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

   Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,
2005, 2006, 2007 The GSL Team.

   Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.2 or
any later version published by the Free Software Foundation; with the
Invariant Sections being "GNU General Public License" and "Free Software
Needs Free Documentation", the Front-Cover text being "A GNU Manual",
and with the Back-Cover Text being (a) (see below).  A copy of the
license is included in the section entitled "GNU Free Documentation
License".

   (a) The Back-Cover Text is: "You have freedom to copy and modify this
GNU Manual, like GNU software."


Indirect:
gsl-ref.info-1: 939
gsl-ref.info-2: 298842
gsl-ref.info-3: 596860
gsl-ref.info-4: 895867
gsl-ref.info-5: 1072596
gsl-ref.info-6: 1311271

Tag Table:
(Indirect)
Node: Top939
Node: Introduction3646
Node: Routines available in GSL4298
Node: GSL is Free Software6213
Node: Obtaining GSL8605
Node: No Warranty9746
Node: Reporting Bugs10252
Node: Further Information11136
Node: Conventions used in this manual12149
Node: Using the library12913
Node: An Example Program13499
Node: Compiling and Linking14203
Node: Linking programs with the library15273
Node: Linking with an alternative BLAS library16418
Node: Shared Libraries17348
Node: ANSI C Compliance18764
Node: Inline functions19857
Node: Long double20900
Node: Portability functions22298
Node: Alternative optimized functions23695
Node: Support for different numeric types25153
Node: Compatibility with C++28216
Node: Aliasing of arrays28788
Node: Thread-safety29539
Node: Deprecated Functions30626
Node: Code Reuse31251
Node: Error Handling31895
Node: Error Reporting32645
Node: Error Codes34537
Node: Error Handlers36393
Node: Using GSL error reporting in your own functions40028
Node: Error Reporting Examples41986
Node: Mathematical Functions43190
Node: Mathematical Constants43951
Node: Infinities and Not-a-number45081
Node: Elementary Functions46149
Node: Small integer powers48404
Node: Testing the Sign of Numbers49966
Node: Testing for Odd and Even Numbers50397
Node: Maximum and Minimum functions50953
Node: Approximate Comparison of Floating Point Numbers53035
Node: Complex Numbers54241
Ref: Complex Numbers-Footnote-155549
Node: Complex numbers55613
Node: Properties of complex numbers57416
Node: Complex arithmetic operators58403
Node: Elementary Complex Functions61149
Node: Complex Trigonometric Functions62969
Node: Inverse Complex Trigonometric Functions64190
Node: Complex Hyperbolic Functions66796
Node: Inverse Complex Hyperbolic Functions68092
Node: Complex Number References and Further Reading70080
Node: Polynomials71476
Node: Polynomial Evaluation72243
Node: Divided Difference Representation of Polynomials72703
Node: Quadratic Equations74372
Node: Cubic Equations76312
Node: General Polynomial Equations77683
Node: Roots of Polynomials Examples80028
Node: Roots of Polynomials References and Further Reading81417
Node: Special Functions82362
Node: Special Function Usage84356
Node: The gsl_sf_result struct85539
Node: Special Function Modes86803
Node: Airy Functions and Derivatives87739
Node: Airy Functions88435
Node: Derivatives of Airy Functions89795
Node: Zeros of Airy Functions91307
Node: Zeros of Derivatives of Airy Functions92026
Node: Bessel Functions92785
Node: Regular Cylindrical Bessel Functions93977
Node: Irregular Cylindrical Bessel Functions95301
Node: Regular Modified Cylindrical Bessel Functions96757
Node: Irregular Modified Cylindrical Bessel Functions99584
Node: Regular Spherical Bessel Functions102552
Node: Irregular Spherical Bessel Functions104764
Node: Regular Modified Spherical Bessel Functions106451
Node: Irregular Modified Spherical Bessel Functions108454
Node: Regular Bessel Function - Fractional Order110517
Node: Irregular Bessel Functions - Fractional Order111515
