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: 292512
gsl-ref.info-3: 589353
gsl-ref.info-4: 887502

Tag Table:
(Indirect)
Node: Top228
Node: Introduction1930
Node: Routines available in GSL2565
Node: GSL is Free Software4203
Node: Obtaining GSL6437
Node: No Warranty7567
Node: Reporting Bugs8000
Node: Further Information8795
Node: Using the library9306
Node: An Example Program9840
Node: ANSI C Compliance10548
Node: Compiling and Linking11607
Node: Shared Libraries14164
Node: Inline functions15117
Node: Long double16115
Node: Portability functions17505
Node: Alternative optimized functions18899
Node: Support for different numeric types20347
Node: Compatibility with C++23405
Node: Aliasing of arrays23717
Node: Thread-safety24458
Node: Code Reuse25525
Node: Error Handling26152
Node: Error Reporting26898
Node: Error Codes28787
Node: Error Handlers30537
Node: Using GSL error reporting in your own functions34183
Node: Error Reporting Examples36131
Node: Mathematical Functions37349
Node: Mathematical Constants38106
Node: Infinities and Not-a-number39227
Node: Elementary Functions40281
Node: Small integer powers42518
Node: Testing the Sign of Numbers44062
Node: Testing for Odd and Even Numbers44484
Node: Maximum and Minimum functions45030
Node: Approximate Comparison of Floating Point Numbers47096
Node: Complex Numbers48295
Node: Complex numbers49636
Node: Properties of complex numbers51424
Node: Complex arithmetic operators52399
Node: Elementary Complex Functions55122
Node: Complex Trigonometric Functions56926
Node: Inverse Complex Trigonometric Functions58133
Node: Complex Hyperbolic Functions60719
Node: Inverse Complex Hyperbolic Functions62001
Node: Complex Number References and Further Reading63825
Node: Polynomials65214
Node: Polynomial Evaluation65977
Node: Divided Difference Representation of Polynomials66428
Node: Quadratic Equations68083
Node: Cubic Equations69850
Node: General Polynomial Equations71195
Node: Roots of Polynomials Examples73063
Node: Roots of Polynomials References and Further Reading74484
Node: Special Functions75245
Node: Special Function Usage77187
Node: The gsl_sf_result struct78363
Node: Special Function Modes79619
Node: Airy Functions and Derivatives80547
Node: Airy Functions81235
Node: Derivatives of Airy Functions82575
Node: Zeros of Airy Functions83914
Node: Zeros of Derivatives of Airy Functions84617
Node: Bessel Functions85360
Node: Regular Cylindrical Bessel Functions86544
Node: Irregular Cylindrical Bessel Functions87850
Node: Regular Modified Cylindrical Bessel Functions89288
Node: Irregular Modified Cylindrical Bessel Functions92091
Node: Regular Spherical Bessel Functions95035
Node: Irregular Spherical Bessel Functions97226
Node: Regular Modified Spherical Bessel Functions98893
Node: Irregular Modified Spherical Bessel Functions100876
Node: Regular Bessel Function - Fractional Order102919
Node: Irregular Bessel Functions - Fractional Order103903
Node: Regular Modified Bessel Functions - Fractional Order104470
Node: Irregular Modified Bessel Functions - Fractional Order105377
Node: Zeros of Regular Bessel Functions106592
Node: Clausen Functions107675
Node: Coulomb Functions108269
Node: Normalized Hydrogenic Bound States108692
Node: Coulomb Wave Functions109698
Node: Coulomb Wave Function Normalization Constant113080
Node: Coupling Coefficients113819
Node: 3-j Symbols114534
Node: 6-j Symbols115124
Node: 9-j Symbols115734
Node: Dawson Function116426
Node: Debye Functions116983
Node: Dilogarithm118260
Node: Real Argument118545
Node: Complex Argument119098
Node: Elementary Operations119552
Node: Elliptic Integrals120364
Node: Definition of Legendre Forms120827
Node: Definition of Carlson Forms121662
Node: Legendre Form of Complete Elliptic Integrals122360
Node: Legendre Form of Incomplete Elliptic Integrals123226
Node: Carlson Forms124943
Node: Elliptic Functions (Jacobi)126468
Node: Error Functions127038
Node: Error Function127479
Node: Complementary Error Function127823
Node: Log Complementary Error Function128268
Node: Probability functions128704
Node: Exponential Functions129910
Node: Exponential Function130283
Node: Relative Exponential Functions131476
