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INFO-DIR-SECTION Software libraries
START-INFO-DIR-ENTRY
* gsl-ref: (gsl-ref).                   GNU Scientific Library - Reference
END-INFO-DIR-ENTRY


Indirect:
gsl-ref.info-1: 707
gsl-ref.info-2: 301602
gsl-ref.info-3: 601000
gsl-ref.info-4: 902430
gsl-ref.info-5: 1443412

Tag Table:
(Indirect)
Node: Top707
Node: Introduction3656
Node: Routines available in GSL4376
Node: GSL is Free Software5989
Node: Obtaining GSL8381
Node: No Warranty9409
Node: Reporting Bugs9915
Ref: Reporting Bugs-Footnote-110867
Node: Further Information10917
Node: Conventions used in this manual11931
Node: Using the library12695
Node: An Example Program13418
Ref: An Example Program-Footnote-114161
Node: Compiling and Linking14268
Node: Linking programs with the library15341
Ref: Linking programs with the library-Footnote-116744
Ref: Linking programs with the library-Footnote-216781
Node: Linking with an alternative BLAS library16834
Node: Shared Libraries17917
Ref: Shared Libraries-Footnote-119392
Node: ANSI C Compliance19440
Node: Inline functions20533
Node: Long double22071
Node: Portability functions23659
Node: Alternative optimized functions25057
Node: Support for different numeric types26515
Node: Compatibility with C++29579
Node: Aliasing of arrays30151
Node: Thread-safety30902
Node: Deprecated Functions31990
Node: Code Reuse32615
Node: Error Handling33260
Node: Error Reporting34060
Node: Error Codes35952
Node: Error Handlers37809
Node: Using GSL error reporting in your own functions41449
Node: Error Reporting Examples43409
Node: Mathematical Functions44621
Node: Mathematical Constants45414
Node: Infinities and Not-a-number46544
Ref: Infinities and Not-a-number-Footnote-147654
Node: Elementary Functions48064
Node: Small integer powers50521
Node: Testing the Sign of Numbers52170
Node: Testing for Odd and Even Numbers52603
Node: Maximum and Minimum functions53162
Node: Approximate Comparison of Floating Point Numbers55443
Node: Complex Numbers56803
Ref: Complex Numbers-Footnote-158148
Node: Representation of complex numbers58212
Node: Properties of complex numbers60152
Node: Complex arithmetic operators61158
Node: Elementary Complex Functions63904
Node: Complex Trigonometric Functions65728
Node: Inverse Complex Trigonometric Functions66949
Node: Complex Hyperbolic Functions69562
Node: Inverse Complex Hyperbolic Functions70858
Node: Complex Number References and Further Reading72846
Node: Polynomials74242
Node: Polynomial Evaluation75046
Node: Divided Difference Representation of Polynomials76457
Node: Quadratic Equations80319
Node: Cubic Equations82256
Node: General Polynomial Equations83839
Node: Roots of Polynomials Examples86196
Node: Roots of Polynomials References and Further Reading87585
Node: Special Functions88631
Node: Special Function Usage90879
Node: The gsl_sf_result struct92063
Node: Special Function Modes93327
Node: Airy Functions and Derivatives94261
Node: Airy Functions94986
Node: Derivatives of Airy Functions96346
Node: Zeros of Airy Functions97858
Node: Zeros of Derivatives of Airy Functions98577
Node: Bessel Functions99336
Node: Regular Cylindrical Bessel Functions100554
Node: Irregular Cylindrical Bessel Functions101878
Node: Regular Modified Cylindrical Bessel Functions103336
Node: Irregular Modified Cylindrical Bessel Functions106164
Node: Regular Spherical Bessel Functions109137
Node: Irregular Spherical Bessel Functions111350
Node: Regular Modified Spherical Bessel Functions113036
Node: Irregular Modified Spherical Bessel Functions115037
Node: Regular Bessel Function - Fractional Order117100
Node: Irregular Bessel Functions - Fractional Order118098
Node: Regular Modified Bessel Functions - Fractional Order118680
Node: Irregular Modified Bessel Functions - Fractional Order119605
Node: Zeros of Regular Bessel Functions120841
Node: Clausen Functions121944
Node: Coulomb Functions122548
Node: Normalized Hydrogenic Bound States123007
Node: Coulomb Wave Functions124120
Node: Coulomb Wave Function Normalization Constant127532
Node: Coupling Coefficients128285
