This is gsl-ref.info, produced by makeinfo version 4.13 from
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START-INFO-DIR-ENTRY
* gsl-ref: (gsl-ref).                   GNU Scientific Library - Reference
END-INFO-DIR-ENTRY

   Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,
2005, 2006, 2007, 2008, 2009, 2010, 2011 The GSL Team.

   Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with the
Invariant Sections being "GNU General Public License" and "Free Software
Needs Free Documentation", the Front-Cover text being "A GNU Manual",
and with the Back-Cover Text being (a) (see below).  A copy of the
license is included in the section entitled "GNU Free Documentation
License".

   (a) The Back-Cover Text is: "You have the freedom to copy and modify
this GNU Manual."


Indirect:
gsl-ref.info-1: 948
gsl-ref.info-2: 300146
gsl-ref.info-3: 598317
gsl-ref.info-4: 898064
gsl-ref.info-5: 1168153
gsl-ref.info-6: 1435602

Tag Table:
(Indirect)
Node: Top948
Node: Introduction3679
Node: Routines available in GSL4331
Node: GSL is Free Software6246
Node: Obtaining GSL8638
Node: No Warranty9665
Node: Reporting Bugs10171
Ref: Reporting Bugs-Footnote-111127
Node: Further Information11177
Node: Conventions used in this manual12190
Node: Using the library12954
Node: An Example Program13540
Ref: An Example Program-Footnote-114283
Node: Compiling and Linking14390
Node: Linking programs with the library15460
Ref: Linking programs with the library-Footnote-116862
Ref: Linking programs with the library-Footnote-216899
Node: Linking with an alternative BLAS library16952
Node: Shared Libraries18034
Ref: Shared Libraries-Footnote-119509
Node: ANSI C Compliance19557
Node: Inline functions20650
Node: Long double22188
Node: Portability functions23776
Node: Alternative optimized functions25173
Node: Support for different numeric types26631
Node: Compatibility with C++29694
Node: Aliasing of arrays30266
Node: Thread-safety31017
Node: Deprecated Functions32104
Node: Code Reuse32729
Node: Error Handling33373
Node: Error Reporting34123
Node: Error Codes36015
Node: Error Handlers37871
Node: Using GSL error reporting in your own functions41508
Node: Error Reporting Examples43466
Node: Mathematical Functions44678
Node: Mathematical Constants45439
Node: Infinities and Not-a-number46569
Ref: Infinities and Not-a-number-Footnote-147676
Node: Elementary Functions48086
Node: Small integer powers50533
Node: Testing the Sign of Numbers52180
Node: Testing for Odd and Even Numbers52611
Node: Maximum and Minimum functions53167
Node: Approximate Comparison of Floating Point Numbers55442
Node: Complex Numbers56801
Ref: Complex Numbers-Footnote-158127
Node: Representation of complex numbers58191
Node: Properties of complex numbers60128
Node: Complex arithmetic operators61133
Node: Elementary Complex Functions63879
Node: Complex Trigonometric Functions65699
Node: Inverse Complex Trigonometric Functions66920
Node: Complex Hyperbolic Functions69526
Node: Inverse Complex Hyperbolic Functions70822
Node: Complex Number References and Further Reading72810
Node: Polynomials74206
Node: Polynomial Evaluation74973
Node: Divided Difference Representation of Polynomials76383
Node: Quadratic Equations78132
Node: Cubic Equations80072
Node: General Polynomial Equations81654
Node: Roots of Polynomials Examples83999
Node: Roots of Polynomials References and Further Reading85388
Node: Special Functions86333
Node: Special Function Usage88327
Node: The gsl_sf_result struct89510
Node: Special Function Modes90774
Node: Airy Functions and Derivatives91710
Node: Airy Functions92411
Node: Derivatives of Airy Functions93771
Node: Zeros of Airy Functions95283
Node: Zeros of Derivatives of Airy Functions96002
Node: Bessel Functions96761
Node: Regular Cylindrical Bessel Functions97953
Node: Irregular Cylindrical Bessel Functions99277
Node: Regular Modified Cylindrical Bessel Functions100735
Node: Irregular Modified Cylindrical Bessel Functions103562
Node: Regular Spherical Bessel Functions106530
Node: Irregular Spherical Bessel Functions108744
Node: Regular Modified Spherical Bessel Functions110431
Node: Irregular Modified Spherical Bessel Functions112434
