This is gsl-ref.info, produced by makeinfo version 4.11 from
gsl-ref.texi.

INFO-DIR-SECTION Software libraries
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, 2008, 2009 The GSL Team.

   Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 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 the freedom to copy and modify
this GNU Manual."


Indirect:
gsl-ref.info-1: 936
gsl-ref.info-2: 300349
gsl-ref.info-3: 599961
gsl-ref.info-4: 899144
gsl-ref.info-5: 1139739
gsl-ref.info-6: 1401858

Tag Table:
(Indirect)
Node: Top936
Node: Introduction3641
Node: Routines available in GSL4293
Node: GSL is Free Software6208
Node: Obtaining GSL8600
Node: No Warranty9627
Node: Reporting Bugs10133
Ref: Reporting Bugs-Footnote-111089
Node: Further Information11139
Node: Conventions used in this manual12152
Node: Using the library12916
Node: An Example Program13502
Ref: An Example Program-Footnote-114245
Node: Compiling and Linking14352
Node: Linking programs with the library15422
Node: Linking with an alternative BLAS library16567
Node: Shared Libraries17649
Ref: Shared Libraries-Footnote-119124
Node: ANSI C Compliance19172
Node: Inline functions20265
Node: Long double21803
Node: Portability functions23391
Node: Alternative optimized functions24788
Node: Support for different numeric types26246
Node: Compatibility with C++29309
Node: Aliasing of arrays29881
Node: Thread-safety30632
Node: Deprecated Functions31719
Node: Code Reuse32344
Node: Error Handling32988
Node: Error Reporting33738
Node: Error Codes35630
Node: Error Handlers37486
Node: Using GSL error reporting in your own functions41123
Node: Error Reporting Examples43081
Node: Mathematical Functions44293
Node: Mathematical Constants45054
Node: Infinities and Not-a-number46184
Ref: Infinities and Not-a-number-Footnote-147291
Node: Elementary Functions47701
Node: Small integer powers50148
Node: Testing the Sign of Numbers51732
Node: Testing for Odd and Even Numbers52163
Node: Maximum and Minimum functions52719
Node: Approximate Comparison of Floating Point Numbers54994
Node: Complex Numbers56353
Ref: Complex Numbers-Footnote-157679
Node: Representation of complex numbers57743
Node: Properties of complex numbers59680
Node: Complex arithmetic operators60685
Node: Elementary Complex Functions63431
Node: Complex Trigonometric Functions65251
Node: Inverse Complex Trigonometric Functions66472
Node: Complex Hyperbolic Functions69078
Node: Inverse Complex Hyperbolic Functions70374
Node: Complex Number References and Further Reading72362
Node: Polynomials73758
Node: Polynomial Evaluation74525
Node: Divided Difference Representation of Polynomials75935
Node: Quadratic Equations77684
Node: Cubic Equations79624
Node: General Polynomial Equations81206
Node: Roots of Polynomials Examples83551
Node: Roots of Polynomials References and Further Reading84940
Node: Special Functions85885
Node: Special Function Usage87879
Node: The gsl_sf_result struct89062
Node: Special Function Modes90326
Node: Airy Functions and Derivatives91262
Node: Airy Functions91958
Node: Derivatives of Airy Functions93318
Node: Zeros of Airy Functions94830
Node: Zeros of Derivatives of Airy Functions95549
Node: Bessel Functions96308
Node: Regular Cylindrical Bessel Functions97500
Node: Irregular Cylindrical Bessel Functions98824
Node: Regular Modified Cylindrical Bessel Functions100282
Node: Irregular Modified Cylindrical Bessel Functions103109
Node: Regular Spherical Bessel Functions106077
Node: Irregular Spherical Bessel Functions108291
Node: Regular Modified Spherical Bessel Functions109978
Node: Irregular Modified Spherical Bessel Functions111981
Node: Regular Bessel Function - Fractional Order114044
Node: Irregular Bessel Functions - Fractional Order115042
Node: Regular Modified Bessel Functions - Fractional Order115624
Node: Irregular Modified Bessel Functions - Fractional Order116549
Node: Zeros of Regular Bessel Functions117785
Node: Clausen Functions118888
Node: Coulomb Functions119492