Node: Regular Modified Bessel Functions - Fractional Order112097
Node: Irregular Modified Bessel Functions - Fractional Order113022
Node: Zeros of Regular Bessel Functions114258
Node: Clausen Functions115361
Node: Coulomb Functions115965
Node: Normalized Hydrogenic Bound States116414
Node: Coulomb Wave Functions117527
Node: Coulomb Wave Function Normalization Constant120937
Node: Coupling Coefficients121690
Node: 3-j Symbols122413
Node: 6-j Symbols123017
Node: 9-j Symbols123641
Node: Dawson Function124347
Node: Debye Functions124914
Node: Dilogarithm126688
Node: Real Argument126983
Node: Complex Argument127552
Node: Elementary Operations128021
Node: Elliptic Integrals128845
Node: Definition of Legendre Forms129417
Node: Definition of Carlson Forms130237
Node: Legendre Form of Complete Elliptic Integrals130934
Node: Legendre Form of Incomplete Elliptic Integrals132502
Node: Carlson Forms134690
Node: Elliptic Functions (Jacobi)136237
Node: Error Functions136818
Node: Error Function137269
Node: Complementary Error Function137642
Node: Log Complementary Error Function138102
Node: Probability functions138554
Node: Exponential Functions139807
Node: Exponential Function140190
Node: Relative Exponential Functions141413
Node: Exponentiation With Error Estimate143084
Node: Exponential Integrals144293
Node: Exponential Integral144775
Node: Ei(x)145425
Node: Hyperbolic Integrals145873
Node: Ei_3(x)146529
Node: Trigonometric Integrals146921
Node: Arctangent Integral147520
Node: Fermi-Dirac Function147920
Node: Complete Fermi-Dirac Integrals148290
Node: Incomplete Fermi-Dirac Integrals150751
Node: Gamma and Beta Functions151394
Node: Gamma Functions151830
Node: Factorials154951
Node: Pochhammer Symbol157504
Node: Incomplete Gamma Functions159016
Node: Beta Functions160265
Node: Incomplete Beta Function161017
Node: Gegenbauer Functions161548
Node: Hypergeometric Functions163198
Node: Laguerre Functions167465
Node: Lambert W Functions169028
Node: Legendre Functions and Spherical Harmonics170066
Node: Legendre Polynomials170655
Node: Associated Legendre Polynomials and Spherical Harmonics172735
Node: Conical Functions175536
Node: Radial Functions for Hyperbolic Space177659
Node: Logarithm and Related Functions179836
Node: Mathieu Functions181460
Node: Mathieu Function Workspace182809
Node: Mathieu Function Characteristic Values183622
Node: Angular Mathieu Functions184690
Node: Radial Mathieu Functions185722
Node: Power Function186960
Node: Psi (Digamma) Function187887
Node: Digamma Function188407
Node: Trigamma Function189237
Node: Polygamma Function189814
Node: Synchrotron Functions190198
Node: Transport Functions190961
Node: Trigonometric Functions192108
Node: Circular Trigonometric Functions192731
Node: Trigonometric Functions for Complex Arguments193740
Node: Hyperbolic Trigonometric Functions194774
Node: Conversion Functions195377
Node: Restriction Functions196160
Node: Trigonometric Functions With Error Estimates197092
Node: Zeta Functions198002
Node: Riemann Zeta Function198460
Node: Riemann Zeta Function Minus One199139
Node: Hurwitz Zeta Function199910
Node: Eta Function200415
Node: Special Functions Examples200974
Node: Special Functions References and Further Reading202668
Node: Vectors and Matrices203775
Node: Data types204534
Node: Blocks205737
Node: Block allocation206653
Node: Reading and writing blocks208137
Node: Example programs for blocks210201
Node: Vectors210828
Node: Vector allocation212714
Node: Accessing vector elements214332
Node: Initializing vector elements216574
Node: Reading and writing vectors217268
Node: Vector views219358
Node: Copying vectors226800
Node: Exchanging elements227660
Node: Vector operations228218
Node: Finding maximum and minimum elements of vectors229732
Node: Vector properties231257
Node: Example programs for vectors231880
Node: Matrices234169
