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: 295768
gsl-ref.info-3: 594317
gsl-ref.info-4: 893991

Tag Table:
(Indirect)
Node: Top228
Node: Introduction2078
Node: Routines available in GSL2726
Node: GSL is Free Software4364
Node: Obtaining GSL6693
Node: No Warranty7833
Node: Reporting Bugs8261
Node: Further Information9057
Node: Conventions used in this manual9759
Node: Using the library10515
Node: An Example Program11072
Node: Compiling and Linking11773
Node: Shared Libraries14657
Node: ANSI C Compliance15757
Node: Inline functions16836
Node: Long double17843
Node: Portability functions19233
Node: Alternative optimized functions20627
Node: Support for different numeric types22075
Node: Compatibility with C++25133
Node: Aliasing of arrays25445
Node: Thread-safety26186
Node: Code Reuse27253
Node: Error Handling27880
Node: Error Reporting28626
Node: Error Codes30515
Node: Error Handlers32265
Node: Using GSL error reporting in your own functions35911
Node: Error Reporting Examples37859
Node: Mathematical Functions39077
Node: Mathematical Constants39834
Node: Infinities and Not-a-number40955
Node: Elementary Functions42009
Node: Small integer powers44246
Node: Testing the Sign of Numbers45790
Node: Testing for Odd and Even Numbers46212
Node: Maximum and Minimum functions46758
Node: Approximate Comparison of Floating Point Numbers48824
Node: Complex Numbers50023
Node: Complex numbers51364
Node: Properties of complex numbers53152
Node: Complex arithmetic operators54127
Node: Elementary Complex Functions56850
Node: Complex Trigonometric Functions58654
Node: Inverse Complex Trigonometric Functions59861
Node: Complex Hyperbolic Functions62447
Node: Inverse Complex Hyperbolic Functions63729
Node: Complex Number References and Further Reading65553
Node: Polynomials66942
Node: Polynomial Evaluation67705
Node: Divided Difference Representation of Polynomials68156
Node: Quadratic Equations69814
Node: Cubic Equations71581
Node: General Polynomial Equations72926
Node: Roots of Polynomials Examples74794
Node: Roots of Polynomials References and Further Reading76215
Node: Special Functions77150
Node: Special Function Usage79092
Node: The gsl_sf_result struct80267
Node: Special Function Modes81523
Node: Airy Functions and Derivatives82451
Node: Airy Functions83139
Node: Derivatives of Airy Functions84479
Node: Zeros of Airy Functions85818
Node: Zeros of Derivatives of Airy Functions86521
Node: Bessel Functions87264
Node: Regular Cylindrical Bessel Functions88448
Node: Irregular Cylindrical Bessel Functions89754
Node: Regular Modified Cylindrical Bessel Functions91192
Node: Irregular Modified Cylindrical Bessel Functions93995
Node: Regular Spherical Bessel Functions96939
Node: Irregular Spherical Bessel Functions99130
Node: Regular Modified Spherical Bessel Functions100797
Node: Irregular Modified Spherical Bessel Functions102780
Node: Regular Bessel Function - Fractional Order104823
Node: Irregular Bessel Functions - Fractional Order105807
Node: Regular Modified Bessel Functions - Fractional Order106374
Node: Irregular Modified Bessel Functions - Fractional Order107281
Node: Zeros of Regular Bessel Functions108496
Node: Clausen Functions109579
Node: Coulomb Functions110173
Node: Normalized Hydrogenic Bound States110596
Node: Coulomb Wave Functions111602
Node: Coulomb Wave Function Normalization Constant114984
Node: Coupling Coefficients115723
Node: 3-j Symbols116438
Node: 6-j Symbols117028
Node: 9-j Symbols117638
Node: Dawson Function118330
Node: Debye Functions118887
Node: Dilogarithm120164
Node: Real Argument120449
Node: Complex Argument121002
Node: Elementary Operations121456
Node: Elliptic Integrals122268
Node: Definition of Legendre Forms122731
Node: Definition of Carlson Forms123566
Node: Legendre Form of Complete Elliptic Integrals124264
Node: Legendre Form of Incomplete Elliptic Integrals125130
Node: Carlson Forms126847
Node: Elliptic Functions (Jacobi)128372
Node: Error Functions128942
Node: Error Function129383
Node: Complementary Error Function129727
Node: Log Complementary Error Function130172
Node: Probability functions130608
Node: Exponential Functions131833
Node: Exponential Function132206
Node: Relative Exponential Functions133399
Node: Exponentiation With Error Estimate135048
