This is gsl-ref.info, produced by makeinfo version 4.2 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


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Tag Table:
(Indirect)
Node: Top228
Node: Introduction1909
Node: Routines available in GSL2528
Node: GSL is Free Software4169
Node: Obtaining GSL6347
Node: An Example Program7525
Node: No Warranty8265
Node: Further Information8706
Node: Using the library9235
Node: ANSI C Compliance9792
Node: Compiling and Linking10854
Node: Shared Libraries13390
Node: Autoconf macros13957
Node: Inline functions16248
Node: Long double17572
Node: Portability functions18965
Node: Alternative optimized functions20422
Node: Support for different numeric types21873
Node: Compatibility with C++24935
Node: Aliasing of arrays25250
Node: Thread-safety25994
Node: Code Reuse27065
Node: Error Handling27695
Node: Error Reporting28444
Node: Error Codes30086
Node: Error Handlers31838
Node: Using GSL error reporting in your own functions35487
Node: Error Reporting Examples37445
Node: Mathematical Functions38689
Node: Mathematical Constants39396
Node: Infinities and Not-a-number40519
Node: Elementary Functions41573
Node: Small integer powers43263
Node: Testing the Sign of Numbers44839
Node: Testing for Odd and Even Numbers45261
Node: Maximum and Minimum functions45807
Node: Complex Numbers47816
Node: Complex numbers49160
Node: Properties of complex numbers50951
Node: Complex arithmetic operators51926
Node: Elementary Complex Functions54649
Node: Complex Trigonometric Functions56453
Node: Inverse Complex Trigonometric Functions57660
Node: Complex Hyperbolic Functions60246
Node: Inverse Complex Hyperbolic Functions61528
Node: Complex Number References and Further Reading63352
Node: Polynomials64741
Node: Polynomial Evaluation65508
Node: Divided Difference Representation of Polynomials65959
Node: Quadratic Equations67617
Node: Cubic Equations69384
Node: General Polynomial Equations70729
Node: Roots of Polynomials Examples72600
Node: Roots of Polynomials References and Further Reading74015
Node: Special Functions74775
Node: Special Function Usage76720
Node: The gsl_sf_result struct77899
Node: Special Function Modes79158
Node: Airy Functions and Derivatives80090
Node: Airy Functions80781
Node: Derivatives of Airy Functions82121
Node: Zeros of Airy Functions83460
Node: Zeros of Derivatives of Airy Functions84163
Node: Bessel Functions84906
Node: Regular Cylindrical Bessel Functions86093
Node: Irregular Cylindrical Bessel Functions87399
Node: Regular Modified Cylindrical Bessel Functions88837
Node: Irregular Modified Cylindrical Bessel Functions91640
Node: Regular Spherical Bessel Functions94584
Node: Irregular Spherical Bessel Functions96775
Node: Regular Modified Spherical Bessel Functions98442
Node: Irregular Modified Spherical Bessel Functions100428
Node: Regular Bessel Function - Fractional Order102474
Node: Irregular Bessel Functions - Fractional Order103458
Node: Regular Modified Bessel Functions - Fractional Order104025
Node: Irregular Modified Bessel Functions - Fractional Order104932
Node: Zeros of Regular Bessel Functions106147
Node: Clausen Functions107157
Node: Coulomb Functions107754
Node: Normalized Hydrogenic Bound States108180
Node: Coulomb Wave Functions109186
Node: Coulomb Wave Function Normalization Constant112571
Node: Coupling Coefficients113313
Node: 3-j Symbols114031
Node: 6-j Symbols114621
Node: 9-j Symbols115231
Node: Dawson Function115923
Node: Debye Functions116482
Node: Dilogarithm117762
Node: Real Argument118050
Node: Complex Argument118603
Node: Elementary Operations119057
Node: Elliptic Integrals119872
Node: Definition of Legendre Forms120338
Node: Definition of Carlson Forms121176
Node: Legendre Form of Complete Elliptic Integrals121877
Node: Legendre Form of Incomplete Elliptic Integrals122743
Node: Carlson Forms124460
Node: Elliptic Functions (Jacobi)125985
Node: Error Functions126558
Node: Error Function127001
Node: Complementary Error Function127345
Node: Log Complementary Error Function127790
Node: Probability functions128226
Node: Exponential Functions128965
Node: Exponential Function129341