Node: Normalized Hydrogenic Bound States119941
Node: Coulomb Wave Functions121054
Node: Coulomb Wave Function Normalization Constant124464
Node: Coupling Coefficients125217
Node: 3-j Symbols125940
Node: 6-j Symbols126544
Node: 9-j Symbols127168
Node: Dawson Function127874
Node: Debye Functions128441
Node: Dilogarithm130215
Node: Real Argument130510
Node: Complex Argument131203
Node: Elementary Operations131672
Node: Elliptic Integrals132496
Node: Definition of Legendre Forms133068
Node: Definition of Carlson Forms133888
Node: Legendre Form of Complete Elliptic Integrals134585
Node: Legendre Form of Incomplete Elliptic Integrals136153
Node: Carlson Forms138341
Node: Elliptic Functions (Jacobi)139888
Node: Error Functions140469
Node: Error Function140920
Node: Complementary Error Function141293
Node: Log Complementary Error Function141753
Node: Probability functions142205
Node: Exponential Functions143458
Node: Exponential Function143841
Node: Relative Exponential Functions145064
Node: Exponentiation With Error Estimate146736
Node: Exponential Integrals147945
Node: Exponential Integral148427
Node: Ei(x)149354
Node: Hyperbolic Integrals149802
Node: Ei_3(x)150458
Node: Trigonometric Integrals150850
Node: Arctangent Integral151449
Node: Fermi-Dirac Function151849
Node: Complete Fermi-Dirac Integrals152219
Node: Incomplete Fermi-Dirac Integrals154787
Node: Gamma and Beta Functions155430
Node: Gamma Functions156003
Node: Factorials159112
Node: Pochhammer Symbol161665
Node: Incomplete Gamma Functions163171
Node: Beta Functions164420
Node: Incomplete Beta Function165172
Node: Gegenbauer Functions165883
Node: Hypergeometric Functions167533
Node: Laguerre Functions171796
Node: Lambert W Functions173359
Node: Legendre Functions and Spherical Harmonics174397
Node: Legendre Polynomials174986
Node: Associated Legendre Polynomials and Spherical Harmonics177041
Node: Conical Functions179878
Node: Radial Functions for Hyperbolic Space182001
Node: Logarithm and Related Functions184178
Node: Mathieu Functions185802
Node: Mathieu Function Workspace187151
Node: Mathieu Function Characteristic Values187965
Node: Angular Mathieu Functions189037
Node: Radial Mathieu Functions190073
Node: Power Function191315
Node: Psi (Digamma) Function192242
Node: Digamma Function192762
Node: Trigamma Function193592
Node: Polygamma Function194169
Node: Synchrotron Functions194553
Node: Transport Functions195316
Node: Trigonometric Functions196463
Node: Circular Trigonometric Functions197086
Node: Trigonometric Functions for Complex Arguments198095
Node: Hyperbolic Trigonometric Functions199131
Node: Conversion Functions199734
Node: Restriction Functions200517
Node: Trigonometric Functions With Error Estimates201449
Node: Zeta Functions202359
Node: Riemann Zeta Function202817
Node: Riemann Zeta Function Minus One203496
Node: Hurwitz Zeta Function204267
Node: Eta Function204772
Node: Special Functions Examples205331
Node: Special Functions References and Further Reading207025
Node: Vectors and Matrices208295
Node: Data types209054
Node: Blocks210257
Node: Block allocation211173
Node: Reading and writing blocks212657
Node: Example programs for blocks214721
Node: Vectors215348
Node: Vector allocation217234
Node: Accessing vector elements218852
Ref: Accessing vector elements-Footnote-1221994
Node: Initializing vector elements222233
Node: Reading and writing vectors222927
Node: Vector views225017
Node: Copying vectors232459
Node: Exchanging elements233319
Node: Vector operations233877
Node: Finding maximum and minimum elements of vectors235330
Node: Vector properties236916
Node: Example programs for vectors237681
Node: Matrices239970
Node: Matrix allocation242828
Node: Accessing matrix elements244495
Node: Initializing matrix elements246444
Node: Reading and writing matrices247240
Node: Matrix views249343
Node: Creating row and column views256483
Node: Copying matrices260954
Node: Copying rows and columns261550
Node: Exchanging rows and columns263227
