This is gsl-ref.info, produced by makeinfo version 4.13 from
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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: 940
gsl-ref.info-2: 298843
gsl-ref.info-3: 596861
gsl-ref.info-4: 895869
gsl-ref.info-5: 1072598
gsl-ref.info-6: 1311273

Tag Table:
(Indirect)
Node: Top940
Node: Introduction3647
Node: Routines available in GSL4299
Node: GSL is Free Software6214
Node: Obtaining GSL8606
Node: No Warranty9747
Node: Reporting Bugs10253
Node: Further Information11137
Node: Conventions used in this manual12150
Node: Using the library12914
Node: An Example Program13500
Node: Compiling and Linking14204
Node: Linking programs with the library15274
Node: Linking with an alternative BLAS library16419
Node: Shared Libraries17349
Node: ANSI C Compliance18765
Node: Inline functions19858
Node: Long double20901
Node: Portability functions22299
Node: Alternative optimized functions23696
Node: Support for different numeric types25154
Node: Compatibility with C++28217
Node: Aliasing of arrays28789
Node: Thread-safety29540
Node: Deprecated Functions30627
Node: Code Reuse31252
Node: Error Handling31896
Node: Error Reporting32646
Node: Error Codes34538
Node: Error Handlers36394
Node: Using GSL error reporting in your own functions40029
Node: Error Reporting Examples41987
Node: Mathematical Functions43191
Node: Mathematical Constants43952
Node: Infinities and Not-a-number45082
Node: Elementary Functions46150
Node: Small integer powers48405
Node: Testing the Sign of Numbers49967
Node: Testing for Odd and Even Numbers50398
Node: Maximum and Minimum functions50954
Node: Approximate Comparison of Floating Point Numbers53036
Node: Complex Numbers54242
Ref: Complex Numbers-Footnote-155550
Node: Complex numbers55614
Node: Properties of complex numbers57417
Node: Complex arithmetic operators58404
Node: Elementary Complex Functions61150
Node: Complex Trigonometric Functions62970
Node: Inverse Complex Trigonometric Functions64191
Node: Complex Hyperbolic Functions66797
Node: Inverse Complex Hyperbolic Functions68093
Node: Complex Number References and Further Reading70081
Node: Polynomials71477
Node: Polynomial Evaluation72244
Node: Divided Difference Representation of Polynomials72704
Node: Quadratic Equations74373
Node: Cubic Equations76313
Node: General Polynomial Equations77684
Node: Roots of Polynomials Examples80029
Node: Roots of Polynomials References and Further Reading81418
Node: Special Functions82363
Node: Special Function Usage84357
Node: The gsl_sf_result struct85540
Node: Special Function Modes86804
Node: Airy Functions and Derivatives87740
Node: Airy Functions88436
Node: Derivatives of Airy Functions89796
Node: Zeros of Airy Functions91308
Node: Zeros of Derivatives of Airy Functions92027
Node: Bessel Functions92786
Node: Regular Cylindrical Bessel Functions93978
Node: Irregular Cylindrical Bessel Functions95302
Node: Regular Modified Cylindrical Bessel Functions96758
Node: Irregular Modified Cylindrical Bessel Functions99585
Node: Regular Spherical Bessel Functions102553
Node: Irregular Spherical Bessel Functions104765
Node: Regular Modified Spherical Bessel Functions106452
Node: Irregular Modified Spherical Bessel Functions108455
Node: Regular Bessel Function - Fractional Order110518
Node: Irregular Bessel Functions - Fractional Order111516
Node: Regular Modified Bessel Functions - Fractional Order112098
Node: Irregular Modified Bessel Functions - Fractional Order113023
Node: Zeros of Regular Bessel Functions114259
Node: Clausen Functions115362
Node: Coulomb Functions115966
Node: Normalized Hydrogenic Bound States116415
Node: Coulomb Wave Functions117528
Node: Coulomb Wave Function Normalization Constant120938
Node: Coupling Coefficients121691
Node: 3-j Symbols122414
Node: 6-j Symbols123018
Node: 9-j Symbols123642
Node: Dawson Function124348
Node: Debye Functions124915
Node: Dilogarithm126689
Node: Real Argument126984
Node: Complex Argument127553
Node: Elementary Operations128022
Node: Elliptic Integrals128846
Node: Definition of Legendre Forms129418
Node: Definition of Carlson Forms130238
Node: Legendre Form of Complete Elliptic Integrals130935
Node: Legendre Form of Incomplete Elliptic Integrals132503
Node: Carlson Forms134691
Node: Elliptic Functions (Jacobi)136238
Node: Error Functions136819
Node: Error Function137270
Node: Complementary Error Function137643
Node: Log Complementary Error Function138103
Node: Probability functions138555
Node: Exponential Functions139808
Node: Exponential Function140191