Node: 3-j Symbols129059
Node: 6-j Symbols129663
Node: 9-j Symbols130287
Node: Dawson Function130993
Node: Debye Functions131560
Node: Dilogarithm133334
Node: Real Argument133656
Node: Complex Argument134350
Node: Elementary Operations134820
Node: Elliptic Integrals135644
Node: Definition of Legendre Forms136239
Node: Definition of Carlson Forms137059
Node: Legendre Form of Complete Elliptic Integrals137756
Node: Legendre Form of Incomplete Elliptic Integrals139309
Node: Carlson Forms141496
Node: Elliptic Functions (Jacobi)143043
Node: Error Functions143624
Node: Error Function144100
Node: Complementary Error Function144473
Node: Log Complementary Error Function144933
Node: Probability functions145385
Node: Exponential Functions146638
Node: Exponential Function147033
Node: Relative Exponential Functions148255
Node: Exponentiation With Error Estimate149927
Node: Exponential Integrals151136
Node: Exponential Integral151692
Node: Ei(x)152613
Node: Hyperbolic Integrals153061
Node: Ei_3(x)153716
Node: Trigonometric Integrals154108
Node: Arctangent Integral154707
Node: Fermi-Dirac Function155107
Node: Complete Fermi-Dirac Integrals155481
Node: Incomplete Fermi-Dirac Integrals158046
Node: Gamma and Beta Functions158689
Node: Gamma Functions159324
Node: Factorials162432
Node: Pochhammer Symbol164985
Node: Incomplete Gamma Functions166486
Node: Beta Functions167735
Node: Incomplete Beta Function168487
Node: Gegenbauer Functions169197
Node: Hypergeometric Functions170847
Node: Laguerre Functions175111
Node: Lambert W Functions176674
Node: Legendre Functions and Spherical Harmonics177714
Node: Legendre Polynomials178326
Node: Associated Legendre Polynomials and Spherical Harmonics180382
Node: Conical Functions183211
Node: Radial Functions for Hyperbolic Space185334
Node: Logarithm and Related Functions187511
Node: Mathieu Functions189135
Node: Mathieu Function Workspace190495
Node: Mathieu Function Characteristic Values191308
Node: Angular Mathieu Functions192380
Node: Radial Mathieu Functions193416
Node: Power Function194653
Node: Psi (Digamma) Function195581
Node: Digamma Function196134
Node: Trigamma Function196964
Node: Polygamma Function197541
Node: Synchrotron Functions197925
Node: Transport Functions198688
Node: Trigonometric Functions199835
Node: Circular Trigonometric Functions200481
Node: Trigonometric Functions for Complex Arguments201490
Node: Hyperbolic Trigonometric Functions202526
Node: Conversion Functions203129
Node: Restriction Functions203912
Node: Trigonometric Functions With Error Estimates204843
Node: Zeta Functions205753
Node: Riemann Zeta Function206211
Node: Riemann Zeta Function Minus One206890
Node: Hurwitz Zeta Function207661
Node: Eta Function208166
Node: Special Functions Examples208725
Node: Special Functions References and Further Reading210420
Node: Vectors and Matrices211688
Node: Data types212531
Node: Blocks213734
Node: Block allocation214667
Node: Reading and writing blocks216071
Node: Example programs for blocks218135
Node: Vectors218762
Node: Vector allocation220730
Node: Accessing vector elements222267
Ref: Accessing vector elements-Footnote-1225408
Node: Initializing vector elements225647
Node: Reading and writing vectors226341
Node: Vector views228431
Node: Copying vectors235897
Node: Exchanging elements236757
Node: Vector operations237315
Node: Finding maximum and minimum elements of vectors239088
Node: Vector properties240675
Node: Example programs for vectors241649
Node: Matrices243938
Node: Matrix allocation246878
Node: Accessing matrix elements248464
Node: Initializing matrix elements250413
Node: Reading and writing matrices251210
Node: Matrix views253313
Node: Creating row and column views260449
Node: Copying matrices264926
Node: Copying rows and columns265522
Node: Exchanging rows and columns267199
Node: Matrix operations268677
Node: Finding maximum and minimum elements of matrices270647
Node: Matrix properties272547
Node: Example programs for matrices273650
Node: Vector and Matrix References and Further Reading277721
Node: Permutations278207