Node: Matrix operations264705
Node: Finding maximum and minimum elements of matrices266345
Node: Matrix properties268249
Node: Example programs for matrices269141
Node: Vector and Matrix References and Further Reading273212
Node: Permutations273698
Node: The Permutation struct274986
Node: Permutation allocation275490
Node: Accessing permutation elements276924
Node: Permutation properties277767
Node: Permutation functions278472
Node: Applying Permutations279729
Node: Reading and writing permutations281655
Ref: Reading and writing permutations-Footnote-1283870
Node: Permutations in cyclic form283982
Node: Permutation Examples287407
Node: Permutation References and Further Reading289950
Node: Combinations290624
Node: The Combination struct291469
Node: Combination allocation292021
Node: Accessing combination elements293806
Node: Combination properties294465
Node: Combination functions295351
Node: Reading and writing combinations296291
Ref: Reading and writing combinations-Footnote-1298525
Node: Combination Examples298637
Node: Combination References and Further Reading299945
Node: Sorting300349
Node: Sorting objects301299
Node: Sorting vectors304210
Node: Selecting the k smallest or largest elements306786
Node: Computing the rank310120
Node: Sorting Examples311321
Node: Sorting References and Further Reading312965
Node: BLAS Support313511
Ref: BLAS Support-Footnote-1316890
Node: GSL BLAS Interface317058
Node: Level 1 GSL BLAS Interface317545
Node: Level 2 GSL BLAS Interface324284
Node: Level 3 GSL BLAS Interface333578
Node: BLAS Examples344718
Node: BLAS References and Further Reading346139
Node: Linear Algebra347486
Node: LU Decomposition348611
Node: QR Decomposition353856
Node: QR Decomposition with Column Pivoting360165
Node: Singular Value Decomposition364620
Node: Cholesky Decomposition368616
Node: Tridiagonal Decomposition of Real Symmetric Matrices371701
Node: Tridiagonal Decomposition of Hermitian Matrices373549
Node: Hessenberg Decomposition of Real Matrices375501
Node: Hessenberg-Triangular Decomposition of Real Matrices377911
Node: Bidiagonalization379031
Node: Householder Transformations381456
Node: Householder solver for linear systems383808
Node: Tridiagonal Systems384713
Node: Balancing387585
Node: Linear Algebra Examples388386
Node: Linear Algebra References and Further Reading390374
Node: Eigensystems392019
Node: Real Symmetric Matrices393233
Node: Complex Hermitian Matrices395747
Node: Real Nonsymmetric Matrices398374
Node: Real Generalized Symmetric-Definite Eigensystems403587
Node: Complex Generalized Hermitian-Definite Eigensystems406459
Node: Real Generalized Nonsymmetric Eigensystems409166
Node: Sorting Eigenvalues and Eigenvectors415750
Node: Eigenvalue and Eigenvector Examples419027
Node: Eigenvalue and Eigenvector References424417
Node: Fast Fourier Transforms425442
Node: Mathematical Definitions426651
Node: Overview of complex data FFTs429056
Node: Radix-2 FFT routines for complex data431999
Node: Mixed-radix FFT routines for complex data436211
Node: Overview of real data FFTs445540
Node: Radix-2 FFT routines for real data447974
Node: Mixed-radix FFT routines for real data452403
Node: FFT References and Further Reading463077
Node: Numerical Integration465946
Node: Numerical Integration Introduction467491
Node: Integrands without weight functions469760
Node: Integrands with weight functions470589
Node: Integrands with singular weight functions471300
Node: QNG non-adaptive Gauss-Kronrod integration472218
Node: QAG adaptive integration473499
Node: QAGS adaptive integration with singularities476130
Node: QAGP adaptive integration with known singular points477930
Node: QAGI adaptive integration on infinite intervals479244
Node: QAWC adaptive integration for Cauchy principal values481537
Node: QAWS adaptive integration for singular functions482712
Node: QAWO adaptive integration for oscillatory functions485934
Node: QAWF adaptive integration for Fourier integrals489713
Node: Numerical integration error codes492338