Node: Relative Exponential Functions130534
Node: Exponentiation With Error Estimate132183
Node: Exponential Integrals133374
Node: Exponential Integral133849
Node: Ei(x)134476
Node: Hyperbolic Integrals134906
Node: Ei_3(x)135543
Node: Trigonometric Integrals135908
Node: Arctangent Integral136489
Node: Fermi-Dirac Function136852
Node: Complete Fermi-Dirac Integrals137205
Node: Incomplete Fermi-Dirac Integrals139636
Node: Gamma Function140263
Node: Gegenbauer Functions147776
Node: Hypergeometric Functions149400
Node: Laguerre Functions153604
Node: Lambert W Functions154858
Node: Legendre Functions and Spherical Harmonics155875
Node: Legendre Polynomials156457
Node: Associated Legendre Polynomials and Spherical Harmonics158274
Node: Conical Functions160682
Node: Radial Functions for Hyperbolic Space162779
Node: Logarithm and Related Functions164937
Node: Power Function166542
Node: Psi (Digamma) Function167474
Node: Digamma Function167978
Node: Trigamma Function168787
Node: Polygamma Function169155
Node: Synchrotron Functions169523
Node: Transport Functions170275
Node: Trigonometric Functions171367
Node: Circular Trigonometric Functions171982
Node: Trigonometric Functions for Complex Arguments172969
Node: Hyperbolic Trigonometric Functions173986
Node: Conversion Functions174571
Node: Restriction Functions175338
Node: Trigonometric Functions With Error Estimates175949
Node: Zeta Functions176693
Node: Riemann Zeta Function177108
Node: Hurwitz Zeta Function177762
Node: Eta Function178244
Node: Special Functions Examples178788
Node: Special Functions References and Further Reading180469
Node: Vectors and Matrices181565
Node: Data types182323
Node: Blocks183521
Node: Block allocation184432
Node: Reading and writing blocks185824
Node: Example programs for blocks187875
Node: Vectors188506
Node: Vector allocation190371
Node: Accessing vector elements191895
Node: Initializing vector elements194010
Node: Reading and writing vectors194689
Node: Vector views196756
Node: Copying vectors203937
Node: Exchanging elements204786
Node: Vector operations205333
Node: Finding maximum and minimum elements of vectors206832
Node: Vector properties208339
Node: Example programs for vectors208687
Node: Matrices210858
Node: Matrix allocation213711
Node: Accessing matrix elements215284
Node: Initializing matrix elements216966
Node: Reading and writing matrices217747
Node: Matrix views219827
Node: Creating row and column views226948
Node: Copying matrices230097
Node: Copying rows and columns230695
Node: Exchanging rows and columns232359
Node: Matrix operations233817
Node: Finding maximum and minimum elements of matrices235433
Node: Matrix properties237120
Node: Example programs for matrices237471
Node: Vector and Matrix References and Further Reading241384
Node: Permutations241862
Node: The Permutation struct243149
Node: Permutation allocation243645
Node: Accessing permutation elements245066
Node: Permutation properties245822
Node: Permutation functions246510
Node: Applying Permutations247755
Node: Reading and writing permutations249667
Node: Permutations in Cyclic Form251839
Node: Permutation Examples255069
Node: Permutation References and Further Reading257507
Node: Combinations258171
Node: The Combination struct258997
Node: Combination allocation259540
Node: Accessing combination elements261043
Node: Combination properties261606
Node: Combination functions262481
Node: Reading and writing combinations263410
Node: Combination Examples265589
Node: Sorting266852
Node: Sorting objects267798
Node: Sorting vectors270700
Node: Selecting the k-th smallest or largest elements273269
Node: Computing the rank276715
Node: Sorting Examples277923
Node: Sorting References and Further Reading279540
Node: BLAS Support280076
Node: GSL BLAS Interface283044
Node: Level 1 GSL BLAS Interface283524
Node: Level 2 GSL BLAS Interface290034
Node: Level 3 GSL BLAS Interface299312
Node: BLAS Examples310385
Node: BLAS References and Further Reading311836
Node: Linear Algebra313180
Node: LU Decomposition314387
Node: QR Decomposition319307
Node: QR Decomposition with Column Pivoting324949
Node: Singular Value Decomposition329321