Node: Regular Bessel Function - Fractional Order114497
Node: Irregular Bessel Functions - Fractional Order115495
Node: Regular Modified Bessel Functions - Fractional Order116077
Node: Irregular Modified Bessel Functions - Fractional Order117002
Node: Zeros of Regular Bessel Functions118238
Node: Clausen Functions119341
Node: Coulomb Functions119945
Node: Normalized Hydrogenic Bound States120394
Node: Coulomb Wave Functions121507
Node: Coulomb Wave Function Normalization Constant124917
Node: Coupling Coefficients125670
Node: 3-j Symbols126393
Node: 6-j Symbols126997
Node: 9-j Symbols127621
Node: Dawson Function128327
Node: Debye Functions128894
Node: Dilogarithm130668
Node: Real Argument130963
Node: Complex Argument131656
Node: Elementary Operations132125
Node: Elliptic Integrals132949
Node: Definition of Legendre Forms133521
Node: Definition of Carlson Forms134341
Node: Legendre Form of Complete Elliptic Integrals135038
Node: Legendre Form of Incomplete Elliptic Integrals136606
Node: Carlson Forms138794
Node: Elliptic Functions (Jacobi)140341
Node: Error Functions140922
Node: Error Function141373
Node: Complementary Error Function141746
Node: Log Complementary Error Function142206
Node: Probability functions142658
Node: Exponential Functions143911
Node: Exponential Function144294
Node: Relative Exponential Functions145517
Node: Exponentiation With Error Estimate147189
Node: Exponential Integrals148398
Node: Exponential Integral148880
Node: Ei(x)149807
Node: Hyperbolic Integrals150255
Node: Ei_3(x)150911
Node: Trigonometric Integrals151303
Node: Arctangent Integral151902
Node: Fermi-Dirac Function152302
Node: Complete Fermi-Dirac Integrals152672
Node: Incomplete Fermi-Dirac Integrals155240
Node: Gamma and Beta Functions155883
Node: Gamma Functions156456
Node: Factorials159565
Node: Pochhammer Symbol162118
Node: Incomplete Gamma Functions163624
Node: Beta Functions164873
Node: Incomplete Beta Function165625
Node: Gegenbauer Functions166336
Node: Hypergeometric Functions167986
Node: Laguerre Functions172249
Node: Lambert W Functions173812
Node: Legendre Functions and Spherical Harmonics174850
Node: Legendre Polynomials175439
Node: Associated Legendre Polynomials and Spherical Harmonics177494
Node: Conical Functions180327
Node: Radial Functions for Hyperbolic Space182450
Node: Logarithm and Related Functions184627
Node: Mathieu Functions186251
Node: Mathieu Function Workspace187600
Node: Mathieu Function Characteristic Values188414
Node: Angular Mathieu Functions189486
Node: Radial Mathieu Functions190522
Node: Power Function191764
Node: Psi (Digamma) Function192691
Node: Digamma Function193211
Node: Trigamma Function194041
Node: Polygamma Function194618
Node: Synchrotron Functions195002
Node: Transport Functions195765
Node: Trigonometric Functions196912
Node: Circular Trigonometric Functions197535
Node: Trigonometric Functions for Complex Arguments198544
Node: Hyperbolic Trigonometric Functions199580
Node: Conversion Functions200183
Node: Restriction Functions200966
Node: Trigonometric Functions With Error Estimates201898
Node: Zeta Functions202808
Node: Riemann Zeta Function203266
Node: Riemann Zeta Function Minus One203945
Node: Hurwitz Zeta Function204716
Node: Eta Function205221
Node: Special Functions Examples205780
Node: Special Functions References and Further Reading207474
Node: Vectors and Matrices208744
Node: Data types209503
Node: Blocks210706
Node: Block allocation211622
Node: Reading and writing blocks213106
Node: Example programs for blocks215170
Node: Vectors215797
Node: Vector allocation217683
Node: Accessing vector elements219301
Ref: Accessing vector elements-Footnote-1222443
Node: Initializing vector elements222682
Node: Reading and writing vectors223376
Node: Vector views225466
Node: Copying vectors232908
Node: Exchanging elements233768
Node: Vector operations234326
Node: Finding maximum and minimum elements of vectors236092
Node: Vector properties237678
Node: Example programs for vectors238652
Node: Matrices240941
Node: Matrix allocation243799
Node: Accessing matrix elements245466
Node: Initializing matrix elements247415
Node: Reading and writing matrices248211