Node: Numerical integration examples493106
Node: Numerical integration References and Further Reading495152
Node: Random Number Generation495881
Node: General comments on random numbers497383
Node: The Random Number Generator Interface499333
Node: Random number generator initialization500691
Node: Sampling from a random number generator503064
Node: Auxiliary random number generator functions506305
Node: Random number environment variables508625
Node: Copying random number generator state511151
Node: Reading and writing random number generator state512126
Node: Random number generator algorithms513520
Node: Unix random number generators523329
Node: Other random number generators527047
Node: Random Number Generator Performance535680
Node: Random Number Generator Examples536998
Node: Random Number References and Further Reading538554
Node: Random Number Acknowledgements539851
Node: Quasi-Random Sequences540337
Node: Quasi-random number generator initialization541444
Node: Sampling from a quasi-random number generator542459
Node: Auxiliary quasi-random number generator functions543156
Node: Saving and resorting quasi-random number generator state544102
Node: Quasi-random number generator algorithms544910
Node: Quasi-random number generator examples546046
Node: Quasi-random number references547031
Node: Random Number Distributions547557
Node: Random Number Distribution Introduction550756
Node: The Gaussian Distribution552551
Node: The Gaussian Tail Distribution555212
Node: The Bivariate Gaussian Distribution556881
Node: The Exponential Distribution558204
Node: The Laplace Distribution559343
Node: The Exponential Power Distribution560440
Node: The Cauchy Distribution561708
Node: The Rayleigh Distribution562957
Node: The Rayleigh Tail Distribution564129
Node: The Landau Distribution565001
Node: The Levy alpha-Stable Distributions565956
Node: The Levy skew alpha-Stable Distribution567014
Node: The Gamma Distribution568626
Node: The Flat (Uniform) Distribution570283
Node: The Lognormal Distribution571435
Node: The Chi-squared Distribution572783
Node: The F-distribution574187
Node: The t-distribution575823
Node: The Beta Distribution577217
Node: The Logistic Distribution578376
Node: The Pareto Distribution579505
Node: Spherical Vector Distributions580675
Node: The Weibull Distribution583509
Node: The Type-1 Gumbel Distribution584703
Node: The Type-2 Gumbel Distribution585940
Node: The Dirichlet Distribution587171
Node: General Discrete Distributions588838
Node: The Poisson Distribution592705
Node: The Bernoulli Distribution593713
Node: The Binomial Distribution594464
Node: The Multinomial Distribution595669
Node: The Negative Binomial Distribution597438
Node: The Pascal Distribution598803
Node: The Geometric Distribution599961
Node: The Hypergeometric Distribution601209
Node: The Logarithmic Distribution602862
Node: Shuffling and Sampling603653
Node: Random Number Distribution Examples606472
Node: Random Number Distribution References and Further Reading609668
Node: Statistics611811
Node: Mean and standard deviation and variance613211
Node: Absolute deviation616719
Node: Higher moments (skewness and kurtosis)618011
Node: Autocorrelation620144
Node: Covariance620958
Node: Correlation621934
Node: Weighted Samples622643
Node: Maximum and Minimum values628493
Node: Median and Percentiles631232
Node: Example statistical programs633647
Node: Statistics References and Further Reading636308
Node: Histograms637516
Node: The histogram struct639276
Node: Histogram allocation641079
Node: Copying Histograms644040
Node: Updating and accessing histogram elements644716
Node: Searching histogram ranges647983
Node: Histogram Statistics648982
Node: Histogram Operations650842
Node: Reading and writing histograms652914
Node: Resampling from histograms655956
Node: The histogram probability distribution struct656754
Node: Example programs for histograms659785
Node: Two dimensional histograms661848
Node: The 2D histogram struct662569
