying matrices226029
Node: Copying rows and columns226627
Node: Exchanging rows and columns228291
Node: Matrix operations229749
Node: Finding maximum and minimum elements of matrices231365
Node: Matrix properties233052
Node: Example programs for matrices233403
Node: Vector and Matrix References and Further Reading237316
Node: Permutations237794
Node: The Permutation struct239044
Node: Permutation allocation239540
Node: Accessing permutation elements240715
Node: Permutation properties241471
Node: Permutation functions242159
Node: Applying Permutations243404
Node: Reading and writing permutations245007
Node: Permutation Examples247172
Node: Permutation References and Further Reading249614
Node: Sorting250027
Node: Sorting objects250973
Node: Sorting vectors253753
Node: Selecting the k-th smallest or largest elements256322
Node: Computing the rank259768
Node: Sorting Examples260976
Node: Sorting References and Further Reading262593
Node: BLAS Support263129
Node: GSL BLAS Interface266097
Node: Level 1 GSL BLAS Interface266577
Node: Level 2 GSL BLAS Interface273087
Node: Level 3 GSL BLAS Interface282365
Node: BLAS Examples293438
Node: BLAS References and Further Reading294889
Node: Linear Algebra296233
Node: LU Decomposition297440
Node: QR Decomposition302275
Node: QR Decomposition with Column Pivoting307917
Node: Singular Value Decomposition312289
Node: Cholesky Decomposition315586
Node: Tridiagonal Decomposition of Real Symmetric Matrices317487
Node: Tridiagonal Decomposition of Hermitian Matrices319295
Node: Bidiagonalization321183
Node: Householder solver for linear systems323495
Node: Tridiagonal Systems324376
Node: Linear Algebra Examples325471
Node: Linear Algebra References and Further Reading327499
Node: Eigensystems328956
Node: Real Symmetric Matrices329995
Node: Complex Hermitian Matrices332211
Node: Sorting Eigenvalues and Eigenvectors334713
Node: Eigenvalue and Eigenvector Examples336032
Node: Eigenvalue and Eigenvector References338382
Node: Fast Fourier Transforms339080
Node: Mathematical Definitions340286
Node: Overview of complex data FFTs342684
Node: Radix-2 FFT routines for complex data345303
Node: Mixed-radix FFT routines for complex data349368
Node: Overview of real data FFTs358613
Node: Radix-2 FFT routines for real data361043
Node: Mixed-radix FFT routines for real data363872
Node: FFT References and Further Reading374532
Node: Numerical Integration377292
Node: Numerical Integration Introduction378834
Node: QNG non-adaptive Gauss-Kronrod integration382297
Node: QAG adaptive integration383557
Node: QAGS adaptive integration with singularities386187
Node: QAGP adaptive integration with known singular points387977
Node: QAGI adaptive integration on infinite intervals389277
Node: QAWC adaptive integration for Cauchy principal values391499
Node: QAWS adaptive integration for singular functions392662
Node: QAWO adaptive integration for oscillatory functions395891
Node: QAWF adaptive integration for Fourier integrals399645
Node: Numerical integration error codes402223
Node: Numerical integration examples402982
Node: Numerical integration References and Further Reading405008
Node: Random Number Generation405724
Node: General comments on random numbers407175
Node: The Random Number Generator Interface409123
Node: Random number generator initialization410474
Node: Sampling from a random number generator412471
Node: Auxiliary random number generator functions414946
Node: Random number environment variables417266
Node: Saving and restoring random number generator state419799
Node: Random number generator algorithms420968
Node: Unix random number generators429830
Node: Numerical Recipes generators433545
Node: Other random number generators434928
Node: Random Number Generator Performance441471
Node: Random Number References and Further Reading442762
Node: Random Number Acknowledgements443959
Node: Quasi-Random Sequences444433
Node: Quasi-random number generator initialization445457
Node: Sampling from a quasi-random number generator446361
Node: Auxiliary quasi-random number generator functions446955
Node: Saving and resorting quasi-random number generator state447887
Node: Quasi-random number generator algorithms448673
Node: Quasi-random number generator examples449439
Node: Quasi-random number references450429
Node: Random Number Distributions450942
Node: The Gaussian Distribution453206
Node: The Gaussian Tail Distribution454819
Node: The Bivariate Gaussian Distribution456432
Node: The Exponential Distribution457711
Node: The Laplace Distribution458414