Node: Exponentiation With Error Estimate133125
Node: Exponential Integrals134316
Node: Exponential Integral134788
Node: Ei(x)135415
Node: Hyperbolic Integrals135847
Node: Ei_3(x)136484
Node: Trigonometric Integrals136849
Node: Arctangent Integral137430
Node: Fermi-Dirac Function137793
Node: Complete Fermi-Dirac Integrals138143
Node: Incomplete Fermi-Dirac Integrals140574
Node: Gamma Function141201
Node: Gegenbauer Functions149179
Node: Hypergeometric Functions150800
Node: Laguerre Functions155001
Node: Lambert W Functions156252
Node: Legendre Functions and Spherical Harmonics157266
Node: Legendre Polynomials157845
Node: Associated Legendre Polynomials and Spherical Harmonics159662
Node: Conical Functions162066
Node: Radial Functions for Hyperbolic Space164160
Node: Logarithm and Related Functions166315
Node: Power Function167917
Node: Psi (Digamma) Function168846
Node: Digamma Function169347
Node: Trigamma Function170156
Node: Polygamma Function170524
Node: Synchrotron Functions170892
Node: Transport Functions171641
Node: Trigonometric Functions172730
Node: Circular Trigonometric Functions173343
Node: Trigonometric Functions for Complex Arguments174330
Node: Hyperbolic Trigonometric Functions175347
Node: Conversion Functions175932
Node: Restriction Functions176699
Node: Trigonometric Functions With Error Estimates177310
Node: Zeta Functions178054
Node: Riemann Zeta Function178466
Node: Hurwitz Zeta Function179117
Node: Eta Function179596
Node: Special Functions Examples180137
Node: Special Functions References and Further Reading181862
Node: Vectors and Matrices182958
Node: Data types183713
Node: Blocks184908
Node: Block allocation185816
Node: Reading and writing blocks187205
Node: Example programs for blocks189253
Node: Vectors189885
Node: Vector allocation191747
Node: Accessing vector elements193268
Node: Initializing vector elements195382
Node: Reading and writing vectors196061
Node: Vector views198125
Node: Copying vectors205303
Node: Exchanging elements206149
Node: Vector operations206693
Node: Finding maximum and minimum elements of vectors208189
Node: Vector properties209696
Node: Example programs for vectors210044
Node: Matrices212228
Node: Matrix allocation215078
Node: Accessing matrix elements216648
Node: Initializing matrix elements218337
Node: Reading and writing matrices219118
Node: Matrix views221195
Node: Creating row and column views228313
Node: Copying matrices231459
Node: Copying rows and columns232041
Node: Exchanging rows and columns233702
Node: Matrix operations235163
Node: Finding maximum and minimum elements of matrices236783
Node: Matrix properties238637
Node: Example programs for matrices238988
Node: Vector and Matrix References and Further Reading242939
Node: Permutations243417
Node: The Permutation struct244701
Node: Permutation allocation245195
Node: Accessing permutation elements246616
Node: Permutation properties247369
Node: Permutation functions248057
Node: Applying Permutations249302
Node: Reading and writing permutations251214
Node: Permutations in Cyclic Form253383
Node: Permutation Examples256610
Node: Permutation References and Further Reading259061
Node: Combinations259725
Node: The Combination struct260595
Node: Combination allocation261135
Node: Accessing combination elements262905
Node: Combination properties263465
Node: Combination functions264340
Node: Reading and writing combinations265268
Node: Combination Examples267444
Node: Combination References and Further Reading268764
Node: Sorting269332
Node: Sorting objects270272
Node: Sorting vectors273171
Node: Selecting the k smallest or largest elements275730
Node: Computing the rank279029
Node: Sorting Examples280235
Node: Sorting References and Further Reading281856
Node: BLAS Support282392
Node: GSL BLAS Interface285360
Node: Level 1 GSL BLAS Interface285837
Node: Level 2 GSL BLAS Interface292512
Node: Level 3 GSL BLAS Interface301766
Node: BLAS Examples312843
Node: BLAS References and Further Reading314296
Node: Linear Algebra315640
Node: LU Decomposition316876
Node: QR Decomposition321857
Node: QR Decomposition with Column Pivoting327496
Node: Singular Value Decomposition331861
Node: Cholesky Decomposition335155