Node: Relative Exponential Functions141414
Node: Exponentiation With Error Estimate143085
Node: Exponential Integrals144294
Node: Exponential Integral144776
Node: Ei(x)145426
Node: Hyperbolic Integrals145874
Node: Ei_3(x)146530
Node: Trigonometric Integrals146922
Node: Arctangent Integral147521
Node: Fermi-Dirac Function147921
Node: Complete Fermi-Dirac Integrals148291
Node: Incomplete Fermi-Dirac Integrals150752
Node: Gamma and Beta Functions151395
Node: Gamma Functions151831
Node: Factorials154952
Node: Pochhammer Symbol157505
Node: Incomplete Gamma Functions159017
Node: Beta Functions160266
Node: Incomplete Beta Function161018
Node: Gegenbauer Functions161549
Node: Hypergeometric Functions163199
Node: Laguerre Functions167466
Node: Lambert W Functions169029
Node: Legendre Functions and Spherical Harmonics170067
Node: Legendre Polynomials170656
Node: Associated Legendre Polynomials and Spherical Harmonics172736
Node: Conical Functions175537
Node: Radial Functions for Hyperbolic Space177660
Node: Logarithm and Related Functions179837
Node: Mathieu Functions181461
Node: Mathieu Function Workspace182810
Node: Mathieu Function Characteristic Values183623
Node: Angular Mathieu Functions184691
Node: Radial Mathieu Functions185723
Node: Power Function186961
Node: Psi (Digamma) Function187888
Node: Digamma Function188408
Node: Trigamma Function189238
Node: Polygamma Function189815
Node: Synchrotron Functions190199
Node: Transport Functions190962
Node: Trigonometric Functions192109
Node: Circular Trigonometric Functions192732
Node: Trigonometric Functions for Complex Arguments193741
Node: Hyperbolic Trigonometric Functions194775
Node: Conversion Functions195378
Node: Restriction Functions196161
Node: Trigonometric Functions With Error Estimates197093
Node: Zeta Functions198003
Node: Riemann Zeta Function198461
Node: Riemann Zeta Function Minus One199140
Node: Hurwitz Zeta Function199911
Node: Eta Function200416
Node: Special Functions Examples200975
Node: Special Functions References and Further Reading202669
Node: Vectors and Matrices203776
Node: Data types204535
Node: Blocks205738
Node: Block allocation206654
Node: Reading and writing blocks208138
Node: Example programs for blocks210202
Node: Vectors210829
Node: Vector allocation212715
Node: Accessing vector elements214333
Node: Initializing vector elements216575
Node: Reading and writing vectors217269
Node: Vector views219359
Node: Copying vectors226801
Node: Exchanging elements227661
Node: Vector operations228219
Node: Finding maximum and minimum elements of vectors229733
Node: Vector properties231258
Node: Example programs for vectors231881
Node: Matrices234170
Node: Matrix allocation237028
Node: Accessing matrix elements238695
Node: Initializing matrix elements240403
Node: Reading and writing matrices241199
Node: Matrix views243302
Node: Creating row and column views250442
Node: Copying matrices253613
Node: Copying rows and columns254209
Node: Exchanging rows and columns255886
Node: Matrix operations257364
Node: Finding maximum and minimum elements of matrices259004
Node: Matrix properties260908
Node: Example programs for matrices261656
Node: Vector and Matrix References and Further Reading265727
Node: Permutations266213
Node: The Permutation struct267501
Node: Permutation allocation268005
Node: Accessing permutation elements269439
Node: Permutation properties270202
Node: Permutation functions270901
Node: Applying Permutations272158
Node: Reading and writing permutations274083
Node: Permutations in cyclic form276265
Node: Permutation Examples279690
Node: Permutation References and Further Reading282233
Node: Combinations282907
Node: The Combination struct283752
Node: Combination allocation284304
Node: Accessing combination elements286089
Node: Combination properties286668
Node: Combination functions287554
Node: Reading and writing combinations288494
Node: Combination Examples290694
Node: Combination References and Further Reading292002
Node: Sorting292406
Node: Sorting objects293356
Node: Sorting vectors296267
Node: Selecting the k smallest or largest elements298843
Node: Computing the rank302177
Node: Sorting Examples303378
Node: Sorting References and Further Reading305022
Node: BLAS Support305568
Node: GSL BLAS Interface308543
Node: Level 1 GSL BLAS Interface309030
Node: Level 2 GSL BLAS Interface315773
Node: Level 3 GSL BLAS Interface325067
Node: BLAS Examples336203
Node: BLAS References and Further Reading337624
Node: Linear Algebra338983
Node: LU Decomposition340165
Node: QR Decomposition345373