Node: Matrix allocation237027
Node: Accessing matrix elements238694
Node: Initializing matrix elements240402
Node: Reading and writing matrices241198
Node: Matrix views243301
Node: Creating row and column views250441
Node: Copying matrices253612
Node: Copying rows and columns254208
Node: Exchanging rows and columns255885
Node: Matrix operations257363
Node: Finding maximum and minimum elements of matrices259003
Node: Matrix properties260907
Node: Example programs for matrices261655
Node: Vector and Matrix References and Further Reading265726
Node: Permutations266212
Node: The Permutation struct267500
Node: Permutation allocation268004
Node: Accessing permutation elements269438
Node: Permutation properties270201
Node: Permutation functions270900
Node: Applying Permutations272157
Node: Reading and writing permutations274082
Node: Permutations in cyclic form276264
Node: Permutation Examples279689
Node: Permutation References and Further Reading282232
Node: Combinations282906
Node: The Combination struct283751
Node: Combination allocation284303
Node: Accessing combination elements286088
Node: Combination properties286667
Node: Combination functions287553
Node: Reading and writing combinations288493
Node: Combination Examples290693
Node: Combination References and Further Reading292001
Node: Sorting292405
Node: Sorting objects293355
Node: Sorting vectors296266
Node: Selecting the k smallest or largest elements298842
Node: Computing the rank302176
Node: Sorting Examples303377
Node: Sorting References and Further Reading305021
Node: BLAS Support305567
Node: GSL BLAS Interface308542
Node: Level 1 GSL BLAS Interface309029
Node: Level 2 GSL BLAS Interface315772
Node: Level 3 GSL BLAS Interface325066
Node: BLAS Examples336202
Node: BLAS References and Further Reading337623
Node: Linear Algebra338982
Node: LU Decomposition340164
Node: QR Decomposition345372
Node: QR Decomposition with Column Pivoting351174
Node: Singular Value Decomposition355584
Node: Cholesky Decomposition359174
Node: Tridiagonal Decomposition of Real Symmetric Matrices361181
Node: Tridiagonal Decomposition of Hermitian Matrices363029
Node: Hessenberg Decomposition of Real Matrices364984
Node: Bidiagonalization367329
Node: Householder Transformations369739
Node: Householder solver for linear systems371587
Node: Tridiagonal Systems372492
Node: Balancing375145
Node: Linear Algebra Examples375946
Node: Linear Algebra References and Further Reading377934
Node: Eigensystems379424
Node: Real Symmetric Matrices380603
Node: Complex Hermitian Matrices382835
Node: Real Nonsymmetric Matrices385343
Node: Sorting Eigenvalues and Eigenvectors390537
Node: Eigenvalue and Eigenvector Examples392404
Node: Eigenvalue and Eigenvector References397790
Node: Fast Fourier Transforms398498
Node: Mathematical Definitions399707
Node: Overview of complex data FFTs402112
Node: Radix-2 FFT routines for complex data405055
Node: Mixed-radix FFT routines for complex data409267
Node: Overview of real data FFTs418596
Node: Radix-2 FFT routines for real data421030
Node: Mixed-radix FFT routines for real data424037
Node: FFT References and Further Reading434617
Node: Numerical Integration437486
Node: Numerical Integration Introduction439031
Node: Integrands without weight functions440965
Node: Integrands with weight functions441794
Node: Integrands with singular weight functions442505
Node: QNG non-adaptive Gauss-Kronrod integration443423
Node: QAG adaptive integration444694
Node: QAGS adaptive integration with singularities447325
Node: QAGP adaptive integration with known singular points449125
Node: QAGI adaptive integration on infinite intervals450439
Node: QAWC adaptive integration for Cauchy principal values452732
Node: QAWS adaptive integration for singular functions453907
Node: QAWO adaptive integration for oscillatory functions457129
Node: QAWF adaptive integration for Fourier integrals460908