Node: Exponential Integrals136239
Node: Exponential Integral136711
Node: Ei(x)137338
Node: Hyperbolic Integrals137769
Node: Ei_3(x)138406
Node: Trigonometric Integrals138771
Node: Arctangent Integral139352
Node: Fermi-Dirac Function139715
Node: Complete Fermi-Dirac Integrals140065
Node: Incomplete Fermi-Dirac Integrals142496
Node: Gamma Function143123
Node: Gegenbauer Functions151103
Node: Hypergeometric Functions152724
Node: Laguerre Functions156925
Node: Lambert W Functions158177
Node: Legendre Functions and Spherical Harmonics159191
Node: Legendre Polynomials159770
Node: Associated Legendre Polynomials and Spherical Harmonics161587
Node: Conical Functions163991
Node: Radial Functions for Hyperbolic Space166085
Node: Logarithm and Related Functions168241
Node: Power Function169843
Node: Psi (Digamma) Function170772
Node: Digamma Function171273
Node: Trigamma Function172082
Node: Polygamma Function172641
Node: Synchrotron Functions173009
Node: Transport Functions173758
Node: Trigonometric Functions174847
Node: Circular Trigonometric Functions175460
Node: Trigonometric Functions for Complex Arguments176447
Node: Hyperbolic Trigonometric Functions177464
Node: Conversion Functions178049
Node: Restriction Functions178816
Node: Trigonometric Functions With Error Estimates179427
Node: Zeta Functions180171
Node: Riemann Zeta Function180619
Node: Riemann Zeta Function Minus One181280
Node: Hurwitz Zeta Function182033
Node: Eta Function182522
Node: Special Functions Examples183063
Node: Special Functions References and Further Reading184788
Node: Vectors and Matrices185884
Node: Data types186639
Node: Blocks187834
Node: Block allocation188742
Node: Reading and writing blocks190131
Node: Example programs for blocks192179
Node: Vectors192811
Node: Vector allocation194673
Node: Accessing vector elements196194
Node: Initializing vector elements198401
Node: Reading and writing vectors199080
Node: Vector views201144
Node: Copying vectors208557
Node: Exchanging elements209403
Node: Vector operations209947
Node: Finding maximum and minimum elements of vectors211443
Node: Vector properties212950
Node: Example programs for vectors213298
Node: Matrices215482
Node: Matrix allocation218332
Node: Accessing matrix elements219902
Node: Initializing matrix elements221594
Node: Reading and writing matrices222375
Node: Matrix views224452
Node: Creating row and column views231570
Node: Copying matrices234716
Node: Copying rows and columns235298
Node: Exchanging rows and columns236959
Node: Matrix operations238420
Node: Finding maximum and minimum elements of matrices240040
Node: Matrix properties241894
Node: Example programs for matrices242245
Node: Vector and Matrix References and Further Reading246195
Node: Permutations246673
Node: The Permutation struct247957
Node: Permutation allocation248451
Node: Accessing permutation elements249872
Node: Permutation properties250625
Node: Permutation functions251313
Node: Applying Permutations252558
Node: Reading and writing permutations254470
Node: Permutations in Cyclic Form256639
Node: Permutation Examples259866
Node: Permutation References and Further Reading262317
Node: Combinations262981
Node: The Combination struct263851
Node: Combination allocation264391
Node: Accessing combination elements266161
Node: Combination properties266721
Node: Combination functions267596
Node: Reading and writing combinations268524
Node: Combination Examples270700
Node: Combination References and Further Reading272020
Node: Sorting272588
Node: Sorting objects273528
Node: Sorting vectors276427
Node: Selecting the k smallest or largest elements278986
Node: Computing the rank282285
Node: Sorting Examples283491
Node: Sorting References and Further Reading285112
Node: BLAS Support285648
Node: GSL BLAS Interface288616
Node: Level 1 GSL BLAS Interface289093
Node: Level 2 GSL BLAS Interface295768
Node: Level 3 GSL BLAS Interface305022
Node: BLAS Examples316099
Node: BLAS References and Further Reading317552
Node: Linear Algebra318896
Node: LU Decomposition320132
Node: QR Decomposition325113
Node: QR Decomposition with Column Pivoting330753
Node: Singular Value Decomposition335120
Node: Cholesky Decomposition338414
Node: Tridiagonal Decomposition of Real Symmetric Matrices340312