Node: The Permutation struct279544
Node: Permutation allocation280047
Node: Accessing permutation elements281483
Node: Permutation properties282326
Node: Permutation functions283031
Node: Applying Permutations284288
Node: Reading and writing permutations286215
Ref: Reading and writing permutations-Footnote-1288431
Node: Permutations in cyclic form288543
Node: Permutation Examples291970
Node: Permutation References and Further Reading294513
Node: Combinations295187
Node: The Combination struct296072
Node: Combination allocation296623
Node: Accessing combination elements298410
Node: Combination properties299069
Node: Combination functions299955
Node: Reading and writing combinations301602
Ref: Reading and writing combinations-Footnote-1303835
Node: Combination Examples303947
Node: Combination References and Further Reading305255
Node: Multisets305658
Node: The Multiset struct306584
Node: Multiset allocation307105
Node: Accessing multiset elements308800
Node: Multiset properties309429
Node: Multiset functions310242
Node: Reading and writing multisets311152
Ref: Reading and writing multisets-Footnote-1313303
Node: Multiset Examples313415
Node: Sorting315523
Node: Sorting objects316522
Node: Sorting vectors319435
Node: Selecting the k smallest or largest elements322596
Node: Computing the rank325937
Node: Sorting Examples327138
Node: Sorting References and Further Reading328782
Node: BLAS Support329328
Ref: BLAS Support-Footnote-1332714
Node: GSL BLAS Interface332883
Node: Level 1 GSL BLAS Interface333376
Node: Level 2 GSL BLAS Interface340116
Node: Level 3 GSL BLAS Interface349406
Node: BLAS Examples360504
Node: BLAS References and Further Reading361925
Node: Linear Algebra363267
Node: LU Decomposition364461
Node: QR Decomposition369697
Node: QR Decomposition with Column Pivoting376006
Node: Singular Value Decomposition380470
Node: Cholesky Decomposition384890
Node: Tridiagonal Decomposition of Real Symmetric Matrices388132
Node: Tridiagonal Decomposition of Hermitian Matrices389980
Node: Hessenberg Decomposition of Real Matrices391932
Node: Hessenberg-Triangular Decomposition of Real Matrices394344
Node: Bidiagonalization395467
Node: Householder Transformations397892
Node: Householder solver for linear systems400244
Node: Tridiagonal Systems401151
Node: Balancing404024
Node: Linear Algebra Examples404827
Node: Linear Algebra References and Further Reading406816
Node: Eigensystems408463
Node: Real Symmetric Matrices409692
Node: Complex Hermitian Matrices412206
Node: Real Nonsymmetric Matrices414835
Node: Real Generalized Symmetric-Definite Eigensystems420570
Node: Complex Generalized Hermitian-Definite Eigensystems423449
Node: Real Generalized Nonsymmetric Eigensystems426163
Node: Sorting Eigenvalues and Eigenvectors432770
Node: Eigenvalue and Eigenvector Examples436048
Node: Eigenvalue and Eigenvector References441439
Node: Fast Fourier Transforms442466
Node: Mathematical Definitions443692
Node: Overview of complex data FFTs446097
Node: Radix-2 FFT routines for complex data449042
Node: Mixed-radix FFT routines for complex data453261
Node: Overview of real data FFTs462594
Node: Radix-2 FFT routines for real data465029
Node: Mixed-radix FFT routines for real data469453
Node: FFT References and Further Reading480138
Node: Numerical Integration483008
Node: Numerical Integration Introduction484806
Node: Integrands without weight functions487081
Node: Integrands with weight functions487911
Node: Integrands with singular weight functions488622
Node: QNG non-adaptive Gauss-Kronrod integration489540
Node: QAG adaptive integration490822
Node: QAGS adaptive integration with singularities493611
Node: QAGP adaptive integration with known singular points495411
Node: QAGI adaptive integration on infinite intervals496725
Node: QAWC adaptive integration for Cauchy principal values499005
Node: QAWS adaptive integration for singular functions500175
Node: QAWO adaptive integration for oscillatory functions503401
Node: QAWF adaptive integration for Fourier integrals507189
Node: CQUAD doubly-adaptive integration509813