Node: Numerical integration error codes463533
Node: Numerical integration examples464301
Node: Numerical integration References and Further Reading466346
Node: Random Number Generation467075
Node: General comments on random numbers468577
Node: The Random Number Generator Interface470527
Node: Random number generator initialization471885
Node: Sampling from a random number generator473901
Node: Auxiliary random number generator functions477066
Node: Random number environment variables479386
Node: Copying random number generator state481912
Node: Reading and writing random number generator state482887
Node: Random number generator algorithms484299
Node: Unix random number generators494108
Node: Other random number generators497826
Node: Random Number Generator Performance506459
Node: Random Number Generator Examples507777
Node: Random Number References and Further Reading509333
Node: Random Number Acknowledgements510630
Node: Quasi-Random Sequences511116
Node: Quasi-random number generator initialization512223
Node: Sampling from a quasi-random number generator513238
Node: Auxiliary quasi-random number generator functions513855
Node: Saving and resorting quasi-random number generator state514801
Node: Quasi-random number generator algorithms515609
Node: Quasi-random number generator examples516384
Node: Quasi-random number references517369
Node: Random Number Distributions517895
Node: Random Number Distribution Introduction521094
Node: The Gaussian Distribution522889
Node: The Gaussian Tail Distribution525551
Node: The Bivariate Gaussian Distribution527220
Node: The Exponential Distribution528543
Node: The Laplace Distribution529682
Node: The Exponential Power Distribution530779
Node: The Cauchy Distribution532047
Node: The Rayleigh Distribution533296
Node: The Rayleigh Tail Distribution534468
Node: The Landau Distribution535340
Node: The Levy alpha-Stable Distributions536295
Node: The Levy skew alpha-Stable Distribution537353
Node: The Gamma Distribution538965
Node: The Flat (Uniform) Distribution540622
Node: The Lognormal Distribution541774
Node: The Chi-squared Distribution543122
Node: The F-distribution544526
Node: The t-distribution546162
Node: The Beta Distribution547556
Node: The Logistic Distribution548715
Node: The Pareto Distribution549844
Node: Spherical Vector Distributions551014
Node: The Weibull Distribution553848
Node: The Type-1 Gumbel Distribution555042
Node: The Type-2 Gumbel Distribution556279
Node: The Dirichlet Distribution557510
Node: General Discrete Distributions559178
Node: The Poisson Distribution563043
Node: The Bernoulli Distribution564051
Node: The Binomial Distribution564802
Node: The Multinomial Distribution566007
Node: The Negative Binomial Distribution567776
Node: The Pascal Distribution569141
Node: The Geometric Distribution570299
Node: The Hypergeometric Distribution571547
Node: The Logarithmic Distribution573200
Node: Shuffling and Sampling573991
Node: Random Number Distribution Examples576810
Node: Random Number Distribution References and Further Reading580006
Node: Statistics582072
Node: Mean and standard deviation and variance583351
Node: Absolute deviation586396
Node: Higher moments (skewness and kurtosis)587688
Node: Autocorrelation589821
Node: Covariance590635
Node: Weighted Samples591616
Node: Maximum and Minimum values596860
Node: Median and Percentiles599599
Node: Example statistical programs602014
Node: Statistics References and Further Reading604673
Node: Histograms605881
Node: The histogram struct607641
Node: Histogram allocation609444
Node: Copying Histograms612405
Node: Updating and accessing histogram elements613081
Node: Searching histogram ranges616348
Node: Histogram Statistics617347
Node: Histogram Operations619207
Node: Reading and writing histograms621279
Node: Resampling from histograms624321
Node: The histogram probability distribution struct625119
