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".


Indirect:
gsl-ref.info-1: 720
gsl-ref.info-2: 50378
gsl-ref.info-3: 98880
gsl-ref.info-4: 147852
gsl-ref.info-5: 195208
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gsl-ref.info-10: 432303
gsl-ref.info-11: 481661
gsl-ref.info-12: 530518
gsl-ref.info-13: 580187
gsl-ref.info-14: 629776
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gsl-ref.info-19: 869693
gsl-ref.info-20: 916449
gsl-ref.info-21: 936366
gsl-ref.info-22: 1046435

Tag Table:
(Indirect)
Node: Top720
Node: Introduction2249
Node: Routines available in GSL2868
Node: GSL is Free Software4509
Node: Obtaining GSL6633
Node: An Example Program7811
Node: No Warranty8551
Node: Further Information8992
Node: Using the library9521
Node: ANSI C Compliance10060
Node: Compiling and Linking11122
Node: Shared Libraries13325
Node: Autoconf macros13892
Node: Inline functions16183
Node: Long double17507
Node: Portability functions18900
Node: Alternative optimized functions20357
Node: Support for different numeric types21808
Node: Compatibility with C++24870
Node: Aliasing of arrays25185
Node: Code Reuse25926
Node: Error Handling26561
Node: Error Reporting27265
Node: Error Handlers31052
Node: Using GSL error reporting in your own functions35230
Node: Mathematical Functions37141
Node: Mathematical Constants37848
Node: Infinities and Not-a-number38971
Node: Elementary Functions40025
Node: Small integer powers41715
Node: Testing the Sign of Numbers43291
Node: Testing for Odd and Even Numbers43713
Node: Maximum and Minimum functions44259
Node: Complex Numbers46268
Node: Complex numbers47612
Node: Properties of complex numbers49403
Node: Complex arithmetic operators50378
Node: Elementary Complex Functions53101
Node: Complex Trigonometric Functions54905
Node: Inverse Complex Trigonometric Functions56112
Node: Complex Hyperbolic Functions58698
Node: Inverse Complex Hyperbolic Functions59980
Node: Complex Number References and Further Reading61804
Node: Polynomials63193
Node: Polynomial Evaluation63960
Node: Divided Difference Representation of Polynomials64411
Node: Quadratic Equations66069
Node: Cubic Equations67836
Node: General Polynomial Equations69181
Node: Roots of Polynomials Examples71052
Node: Roots of Polynomials References and Further Reading72467
Node: Special Functions73227
Node: Special Function Usage75172
Node: The gsl_sf_result struct76351
Node: Special Function Modes77610
Node: Airy Functions and Derivatives78542
Node: Airy Functions79233
Node: Derivatives of Airy Functions80573
Node: Zeros of Airy Functions81912
Node: Zeros of Derivatives of Airy Functions82615
Node: Bessel Functions83358
Node: Regular Cylindrical Bessel Functions84545
Node: Irregular Cylindrical Bessel Functions85851
Node: Regular Modified Cylindrical Bessel Functions87289
Node: Irregular Modified Cylindrical Bessel Functions90092
Node: Regular Spherical Bessel Functions93036
Node: Irregular Spherical Bessel Functions95227
Node: Regular Modified Spherical Bessel Functions96894
Node: Irregular Modified Spherical Bessel Functions98880
Node: Regular Bessel Function - Fractional Order100926
Node: Irregular Bessel Functions - Fractional Order101910
Node: Regular Modified Bessel Functions - Fractional Order102477
Node: Irregular Modified Bessel Functions - Fractional Order103384
Node: Zeros of Regular Bessel Functions104599
Node: Clausen Functions105609
Node: Coulomb Functions106206
Node: Normalized Hydrogenic Bound States106632
Node: Coulomb Wave Functions107638
Node: Coulomb Wave Function Normalization Constant111023
Node: Coupling Coefficients111765
Node: 3-j Symbols112483
Node: 6-j Symbols113073
Node: 9-j Symbols113683
Node: Dawson Function114375
Node: Debye Functions114934
Node: Dilogarithm116214
Node: Real Argument116502
Node: Complex Argument117055
Node: Elementary Operations117509
Node: Elliptic Integrals118324
Node: Definition of Legendre Forms118790
Node: Definition of Carlson Forms119628
Node: Legendre Form of Complete Elliptic Integrals120329
Node: Legendre Form of Incomplete Elliptic Integrals121195
Node: Carlson Forms122912
Node: Elliptic Functions (Jacobi)124437
Node: Error Functions125010