Node: Fixed order Gauss-Legendre integration513071
Node: Numerical integration error codes515059
Node: Numerical integration examples515815
Node: Numerical integration References and Further Reading517861
Node: Random Number Generation518852
Node: General comments on random numbers520386
Node: The Random Number Generator Interface522338
Node: Random number generator initialization523696
Node: Sampling from a random number generator526067
Node: Auxiliary random number generator functions529311
Node: Random number environment variables531631
Node: Copying random number generator state534156
Node: Reading and writing random number generator state535130
Node: Random number generator algorithms536524
Node: Unix random number generators546466
Node: Other random number generators550180
Node: Random Number Generator Performance558831
Node: Random Number Generator Examples559952
Node: Random Number References and Further Reading561508
Node: Random Number Acknowledgements562803
Node: Quasi-Random Sequences563289
Node: Quasi-random number generator initialization564409
Node: Sampling from a quasi-random number generator565424
Node: Auxiliary quasi-random number generator functions566121
Node: Saving and resorting quasi-random number generator state567067
Node: Quasi-random number generator algorithms567875
Node: Quasi-random number generator examples569013
Node: Quasi-random number references569998
Node: Random Number Distributions570524
Node: Random Number Distribution Introduction573855
Node: The Gaussian Distribution575650
Node: The Gaussian Tail Distribution578310
Node: The Bivariate Gaussian Distribution579974
Node: The Exponential Distribution581288
Node: The Laplace Distribution582427
Node: The Exponential Power Distribution583519
Node: The Cauchy Distribution584787
Node: The Rayleigh Distribution586036
Node: The Rayleigh Tail Distribution587208
Node: The Landau Distribution588081
Node: The Levy alpha-Stable Distributions589036
Node: The Levy skew alpha-Stable Distribution590094
Node: The Gamma Distribution591706
Node: The Flat (Uniform) Distribution593361
Node: The Lognormal Distribution594509
Node: The Chi-squared Distribution595857
Node: The F-distribution597262
Node: The t-distribution598899
Node: The Beta Distribution601000
Node: The Logistic Distribution602159
Node: The Pareto Distribution603288
Node: Spherical Vector Distributions604458
Node: The Weibull Distribution607294
Node: The Type-1 Gumbel Distribution608488
Node: The Type-2 Gumbel Distribution609724
Node: The Dirichlet Distribution610955
Node: General Discrete Distributions612623
Node: The Poisson Distribution616491
Node: The Bernoulli Distribution617498
Node: The Binomial Distribution618249
Node: The Multinomial Distribution619452
Node: The Negative Binomial Distribution621226
Node: The Pascal Distribution622591
Node: The Geometric Distribution623749
Node: The Hypergeometric Distribution624997
Node: The Logarithmic Distribution626650
Node: Shuffling and Sampling627442
Node: Random Number Distribution Examples630254
Node: Random Number Distribution References and Further Reading633450
Node: Statistics635594
Node: Mean and standard deviation and variance637080
Node: Absolute deviation640588
Node: Higher moments (skewness and kurtosis)641880
Node: Autocorrelation644013
Node: Covariance644826
Node: Correlation645792
Node: Weighted Samples647161
Node: Maximum and Minimum values653011
Node: Median and Percentiles655750
Node: Example statistical programs658165
Node: Statistics References and Further Reading660825
Node: Histograms662033
Node: The histogram struct663886
Node: Histogram allocation665690
Node: Copying Histograms668647
Node: Updating and accessing histogram elements669323
Node: Searching histogram ranges672592
Node: Histogram Statistics673592
Node: Histogram Operations675458
Node: Reading and writing histograms677533
Node: Resampling from histograms680575
Node: The histogram probability distribution struct681374
Node: Example programs for histograms684408
Node: Two dimensional histograms686471
Node: The 2D histogram struct687192