Node: Example programs for histograms628150
Node: Two dimensional histograms630213
Node: The 2D histogram struct630934
Node: 2D Histogram allocation632742
Node: Copying 2D Histograms634813
Node: Updating and accessing 2D histogram elements635518
Node: Searching 2D histogram ranges639173
Node: 2D Histogram Statistics640192
Node: 2D Histogram Operations643051
Node: Reading and writing 2D histograms645225
Node: Resampling from 2D histograms648852
Node: Example programs for 2D histograms651871
Node: N-tuples653699
Node: The ntuple struct654955
Node: Creating ntuples655433
Node: Opening an existing ntuple file656100
Node: Writing ntuples656728
Node: Reading ntuples657189
Node: Closing an ntuple file657520
Node: Histogramming ntuple values657860
Node: Example ntuple programs659866
Node: Ntuple References and Further Reading663195
Node: Monte Carlo Integration663516
Node: Monte Carlo Interface664761
Node: PLAIN Monte Carlo667384
Node: MISER669822
Node: VEGAS675660
Node: Monte Carlo Examples683995
Node: Monte Carlo Integration References and Further Reading689938
Node: Simulated Annealing690720
Node: Simulated Annealing algorithm691927
Node: Simulated Annealing functions693081
Node: Examples with Simulated Annealing697607
Node: Trivial example698161
Node: Traveling Salesman Problem700812
Node: Simulated Annealing References and Further Reading704125
Node: Ordinary Differential Equations704536
Node: Defining the ODE System705357
Node: Stepping Functions707549
Node: Adaptive Step-size Control711728
Node: Evolution717186
Node: ODE Example programs719864
Node: ODE References and Further Reading724934
Node: Interpolation725573
Node: Introduction to Interpolation726586
Node: Interpolation Functions727027
Node: Interpolation Types728203
Node: Index Look-up and Acceleration730813
Node: Evaluation of Interpolating Functions732443
Node: Higher-level Interface734827
Node: Interpolation Example programs736866
Node: Interpolation References and Further Reading740113
Node: Numerical Differentiation740686
Node: Numerical Differentiation functions741275
Node: Numerical Differentiation Examples744133
Node: Numerical Differentiation References745546
Node: Chebyshev Approximations746097
Node: Chebyshev Definitions747113
Node: Creation and Calculation of Chebyshev Series747903
Node: Chebyshev Series Evaluation748875
Node: Derivatives and Integrals750259
Node: Chebyshev Approximation examples751501
Node: Chebyshev Approximation References and Further Reading752997
Node: Series Acceleration753446
Node: Acceleration functions754211
Node: Acceleration functions without error estimation756536
Node: Example of accelerating a series759146
Node: Series Acceleration References761492
Node: Wavelet Transforms762380
Node: DWT Definitions762921
Node: DWT Initialization763873
Node: DWT Transform Functions766452
Node: DWT in one dimension766987
Node: DWT in two dimension769006
Node: DWT Examples773607
Node: DWT References775424
Node: Discrete Hankel Transforms777587
Node: Discrete Hankel Transform Definition778055
Node: Discrete Hankel Transform Functions780194
Node: Discrete Hankel Transform References781725
Node: One dimensional Root-Finding782129
Node: Root Finding Overview783389
Node: Root Finding Caveats785247
Node: Initializing the Solver787014
Node: Providing the function to solve789647
Node: Search Bounds and Guesses793413
Node: Root Finding Iteration794274
Node: Search Stopping Parameters796123
Node: Root Bracketing Algorithms798637
Node: Root Finding Algorithms using Derivatives801935
Node: Root Finding Examples805438
Node: Root Finding References and Further Reading812726
Node: One dimensional Minimization813365
Node: Minimization Overview814667
Node: Minimization Caveats816373
Node: Initializing the Minimizer817710
Node: Providing the function to minimize819951
Node: Minimization Iteration820429