Node: Tridiagonal Decomposition of Hermitian Matrices342147
Node: Bidiagonalization344062
Node: Householder Transformations346464
Node: Householder solver for linear systems348296
Node: Tridiagonal Systems349187
Node: Linear Algebra Examples351682
Node: Linear Algebra References and Further Reading353713
Node: Eigensystems355191
Node: Real Symmetric Matrices356230
Node: Complex Hermitian Matrices358446
Node: Sorting Eigenvalues and Eigenvectors360948
Node: Eigenvalue and Eigenvector Examples362267
Node: Eigenvalue and Eigenvector References364632
Node: Fast Fourier Transforms365330
Node: Mathematical Definitions366533
Node: Overview of complex data FFTs368928
Node: Radix-2 FFT routines for complex data371866
Node: Mixed-radix FFT routines for complex data376105
Node: Overview of real data FFTs385483
Node: Radix-2 FFT routines for real data387910
Node: Mixed-radix FFT routines for real data390736
Node: FFT References and Further Reading401385
Node: Numerical Integration404242
Node: Numerical Integration Introduction405781
Node: QNG non-adaptive Gauss-Kronrod integration409235
Node: QAG adaptive integration410494
Node: QAGS adaptive integration with singularities413121
Node: QAGP adaptive integration with known singular points414908
Node: QAGI adaptive integration on infinite intervals416208
Node: QAWC adaptive integration for Cauchy principal values418430
Node: QAWS adaptive integration for singular functions419593
Node: QAWO adaptive integration for oscillatory functions422818
Node: QAWF adaptive integration for Fourier integrals426568
Node: Numerical integration error codes429146
Node: Numerical integration examples429902
Node: Numerical integration References and Further Reading431935
Node: Random Number Generation432651
Node: General comments on random numbers434147
Node: The Random Number Generator Interface436087
Node: Random number generator initialization437435
Node: Sampling from a random number generator439432
Node: Auxiliary random number generator functions441904
Node: Random number environment variables444226
Node: Copying random number generator state446751
Node: Reading and writing random number generator state447703
Node: Random number generator algorithms449103
Node: Unix random number generators458488
Node: Other random number generators462202
Node: Random Number Generator Performance471486
Node: Random Number Generator Examples472797
Node: Random Number References and Further Reading474374
Node: Random Number Acknowledgements475871
Node: Quasi-Random Sequences476345
Node: Quasi-random number generator initialization477365
Node: Sampling from a quasi-random number generator478263
Node: Auxiliary quasi-random number generator functions478857
Node: Saving and resorting quasi-random number generator state479790
Node: Quasi-random number generator algorithms480576
Node: Quasi-random number generator examples481339
Node: Quasi-random number references482329
Node: Random Number Distributions482839
Node: Random Number Distribution Introduction485684
Node: The Gaussian Distribution486736
Node: The Gaussian Tail Distribution489146
Node: The Bivariate Gaussian Distribution490761
Node: The Exponential Distribution492060
Node: The Laplace Distribution493181
Node: The Exponential Power Distribution494260
Node: The Cauchy Distribution495212
Node: The Rayleigh Distribution496444
Node: The Rayleigh Tail Distribution497598
Node: The Landau Distribution498454
Node: The Levy alpha-Stable Distributions499392
Node: The Levy skew alpha-Stable Distribution500435
Node: The Gamma Distribution502032
Node: The Flat (Uniform) Distribution503177
Node: The Lognormal Distribution504299
Node: The Chi-squared Distribution505627
Node: The F-distribution507011
Node: The t-distribution508433
Node: The Beta Distribution509807
Node: The Logistic Distribution510777
Node: The Pareto Distribution511886
Node: Spherical Vector Distributions513026
Node: The Weibull Distribution515809
Node: The Type-1 Gumbel Distribution516983
Node: The Type-2 Gumbel Distribution518200
Node: The Dirichlet Distribution519411
Node: General Discrete Distributions521062
Node: The Poisson Distribution524909
Node: The Bernoulli Distribution525624
Node: The Binomial Distribution526350
Node: The Multinomial Distribution527212