Node: Error Function125453
Node: Complementary Error Function125797
Node: Log Complementary Error Function126242
Node: Probability functions126678
Node: Exponential Functions127417
Node: Exponential Function127793
Node: Relative Exponential Functions128986
Node: Exponentiation With Error Estimate130635
Node: Exponential Integrals131826
Node: Exponential Integral132301
Node: Ei(x)132928
Node: Hyperbolic Integrals133358
Node: Ei_3(x)133995
Node: Trigonometric Integrals134360
Node: Arctangent Integral134941
Node: Fermi-Dirac Function135304
Node: Complete Fermi-Dirac Integrals135657
Node: Incomplete Fermi-Dirac Integrals138088
Node: Gamma Function138715
Node: Gegenbauer Functions146228
Node: Hypergeometric Functions147852
Node: Laguerre Functions152056
Node: Lambert W Functions153310
Node: Legendre Functions and Spherical Harmonics154327
Node: Legendre Polynomials154909
Node: Associated Legendre Polynomials and Spherical Harmonics156726
Node: Conical Functions159134
Node: Radial Functions for Hyperbolic Space161231
Node: Logarithm and Related Functions163389
Node: Power Function164994
Node: Psi (Digamma) Function165926
Node: Digamma Function166430
Node: Trigamma Function167239
Node: Polygamma Function167607
Node: Synchrotron Functions167975
Node: Transport Functions168727
Node: Trigonometric Functions169819
Node: Circular Trigonometric Functions170434
Node: Trigonometric Functions for Complex Arguments171421
Node: Hyperbolic Trigonometric Functions172438
Node: Conversion Functions173023
Node: Restriction Functions173790
Node: Trigonometric Functions With Error Estimates174401
Node: Zeta Functions175145
Node: Riemann Zeta Function175560
Node: Hurwitz Zeta Function176214
Node: Eta Function176696
Node: Special Functions Examples177240
Node: Special Functions References and Further Reading178921
Node: Vectors and Matrices180017
Node: Data types180775
Node: Blocks181973
Node: Block allocation182884
Node: Reading and writing blocks184276
Node: Example programs for blocks186327
Node: Vectors186958
Node: Vector allocation188823
Node: Accessing vector elements190347
Node: Initializing vector elements192462
Node: Reading and writing vectors193141
Node: Vector views195208
Node: Copying vectors202389
Node: Exchanging elements203238
Node: Vector operations203785
Node: Finding maximum and minimum elements of vectors205284
Node: Vector properties206791
Node: Example programs for vectors207139
Node: Matrices208875
Node: Matrix allocation211728
Node: Accessing matrix elements213301
Node: Initializing matrix elements214983
Node: Reading and writing matrices215764
Node: Matrix views217844
Node: Creating row and column views224965
Node: Copying matrices228114
Node: Copying rows and columns228712
Node: Exchanging rows and columns230376
Node: Matrix operations231834
Node: Finding maximum and minimum elements of matrices233450
Node: Matrix properties235137
Node: Example programs for matrices235488
Node: Vector and Matrix References and Further Reading239401
Node: Permutations239879
Node: The Permutation struct241134
Node: Permutation allocation241630
Node: Accessing permutation elements243051
Node: Permutation properties243807
Node: Permutation functions244495
Node: Applying Permutations245740
Node: Reading and writing permutations247343
Node: Permutation Examples249508
Node: Permutation References and Further Reading251950
Node: Combinations252363
Node: The Combination struct253189
Node: Combination allocation253732
Node: Accessing combination elements255235
Node: Combination properties255798
Node: Combination functions256673
Node: Reading and writing combinations257602
Node: Combination Examples259781
Node: Sorting261058
Node: Sorting objects262004
Node: Sorting vectors264906
Node: Selecting the k-th smallest or largest elements267475
Node: Computing the rank270921
Node: Sorting Examples272129
Node: Sorting References and Further Reading273746
Node: BLAS Support274282
Node: GSL BLAS Interface277250
Node: Level 1 GSL BLAS Interface277730
Node: Level 2 GSL BLAS Interface284240
Node: Level 3 GSL BLAS Interface293518
Node: BLAS Examples304591
Node: BLAS References and Further Reading306042
Node: Linear Algebra307386