Node: QR Decomposition with Column Pivoting351175
Node: Singular Value Decomposition355585
Node: Cholesky Decomposition359175
Node: Tridiagonal Decomposition of Real Symmetric Matrices361182
Node: Tridiagonal Decomposition of Hermitian Matrices363030
Node: Hessenberg Decomposition of Real Matrices364985
Node: Bidiagonalization367330
Node: Householder Transformations369740
Node: Householder solver for linear systems371588
Node: Tridiagonal Systems372493
Node: Balancing375146
Node: Linear Algebra Examples375947
Node: Linear Algebra References and Further Reading377935
Node: Eigensystems379425
Node: Real Symmetric Matrices380604
Node: Complex Hermitian Matrices382836
Node: Real Nonsymmetric Matrices385344
Node: Sorting Eigenvalues and Eigenvectors390538
Node: Eigenvalue and Eigenvector Examples392405
Node: Eigenvalue and Eigenvector References397791
Node: Fast Fourier Transforms398499
Node: Mathematical Definitions399708
Node: Overview of complex data FFTs402113
Node: Radix-2 FFT routines for complex data405056
Node: Mixed-radix FFT routines for complex data409268
Node: Overview of real data FFTs418597
Node: Radix-2 FFT routines for real data421031
Node: Mixed-radix FFT routines for real data424038
Node: FFT References and Further Reading434618
Node: Numerical Integration437487
Node: Numerical Integration Introduction439032
Node: Integrands without weight functions440966
Node: Integrands with weight functions441795
Node: Integrands with singular weight functions442506
Node: QNG non-adaptive Gauss-Kronrod integration443424
Node: QAG adaptive integration444695
Node: QAGS adaptive integration with singularities447326
Node: QAGP adaptive integration with known singular points449126
Node: QAGI adaptive integration on infinite intervals450440
Node: QAWC adaptive integration for Cauchy principal values452733
Node: QAWS adaptive integration for singular functions453908
Node: QAWO adaptive integration for oscillatory functions457130
Node: QAWF adaptive integration for Fourier integrals460909
Node: Numerical integration error codes463534
Node: Numerical integration examples464302
Node: Numerical integration References and Further Reading466347
Node: Random Number Generation467076
Node: General comments on random numbers468578
Node: The Random Number Generator Interface470528
Node: Random number generator initialization471886
Node: Sampling from a random number generator473902
Node: Auxiliary random number generator functions477067
Node: Random number environment variables479387
Node: Copying random number generator state481913
Node: Reading and writing random number generator state482888
Node: Random number generator algorithms484300
Node: Unix random number generators494109
Node: Other random number generators497827
Node: Random Number Generator Performance506460
Node: Random Number Generator Examples507778
Node: Random Number References and Further Reading509334
Node: Random Number Acknowledgements510631
Node: Quasi-Random Sequences511117
Node: Quasi-random number generator initialization512224
Node: Sampling from a quasi-random number generator513239
Node: Auxiliary quasi-random number generator functions513856
Node: Saving and resorting quasi-random number generator state514802
Node: Quasi-random number generator algorithms515610
Node: Quasi-random number generator examples516385
Node: Quasi-random number references517370
Node: Random Number Distributions517896
Node: Random Number Distribution Introduction521095
Node: The Gaussian Distribution522890
Node: The Gaussian Tail Distribution525552
Node: The Bivariate Gaussian Distribution527221
Node: The Exponential Distribution528544
Node: The Laplace Distribution529683
Node: The Exponential Power Distribution530780
Node: The Cauchy Distribution532048
Node: The Rayleigh Distribution533297
Node: The Rayleigh Tail Distribution534469
Node: The Landau Distribution535341
Node: The Levy alpha-Stable Distributions536296
Node: The Levy skew alpha-Stable Distribution537354
Node: The Gamma Distribution538966
Node: The Flat (Uniform) Distribution540623
Node: The Lognormal Distribution541775
Node: The Chi-squared Distribution543123
Node: The F-distribution544527
Node: The t-distribution546163
Node: The Beta Distribution547557
Node: The Logistic Distribution548716
Node: The Pareto Distribution549845
Node: Spherical Vector Distributions551015
Node: The Weibull Distribution553849
Node: The Type-1 Gumbel Distribution555043
Node: The Type-2 Gumbel Distribution556280
Node: The Dirichlet Distribution557511
Node: General Discrete Distributions559179