Node: The Exponential Power Distribution459103
Node: The Cauchy Distribution460056
Node: The Rayleigh Distribution460889
Node: The Rayleigh Tail Distribution461615
Node: The Landau Distribution462471
Node: The Levy alpha-Stable Distributions463409
Node: The Levy skew alpha-Stable Distribution464452
Node: The Gamma Distribution466049
Node: The Flat (Uniform) Distribution466759
Node: The Lognormal Distribution467463
Node: The Chi-squared Distribution468262
Node: The F-distribution469238
Node: The t-distribution470369
Node: The Beta Distribution471349
Node: The Logistic Distribution472049
Node: The Pareto Distribution472750
Node: The Spherical Distribution (2D & 3D)473453
Node: The Weibull Distribution476262
Node: The Type-1 Gumbel Distribution476993
Node: The Type-2 Gumbel Distribution477760
Node: General Discrete Distributions478525
Node: The Poisson Distribution482375
Node: The Bernoulli Distribution483090
Node: The Binomial Distribution483816
Node: The Negative Binomial Distribution484684
Node: The Pascal Distribution485685
Node: The Geometric Distribution486508
Node: The Hypergeometric Distribution487312
Node: The Logarithmic Distribution488277
Node: Shuffling and Sampling489053
Node: Random Number Distribution Examples491892
Node: Random Number Distribution References and Further Reading494291
Node: Statistics495494
Node: Mean and standard deviation and variance496761
Node: Absolute deviation499806
Node: Higher moments (skewness and kurtosis)501090
Node: Autocorrelation503217
Node: Covariance504020
Node: Weighted Samples504839
Node: Maximum and Minimum values510050
Node: Median and Percentiles512486
Node: Example statistical programs514896
Node: Statistics References and Further Reading517630
Node: Histograms518814
Node: The histogram struct520568
Node: Histogram allocation522368
Node: Copying Histograms525349
Node: Updating and accessing histogram elements526013
Node: Searching histogram ranges529262
Node: Histogram Statistics530253
Node: Histogram Operations531927
Node: Reading and writing histograms533970
Node: Resampling from histograms536991
Node: The histogram probability distribution struct537782
Node: Example programs for histograms540809
Node: Two dimensional histograms542930
Node: The 2D histogram struct543642
Node: 2D Histogram allocation545432
Node: Copying 2D Histograms547490
Node: Updating and accessing 2D histogram elements548181
Node: Searching 2D histogram ranges551807
Node: 2D Histogram Statistics552816
Node: 2D Histogram Operations553948
Node: Reading and writing 2D histograms556098
Node: Resampling from 2D histograms559742
Node: Example programs for 2D histograms562747
Node: N-tuples564796
Node: The ntuple struct566056
Node: Creating ntuples566527
Node: Opening an existing ntuple file567184
Node: Writing ntuples567802
Node: Reading ntuples568250
Node: Closing an ntuple file568569
Node: Histogramming ntuple values568898
Node: Example ntuple programs570894
Node: Ntuple References and Further Reading574446
Node: Monte Carlo Integration574757
Node: Monte Carlo Interface576001
Node: PLAIN Monte Carlo578635
Node: MISER581062
Node: VEGAS586885
Node: Monte Carlo Examples595182
Node: Monte Carlo Integration References and Further Reading601210
Node: Simulated Annealing601962
Node: Simulated Annealing algorithm603139
Node: Simulated Annealing functions604634
Node: Examples with Simulated Annealing607025
Node: Trivial example607565
Node: Traveling Salesman Problem610011
Node: Ordinary Differential Equations613429
Node: Defining the ODE System614247
Node: Stepping Functions615625
Node: Adaptive Step-size Control619136
Node: Evolution623826
Node: ODE Example programs625881
Node: ODE References and Further Reading629352
Node: Interpolation629985
Node: Introduction to Interpolation630995
Node: Interpolation Functions631425
Node: Interpolation Types632591
Node: Index Look-up and Acceleration634032
Node: Evaluation of interpolating functions635645
Node: Higher-level interface637997
Node: Interpolation Example programs639845
Node: Interpolation References and Further Reading641582
Node: Numerical Differentiation642012
Node: Numerical Differentiation functions642592
Node: Numerical Differentiation Example644199
Node: Numerical Differentiation References645611
Node: Chebyshev Approximations646009
Node: The gsl_cheb_series struct646965
Node: Creation and Calculation of Chebyshev Series647610
Node: Chebyshev Series Evaluation648574
Node: Derivatives and Integrals649934
Node: Chebyshev Approximation examples651167
Node: Chebyshev Approximation References and Further Reading652701