Node: Matrix views250314
Node: Creating row and column views257454
Node: Copying matrices261924
Node: Copying rows and columns262520
Node: Exchanging rows and columns264197
Node: Matrix operations265675
Node: Finding maximum and minimum elements of matrices267642
Node: Matrix properties269546
Node: Example programs for matrices270648
Node: Vector and Matrix References and Further Reading274719
Node: Permutations275205
Node: The Permutation struct276493
Node: Permutation allocation276997
Node: Accessing permutation elements278431
Node: Permutation properties279274
Node: Permutation functions279979
Node: Applying Permutations281236
Node: Reading and writing permutations283162
Ref: Reading and writing permutations-Footnote-1285377
Node: Permutations in cyclic form285489
Node: Permutation Examples288914
Node: Permutation References and Further Reading291457
Node: Combinations292131
Node: The Combination struct292978
Node: Combination allocation293530
Node: Accessing combination elements295315
Node: Combination properties295974
Node: Combination functions296860
Node: Reading and writing combinations297800
Ref: Reading and writing combinations-Footnote-1300034
Node: Combination Examples300146
Node: Combination References and Further Reading301454
Node: Multisets301858
Node: The Multiset struct302784
Node: Multiset allocation303306
Node: Accessing multiset elements304997
Node: Multiset properties305626
Node: Multiset functions306439
Node: Reading and writing multisets307349
Ref: Reading and writing multisets-Footnote-1309500
Node: Multiset Examples309612
Node: Sorting311720
Node: Sorting objects312667
Node: Sorting vectors315578
Node: Selecting the k smallest or largest elements318154
Node: Computing the rank321488
Node: Sorting Examples322689
Node: Sorting References and Further Reading324333
Node: BLAS Support324879
Ref: BLAS Support-Footnote-1328254
Node: GSL BLAS Interface328422
Node: Level 1 GSL BLAS Interface328909
Node: Level 2 GSL BLAS Interface335648
Node: Level 3 GSL BLAS Interface344944
Node: BLAS Examples356084
Node: BLAS References and Further Reading357505
Node: Linear Algebra358852
Node: LU Decomposition359977
Node: QR Decomposition365222
Node: QR Decomposition with Column Pivoting371531
Node: Singular Value Decomposition375986
Node: Cholesky Decomposition379982
Node: Tridiagonal Decomposition of Real Symmetric Matrices383222
Node: Tridiagonal Decomposition of Hermitian Matrices385070
Node: Hessenberg Decomposition of Real Matrices387022
Node: Hessenberg-Triangular Decomposition of Real Matrices389432
Node: Bidiagonalization390552
Node: Householder Transformations392977
Node: Householder solver for linear systems395329
Node: Tridiagonal Systems396234
Node: Balancing399106
Node: Linear Algebra Examples399907
Node: Linear Algebra References and Further Reading401895
Node: Eigensystems403542
Node: Real Symmetric Matrices404756
Node: Complex Hermitian Matrices407270
Node: Real Nonsymmetric Matrices409897
Node: Real Generalized Symmetric-Definite Eigensystems415610
Node: Complex Generalized Hermitian-Definite Eigensystems418482
Node: Real Generalized Nonsymmetric Eigensystems421189
Node: Sorting Eigenvalues and Eigenvectors427773
Node: Eigenvalue and Eigenvector Examples431050
Node: Eigenvalue and Eigenvector References436440
Node: Fast Fourier Transforms437465
Node: Mathematical Definitions438674
Node: Overview of complex data FFTs441079
Node: Radix-2 FFT routines for complex data444022
Node: Mixed-radix FFT routines for complex data448234
Node: Overview of real data FFTs457563
Node: Radix-2 FFT routines for real data459997
Node: Mixed-radix FFT routines for real data464426
Node: FFT References and Further Reading475100
Node: Numerical Integration477969
Node: Numerical Integration Introduction479735
Node: Integrands without weight functions482004
Node: Integrands with weight functions482833
Node: Integrands with singular weight functions483544
Node: QNG non-adaptive Gauss-Kronrod integration484462
Node: QAG adaptive integration485743
Node: QAGS adaptive integration with singularities488374
Node: QAGP adaptive integration with known singular points490174