Node: The Poisson Distribution563044
Node: The Bernoulli Distribution564052
Node: The Binomial Distribution564803
Node: The Multinomial Distribution566008
Node: The Negative Binomial Distribution567777
Node: The Pascal Distribution569142
Node: The Geometric Distribution570300
Node: The Hypergeometric Distribution571548
Node: The Logarithmic Distribution573201
Node: Shuffling and Sampling573992
Node: Random Number Distribution Examples576811
Node: Random Number Distribution References and Further Reading580007
Node: Statistics582073
Node: Mean and standard deviation and variance583352
Node: Absolute deviation586397
Node: Higher moments (skewness and kurtosis)587689
Node: Autocorrelation589822
Node: Covariance590636
Node: Weighted Samples591617
Node: Maximum and Minimum values596861
Node: Median and Percentiles599600
Node: Example statistical programs602015
Node: Statistics References and Further Reading604674
Node: Histograms605882
Node: The histogram struct607642
Node: Histogram allocation609445
Node: Copying Histograms612406
Node: Updating and accessing histogram elements613082
Node: Searching histogram ranges616349
Node: Histogram Statistics617348
Node: Histogram Operations619208
Node: Reading and writing histograms621280
Node: Resampling from histograms624322
Node: The histogram probability distribution struct625120
Node: Example programs for histograms628151
Node: Two dimensional histograms630214
Node: The 2D histogram struct630935
Node: 2D Histogram allocation632743
Node: Copying 2D Histograms634814
Node: Updating and accessing 2D histogram elements635519
Node: Searching 2D histogram ranges639175
Node: 2D Histogram Statistics640194
Node: 2D Histogram Operations643053
Node: Reading and writing 2D histograms645227
Node: Resampling from 2D histograms648854
Node: Example programs for 2D histograms651873
Node: N-tuples653701
Node: The ntuple struct654957
Node: Creating ntuples655435
Node: Opening an existing ntuple file656102
Node: Writing ntuples656730
Node: Reading ntuples657191
Node: Closing an ntuple file657522
Node: Histogramming ntuple values657862
Node: Example ntuple programs659868
Node: Ntuple References and Further Reading663197
Node: Monte Carlo Integration663518
Node: Monte Carlo Interface664763
Node: PLAIN Monte Carlo667386
Node: MISER669824
Node: VEGAS675662
Node: Monte Carlo Examples683997
Node: Monte Carlo Integration References and Further Reading689940
Node: Simulated Annealing690722
Node: Simulated Annealing algorithm691929
Node: Simulated Annealing functions693083
Node: Examples with Simulated Annealing697609
Node: Trivial example698163
Node: Traveling Salesman Problem700814
Node: Simulated Annealing References and Further Reading704127
Node: Ordinary Differential Equations704538
Node: Defining the ODE System705359
Node: Stepping Functions707551
Node: Adaptive Step-size Control711730
Node: Evolution717188
Node: ODE Example programs719866
Node: ODE References and Further Reading724936
Node: Interpolation725575
Node: Introduction to Interpolation726588
Node: Interpolation Functions727029
Node: Interpolation Types728205
Node: Index Look-up and Acceleration730815
Node: Evaluation of Interpolating Functions732445
Node: Higher-level Interface734829
Node: Interpolation Example programs736868
Node: Interpolation References and Further Reading740115
Node: Numerical Differentiation740688
Node: Numerical Differentiation functions741277
Node: Numerical Differentiation Examples744135
Node: Numerical Differentiation References745548
Node: Chebyshev Approximations746099
Node: Chebyshev Definitions747115
Node: Creation and Calculation of Chebyshev Series747905
Node: Chebyshev Series Evaluation748877
Node: Derivatives and Integrals750261
Node: Chebyshev Approximation examples751503
Node: Chebyshev Approximation References and Further Reading752999
Node: Series Acceleration753448
Node: Acceleration functions754213
Node: Acceleration functions without error estimation756538
Node: Example of accelerating a series759148
Node: Series Acceleration References761494
Node: Wavelet Transforms762382
Node: DWT Definitions762923
Node: DWT Initialization763875
Node: DWT Transform Functions766454
Node: DWT in one dimension766989
Node: DWT in two dimension769008
Node: DWT Examples773609
Node: DWT References775426
Node: Discrete Hankel Transforms777589
Node: Discrete Hankel Transform Definition778057
Node: Discrete Hankel Transform Functions780196
Node: Discrete Hankel Transform References781727
Node: One dimensional Root-Finding782131