Node: 2D Histogram allocation689002
Node: Copying 2D Histograms691076
Node: Updating and accessing 2D histogram elements691781
Node: Searching 2D histogram ranges695438
Node: 2D Histogram Statistics696452
Node: 2D Histogram Operations699317
Node: Reading and writing 2D histograms701495
Node: Resampling from 2D histograms705124
Node: Example programs for 2D histograms708145
Node: N-tuples709972
Node: The ntuple struct711295
Node: Creating ntuples711774
Node: Opening an existing ntuple file712441
Node: Writing ntuples713070
Node: Reading ntuples713531
Node: Closing an ntuple file713862
Node: Histogramming ntuple values714202
Node: Example ntuple programs716212
Node: Ntuple References and Further Reading719541
Node: Monte Carlo Integration719862
Node: Monte Carlo Interface721173
Node: PLAIN Monte Carlo723800
Node: MISER726255
Ref: MISER-Footnote-1732935
Node: VEGAS733060
Node: Monte Carlo Examples742621
Node: Monte Carlo Integration References and Further Reading748608
Node: Simulated Annealing749390
Node: Simulated Annealing algorithm750606
Node: Simulated Annealing functions751758
Node: Examples with Simulated Annealing756288
Node: Trivial example756857
Node: Traveling Salesman Problem759508
Node: Simulated Annealing References and Further Reading762821
Node: Ordinary Differential Equations763232
Node: Defining the ODE System764472
Node: Stepping Functions767300
Node: Adaptive Step-size Control774270
Node: Evolution780347
Node: Driver784476
Node: ODE Example programs788710
Node: ODE References and Further Reading793756
Node: Interpolation795520
Node: Introduction to Interpolation796721
Node: Interpolation Functions797162
Node: Interpolation Types798369
Node: Index Look-up and Acceleration801091
Node: Evaluation of Interpolating Functions803143
Node: Higher-level Interface805639
Node: Interpolation Example programs807679
Node: Interpolation References and Further Reading810899
Node: Numerical Differentiation811471
Node: Numerical Differentiation functions812066
Node: Numerical Differentiation Examples814923
Node: Numerical Differentiation References816336
Node: Chebyshev Approximations816887
Node: Chebyshev Definitions817968
Node: Creation and Calculation of Chebyshev Series818757
Node: Auxiliary Functions for Chebyshev Series819742
Node: Chebyshev Series Evaluation820482
Node: Derivatives and Integrals821862
Node: Chebyshev Approximation Examples823100
Node: Chebyshev Approximation References and Further Reading824596
Node: Series Acceleration825046
Node: Acceleration functions825823
Node: Acceleration functions without error estimation828150
Node: Example of accelerating a series830774
Node: Series Acceleration References833120
Node: Wavelet Transforms834008
Node: DWT Definitions834607
Node: DWT Initialization835559
Node: DWT Transform Functions838207
Node: DWT in one dimension838758
Node: DWT in two dimension840779
Node: DWT Examples845358
Node: DWT References847175
Node: Discrete Hankel Transforms849339
Node: Discrete Hankel Transform Definition849813
Node: Discrete Hankel Transform Functions852016
Node: Discrete Hankel Transform References853681
Node: One dimensional Root-Finding854085
Node: Root Finding Overview855391
Node: Root Finding Caveats857247
Node: Initializing the Solver859016
Node: Providing the function to solve861649
Node: Search Bounds and Guesses865203
Node: Root Finding Iteration866066
Node: Search Stopping Parameters867917
Node: Root Bracketing Algorithms870428
Node: Root Finding Algorithms using Derivatives873726
Ref: Root Finding Algorithms using Derivatives-Footnote-1877269
Node: Root Finding Examples877425
Node: Root Finding References and Further Reading884713
Node: One dimensional Minimization885352
Node: Minimization Overview886695
Node: Minimization Caveats888402
Node: Initializing the Minimizer889740
Node: Providing the function to minimize891981
Node: Minimization Iteration892459
Node: Minimization Stopping Parameters894597
Node: Minimization Algorithms896202
Node: Minimization Examples898796
Node: Minimization References and Further Reading902430