Node: Cholesky Decomposition332618
Node: Tridiagonal Decomposition of Real Symmetric Matrices334519
Node: Tridiagonal Decomposition of Hermitian Matrices336357
Node: Bidiagonalization338275
Node: Householder solver for linear systems340587
Node: Tridiagonal Systems341468
Node: Linear Algebra Examples342563
Node: Linear Algebra References and Further Reading344591
Node: Eigensystems346048
Node: Real Symmetric Matrices347087
Node: Complex Hermitian Matrices349303
Node: Sorting Eigenvalues and Eigenvectors351805
Node: Eigenvalue and Eigenvector Examples353124
Node: Eigenvalue and Eigenvector References355474
Node: Fast Fourier Transforms356172
Node: Mathematical Definitions357378
Node: Overview of complex data FFTs359776
Node: Radix-2 FFT routines for complex data362395
Node: Mixed-radix FFT routines for complex data366460
Node: Overview of real data FFTs375705
Node: Radix-2 FFT routines for real data378135
Node: Mixed-radix FFT routines for real data380964
Node: FFT References and Further Reading391624
Node: Numerical Integration394384
Node: Numerical Integration Introduction395926
Node: QNG non-adaptive Gauss-Kronrod integration399389
Node: QAG adaptive integration400649
Node: QAGS adaptive integration with singularities403279
Node: QAGP adaptive integration with known singular points405069
Node: QAGI adaptive integration on infinite intervals406369
Node: QAWC adaptive integration for Cauchy principal values408591
Node: QAWS adaptive integration for singular functions409754
Node: QAWO adaptive integration for oscillatory functions412983
Node: QAWF adaptive integration for Fourier integrals416737
Node: Numerical integration error codes419315
Node: Numerical integration examples420074
Node: Numerical integration References and Further Reading422100
Node: Random Number Generation422816
Node: General comments on random numbers424304
Node: The Random Number Generator Interface426252
Node: Random number generator initialization427603
Node: Sampling from a random number generator429600
Node: Auxiliary random number generator functions432075
Node: Random number environment variables434395
Node: Saving and restoring random number generator state436928
Node: Random number generator algorithms438097
Node: Unix random number generators447442
Node: Numerical Recipes generators451157
Node: Other random number generators452540
Node: Random Number Generator Performance461829
Node: Random Number Generator Examples463108
Node: Random Number References and Further Reading464684
Node: Random Number Acknowledgements465878
Node: Quasi-Random Sequences466352
Node: Quasi-random number generator initialization467376
Node: Sampling from a quasi-random number generator468274
Node: Auxiliary quasi-random number generator functions468868
Node: Saving and resorting quasi-random number generator state469800
Node: Quasi-random number generator algorithms470586
Node: Quasi-random number generator examples471352
Node: Quasi-random number references472342
Node: Random Number Distributions472855
Node: The Gaussian Distribution475119
Node: The Gaussian Tail Distribution476704
Node: The Bivariate Gaussian Distribution478319
Node: The Exponential Distribution479598
Node: The Laplace Distribution480301
Node: The Exponential Power Distribution480990
Node: The Cauchy Distribution481943
Node: The Rayleigh Distribution482776
Node: The Rayleigh Tail Distribution483502
Node: The Landau Distribution484358
Node: The Levy alpha-Stable Distributions485296
Node: The Levy skew alpha-Stable Distribution486339
Node: The Gamma Distribution487936
Node: The Flat (Uniform) Distribution488646
Node: The Lognormal Distribution489350
Node: The Chi-squared Distribution490149
Node: The F-distribution491125
Node: The t-distribution492256
Node: The Beta Distribution493236
Node: The Logistic Distribution493936
Node: The Pareto Distribution494637
Node: The Spherical Distribution (2D & 3D)495340
Node: The Weibull Distribution498149
Node: The Type-1 Gumbel Distribution498880
Node: The Type-2 Gumbel Distribution499647
Node: General Discrete Distributions500412
Node: The Poisson Distribution504268
Node: The Bernoulli Distribution504983