Node: 2D Histogram allocation664377
Node: Copying 2D Histograms666448
Node: Updating and accessing 2D histogram elements667153
Node: Searching 2D histogram ranges670809
Node: 2D Histogram Statistics671828
Node: 2D Histogram Operations674687
Node: Reading and writing 2D histograms676861
Node: Resampling from 2D histograms680490
Node: Example programs for 2D histograms683509
Node: N-tuples685337
Node: The ntuple struct686593
Node: Creating ntuples687071
Node: Opening an existing ntuple file687738
Node: Writing ntuples688366
Node: Reading ntuples688827
Node: Closing an ntuple file689158
Node: Histogramming ntuple values689498
Node: Example ntuple programs691506
Node: Ntuple References and Further Reading694835
Node: Monte Carlo Integration695156
Node: Monte Carlo Interface696401
Node: PLAIN Monte Carlo699024
Node: MISER701474
Ref: MISER-Footnote-1708150
Node: VEGAS708275
Node: Monte Carlo Examples717826
Node: Monte Carlo Integration References and Further Reading723811
Node: Simulated Annealing724593
Node: Simulated Annealing algorithm725800
Node: Simulated Annealing functions726954
Node: Examples with Simulated Annealing731489
Node: Trivial example732043
Node: Traveling Salesman Problem734694
Node: Simulated Annealing References and Further Reading738007
Node: Ordinary Differential Equations738418
Node: Defining the ODE System739239
Node: Stepping Functions741431
Node: Adaptive Step-size Control745776
Node: Evolution751234
Node: ODE Example programs754851
Node: ODE References and Further Reading760090
Node: Interpolation760729
Node: Introduction to Interpolation761900
Node: Interpolation Functions762341
Node: Interpolation Types763548
Node: Index Look-up and Acceleration766157
Node: Evaluation of Interpolating Functions768209
Node: Higher-level Interface770593
Node: Interpolation Example programs772632
Node: Interpolation References and Further Reading775848
Node: Numerical Differentiation776421
Node: Numerical Differentiation functions777010
Node: Numerical Differentiation Examples779868
Node: Numerical Differentiation References781281
Node: Chebyshev Approximations781832
Node: Chebyshev Definitions782893
Node: Creation and Calculation of Chebyshev Series783683
Node: Auxiliary Functions for Chebyshev Series784668
Node: Chebyshev Series Evaluation785408
Node: Derivatives and Integrals786788
Node: Chebyshev Approximation Examples788030
Node: Chebyshev Approximation References and Further Reading789526
Node: Series Acceleration789975
Node: Acceleration functions790740
Node: Acceleration functions without error estimation793065
Node: Example of accelerating a series795675
Node: Series Acceleration References798021
Node: Wavelet Transforms798909
Node: DWT Definitions799450
Node: DWT Initialization800402
Node: DWT Transform Functions802981
Node: DWT in one dimension803516
Node: DWT in two dimension805535
Node: DWT Examples810113
Node: DWT References811930
Node: Discrete Hankel Transforms814093
Node: Discrete Hankel Transform Definition814561
Node: Discrete Hankel Transform Functions816700
Node: Discrete Hankel Transform References818237
Node: One dimensional Root-Finding818641
Node: Root Finding Overview819901
Node: Root Finding Caveats821759
Node: Initializing the Solver823526
Node: Providing the function to solve826159
Node: Search Bounds and Guesses829925
Node: Root Finding Iteration830788
Node: Search Stopping Parameters832637
Node: Root Bracketing Algorithms835151
Node: Root Finding Algorithms using Derivatives838449
Ref: Root Finding Algorithms using Derivatives-Footnote-1841991
Node: Root Finding Examples842146
Node: Root Finding References and Further Reading849434
Node: One dimensional Minimization850073
Node: Minimization Overview851375
Node: Minimization Caveats853081
Node: Initializing the Minimizer854418
Node: Providing the function to minimize856659
Node: Minimization Iteration857137
Node: Minimization Stopping Parameters859273
Node: Minimization Algorithms860882
Node: Minimization Examples863486
