This is gsl-ref.info, produced by makeinfo version 4.6 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


Indirect:
gsl-ref.info-1: 228
gsl-ref.info-2: 295370
gsl-ref.info-3: 593602
gsl-ref.info-4: 893552

Tag Table:
(Indirect)
Node: Top228
Node: Introduction2055
Node: Routines available in GSL2703
Node: GSL is Free Software4341
Node: Obtaining GSL6670
Node: No Warranty7782
Node: Reporting Bugs8210
Node: Further Information9006
Node: Conventions used in this manual9778
Node: Using the library10534
Node: An Example Program11091
Node: Compiling and Linking11792
Node: Shared Libraries14676
Node: ANSI C Compliance15776
Node: Inline functions16855
Node: Long double17862
Node: Portability functions19252
Node: Alternative optimized functions20646
Node: Support for different numeric types22094
Node: Compatibility with C++25152
Node: Aliasing of arrays25464
Node: Thread-safety26205
Node: Code Reuse27272
Node: Error Handling27899
Node: Error Reporting28645
Node: Error Codes30534
Node: Error Handlers32284
Node: Using GSL error reporting in your own functions35930
Node: Error Reporting Examples37878
Node: Mathematical Functions39096
Node: Mathematical Constants39853
Node: Infinities and Not-a-number40974
Node: Elementary Functions42028
Node: Small integer powers44265
Node: Testing the Sign of Numbers45809
Node: Testing for Odd and Even Numbers46231
Node: Maximum and Minimum functions46777
Node: Approximate Comparison of Floating Point Numbers48843
Node: Complex Numbers50042
Node: Complex numbers51383
Node: Properties of complex numbers53171
Node: Complex arithmetic operators54146
Node: Elementary Complex Functions56869
Node: Complex Trigonometric Functions58673
Node: Inverse Complex Trigonometric Functions59880
Node: Complex Hyperbolic Functions62466
Node: Inverse Complex Hyperbolic Functions63748
Node: Complex Number References and Further Reading65572
Node: Polynomials66961
Node: Polynomial Evaluation67724
Node: Divided Difference Representation of Polynomials68175
Node: Quadratic Equations69830
Node: Cubic Equations71597
Node: General Polynomial Equations72942
Node: Roots of Polynomials Examples74810
Node: Roots of Polynomials References and Further Reading76231
Node: Special Functions76992
Node: Special Function Usage78934
Node: The gsl_sf_result struct80110
Node: Special Function Modes81366
Node: Airy Functions and Derivatives82294
Node: Airy Functions82982
Node: Derivatives of Airy Functions84322
Node: Zeros of Airy Functions85661
Node: Zeros of Derivatives of Airy Functions86364
Node: Bessel Functions87107
Node: Regular Cylindrical Bessel Functions88291
Node: Irregular Cylindrical Bessel Functions89597
Node: Regular Modified Cylindrical Bessel Functions91035
Node: Irregular Modified Cylindrical Bessel Functions93838
Node: Regular Spherical Bessel Functions96782
Node: Irregular Spherical Bessel Functions98973
Node: Regular Modified Spherical Bessel Functions100640
Node: Irregular Modified Spherical Bessel Functions102623
Node: Regular Bessel Function - Fractional Order104666
Node: Irregular Bessel Functions - Fractional Order105650
Node: Regular Modified Bessel Functions - Fractional Order106217
Node: Irregular Modified Bessel Functions - Fractional Order107124
Node: Zeros of Regular Bessel Functions108339
Node: Clausen Functions109422
Node: Coulomb Functions110016
Node: Normalized Hydrogenic Bound States110439
Node: Coulomb Wave Functions111445
Node: Coulomb Wave Function Normalization Constant114827
Node: Coupling Coefficients115566
Node: 3-j Symbols116281
Node: 6-j Symbols116871
Node: 9-j Symbols117481
Node: Dawson Function118173
Node: Debye Functions118730
Node: Dilogarithm120007
Node: Real Argument120292
Node: Complex Argument120845
Node: Elementary Operations121299
Node: Elliptic Integrals122111
Node: Definition of Legendre Forms122574
Node: Definition of Carlson Forms123409
Node: Legendre Form of Complete Elliptic Integrals124107
Node: Legendre Form of Incomplete Elliptic Integrals124973
Node: Carlson Forms126690
Node: Elliptic Functions (Jacobi)128215
Node: Error Functions128785
Node: Error Function129226
Node: Complementary Error Function129570
Node: Log Complementary Error Function130015
Node: Probability functions130451