Node: The Negative Binomial Distribution528848
Node: The Pascal Distribution529851
Node: The Geometric Distribution530674
Node: The Hypergeometric Distribution531478
Node: The Logarithmic Distribution532465
Node: Shuffling and Sampling533241
Node: Random Number Distribution Examples536079
Node: Random Number Distribution References and Further Reading539303
Node: Statistics541357
Node: Mean and standard deviation and variance542631
Node: Absolute deviation545674
Node: Higher moments (skewness and kurtosis)546958
Node: Autocorrelation549085
Node: Covariance549888
Node: Weighted Samples550826
Node: Maximum and Minimum values556082
Node: Median and Percentiles558518
Node: Example statistical programs560925
Node: Statistics References and Further Reading563635
Node: Histograms564819
Node: The histogram struct566573
Node: Histogram allocation568370
Node: Copying Histograms571348
Node: Updating and accessing histogram elements572012
Node: Searching histogram ranges575261
Node: Histogram Statistics576249
Node: Histogram Operations578092
Node: Reading and writing histograms580135
Node: Resampling from histograms583153
Node: The histogram probability distribution struct583941
Node: Example programs for histograms586955
Node: Two dimensional histograms589075
Node: The 2D histogram struct589784
Node: 2D Histogram allocation591571
Node: Copying 2D Histograms593626
Node: Updating and accessing 2D histogram elements594317
Node: Searching 2D histogram ranges597947
Node: 2D Histogram Statistics598952
Node: 2D Histogram Operations601733
Node: Reading and writing 2D histograms603883
Node: Resampling from 2D histograms607524
Node: Example programs for 2D histograms610526
Node: N-tuples612591
Node: The ntuple struct613841
Node: Creating ntuples614309
Node: Opening an existing ntuple file614965
Node: Writing ntuples615582
Node: Reading ntuples616031
Node: Closing an ntuple file616351
Node: Histogramming ntuple values616680
Node: Example ntuple programs618673
Node: Ntuple References and Further Reading622114
Node: Monte Carlo Integration622425
Node: Monte Carlo Interface623666
Node: PLAIN Monte Carlo626299
Node: MISER628723
Node: VEGAS634546
Node: Monte Carlo Examples642839
Node: Monte Carlo Integration References and Further Reading648867
Node: Simulated Annealing649619
Node: Simulated Annealing algorithm650765
Node: Simulated Annealing functions651935
Node: Examples with Simulated Annealing656434
Node: Trivial example656919
Node: Traveling Salesman Problem659688
Node: Ordinary Differential Equations663098
Node: Defining the ODE System663913
Node: Stepping Functions665774
Node: Adaptive Step-size Control669196
Node: Evolution674655
Node: ODE Example programs676704
Node: ODE References and Further Reading681742
Node: Interpolation682371
Node: Introduction to Interpolation683378
Node: Interpolation Functions683809
Node: Interpolation Types684972
Node: Index Look-up and Acceleration686938
Node: Evaluation of Interpolating Functions688554
Node: Higher-level Interface690920
Node: Interpolation Example programs692780
Node: Interpolation References and Further Reading694485
Node: Numerical Differentiation694915
Node: Numerical Differentiation functions695498
Node: Numerical Differentiation Examples698332
Node: Numerical Differentiation References699776
Node: Chebyshev Approximations700317
Node: The gsl_cheb_series struct701332
Node: Creation and Calculation of Chebyshev Series702136
Node: Chebyshev Series Evaluation703100
Node: Derivatives and Integrals704460
Node: Chebyshev Approximation examples705690
Node: Chebyshev Approximation References and Further Reading707223
Node: Series Acceleration707662
Node: Acceleration functions708421
Node: Acceleration functions without error estimation710650
Node: Example of accelerating a series713256
Node: Series Acceleration References715668
Node: Wavelet Transforms716549
Node: DWT Definitions717084
Node: DWT Initialization718023
Node: DWT Transform Functions720617
Node: DWT in one dimension721142
Node: DWT in two dimension723128
Node: DWT Examples727719
Node: DWT References729423
Node: Discrete Hankel Transforms731582
Node: Discrete Hankel Transform Definition732044
Node: Discrete Hankel Transform Functions733880
Node: Discrete Hankel Transform References735384