Node: Root Finding Overview783391
Node: Root Finding Caveats785249
Node: Initializing the Solver787016
Node: Providing the function to solve789649
Node: Search Bounds and Guesses793415
Node: Root Finding Iteration794276
Node: Search Stopping Parameters796125
Node: Root Bracketing Algorithms798639
Node: Root Finding Algorithms using Derivatives801937
Node: Root Finding Examples805440
Node: Root Finding References and Further Reading812728
Node: One dimensional Minimization813367
Node: Minimization Overview814669
Node: Minimization Caveats816375
Node: Initializing the Minimizer817712
Node: Providing the function to minimize819953
Node: Minimization Iteration820431
Node: Minimization Stopping Parameters822567
Node: Minimization Algorithms824176
Node: Minimization Examples826615
Node: Minimization References and Further Reading829559
Node: Multidimensional Root-Finding830015
Node: Overview of Multidimensional Root Finding831504
Node: Initializing the Multidimensional Solver833691
Node: Providing the multidimensional system of equations to solve836889
Node: Iteration of the multidimensional solver841794
Node: Search Stopping Parameters for the multidimensional solver843979
Node: Algorithms using Derivatives845716
Node: Algorithms without Derivatives850462
Node: Example programs for Multidimensional Root finding853550
Node: References and Further Reading for Multidimensional Root Finding862163
Node: Multidimensional Minimization863402
Node: Multimin Overview864694
Node: Multimin Caveats866666
Node: Initializing the Multidimensional Minimizer867415
Node: Providing a function to minimize870576
Node: Multimin Iteration874241
Node: Multimin Stopping Criteria876232
Node: Multimin Algorithms877784
Node: Multimin Examples882743
Node: Multimin References and Further Reading889360
Node: Least-Squares Fitting890223
Node: Fitting Overview891222
Node: Linear regression893438
Node: Linear fitting without a constant term895869
Node: Multi-parameter fitting898060
Node: Fitting Examples902965
Node: Fitting References and Further Reading909790
Node: Nonlinear Least-Squares Fitting910612
Node: Overview of Nonlinear Least-Squares Fitting912062
Node: Initializing the Nonlinear Least-Squares Solver913529
Node: Providing the Function to be Minimized916382
Node: Iteration of the Minimization Algorithm919319
Node: Search Stopping Parameters for Minimization Algorithms921169
Node: Minimization Algorithms using Derivatives923264
Node: Minimization Algorithms without Derivatives926512
Node: Computing the covariance matrix of best fit parameters926904
Node: Example programs for Nonlinear Least-Squares Fitting928938
Node: References and Further Reading for Nonlinear Least-Squares Fitting936666
Node: Basis Splines937402
Node: Overview of B-splines937977
Node: Initializing the B-splines solver939262
Node: Constructing the knots vector940005
Node: Evaluation of B-spline basis functions940792
Node: Example programs for B-splines941525
Node: References and Further Reading945222
Node: Physical Constants945736
Node: Fundamental Constants947146
Node: Astronomy and Astrophysics948285
Node: Atomic and Nuclear Physics948950
Node: Measurement of Time950587
Node: Imperial Units951017
Node: Speed and Nautical Units951459
Node: Printers Units951963
Node: Volume Area and Length952286
Node: Mass and Weight952972
Node: Thermal Energy and Power953791
Node: Pressure954214
Node: Viscosity954827
Node: Light and Illumination955103
Node: Radioactivity955695
Node: Force and Energy956030
Node: Prefixes956434
Node: Physical Constant Examples957177
Node: Physical Constant References and Further Reading958966
Node: IEEE floating-point arithmetic959677
Node: Representation of floating point numbers960263
Node: Setting up your IEEE environment964744
Node: IEEE References and Further Reading971353
Node: Debugging Numerical Programs972508
Node: Using gdb972992
Node: Examining floating point registers976335
Node: Handling floating point exceptions977620
Node: GCC warning options for numerical programs979032
Node: Debugging References983225
Node: Contributors to GSL983937
Node: Autoconf Macros988120
Node: GSL CBLAS Library992105
Node: Level 1 CBLAS Functions992632
Node: Level 2 CBLAS Functions997934
Node: Level 3 CBLAS Functions1014604
Node: GSL CBLAS Examples1024266
Node: Free Software Needs Free Documentation1025828
Node: GNU General Public License1030897
Node: GNU Free Documentation License1050167
Node: Function Index1072598
Node: Variable Index1306455
Node: Type Index1307627
Node: Concept Index1311273

End Tag Table