Node: Tridiagonal Decomposition of Real Symmetric Matrices337053
Node: Tridiagonal Decomposition of Hermitian Matrices338888
Node: Bidiagonalization340803
Node: Householder Transformations343205
Node: Householder solver for linear systems345039
Node: Tridiagonal Systems345930
Node: Linear Algebra Examples347025
Node: Linear Algebra References and Further Reading349056
Node: Eigensystems350534
Node: Real Symmetric Matrices351570
Node: Complex Hermitian Matrices353786
Node: Sorting Eigenvalues and Eigenvectors356288
Node: Eigenvalue and Eigenvector Examples357607
Node: Eigenvalue and Eigenvector References359972
Node: Fast Fourier Transforms360670
Node: Mathematical Definitions361873
Node: Overview of complex data FFTs364268
Node: Radix-2 FFT routines for complex data366905
Node: Mixed-radix FFT routines for complex data371144
Node: Overview of real data FFTs380523
Node: Radix-2 FFT routines for real data382950
Node: Mixed-radix FFT routines for real data385776
Node: FFT References and Further Reading396425
Node: Numerical Integration399282
Node: Numerical Integration Introduction400821
Node: QNG non-adaptive Gauss-Kronrod integration404275
Node: QAG adaptive integration405534
Node: QAGS adaptive integration with singularities408161
Node: QAGP adaptive integration with known singular points409948
Node: QAGI adaptive integration on infinite intervals411248
Node: QAWC adaptive integration for Cauchy principal values413470
Node: QAWS adaptive integration for singular functions414633
Node: QAWO adaptive integration for oscillatory functions417858
Node: QAWF adaptive integration for Fourier integrals421608
Node: Numerical integration error codes424186
Node: Numerical integration examples424942
Node: Numerical integration References and Further Reading426975
Node: Random Number Generation427691
Node: General comments on random numbers429187
Node: The Random Number Generator Interface431127
Node: Random number generator initialization432475
Node: Sampling from a random number generator434472
Node: Auxiliary random number generator functions436944
Node: Random number environment variables439266
Node: Copying random number generator state441791
Node: Reading and writing random number generator state442743
Node: Random number generator algorithms444143
Node: Unix random number generators453528
Node: Other random number generators457242
Node: Random Number Generator Performance466527
Node: Random Number Generator Examples467838
Node: Random Number References and Further Reading469415
Node: Random Number Acknowledgements470912
Node: Quasi-Random Sequences471386
Node: Quasi-random number generator initialization472406
Node: Sampling from a quasi-random number generator473304
Node: Auxiliary quasi-random number generator functions473898
Node: Saving and resorting quasi-random number generator state474831
Node: Quasi-random number generator algorithms475617
Node: Quasi-random number generator examples476380
Node: Quasi-random number references477370
Node: Random Number Distributions477880
Node: Random Number Distribution Introduction480731
Node: The Gaussian Distribution481778
Node: The Gaussian Tail Distribution484188
Node: The Bivariate Gaussian Distribution485803
Node: The Exponential Distribution487102
Node: The Laplace Distribution488223
Node: The Exponential Power Distribution489302
Node: The Cauchy Distribution490254
Node: The Rayleigh Distribution491486
Node: The Rayleigh Tail Distribution492640
Node: The Landau Distribution493496
Node: The Levy alpha-Stable Distributions494434
Node: The Levy skew alpha-Stable Distribution495477
Node: The Gamma Distribution497074
Node: The Flat (Uniform) Distribution498219
Node: The Lognormal Distribution499341
Node: The Chi-squared Distribution500669
Node: The F-distribution502051
Node: The t-distribution503473
Node: The Beta Distribution504847
Node: The Logistic Distribution505817
Node: The Pareto Distribution506926
Node: The Spherical Distribution (2D & 3D)508072
Node: The Weibull Distribution510862
Node: The Type-1 Gumbel Distribution512042
Node: The Type-2 Gumbel Distribution513259
Node: The Dirichlet Distribution514470
Node: General Discrete Distributions516121
Node: The Poisson Distribution519969