Node: Exponential Functions131676
Node: Exponential Function132049
Node: Relative Exponential Functions133242
Node: Exponentiation With Error Estimate134891
Node: Exponential Integrals136082
Node: Exponential Integral136554
Node: Ei(x)137181
Node: Hyperbolic Integrals137613
Node: Ei_3(x)138250
Node: Trigonometric Integrals138615
Node: Arctangent Integral139196
Node: Fermi-Dirac Function139559
Node: Complete Fermi-Dirac Integrals139909
Node: Incomplete Fermi-Dirac Integrals142340
Node: Gamma Function142967
Node: Gegenbauer Functions150945
Node: Hypergeometric Functions152566
Node: Laguerre Functions156767
Node: Lambert W Functions158018
Node: Legendre Functions and Spherical Harmonics159032
Node: Legendre Polynomials159611
Node: Associated Legendre Polynomials and Spherical Harmonics161428
Node: Conical Functions163832
Node: Radial Functions for Hyperbolic Space165926
Node: Logarithm and Related Functions168081
Node: Power Function169683
Node: Psi (Digamma) Function170612
Node: Digamma Function171113
Node: Trigamma Function171922
Node: Polygamma Function172481
Node: Synchrotron Functions172849
Node: Transport Functions173598
Node: Trigonometric Functions174687
Node: Circular Trigonometric Functions175300
Node: Trigonometric Functions for Complex Arguments176287
Node: Hyperbolic Trigonometric Functions177304
Node: Conversion Functions177889
Node: Restriction Functions178656
Node: Trigonometric Functions With Error Estimates179267
Node: Zeta Functions180011
Node: Riemann Zeta Function180459
Node: Riemann Zeta Function Minus One181120
Node: Hurwitz Zeta Function181873
Node: Eta Function182362
Node: Special Functions Examples182903
Node: Special Functions References and Further Reading184628
Node: Vectors and Matrices185724
Node: Data types186479
Node: Blocks187674
Node: Block allocation188582
Node: Reading and writing blocks189971
Node: Example programs for blocks192019
Node: Vectors192651
Node: Vector allocation194513
Node: Accessing vector elements196034
Node: Initializing vector elements198241
Node: Reading and writing vectors198920
Node: Vector views200984
Node: Copying vectors208162
Node: Exchanging elements209008
Node: Vector operations209552
Node: Finding maximum and minimum elements of vectors211048
Node: Vector properties212555
Node: Example programs for vectors212903
Node: Matrices215087
Node: Matrix allocation217937
Node: Accessing matrix elements219507
Node: Initializing matrix elements221196
Node: Reading and writing matrices221977
Node: Matrix views224054
Node: Creating row and column views231172
Node: Copying matrices234318
Node: Copying rows and columns234900
Node: Exchanging rows and columns236561
Node: Matrix operations238022
Node: Finding maximum and minimum elements of matrices239642
Node: Matrix properties241496
Node: Example programs for matrices241847
Node: Vector and Matrix References and Further Reading245797
Node: Permutations246275
Node: The Permutation struct247559
Node: Permutation allocation248053
Node: Accessing permutation elements249474
Node: Permutation properties250227
Node: Permutation functions250915
Node: Applying Permutations252160
Node: Reading and writing permutations254072
Node: Permutations in Cyclic Form256241
Node: Permutation Examples259468
Node: Permutation References and Further Reading261919
Node: Combinations262583
Node: The Combination struct263453
Node: Combination allocation263993
Node: Accessing combination elements265763
Node: Combination properties266323
Node: Combination functions267198
Node: Reading and writing combinations268126
Node: Combination Examples270302
Node: Combination References and Further Reading271622
Node: Sorting272190
Node: Sorting objects273130
Node: Sorting vectors276029
Node: Selecting the k smallest or largest elements278588
Node: Computing the rank281887
Node: Sorting Examples283093
Node: Sorting References and Further Reading284714
Node: BLAS Support285250
Node: GSL BLAS Interface288218
Node: Level 1 GSL BLAS Interface288695
Node: Level 2 GSL BLAS Interface295370
Node: Level 3 GSL BLAS Interface304624
Node: BLAS Examples315701
Node: BLAS References and Further Reading317154
Node: Linear Algebra318498
Node: LU Decomposition319734
Node: QR Decomposition324715