Node: One dimensional Root-Finding735778
Node: Root Finding Overview737032
Node: Root Finding Caveats738880
Node: Initializing the Solver740634
Node: Providing the function to solve743249
Node: Search Bounds and Guesses747048
Node: Root Finding Iteration747899
Node: Search Stopping Parameters749732
Node: Root Bracketing Algorithms752233
Node: Root Finding Algorithms using Derivatives755518
Node: Root Finding Examples759008
Node: Root Finding References and Further Reading766362
Node: One dimensional Minimization766989
Node: Minimization Overview768285
Node: Minimization Caveats769971
Node: Initializing the Minimizer771298
Node: Providing the function to minimize773525
Node: Minimization Iteration773993
Node: Minimization Stopping Parameters776105
Node: Minimization Algorithms777703
Node: Minimization Examples780132
Node: Minimization References and Further Reading783128
Node: Multidimensional Root-Finding783574
Node: Overview of Multidimensional Root Finding785057
Node: Initializing the Multidimensional Solver787234
Node: Providing the multidimensional system of equations to solve790404
Node: Iteration of the multidimensional solver795347
Node: Search Stopping Parameters for the multidimensional solver797514
Node: Algorithms using Derivatives799239
Node: Algorithms without Derivatives803971
Node: Example programs for Multidimensional Root finding806750
Node: References and Further Reading for Multidimensional Root Finding815537
Node: Multidimensional Minimization816766
Node: Multimin Overview818052
Node: Multimin Caveats820040
Node: Initializing the Multidimensional Minimizer820779
Node: Providing a function to minimize823678
Node: Multimin Iteration827375
Node: Multimin Stopping Criteria829344
Node: Multimin Algorithms830884
Node: Multimin Examples835132
Node: Multimin References and Further Reading841889
Node: Least-Squares Fitting842499
Node: Linear regression843431
Node: Linear fitting without a constant term846021
Node: Multi-parameter fitting848410
Node: Fitting Examples852159
Node: Fitting References and Further Reading858989
Node: Nonlinear Least-Squares Fitting859799
Node: Overview of Nonlinear Least-Squares Fitting861247
Node: Initializing the Nonlinear Least-Squares Solver862127
Node: Providing the Function to be Minimized864786
Node: Iteration of the Minimization Algorithm867427
Node: Search Stopping Parameters for Minimization Algorithms869241
Node: Minimization Algorithms using Derivatives871323
Node: Minimization Algorithms without Derivatives874560
Node: Computing the covariance matrix of best fit parameters874942
Node: Example programs for Nonlinear Least-Squares Fitting876000
Node: References and Further Reading for Nonlinear Least-Squares Fitting883340
Node: Physical Constants884064
Node: Fundamental Constants885460
Node: Astronomy and Astrophysics886843
Node: Atomic and Nuclear Physics887498
Node: Measurement of Time889054
Node: Imperial Units889474
Node: Nautical Units889896
Node: Printers Units890214
Node: Volume890501
Node: Mass and Weight891019
Node: Thermal Energy and Power891812
Node: Pressure892223
Node: Viscosity892824
Node: Light and Illumination893088
Node: Radioactivity893668
Node: Force and Energy893991
Node: Prefixes894383
Node: Physical Constant Examples895114
Node: Physical Constant References and Further Reading896906
Node: IEEE floating-point arithmetic897262
Node: Representation of floating point numbers897842
Node: Setting up your IEEE environment902355
Node: IEEE References and Further Reading908291
Node: Debugging Numerical Programs909292
Node: Using gdb909754
Node: Examining floating point registers913108
Node: Handling floating point exceptions914385
Node: GCC warning options for numerical programs915791
Node: Debugging References919976
Node: Contributors to GSL920518
Node: Autoconf Macros922724
Node: GSL CBLAS Library926774
Node: Level 1 CBLAS Functions927279
Node: Level 2 CBLAS Functions932425
Node: Level 3 CBLAS Functions948787
Node: GSL CBLAS Examples958306
Node: Free Software Needs Free Documentation959907
Node: GNU General Public License964974
Node: GNU Free Documentation License984267
Node: Function Index1006703
Node: Variable Index1126445
Node: Type Index1127255
Node: Concept Index1129184

End Tag Table