Node: Minimization References and Further Reading866413
Node: Multidimensional Root-Finding866869
Node: Overview of Multidimensional Root Finding868358
Node: Initializing the Multidimensional Solver870545
Node: Providing the multidimensional system of equations to solve873776
Node: Iteration of the multidimensional solver878681
Node: Search Stopping Parameters for the multidimensional solver880960
Node: Algorithms using Derivatives882697
Node: Algorithms without Derivatives887443
Node: Example programs for Multidimensional Root finding890531
Node: References and Further Reading for Multidimensional Root Finding899144
Node: Multidimensional Minimization900383
Node: Multimin Overview901736
Node: Multimin Caveats903813
Node: Initializing the Multidimensional Minimizer904562
Node: Providing a function to minimize907723
Node: Multimin Iteration911775
Node: Multimin Stopping Criteria913766
Node: Multimin Algorithms with Derivatives915335
Node: Multimin Algorithms without Derivatives918863
Node: Multimin Examples921788
Node: Multimin References and Further Reading928354
Node: Least-Squares Fitting929219
Node: Fitting Overview930218
Node: Linear regression932552
Node: Linear fitting without a constant term935154
Node: Multi-parameter fitting937347
Node: Fitting Examples942997
Node: Fitting References and Further Reading949822
Node: Nonlinear Least-Squares Fitting950644
Node: Overview of Nonlinear Least-Squares Fitting952094
Node: Initializing the Nonlinear Least-Squares Solver953561
Node: Providing the Function to be Minimized956426
Node: Iteration of the Minimization Algorithm959363
Node: Search Stopping Parameters for Minimization Algorithms961213
Node: Minimization Algorithms using Derivatives963308
Node: Minimization Algorithms without Derivatives966751
Node: Computing the covariance matrix of best fit parameters967143
Node: Example programs for Nonlinear Least-Squares Fitting969177
Node: References and Further Reading for Nonlinear Least-Squares Fitting976905
Node: Basis Splines977641
Node: Overview of B-splines978541
Node: Initializing the B-splines solver979850
Node: Constructing the knots vector981226
Node: Evaluation of B-spline basis functions982013
Node: Evaluation of B-spline basis function derivatives983670
Node: Obtaining Greville abscissae for B-spline basis functions985662
Node: Example programs for B-splines986700
Node: References and Further Reading990712
Node: Physical Constants991517
Node: Fundamental Constants992927
Node: Astronomy and Astrophysics994066
Node: Atomic and Nuclear Physics994731
Node: Measurement of Time996382
Node: Imperial Units996812
Node: Speed and Nautical Units997254
Node: Printers Units997758
Node: Volume Area and Length998081
Node: Mass and Weight998767
Node: Thermal Energy and Power999586
Node: Pressure1000009
Node: Viscosity1000622
Node: Light and Illumination1000898
Node: Radioactivity1001490
Node: Force and Energy1001825
Node: Prefixes1002229
Node: Physical Constant Examples1002972
Node: Physical Constant References and Further Reading1004761
Node: IEEE floating-point arithmetic1005491
Node: Representation of floating point numbers1006077
Node: Setting up your IEEE environment1010558
Node: IEEE References and Further Reading1017550
Node: Debugging Numerical Programs1018705
Node: Using gdb1019189
Node: Examining floating point registers1022532
Node: Handling floating point exceptions1023817
Node: GCC warning options for numerical programs1025229
Node: Debugging References1029191
Node: Contributors to GSL1029903
Node: Autoconf Macros1034138
Node: GSL CBLAS Library1038167
Node: Level 1 CBLAS Functions1038694
Node: Level 2 CBLAS Functions1043996
Node: Level 3 CBLAS Functions1060666
Node: GSL CBLAS Examples1070328
Node: Free Software Needs Free Documentation1071890
Node: GNU General Public License1076959
Node: GNU Free Documentation License1114571
Node: Function Index1139739
Node: Variable Index1384156
Node: Type Index1387459
Node: Concept Index1401858

End Tag Table