Node: The Binomial Distribution505709
Node: The Negative Binomial Distribution506577
Node: The Pascal Distribution507578
Node: The Geometric Distribution508401
Node: The Hypergeometric Distribution509205
Node: The Logarithmic Distribution510170
Node: Shuffling and Sampling510946
Node: Random Number Distribution Examples513785
Node: Random Number Distribution References and Further Reading516184
Node: Statistics517387
Node: Mean and standard deviation and variance518664
Node: Absolute deviation521709
Node: Higher moments (skewness and kurtosis)522993
Node: Autocorrelation525120
Node: Covariance525923
Node: Weighted Samples526742
Node: Maximum and Minimum values532001
Node: Median and Percentiles534437
Node: Example statistical programs536847
Node: Statistics References and Further Reading539581
Node: Histograms540765
Node: The histogram struct542519
Node: Histogram allocation544319
Node: Copying Histograms547300
Node: Updating and accessing histogram elements547964
Node: Searching histogram ranges551213
Node: Histogram Statistics552204
Node: Histogram Operations554047
Node: Reading and writing histograms556090
Node: Resampling from histograms559111
Node: The histogram probability distribution struct559902
Node: Example programs for histograms562929
Node: Two dimensional histograms565050
Node: The 2D histogram struct565762
Node: 2D Histogram allocation567552
Node: Copying 2D Histograms569610
Node: Updating and accessing 2D histogram elements570301
Node: Searching 2D histogram ranges573927
Node: 2D Histogram Statistics574936
Node: 2D Histogram Operations577717
Node: Reading and writing 2D histograms579867
Node: Resampling from 2D histograms583511
Node: Example programs for 2D histograms586516
Node: N-tuples588574
Node: The ntuple struct589834
Node: Creating ntuples590305
Node: Opening an existing ntuple file590962
Node: Writing ntuples591580
Node: Reading ntuples592028
Node: Closing an ntuple file592347
Node: Histogramming ntuple values592676
Node: Example ntuple programs594672
Node: Ntuple References and Further Reading598224
Node: Monte Carlo Integration598535
Node: Monte Carlo Interface599779
Node: PLAIN Monte Carlo602406
Node: MISER604833
Node: VEGAS610656
Node: Monte Carlo Examples618953
Node: Monte Carlo Integration References and Further Reading624981
Node: Simulated Annealing625733
Node: Simulated Annealing algorithm626882
Node: Simulated Annealing functions628055
Node: Examples with Simulated Annealing632552
Node: Trivial example633090
Node: Traveling Salesman Problem635777
Node: Ordinary Differential Equations639195
Node: Defining the ODE System640013
Node: Stepping Functions641827
Node: Adaptive Step-size Control645382
Node: Evolution650072
Node: ODE Example programs652127
Node: ODE References and Further Reading657125
Node: Interpolation657758
Node: Introduction to Interpolation658768
Node: Interpolation Functions659198
Node: Interpolation Types660364
Node: Index Look-up and Acceleration662167
Node: Evaluation of interpolating functions663780
Node: Higher-level interface666132
Node: Interpolation Example programs667980
Node: Interpolation References and Further Reading669710
Node: Numerical Differentiation670140
Node: Numerical Differentiation functions670720
Node: Numerical Differentiation Example672327
Node: Numerical Differentiation References673739
Node: Chebyshev Approximations674137
Node: The gsl_cheb_series struct675093
Node: Creation and Calculation of Chebyshev Series675738
Node: Chebyshev Series Evaluation676702
Node: Derivatives and Integrals678062
Node: Chebyshev Approximation examples679295
Node: Chebyshev Approximation References and Further Reading680829
Node: Series Acceleration681268
Node: Acceleration functions682038
Node: Acceleration functions without error estimation684270
Node: Example of accelerating a series686876
Node: Series Acceleration References689317
Node: Discrete Hankel Transforms690196
Node: Discrete Hankel Transform Definition690662
Node: Discrete Hankel Transform Functions692500
Node: Discrete Hankel Transform References694004
Node: One dimensional Root-Finding694398
Node: Root Finding Overview695655