Node: QAGI adaptive integration on infinite intervals491488
Node: QAWC adaptive integration for Cauchy principal values493781
Node: QAWS adaptive integration for singular functions494956
Node: QAWO adaptive integration for oscillatory functions498178
Node: QAWF adaptive integration for Fourier integrals501957
Node: CQUAD doubly-adaptive integration504582
Node: Fixed order Gauss-Legendre integration507819
Node: Numerical integration error codes509797
Node: Numerical integration examples510556
Node: Numerical integration References and Further Reading512602
Node: Random Number Generation513593
Node: General comments on random numbers515095
Node: The Random Number Generator Interface517045
Node: Random number generator initialization518403
Node: Sampling from a random number generator520776
Node: Auxiliary random number generator functions524017
Node: Random number environment variables526337
Node: Copying random number generator state528863
Node: Reading and writing random number generator state529838
Node: Random number generator algorithms531232
Node: Unix random number generators541167
Node: Other random number generators544885
Node: Random Number Generator Performance553519
Node: Random Number Generator Examples554640
Node: Random Number References and Further Reading556196
Node: Random Number Acknowledgements557493
Node: Quasi-Random Sequences557979
Node: Quasi-random number generator initialization559086
Node: Sampling from a quasi-random number generator560101
Node: Auxiliary quasi-random number generator functions560798
Node: Saving and resorting quasi-random number generator state561744
Node: Quasi-random number generator algorithms562552
Node: Quasi-random number generator examples563688
Node: Quasi-random number references564673
Node: Random Number Distributions565199
Node: Random Number Distribution Introduction568398
Node: The Gaussian Distribution570193
Node: The Gaussian Tail Distribution572854
Node: The Bivariate Gaussian Distribution574523
Node: The Exponential Distribution575846
Node: The Laplace Distribution576985
Node: The Exponential Power Distribution578082
Node: The Cauchy Distribution579350
Node: The Rayleigh Distribution580599
Node: The Rayleigh Tail Distribution581771
Node: The Landau Distribution582643
Node: The Levy alpha-Stable Distributions583598
Node: The Levy skew alpha-Stable Distribution584656
Node: The Gamma Distribution586268
Node: The Flat (Uniform) Distribution587925
Node: The Lognormal Distribution589077
Node: The Chi-squared Distribution590425
Node: The F-distribution591829
Node: The t-distribution593465
Node: The Beta Distribution594859
Node: The Logistic Distribution596018
Node: The Pareto Distribution597147
Node: Spherical Vector Distributions598317
Node: The Weibull Distribution601151
Node: The Type-1 Gumbel Distribution602345
Node: The Type-2 Gumbel Distribution603582
Node: The Dirichlet Distribution604813
Node: General Discrete Distributions606480
Node: The Poisson Distribution610347
Node: The Bernoulli Distribution611355
Node: The Binomial Distribution612106
Node: The Multinomial Distribution613311
Node: The Negative Binomial Distribution615080
Node: The Pascal Distribution616445
Node: The Geometric Distribution617603
Node: The Hypergeometric Distribution618851
Node: The Logarithmic Distribution620504
Node: Shuffling and Sampling621295
Node: Random Number Distribution Examples624114
Node: Random Number Distribution References and Further Reading627310
Node: Statistics629453
Node: Mean and standard deviation and variance630853
Node: Absolute deviation634361
Node: Higher moments (skewness and kurtosis)635653
Node: Autocorrelation637786
Node: Covariance638600
Node: Correlation639576
Node: Weighted Samples640285
Node: Maximum and Minimum values646135
Node: Median and Percentiles648874
Node: Example statistical programs651289
Node: Statistics References and Further Reading653949
Node: Histograms655157
Node: The histogram struct656917
Node: Histogram allocation658720
Node: Copying Histograms661681
Node: Updating and accessing histogram elements662357
Node: Searching histogram ranges665624
Node: Histogram Statistics666623
Node: Histogram Operations668483