Node: QR Decomposition with Column Pivoting330354
Node: Singular Value Decomposition334719
Node: Cholesky Decomposition338013
Node: Tridiagonal Decomposition of Real Symmetric Matrices339911
Node: Tridiagonal Decomposition of Hermitian Matrices341746
Node: Bidiagonalization343661
Node: Householder Transformations346063
Node: Householder solver for linear systems347895
Node: Tridiagonal Systems348786
Node: Linear Algebra Examples351281
Node: Linear Algebra References and Further Reading353312
Node: Eigensystems354790
Node: Real Symmetric Matrices355826
Node: Complex Hermitian Matrices358042
Node: Sorting Eigenvalues and Eigenvectors360544
Node: Eigenvalue and Eigenvector Examples361863
Node: Eigenvalue and Eigenvector References364228
Node: Fast Fourier Transforms364926
Node: Mathematical Definitions366129
Node: Overview of complex data FFTs368524
Node: Radix-2 FFT routines for complex data371161
Node: Mixed-radix FFT routines for complex data375400
Node: Overview of real data FFTs384779
Node: Radix-2 FFT routines for real data387206
Node: Mixed-radix FFT routines for real data390032
Node: FFT References and Further Reading400681
Node: Numerical Integration403538
Node: Numerical Integration Introduction405077
Node: QNG non-adaptive Gauss-Kronrod integration408531
Node: QAG adaptive integration409790
Node: QAGS adaptive integration with singularities412417
Node: QAGP adaptive integration with known singular points414204
Node: QAGI adaptive integration on infinite intervals415504
Node: QAWC adaptive integration for Cauchy principal values417726
Node: QAWS adaptive integration for singular functions418889
Node: QAWO adaptive integration for oscillatory functions422114
Node: QAWF adaptive integration for Fourier integrals425864
Node: Numerical integration error codes428442
Node: Numerical integration examples429198
Node: Numerical integration References and Further Reading431231
Node: Random Number Generation431947
Node: General comments on random numbers433443
Node: The Random Number Generator Interface435383
Node: Random number generator initialization436731
Node: Sampling from a random number generator438728
Node: Auxiliary random number generator functions441200
Node: Random number environment variables443522
Node: Copying random number generator state446047
Node: Reading and writing random number generator state446999
Node: Random number generator algorithms448399
Node: Unix random number generators457784
Node: Other random number generators461498
Node: Random Number Generator Performance470782
Node: Random Number Generator Examples472093
Node: Random Number References and Further Reading473670
Node: Random Number Acknowledgements475167
Node: Quasi-Random Sequences475641
Node: Quasi-random number generator initialization476661
Node: Sampling from a quasi-random number generator477559
Node: Auxiliary quasi-random number generator functions478153
Node: Saving and resorting quasi-random number generator state479086
Node: Quasi-random number generator algorithms479872
Node: Quasi-random number generator examples480635
Node: Quasi-random number references481625
Node: Random Number Distributions482135
Node: Random Number Distribution Introduction484980
Node: The Gaussian Distribution486032
Node: The Gaussian Tail Distribution488442
Node: The Bivariate Gaussian Distribution490057
Node: The Exponential Distribution491356
Node: The Laplace Distribution492477
Node: The Exponential Power Distribution493556
Node: The Cauchy Distribution494508
Node: The Rayleigh Distribution495740
Node: The Rayleigh Tail Distribution496894
Node: The Landau Distribution497750
Node: The Levy alpha-Stable Distributions498688
Node: The Levy skew alpha-Stable Distribution499731
Node: The Gamma Distribution501328
Node: The Flat (Uniform) Distribution502473
Node: The Lognormal Distribution503595
Node: The Chi-squared Distribution504923
Node: The F-distribution506307
Node: The t-distribution507729
Node: The Beta Distribution509103
Node: The Logistic Distribution510073
Node: The Pareto Distribution511182
Node: Spherical Vector Distributions512322
Node: The Weibull Distribution515095
Node: The Type-1 Gumbel Distribution516269
Node: The Type-2 Gumbel Distribution517486
Node: The Dirichlet Distribution518697