Node: Minimization Stopping Parameters822565
Node: Minimization Algorithms824174
Node: Minimization Examples826613
Node: Minimization References and Further Reading829557
Node: Multidimensional Root-Finding830013
Node: Overview of Multidimensional Root Finding831502
Node: Initializing the Multidimensional Solver833689
Node: Providing the multidimensional system of equations to solve836887
Node: Iteration of the multidimensional solver841792
Node: Search Stopping Parameters for the multidimensional solver843977
Node: Algorithms using Derivatives845714
Node: Algorithms without Derivatives850460
Node: Example programs for Multidimensional Root finding853548
Node: References and Further Reading for Multidimensional Root Finding862161
Node: Multidimensional Minimization863400
Node: Multimin Overview864692
Node: Multimin Caveats866664
Node: Initializing the Multidimensional Minimizer867413
Node: Providing a function to minimize870574
Node: Multimin Iteration874239
Node: Multimin Stopping Criteria876230
Node: Multimin Algorithms877782
Node: Multimin Examples882741
Node: Multimin References and Further Reading889358
Node: Least-Squares Fitting890221
Node: Fitting Overview891220
Node: Linear regression893436
Node: Linear fitting without a constant term895867
Node: Multi-parameter fitting898058
Node: Fitting Examples902963
Node: Fitting References and Further Reading909788
Node: Nonlinear Least-Squares Fitting910610
Node: Overview of Nonlinear Least-Squares Fitting912060
Node: Initializing the Nonlinear Least-Squares Solver913527
Node: Providing the Function to be Minimized916380
Node: Iteration of the Minimization Algorithm919317
Node: Search Stopping Parameters for Minimization Algorithms921167
Node: Minimization Algorithms using Derivatives923262
Node: Minimization Algorithms without Derivatives926510
Node: Computing the covariance matrix of best fit parameters926902
Node: Example programs for Nonlinear Least-Squares Fitting928936
Node: References and Further Reading for Nonlinear Least-Squares Fitting936664
Node: Basis Splines937400
Node: Overview of B-splines937975
Node: Initializing the B-splines solver939260
Node: Constructing the knots vector940003
Node: Evaluation of B-spline basis functions940790
Node: Example programs for B-splines941523
Node: References and Further Reading945220
Node: Physical Constants945734
Node: Fundamental Constants947144
Node: Astronomy and Astrophysics948283
Node: Atomic and Nuclear Physics948948
Node: Measurement of Time950585
Node: Imperial Units951015
Node: Speed and Nautical Units951457
Node: Printers Units951961
Node: Volume Area and Length952284
Node: Mass and Weight952970
Node: Thermal Energy and Power953789
Node: Pressure954212
Node: Viscosity954825
Node: Light and Illumination955101
Node: Radioactivity955693
Node: Force and Energy956028
Node: Prefixes956432
Node: Physical Constant Examples957175
Node: Physical Constant References and Further Reading958964
Node: IEEE floating-point arithmetic959675
Node: Representation of floating point numbers960261
Node: Setting up your IEEE environment964742
Node: IEEE References and Further Reading971351
Node: Debugging Numerical Programs972506
Node: Using gdb972990
Node: Examining floating point registers976333
Node: Handling floating point exceptions977618
Node: GCC warning options for numerical programs979030
Node: Debugging References983223
Node: Contributors to GSL983935
Node: Autoconf Macros988118
Node: GSL CBLAS Library992103
Node: Level 1 CBLAS Functions992630
Node: Level 2 CBLAS Functions997932
Node: Level 3 CBLAS Functions1014602
Node: GSL CBLAS Examples1024264
Node: Free Software Needs Free Documentation1025826
Node: GNU General Public License1030895
Node: GNU Free Documentation License1050165
Node: Function Index1072596
Node: Variable Index1306453
Node: Type Index1307625
Node: Concept Index1311271

End Tag Table