Node: Reading and writing histograms670555
Node: Resampling from histograms673597
Node: The histogram probability distribution struct674395
Node: Example programs for histograms677426
Node: Two dimensional histograms679489
Node: The 2D histogram struct680210
Node: 2D Histogram allocation682018
Node: Copying 2D Histograms684089
Node: Updating and accessing 2D histogram elements684794
Node: Searching 2D histogram ranges688450
Node: 2D Histogram Statistics689469
Node: 2D Histogram Operations692328
Node: Reading and writing 2D histograms694502
Node: Resampling from 2D histograms698131
Node: Example programs for 2D histograms701150
Node: N-tuples702978
Node: The ntuple struct704234
Node: Creating ntuples704712
Node: Opening an existing ntuple file705379
Node: Writing ntuples706007
Node: Reading ntuples706468
Node: Closing an ntuple file706799
Node: Histogramming ntuple values707139
Node: Example ntuple programs709147
Node: Ntuple References and Further Reading712476
Node: Monte Carlo Integration712797
Node: Monte Carlo Interface714042
Node: PLAIN Monte Carlo716665
Node: MISER719119
Ref: MISER-Footnote-1725795
Node: VEGAS725920
Node: Monte Carlo Examples735471
Node: Monte Carlo Integration References and Further Reading741456
Node: Simulated Annealing742238
Node: Simulated Annealing algorithm743445
Node: Simulated Annealing functions744599
Node: Examples with Simulated Annealing749134
Node: Trivial example749688
Node: Traveling Salesman Problem752339
Node: Simulated Annealing References and Further Reading755652
Node: Ordinary Differential Equations756063
Node: Defining the ODE System757254
Node: Stepping Functions760080
Node: Adaptive Step-size Control767022
Node: Evolution773094
Node: Driver777211
Node: ODE Example programs781150
Node: ODE References and Further Reading786218
Node: Interpolation787978
Node: Introduction to Interpolation789149
Node: Interpolation Functions789590
Node: Interpolation Types790797
Node: Index Look-up and Acceleration793520
Node: Evaluation of Interpolating Functions795572
Node: Higher-level Interface798073
Node: Interpolation Example programs800112
Node: Interpolation References and Further Reading803328
Node: Numerical Differentiation803901
Node: Numerical Differentiation functions804490
Node: Numerical Differentiation Examples807348
Node: Numerical Differentiation References808761
Node: Chebyshev Approximations809312
Node: Chebyshev Definitions810373
Node: Creation and Calculation of Chebyshev Series811163
Node: Auxiliary Functions for Chebyshev Series812148
Node: Chebyshev Series Evaluation812888
Node: Derivatives and Integrals814268
Node: Chebyshev Approximation Examples815510
Node: Chebyshev Approximation References and Further Reading817006
Node: Series Acceleration817455
Node: Acceleration functions818220
Node: Acceleration functions without error estimation820545
Node: Example of accelerating a series823155
Node: Series Acceleration References825501
Node: Wavelet Transforms826389
Node: DWT Definitions826930
Node: DWT Initialization827882
Node: DWT Transform Functions830531
Node: DWT in one dimension831066
Node: DWT in two dimension833085
Node: DWT Examples837663
Node: DWT References839480
Node: Discrete Hankel Transforms841643
Node: Discrete Hankel Transform Definition842111
Node: Discrete Hankel Transform Functions844310
Node: Discrete Hankel Transform References845974
Node: One dimensional Root-Finding846378
Node: Root Finding Overview847638
Node: Root Finding Caveats849496
Node: Initializing the Solver851263
Node: Providing the function to solve853896
Node: Search Bounds and Guesses857444
Node: Root Finding Iteration858307
Node: Search Stopping Parameters860156
Node: Root Bracketing Algorithms862670
Node: Root Finding Algorithms using Derivatives865968
Ref: Root Finding Algorithms using Derivatives-Footnote-1869510
Node: Root Finding Examples869665
Node: Root Finding References and Further Reading876953
Node: One dimensional Minimization877592
Node: Minimization Overview878894
Node: Minimization Caveats880600
Node: Initializing the Minimizer881937
Node: Providing the function to minimize884178
Node: Minimization Iteration884656