Node: The Bernoulli Distribution520684
Node: The Binomial Distribution521410
Node: The Multinomial Distribution522272
Node: The Negative Binomial Distribution523908
Node: The Pascal Distribution524911
Node: The Geometric Distribution525734
Node: The Hypergeometric Distribution526538
Node: The Logarithmic Distribution527503
Node: Shuffling and Sampling528279
Node: Random Number Distribution Examples531115
Node: Random Number Distribution References and Further Reading534339
Node: Statistics536393
Node: Mean and standard deviation and variance537667
Node: Absolute deviation540710
Node: Higher moments (skewness and kurtosis)541994
Node: Autocorrelation544121
Node: Covariance544924
Node: Weighted Samples545862
Node: Maximum and Minimum values551118
Node: Median and Percentiles553554
Node: Example statistical programs555961
Node: Statistics References and Further Reading558671
Node: Histograms559855
Node: The histogram struct561609
Node: Histogram allocation563406
Node: Copying Histograms566384
Node: Updating and accessing histogram elements567048
Node: Searching histogram ranges570297
Node: Histogram Statistics571285
Node: Histogram Operations573128
Node: Reading and writing histograms575171
Node: Resampling from histograms578189
Node: The histogram probability distribution struct578977
Node: Example programs for histograms581991
Node: Two dimensional histograms584111
Node: The 2D histogram struct584820
Node: 2D Histogram allocation586607
Node: Copying 2D Histograms588662
Node: Updating and accessing 2D histogram elements589353
Node: Searching 2D histogram ranges592983
Node: 2D Histogram Statistics593989
Node: 2D Histogram Operations596770
Node: Reading and writing 2D histograms598920
Node: Resampling from 2D histograms602561
Node: Example programs for 2D histograms605563
Node: N-tuples607615
Node: The ntuple struct608865
Node: Creating ntuples609333
Node: Opening an existing ntuple file609990
Node: Writing ntuples610608
Node: Reading ntuples611057
Node: Closing an ntuple file611377
Node: Histogramming ntuple values611706
Node: Example ntuple programs613699
Node: Ntuple References and Further Reading617140
Node: Monte Carlo Integration617451
Node: Monte Carlo Interface618692
Node: PLAIN Monte Carlo621335
Node: MISER623759
Node: VEGAS629579
Node: Monte Carlo Examples637872
Node: Monte Carlo Integration References and Further Reading643899
Node: Simulated Annealing644651
Node: Simulated Annealing algorithm645797
Node: Simulated Annealing functions646967
Node: Examples with Simulated Annealing651462
Node: Trivial example651947
Node: Traveling Salesman Problem654716
Node: Ordinary Differential Equations658131
Node: Defining the ODE System658946
Node: Stepping Functions660807
Node: Adaptive Step-size Control664361
Node: Evolution669701
Node: ODE Example programs671750
Node: ODE References and Further Reading676793
Node: Interpolation677422
Node: Introduction to Interpolation678429
Node: Interpolation Functions678860
Node: Interpolation Types680023
Node: Index Look-up and Acceleration681989
Node: Evaluation of Interpolating Functions683605
Node: Higher-level Interface685971
Node: Interpolation Example programs687831
Node: Interpolation References and Further Reading689536
Node: Numerical Differentiation689966
Node: Numerical Differentiation functions690547
Node: Numerical Differentiation Examples692155
Node: Numerical Differentiation References693577
Node: Chebyshev Approximations693976
Node: The gsl_cheb_series struct694991
Node: Creation and Calculation of Chebyshev Series695795
Node: Chebyshev Series Evaluation696759
Node: Derivatives and Integrals698119
Node: Chebyshev Approximation examples699349
Node: Chebyshev Approximation References and Further Reading700882
Node: Series Acceleration701321
Node: Acceleration functions702088
Node: Acceleration functions without error estimation704317
Node: Example of accelerating a series706923
Node: Series Acceleration References709335
Node: Discrete Hankel Transforms710214
Node: Discrete Hankel Transform Definition710677
Node: Discrete Hankel Transform Functions712513
Node: Discrete Hankel Transform References714017
Node: One dimensional Root-Finding714411