Node: LU Decomposition308593
Node: QR Decomposition313513
Node: QR Decomposition with Column Pivoting319155
Node: Singular Value Decomposition323527
Node: Cholesky Decomposition326824
Node: Tridiagonal Decomposition of Real Symmetric Matrices328725
Node: Tridiagonal Decomposition of Hermitian Matrices330563
Node: Bidiagonalization332481
Node: Householder solver for linear systems334793
Node: Tridiagonal Systems335674
Node: Linear Algebra Examples336769
Node: Linear Algebra References and Further Reading338797
Node: Eigensystems340254
Node: Real Symmetric Matrices341293
Node: Complex Hermitian Matrices343509
Node: Sorting Eigenvalues and Eigenvectors346011
Node: Eigenvalue and Eigenvector Examples347330
Node: Eigenvalue and Eigenvector References349680
Node: Fast Fourier Transforms350378
Node: Mathematical Definitions351584
Node: Overview of complex data FFTs353982
Node: Radix-2 FFT routines for complex data356601
Node: Mixed-radix FFT routines for complex data360666
Node: Overview of real data FFTs369911
Node: Radix-2 FFT routines for real data372341
Node: Mixed-radix FFT routines for real data375170
Node: FFT References and Further Reading385830
Node: Numerical Integration388590
Node: Numerical Integration Introduction390132
Node: QNG non-adaptive Gauss-Kronrod integration393595
Node: QAG adaptive integration394855
Node: QAGS adaptive integration with singularities397485
Node: QAGP adaptive integration with known singular points399275
Node: QAGI adaptive integration on infinite intervals400575
Node: QAWC adaptive integration for Cauchy principal values402797
Node: QAWS adaptive integration for singular functions403960
Node: QAWO adaptive integration for oscillatory functions407189
Node: QAWF adaptive integration for Fourier integrals410943
Node: Numerical integration error codes413521
Node: Numerical integration examples414280
Node: Numerical integration References and Further Reading416306
Node: Random Number Generation417022
Node: General comments on random numbers418510
Node: The Random Number Generator Interface420458
Node: Random number generator initialization421809
Node: Sampling from a random number generator423806
Node: Auxiliary random number generator functions426281
Node: Random number environment variables428601
Node: Saving and restoring random number generator state431134
Node: Random number generator algorithms432303
Node: Unix random number generators441165
Node: Numerical Recipes generators444880
Node: Other random number generators446263
Node: Random Number Generator Performance455552
Node: Random Number Generator Examples456831
Node: Random Number References and Further Reading458407
Node: Random Number Acknowledgements459601
Node: Quasi-Random Sequences460075
Node: Quasi-random number generator initialization461099
Node: Sampling from a quasi-random number generator462003
Node: Auxiliary quasi-random number generator functions462597
Node: Saving and resorting quasi-random number generator state463529
Node: Quasi-random number generator algorithms464315
Node: Quasi-random number generator examples465081
Node: Quasi-random number references466071
Node: Random Number Distributions466584
Node: The Gaussian Distribution468848
Node: The Gaussian Tail Distribution470431
Node: The Bivariate Gaussian Distribution472044
Node: The Exponential Distribution473323
Node: The Laplace Distribution474026
Node: The Exponential Power Distribution474715
Node: The Cauchy Distribution475668
Node: The Rayleigh Distribution476501
Node: The Rayleigh Tail Distribution477227
Node: The Landau Distribution478083
Node: The Levy alpha-Stable Distributions479021
Node: The Levy skew alpha-Stable Distribution480064
Node: The Gamma Distribution481661
Node: The Flat (Uniform) Distribution482371
Node: The Lognormal Distribution483075
Node: The Chi-squared Distribution483874
Node: The F-distribution484850
Node: The t-distribution485981
Node: The Beta Distribution486961
Node: The Logistic Distribution487661
Node: The Pareto Distribution488362
Node: The Spherical Distribution (2D & 3D)489065
Node: The Weibull Distribution491874
Node: The Type-1 Gumbel Distribution492605