Node: General Discrete Distributions520348
Node: The Poisson Distribution524196
Node: The Bernoulli Distribution524911
Node: The Binomial Distribution525637
Node: The Multinomial Distribution526499
Node: The Negative Binomial Distribution528135
Node: The Pascal Distribution529138
Node: The Geometric Distribution529961
Node: The Hypergeometric Distribution530765
Node: The Logarithmic Distribution531752
Node: Shuffling and Sampling532528
Node: Random Number Distribution Examples535364
Node: Random Number Distribution References and Further Reading538588
Node: Statistics540642
Node: Mean and standard deviation and variance541916
Node: Absolute deviation544959
Node: Higher moments (skewness and kurtosis)546243
Node: Autocorrelation548370
Node: Covariance549173
Node: Weighted Samples550111
Node: Maximum and Minimum values555367
Node: Median and Percentiles557803
Node: Example statistical programs560210
Node: Statistics References and Further Reading562920
Node: Histograms564104
Node: The histogram struct565858
Node: Histogram allocation567655
Node: Copying Histograms570633
Node: Updating and accessing histogram elements571297
Node: Searching histogram ranges574546
Node: Histogram Statistics575534
Node: Histogram Operations577377
Node: Reading and writing histograms579420
Node: Resampling from histograms582438
Node: The histogram probability distribution struct583226
Node: Example programs for histograms586240
Node: Two dimensional histograms588360
Node: The 2D histogram struct589069
Node: 2D Histogram allocation590856
Node: Copying 2D Histograms592911
Node: Updating and accessing 2D histogram elements593602
Node: Searching 2D histogram ranges597232
Node: 2D Histogram Statistics598238
Node: 2D Histogram Operations601019
Node: Reading and writing 2D histograms603169
Node: Resampling from 2D histograms606810
Node: Example programs for 2D histograms609812
Node: N-tuples611864
Node: The ntuple struct613114
Node: Creating ntuples613582
Node: Opening an existing ntuple file614239
Node: Writing ntuples614857
Node: Reading ntuples615306
Node: Closing an ntuple file615626
Node: Histogramming ntuple values615955
Node: Example ntuple programs617948
Node: Ntuple References and Further Reading621389
Node: Monte Carlo Integration621700
Node: Monte Carlo Interface622941
Node: PLAIN Monte Carlo625572
Node: MISER627996
Node: VEGAS633816
Node: Monte Carlo Examples642109
Node: Monte Carlo Integration References and Further Reading648136
Node: Simulated Annealing648888
Node: Simulated Annealing algorithm650034
Node: Simulated Annealing functions651204
Node: Examples with Simulated Annealing655699
Node: Trivial example656184
Node: Traveling Salesman Problem658953
Node: Ordinary Differential Equations662368
Node: Defining the ODE System663183
Node: Stepping Functions665044
Node: Adaptive Step-size Control668462
Node: Evolution673922
Node: ODE Example programs675971
Node: ODE References and Further Reading681009
Node: Interpolation681638
Node: Introduction to Interpolation682645
Node: Interpolation Functions683076
Node: Interpolation Types684239
Node: Index Look-up and Acceleration686205
Node: Evaluation of Interpolating Functions687821
Node: Higher-level Interface690187
Node: Interpolation Example programs692047
Node: Interpolation References and Further Reading693752
Node: Numerical Differentiation694182
Node: Numerical Differentiation functions694764
Node: Numerical Differentiation Examples697598
Node: Numerical Differentiation References699042
Node: Chebyshev Approximations699583
Node: The gsl_cheb_series struct700598
Node: Creation and Calculation of Chebyshev Series701402
Node: Chebyshev Series Evaluation702366
Node: Derivatives and Integrals703726
Node: Chebyshev Approximation examples704956
Node: Chebyshev Approximation References and Further Reading706489
Node: Series Acceleration706928
Node: Acceleration functions707695
Node: Acceleration functions without error estimation709924
Node: Example of accelerating a series712530
Node: Series Acceleration References714942
Node: Discrete Hankel Transforms715821
Node: Discrete Hankel Transform Definition716284
Node: Discrete Hankel Transform Functions718120
Node: Discrete Hankel Transform References719624