Node: Root Finding Caveats697506
Node: Initializing the Solver699264
Node: Providing the function to solve701881
Node: Search Bounds and Guesses705685
Node: Root Finding Iteration706539
Node: Search Stopping Parameters708375
Node: Root Bracketing Algorithms710883
Node: Root Finding Algorithms using Derivatives714172
Node: Root Finding Examples717643
Node: Root Finding References and Further Reading724991
Node: One dimensional Minimization725618
Node: Minimization Overview726917
Node: Minimization Caveats728607
Node: Initializing the Minimizer729937
Node: Providing the function to minimize732164
Node: Minimization Iteration732635
Node: Minimization Stopping Parameters734750
Node: Minimization Algorithms736351
Node: Minimization Examples738783
Node: Minimization References and Further Reading741752
Node: Multidimensional Root-Finding742198
Node: Overview of Multidimensional Root Finding743684
Node: Initializing the Multidimensional Solver745864
Node: Providing the multidimensional system of equations to solve749029
Node: Iteration of the multidimensional solver753905
Node: Search Stopping Parameters for the multidimensional solver756075
Node: Algorithms using Derivatives757807
Node: Algorithms without Derivatives762542
Node: Example programs for Multidimensional Root finding765324
Node: References and Further Reading for Multidimensional Root Finding774048
Node: Multidimensional Minimization775277
Node: Multimin Overview776566
Node: Multimin Caveats778144
Node: Initializing the Multidimensional Minimizer778886
Node: Providing a function to minimize781041
Node: Multimin Iteration784259
Node: Multimin Stopping Criteria785807
Node: Multimin Algorithms786998
Node: Multimin Examples789761
Node: Multimin References and Further Reading792856
Node: Least-Squares Fitting793342
Node: Linear regression794273
Node: Linear fitting without a constant term796866
Node: Multi-parameter fitting799258
Node: Fitting Examples803010
Node: Fitting References and Further Reading809785
Node: Nonlinear Least-Squares Fitting810594
Node: Overview of Nonlinear Least-Squares Fitting812045
Node: Initializing the Nonlinear Least-Squares Solver812928
Node: Providing the Function to be Minimized815589
Node: Iteration of the Minimization Algorithm818228
Node: Search Stopping Parameters for Minimization Algorithms819555
Node: Minimization Algorithms using Derivatives821644
Node: Minimization Algorithms without Derivatives824880
Node: Computing the covariance matrix of best fit parameters825265
Node: Example programs for Nonlinear Least-Squares Fitting826323
Node: References and Further Reading for Nonlinear Least-Squares Fitting833262
Node: Physical Constants833985
Node: Fundamental Constants835362
Node: Astronomy and Astrophysics836372
Node: Atomic and Nuclear Physics837021
Node: Measurement of Time838480
Node: Imperial Units838896
Node: Nautical Units839313
Node: Printers Units839628
Node: Volume839913
Node: Mass and Weight840424
Node: Thermal Energy and Power841206
Node: Pressure841613
Node: Viscosity842207
Node: Light and Illumination842469
Node: Radioactivity843042
Node: Force and Energy843362
Node: Prefixes843750
Node: Physical Constant Examples844484
Node: Physical Constant References and Further Reading846269
Node: IEEE floating-point arithmetic846625
Node: Representation of floating point numbers847208
Node: Setting up your IEEE environment851711
Node: IEEE References and Further Reading857798
Node: Debugging Numerical Programs858796
Node: Using gdb859258
Node: Examining floating point registers862614
Node: Handling floating point exceptions863902
Node: GCC warning options for numerical programs865311
Node: Debugging References869498
Node: Contributors to GSL870040
Node: Autoconf Macros871803
Node: GSL CBLAS Library872602
Node: Level 1 CBLAS Functions873086
Node: Level 2 CBLAS Functions878232
Node: Level 3 CBLAS Functions894594
Node: GSL CBLAS Examples904113
Node: Reporting Bugs905709
Node: GNU General Public License906425
Node: GNU Free Documentation License925700
Node: Function Index945616
Node: Variable Index1056683
Node: Type Index1057493
Node: Concept Index1059347

End Tag Table