Node: The Type-2 Gumbel Distribution493372
Node: General Discrete Distributions494137
Node: The Poisson Distribution497987
Node: The Bernoulli Distribution498702
Node: The Binomial Distribution499428
Node: The Negative Binomial Distribution500296
Node: The Pascal Distribution501297
Node: The Geometric Distribution502120
Node: The Hypergeometric Distribution502924
Node: The Logarithmic Distribution503889
Node: Shuffling and Sampling504665
Node: Random Number Distribution Examples507504
Node: Random Number Distribution References and Further Reading509903
Node: Statistics511106
Node: Mean and standard deviation and variance512383
Node: Absolute deviation515428
Node: Higher moments (skewness and kurtosis)516712
Node: Autocorrelation518839
Node: Covariance519642
Node: Weighted Samples520461
Node: Maximum and Minimum values525672
Node: Median and Percentiles528108
Node: Example statistical programs530518
Node: Statistics References and Further Reading533252
Node: Histograms534436
Node: The histogram struct536190
Node: Histogram allocation537990
Node: Copying Histograms540971
Node: Updating and accessing histogram elements541635
Node: Searching histogram ranges544884
Node: Histogram Statistics545875
Node: Histogram Operations547718
Node: Reading and writing histograms549761
Node: Resampling from histograms552782
Node: The histogram probability distribution struct553573
Node: Example programs for histograms556600
Node: Two dimensional histograms558721
Node: The 2D histogram struct559433
Node: 2D Histogram allocation561223
Node: Copying 2D Histograms563281
Node: Updating and accessing 2D histogram elements563972
Node: Searching 2D histogram ranges567598
Node: 2D Histogram Statistics568607
Node: 2D Histogram Operations571388
Node: Reading and writing 2D histograms573538
Node: Resampling from 2D histograms577182
Node: Example programs for 2D histograms580187
Node: N-tuples582245
Node: The ntuple struct583505
Node: Creating ntuples583976
Node: Opening an existing ntuple file584633
Node: Writing ntuples585251
Node: Reading ntuples585699
Node: Closing an ntuple file586018
Node: Histogramming ntuple values586347
Node: Example ntuple programs588343
Node: Ntuple References and Further Reading591895
Node: Monte Carlo Integration592206
Node: Monte Carlo Interface593450
Node: PLAIN Monte Carlo596084
Node: MISER598511
Node: VEGAS604334
Node: Monte Carlo Examples612631
Node: Monte Carlo Integration References and Further Reading618659
Node: Simulated Annealing619411
Node: Simulated Annealing algorithm620560
Node: Simulated Annealing functions622080
Node: Examples with Simulated Annealing626551
Node: Trivial example627089
Node: Traveling Salesman Problem629776
Node: Ordinary Differential Equations633194
Node: Defining the ODE System634012
Node: Stepping Functions635826
Node: Adaptive Step-size Control639381
Node: Evolution644071
Node: ODE Example programs646126
Node: ODE References and Further Reading650972
Node: Interpolation651605
Node: Introduction to Interpolation652615
Node: Interpolation Functions653045
Node: Interpolation Types654211
Node: Index Look-up and Acceleration656014
Node: Evaluation of interpolating functions657627
Node: Higher-level interface659979
Node: Interpolation Example programs661827
Node: Interpolation References and Further Reading663557
Node: Numerical Differentiation663987
Node: Numerical Differentiation functions664567
Node: Numerical Differentiation Example666174
Node: Numerical Differentiation References667586
Node: Chebyshev Approximations667984
Node: The gsl_cheb_series struct668940
Node: Creation and Calculation of Chebyshev Series669585
Node: Chebyshev Series Evaluation670549
Node: Derivatives and Integrals671909
Node: Chebyshev Approximation examples673142
Node: Chebyshev Approximation References and Further Reading674676
Node: Series Acceleration675115
Node: Acceleration functions675885
Node: Acceleration functions without error estimation678117
Node: Example of accelerating a series680723
Node: Series Acceleration References683164
Node: Discrete Hankel Transforms684043
Node: Discrete Hankel Transform Definition684509
Node: Discrete Hankel Transform Functions686347