Node: One dimensional Root-Finding720018
Node: Root Finding Overview721272
Node: Root Finding Caveats723120
Node: Initializing the Solver724874
Node: Providing the function to solve727489
Node: Search Bounds and Guesses731290
Node: Root Finding Iteration732141
Node: Search Stopping Parameters733974
Node: Root Bracketing Algorithms736475
Node: Root Finding Algorithms using Derivatives739761
Node: Root Finding Examples743252
Node: Root Finding References and Further Reading750606
Node: One dimensional Minimization751233
Node: Minimization Overview752529
Node: Minimization Caveats754215
Node: Initializing the Minimizer755542
Node: Providing the function to minimize757769
Node: Minimization Iteration758237
Node: Minimization Stopping Parameters760349
Node: Minimization Algorithms761947
Node: Minimization Examples764376
Node: Minimization References and Further Reading767372
Node: Multidimensional Root-Finding767818
Node: Overview of Multidimensional Root Finding769301
Node: Initializing the Multidimensional Solver771478
Node: Providing the multidimensional system of equations to solve774648
Node: Iteration of the multidimensional solver779592
Node: Search Stopping Parameters for the multidimensional solver781759
Node: Algorithms using Derivatives783484
Node: Algorithms without Derivatives788217
Node: Example programs for Multidimensional Root finding790996
Node: References and Further Reading for Multidimensional Root Finding799783
Node: Multidimensional Minimization801012
Node: Multimin Overview802298
Node: Multimin Caveats804286
Node: Initializing the Multidimensional Minimizer805025
Node: Providing a function to minimize807924
Node: Multimin Iteration811622
Node: Multimin Stopping Criteria813591
Node: Multimin Algorithms815131
Node: Multimin Examples819380
Node: Multimin References and Further Reading826137
Node: Least-Squares Fitting826747
Node: Linear regression827678
Node: Linear fitting without a constant term830268
Node: Multi-parameter fitting832657
Node: Fitting Examples836406
Node: Fitting References and Further Reading843236
Node: Nonlinear Least-Squares Fitting844045
Node: Overview of Nonlinear Least-Squares Fitting845493
Node: Initializing the Nonlinear Least-Squares Solver846373
Node: Providing the Function to be Minimized849032
Node: Iteration of the Minimization Algorithm851668
Node: Search Stopping Parameters for Minimization Algorithms852992
Node: Minimization Algorithms using Derivatives855074
Node: Minimization Algorithms without Derivatives858307
Node: Computing the covariance matrix of best fit parameters858689
Node: Example programs for Nonlinear Least-Squares Fitting859747
Node: References and Further Reading for Nonlinear Least-Squares Fitting867141
Node: Physical Constants867864
Node: Fundamental Constants869260
Node: Astronomy and Astrophysics870643
Node: Atomic and Nuclear Physics871298
Node: Measurement of Time872854
Node: Imperial Units873274
Node: Nautical Units873696
Node: Printers Units874014
Node: Volume874301
Node: Mass and Weight874819
Node: Thermal Energy and Power875612
Node: Pressure876023
Node: Viscosity876624
Node: Light and Illumination876888
Node: Radioactivity877468
Node: Force and Energy877791
Node: Prefixes878183
Node: Physical Constant Examples878914
Node: Physical Constant References and Further Reading880706
Node: IEEE floating-point arithmetic881062
Node: Representation of floating point numbers881642
Node: Setting up your IEEE environment886155
Node: IEEE References and Further Reading892092
Node: Debugging Numerical Programs893090
Node: Using gdb893552
Node: Examining floating point registers896906
Node: Handling floating point exceptions898183
Node: GCC warning options for numerical programs899589
Node: Debugging References903774
Node: Contributors to GSL904316
Node: Autoconf Macros906324
Node: GSL CBLAS Library910374
Node: Level 1 CBLAS Functions910879
Node: Level 2 CBLAS Functions916025
Node: Level 3 CBLAS Functions932387
Node: GSL CBLAS Examples941906
Node: Free Software Needs Free Documentation943507
Node: GNU General Public License948574
Node: GNU Free Documentation License967867
Node: Function Index990303
Node: Variable Index1108421
Node: Type Index1109231
Node: Concept Index1111160

End Tag Table