Node: Root Finding Overview715665
Node: Root Finding Caveats717513
Node: Initializing the Solver719267
Node: Providing the function to solve721882
Node: Search Bounds and Guesses725683
Node: Root Finding Iteration726534
Node: Search Stopping Parameters728367
Node: Root Bracketing Algorithms730868
Node: Root Finding Algorithms using Derivatives734154
Node: Root Finding Examples737645
Node: Root Finding References and Further Reading744999
Node: One dimensional Minimization745626
Node: Minimization Overview746922
Node: Minimization Caveats748608
Node: Initializing the Minimizer749935
Node: Providing the function to minimize752162
Node: Minimization Iteration752630
Node: Minimization Stopping Parameters754742
Node: Minimization Algorithms756340
Node: Minimization Examples758769
Node: Minimization References and Further Reading761765
Node: Multidimensional Root-Finding762211
Node: Overview of Multidimensional Root Finding763694
Node: Initializing the Multidimensional Solver765871
Node: Providing the multidimensional system of equations to solve769041
Node: Iteration of the multidimensional solver773985
Node: Search Stopping Parameters for the multidimensional solver776152
Node: Algorithms using Derivatives777877
Node: Algorithms without Derivatives782610
Node: Example programs for Multidimensional Root finding785389
Node: References and Further Reading for Multidimensional Root Finding794176
Node: Multidimensional Minimization795405
Node: Multimin Overview796691
Node: Multimin Caveats798679
Node: Initializing the Multidimensional Minimizer799418
Node: Providing a function to minimize802317
Node: Multimin Iteration806015
Node: Multimin Stopping Criteria807984
Node: Multimin Algorithms809524
Node: Multimin Examples813773
Node: Multimin References and Further Reading820530
Node: Least-Squares Fitting821140
Node: Linear regression822071
Node: Linear fitting without a constant term824661
Node: Multi-parameter fitting827050
Node: Fitting Examples830799
Node: Fitting References and Further Reading837629
Node: Nonlinear Least-Squares Fitting838438
Node: Overview of Nonlinear Least-Squares Fitting839886
Node: Initializing the Nonlinear Least-Squares Solver840766
Node: Providing the Function to be Minimized843425
Node: Iteration of the Minimization Algorithm846061
Node: Search Stopping Parameters for Minimization Algorithms847385
Node: Minimization Algorithms using Derivatives849467
Node: Minimization Algorithms without Derivatives852700
Node: Computing the covariance matrix of best fit parameters853082
Node: Example programs for Nonlinear Least-Squares Fitting854140
Node: References and Further Reading for Nonlinear Least-Squares Fitting861534
Node: Physical Constants862257
Node: Fundamental Constants863653
Node: Astronomy and Astrophysics864675
Node: Atomic and Nuclear Physics865330
Node: Measurement of Time866804
Node: Imperial Units867224
Node: Nautical Units867646
Node: Printers Units867964
Node: Volume868251
Node: Mass and Weight868769
Node: Thermal Energy and Power869562
Node: Pressure869973
Node: Viscosity870574
Node: Light and Illumination870838
Node: Radioactivity871418
Node: Force and Energy871741
Node: Prefixes872133
Node: Physical Constant Examples872864
Node: Physical Constant References and Further Reading874656
Node: IEEE floating-point arithmetic875012
Node: Representation of floating point numbers875592
Node: Setting up your IEEE environment880105
Node: IEEE References and Further Reading886042
Node: Debugging Numerical Programs887040
Node: Using gdb887502
Node: Examining floating point registers890856
Node: Handling floating point exceptions892133
Node: GCC warning options for numerical programs893539
Node: Debugging References897724
Node: Contributors to GSL898266
Node: Autoconf Macros900274
Node: GSL CBLAS Library904324
Node: Level 1 CBLAS Functions904829
Node: Level 2 CBLAS Functions909975
Node: Level 3 CBLAS Functions926337
Node: GSL CBLAS Examples935856
Node: Free Software Needs Free Documentation937457
Node: GNU General Public License942524
Node: GNU Free Documentation License961817
Node: Function Index981730
Node: Variable Index1099332
Node: Type Index1100142
Node: Concept Index1102071

End Tag Table