Node: Minimization Stopping Parameters886792
Node: Minimization Algorithms888401
Node: Minimization Examples891005
Node: Minimization References and Further Reading893932
Node: Multidimensional Root-Finding894388
Node: Overview of Multidimensional Root Finding895877
Node: Initializing the Multidimensional Solver898064
Node: Providing the multidimensional system of equations to solve901295
Node: Iteration of the multidimensional solver906200
Node: Search Stopping Parameters for the multidimensional solver908479
Node: Algorithms using Derivatives910216
Node: Algorithms without Derivatives915045
Node: Example programs for Multidimensional Root finding918133
Node: References and Further Reading for Multidimensional Root Finding926746
Node: Multidimensional Minimization927985
Node: Multimin Overview929338
Node: Multimin Caveats931415
Node: Initializing the Multidimensional Minimizer932164
Node: Providing a function to minimize935325
Node: Multimin Iteration939377
Node: Multimin Stopping Criteria941576
Node: Multimin Algorithms with Derivatives943145
Node: Multimin Algorithms without Derivatives946673
Node: Multimin Examples949673
Node: Multimin References and Further Reading956239
Node: Least-Squares Fitting957104
Node: Fitting Overview958103
Node: Linear regression960437
Node: Linear fitting without a constant term963039
Node: Multi-parameter fitting965232
Node: Fitting Examples971046
Node: Fitting References and Further Reading977871
Node: Nonlinear Least-Squares Fitting978693
Node: Overview of Nonlinear Least-Squares Fitting980143
Node: Initializing the Nonlinear Least-Squares Solver981610
Node: Providing the Function to be Minimized984475
Node: Iteration of the Minimization Algorithm987412
Node: Search Stopping Parameters for Minimization Algorithms989262
Node: Minimization Algorithms using Derivatives991357
Ref: Minimization Algorithms using Derivatives-Footnote-1994838
Node: Minimization Algorithms without Derivatives994927
Node: Computing the covariance matrix of best fit parameters995319
Node: Example programs for Nonlinear Least-Squares Fitting997353
Node: References and Further Reading for Nonlinear Least-Squares Fitting1005081
Node: Basis Splines1005817
Node: Overview of B-splines1006717
Node: Initializing the B-splines solver1008026
Node: Constructing the knots vector1009402
Node: Evaluation of B-spline basis functions1010189
Node: Evaluation of B-spline basis function derivatives1011846
Node: Obtaining Greville abscissae for B-spline basis functions1013838
Node: Example programs for B-splines1014880
Node: References and Further Reading1018892
Node: Physical Constants1019697
Node: Fundamental Constants1021107
Node: Astronomy and Astrophysics1022246
Node: Atomic and Nuclear Physics1022911
Node: Measurement of Time1024562
Node: Imperial Units1024992
Node: Speed and Nautical Units1025434
Node: Printers Units1025938
Node: Volume Area and Length1026261
Node: Mass and Weight1026947
Node: Thermal Energy and Power1027766
Node: Pressure1028189
Node: Viscosity1028802
Node: Light and Illumination1029078
Node: Radioactivity1029670
Node: Force and Energy1030005
Node: Prefixes1030409
Node: Physical Constant Examples1031152
Node: Physical Constant References and Further Reading1032941
Node: IEEE floating-point arithmetic1033671
Node: Representation of floating point numbers1034257
Node: Setting up your IEEE environment1038738
Node: IEEE References and Further Reading1045730
Node: Debugging Numerical Programs1046885
Node: Using gdb1047369
Node: Examining floating point registers1050712
Node: Handling floating point exceptions1051997
Node: GCC warning options for numerical programs1053409
Node: Debugging References1057371
Node: Contributors to GSL1058083
Node: Autoconf Macros1062552
Node: GSL CBLAS Library1066581
Node: Level 1 CBLAS Functions1067108
Node: Level 2 CBLAS Functions1072410
Node: Level 3 CBLAS Functions1089080
Node: GSL CBLAS Examples1098742
Node: Free Software Needs Free Documentation1100304
Node: GNU General Public License1105373
Node: GNU Free Documentation License1142985
Node: Function Index1168153
Node: Variable Index1417524
Node: Type Index1420827
Node: Concept Index1435602

End Tag Table