Node: Series Acceleration653140
Node: Acceleration functions653910
Node: Acceleration functions without error estimation656142
Node: Example of accelerating a series658748
Node: Series Acceleration References661189
Node: Discrete Hankel Transforms662068
Node: Discrete Hankel Transform Definition662534
Node: Discrete Hankel Transform Functions664372
Node: Discrete Hankel Transform References665876
Node: One dimensional Root-Finding666270
Node: Root Finding Overview667527
Node: Root Finding Caveats669378
Node: Initializing the Solver671136
Node: Providing the function to solve673753
Node: Search Bounds and Guesses677557
Node: Root Finding Iteration678411
Node: Search Stopping Parameters680247
Node: Root Bracketing Algorithms682751
Node: Root Finding Algorithms using Derivatives686040
Node: Root Finding Examples689511
Node: Root Finding References and Further Reading696859
Node: One dimensional Minimization697486
Node: Minimization Overview698785
Node: Minimization Caveats700459
Node: Initializing the Minimizer701789
Node: Providing the function to minimize704008
Node: Minimization Iteration704479
Node: Minimization Stopping Parameters706153
Node: Minimization Algorithms707750
Node: Minimization Examples710182
Node: Minimization References and Further Reading713149
Node: Multidimensional Root-Finding713527
Node: Overview of Multidimensional Root Finding715013
Node: Initializing the Multidimensional Solver717193
Node: Providing the multidimensional system of equations to solve720358
Node: Iteration of the multidimensional solver725234
Node: Search Stopping Parameters for the multidimensional solver726837
Node: Algorithms using Derivatives728565
Node: Algorithms without Derivatives733300
Node: Example programs for Multidimensional Root finding736082
Node: References and Further Reading for Multidimensional Root Finding744806
Node: Multidimensional Minimization746035
Node: Multimin Overview747324
Node: Multimin Caveats748545
Node: Initializing the Multidimensional Minimizer749287
Node: Providing a function to minimize751436
Node: Multimin Iteration754654
Node: Multimin Stopping Criteria756189
Node: Multimin Algorithms757376
Node: Multimin Examples760134
Node: Multimin References and Further Reading763229
Node: Least-Squares Fitting763715
Node: Linear regression764646
Node: Linear fitting without a constant term767239
Node: Multi-parameter fitting769631
Node: Fitting Examples773383
Node: Fitting References and Further Reading780157
Node: Nonlinear Least-Squares Fitting780966
Node: Overview of Nonlinear Least-Squares Fitting782417
Node: Initializing the Nonlinear Least-Squares Solver783300
Node: Providing the Function to be Minimized785961
Node: Iteration of the Minimization Algorithm788600
Node: Search Stopping Parameters for Minimization Algorithms789927
Node: Minimization Algorithms using Derivatives792012
Node: Minimization Algorithms without Derivatives795248
Node: Computing the covariance matrix of best fit parameters795633
Node: Example programs for Nonlinear Least-Squares Fitting796691
Node: References and Further Reading for Nonlinear Least-Squares Fitting803607
Node: Physical Constants804330
Node: Fundamental Constants805673
Node: Astronomy and Astrophysics806517
Node: Atomic and Nuclear Physics807166
Node: Measurement of Time808391
Node: Imperial Units808807
Node: Nautical Units809224
Node: Printers Units809539
Node: Volume809824
Node: Mass and Weight810335
Node: Thermal Energy and Power811117
Node: Pressure811524
Node: Viscosity812118
Node: Light and Illumination812380
Node: Radioactivity812953
Node: Physical Constant Examples813283
Node: Physical Constant References and Further Reading815073
Node: IEEE floating-point arithmetic815429
Node: Representation of floating point numbers816012
Node: Setting up your IEEE environment820515
Node: IEEE References and Further Reading826602
Node: Debugging Numerical Programs827600
Node: Using gdb828062
Node: Examining floating point registers831418
Node: Handling floating point exceptions832706
Node: GCC warning options for numerical programs834115
Node: Debugging References838302
Node: Contributors to GSL838844
Node: Autoconf Macros840412
Node: GSL CBLAS Library841211
Node: Level 1 CBLAS Functions841707
Node: Level 2 CBLAS Functions846853
Node: Level 3 CBLAS Functions863215
Node: GSL CBLAS Examples872734
Node: GNU General Public License874330
Node: GNU Free Documentation License893609
Node: Function Index913526
Node: Variable Index1020928
Node: Type Index1021738
Node: Concept Index1023376

End Tag Table