Node: Multidimensional Root-Finding902886
Node: Overview of Multidimensional Root Finding904394
Node: Initializing the Multidimensional Solver906581
Node: Providing the multidimensional system of equations to solve909811
Node: Iteration of the multidimensional solver914723
Node: Search Stopping Parameters for the multidimensional solver917004
Node: Algorithms using Derivatives918742
Node: Algorithms without Derivatives923567
Node: Example programs for Multidimensional Root finding926657
Node: References and Further Reading for Multidimensional Root Finding935281
Node: Multidimensional Minimization936520
Node: Multimin Overview937930
Node: Multimin Caveats940010
Node: Initializing the Multidimensional Minimizer940759
Node: Providing a function to minimize943993
Node: Multimin Iteration948054
Node: Multimin Stopping Criteria950248
Node: Multimin Algorithms with Derivatives951819
Node: Multimin Algorithms without Derivatives955350
Node: Multimin Examples958352
Node: Multimin References and Further Reading964922
Node: Least-Squares Fitting965786
Node: Fitting Overview966872
Node: Linear regression969205
Node: Linear fitting without a constant term971807
Node: Multi-parameter fitting974001
Node: Robust linear regression979860
Node: Troubleshooting990108
Node: Fitting Examples990731
Node: Fitting References and Further Reading1001255
Node: Nonlinear Least-Squares Fitting1002627
Node: Overview of Nonlinear Least-Squares Fitting1004151
Node: Initializing the Nonlinear Least-Squares Solver1005618
Node: Providing the Function to be Minimized1008483
Node: Finite Difference Jacobian1011946
Node: Iteration of the Minimization Algorithm1013817
Node: Search Stopping Parameters for Minimization Algorithms1015657
Node: High Level Driver1017730
Node: Minimization Algorithms using Derivatives1018636
Ref: Minimization Algorithms using Derivatives-Footnote-11022084
Node: Minimization Algorithms without Derivatives1022173
Node: Computing the covariance matrix of best fit parameters1022565
Node: Example programs for Nonlinear Least-Squares Fitting1024602
Node: References and Further Reading for Nonlinear Least-Squares Fitting1032335
Node: Basis Splines1033071
Node: Overview of B-splines1033950
Node: Initializing the B-splines solver1035266
Node: Constructing the knots vector1036647
Node: Evaluation of B-spline basis functions1037435
Node: Evaluation of B-spline basis function derivatives1039083
Node: Working with the Greville abscissae1041053
Node: Example programs for B-splines1042047
Node: References and Further Reading1046042
Node: Physical Constants1046848
Node: Fundamental Constants1048427
Node: Astronomy and Astrophysics1049567
Node: Atomic and Nuclear Physics1050232
Node: Measurement of Time1051883
Node: Imperial Units1052313
Node: Speed and Nautical Units1052755
Node: Printers Units1053259
Node: Volume Area and Length1053582
Node: Mass and Weight1054268
Node: Thermal Energy and Power1055087
Node: Pressure1055510
Node: Viscosity1056123
Node: Light and Illumination1056399
Node: Radioactivity1056991
Node: Force and Energy1057326
Node: Prefixes1057730
Node: Physical Constant Examples1058473
Node: Physical Constant References and Further Reading1060262
Node: IEEE floating-point arithmetic1060992
Node: Representation of floating point numbers1061584
Node: Setting up your IEEE environment1066070
Node: IEEE References and Further Reading1073043
Node: Debugging Numerical Programs1074203
Node: Using gdb1074720
Node: Examining floating point registers1078063
Node: Handling floating point exceptions1079348
Node: GCC warning options for numerical programs1080760
Node: Debugging References1084708
Node: Contributors to GSL1085420
Node: Autoconf Macros1089914
Node: GSL CBLAS Library1093946
Node: Level 1 CBLAS Functions1094486
Node: Level 2 CBLAS Functions1099788
Node: Level 3 CBLAS Functions1116418
Node: GSL CBLAS Examples1126080
Node: GNU General Public License1127643
Node: GNU Free Documentation License1165217
Node: Function Index1190366
Node: Variable Index1443412
Node: Type Index1446715
Node: Concept Index1461784

End Tag Table