Node: Discrete Hankel Transform References687851
Node: One dimensional Root-Finding688245
Node: Root Finding Overview689502
Node: Root Finding Caveats691353
Node: Initializing the Solver693111
Node: Providing the function to solve695728
Node: Search Bounds and Guesses699532
Node: Root Finding Iteration700386
Node: Search Stopping Parameters702222
Node: Root Bracketing Algorithms704730
Node: Root Finding Algorithms using Derivatives708019
Node: Root Finding Examples711490
Node: Root Finding References and Further Reading718838
Node: One dimensional Minimization719465
Node: Minimization Overview720764
Node: Minimization Caveats722438
Node: Initializing the Minimizer723768
Node: Providing the function to minimize725987
Node: Minimization Iteration726458
Node: Minimization Stopping Parameters728106
Node: Minimization Algorithms729707
Node: Minimization Examples732139
Node: Minimization References and Further Reading735106
Node: Multidimensional Root-Finding735552
Node: Overview of Multidimensional Root Finding737038
Node: Initializing the Multidimensional Solver739218
Node: Providing the multidimensional system of equations to solve742383
Node: Iteration of the multidimensional solver747259
Node: Search Stopping Parameters for the multidimensional solver748862
Node: Algorithms using Derivatives750594
Node: Algorithms without Derivatives755329
Node: Example programs for Multidimensional Root finding758111
Node: References and Further Reading for Multidimensional Root Finding766835
Node: Multidimensional Minimization768064
Node: Multimin Overview769353
Node: Multimin Caveats770931
Node: Initializing the Multidimensional Minimizer771673
Node: Providing a function to minimize773828
Node: Multimin Iteration777046
Node: Multimin Stopping Criteria778576
Node: Multimin Algorithms779767
Node: Multimin Examples782530
Node: Multimin References and Further Reading785625
Node: Least-Squares Fitting786111
Node: Linear regression787042
Node: Linear fitting without a constant term789635
Node: Multi-parameter fitting792027
Node: Fitting Examples795779
Node: Fitting References and Further Reading802553
Node: Nonlinear Least-Squares Fitting803362
Node: Overview of Nonlinear Least-Squares Fitting804813
Node: Initializing the Nonlinear Least-Squares Solver805696
Node: Providing the Function to be Minimized808357
Node: Iteration of the Minimization Algorithm810996
Node: Search Stopping Parameters for Minimization Algorithms812323
Node: Minimization Algorithms using Derivatives814412
Node: Minimization Algorithms without Derivatives817648
Node: Computing the covariance matrix of best fit parameters818033
Node: Example programs for Nonlinear Least-Squares Fitting819091
Node: References and Further Reading for Nonlinear Least-Squares Fitting826030
Node: Physical Constants826753
Node: Fundamental Constants828096
Node: Astronomy and Astrophysics829106
Node: Atomic and Nuclear Physics829755
Node: Measurement of Time831036
Node: Imperial Units831452
Node: Nautical Units831869
Node: Printers Units832184
Node: Volume832469
Node: Mass and Weight832980
Node: Thermal Energy and Power833762
Node: Pressure834169
Node: Viscosity834763
Node: Light and Illumination835025
Node: Radioactivity835598
Node: Physical Constant Examples835928
Node: Physical Constant References and Further Reading837718
Node: IEEE floating-point arithmetic838074
Node: Representation of floating point numbers838657
Node: Setting up your IEEE environment843160
Node: IEEE References and Further Reading849247
Node: Debugging Numerical Programs850245
Node: Using gdb850707
Node: Examining floating point registers854063
Node: Handling floating point exceptions855351
Node: GCC warning options for numerical programs856760
Node: Debugging References860947
Node: Contributors to GSL861489
Node: Autoconf Macros863252
Node: GSL CBLAS Library864051
Node: Level 1 CBLAS Functions864547
Node: Level 2 CBLAS Functions869693
Node: Level 3 CBLAS Functions886055
Node: GSL CBLAS Examples895574
Node: GNU General Public License897170
Node: GNU Free Documentation License916449
Node: Function Index936366
Node: Variable Index1046435
Node: Type Index1047245
Node: Concept Index1049099

End Tag Table
