This is gsl-ref.info, produced by makeinfo version 4.11 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, 2008, 2009, 2010 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: 942
gsl-ref.info-2: 300372
gsl-ref.info-3: 600243
gsl-ref.info-4: 899105
gsl-ref.info-5: 1151767
gsl-ref.info-6: 1416298

Tag Table:
(Indirect)
Node: Top942
Node: Introduction3667
Node: Routines available in GSL4319
Node: GSL is Free Software6234
Node: Obtaining GSL8626
Node: No Warranty9653
Node: Reporting Bugs10159
Ref: Reporting Bugs-Footnote-111115
Node: Further Information11165
Node: Conventions used in this manual12178
Node: Using the library12942
Node: An Example Program13528
Ref: An Example Program-Footnote-114271
Node: Compiling and Linking14378
Node: Linking programs with the library15448
Node: Linking with an alternative BLAS library16593
Node: Shared Libraries17675
Ref: Shared Libraries-Footnote-119150
Node: ANSI C Compliance19198
Node: Inline functions20291
Node: Long double21829
Node: Portability functions23417
Node: Alternative optimized functions24814
Node: Support for different numeric types26272
Node: Compatibility with C++29335
Node: Aliasing of arrays29907
Node: Thread-safety30658
Node: Deprecated Functions31745
Node: Code Reuse32370
Node: Error Handling33014
Node: Error Reporting33764
Node: Error Codes35656
Node: Error Handlers37512
Node: Using GSL error reporting in your own functions41149
Node: Error Reporting Examples43107
Node: Mathematical Functions44319
Node: Mathematical Constants45080
Node: Infinities and Not-a-number46210
Ref: Infinities and Not-a-number-Footnote-147317
Node: Elementary Functions47727
Node: Small integer powers50174
Node: Testing the Sign of Numbers51758
Node: Testing for Odd and Even Numbers52189
Node: Maximum and Minimum functions52745
Node: Approximate Comparison of Floating Point Numbers55020
Node: Complex Numbers56379
Ref: Complex Numbers-Footnote-157705
Node: Representation of complex numbers57769
Node: Properties of complex numbers59706
Node: Complex arithmetic operators60711
Node: Elementary Complex Functions63457
Node: Complex Trigonometric Functions65277
Node: Inverse Complex Trigonometric Functions66498
Node: Complex Hyperbolic Functions69104
Node: Inverse Complex Hyperbolic Functions70400
Node: Complex Number References and Further Reading72388
Node: Polynomials73784
Node: Polynomial Evaluation74551
Node: Divided Difference Representation of Polynomials75961
Node: Quadratic Equations77710
Node: Cubic Equations79650
Node: General Polynomial Equations81232
Node: Roots of Polynomials Examples83577
Node: Roots of Polynomials References and Further Reading84966
Node: Special Functions85911
Node: Special Function Usage87905
Node: The gsl_sf_result struct89088
Node: Special Function Modes90352
Node: Airy Functions and Derivatives91288
Node: Airy Functions91984
Node: Derivatives of Airy Functions93344
Node: Zeros of Airy Functions94856
Node: Zeros of Derivatives of Airy Functions95575
Node: Bessel Functions96334
Node: Regular Cylindrical Bessel Functions97526
Node: Irregular Cylindrical Bessel Functions98850
Node: Regular Modified Cylindrical Bessel Functions100308
Node: Irregular Modified Cylindrical Bessel Functions103135
Node: Regular Spherical Bessel Functions106103
Node: Irregular Spherical Bessel Functions108317
Node: Regular Modified Spherical Bessel Functions110004
Node: Irregular Modified Spherical Bessel Functions112007
Node: Regular Bessel Function - Fractional Order114070
Node: Irregular Bessel Functions - Fractional Order115068
Node: Regular Modified Bessel Functions - Fractional Order115650
Node: Irregular Modified Bessel Functions - Fractional Order116575
Node: Zeros of Regular Bessel Functions117811
Node: Clausen Functions118914
Node: Coulomb Functions119518
Node: Normalized Hydrogenic Bound States119967
Node: Coulomb Wave Functions121080
Node: Coulomb Wave Function Normalization Constant124490
Node: Coupling Coefficients125243
Node: 3-j Symbols125966
Node: 6-j Symbols126570
Node: 9-j Symbols127194
Node: Dawson Function127900
Node: Debye Functions128467
Node: Dilogarithm130241
Node: Real Argument130536
Node: Complex Argument131229
Node: Elementary Operations131698
Node: Elliptic Integrals132522
Node: Definition of Legendre Forms133094
Node: Definition of Carlson Forms133914
Node: Legendre Form of Complete Elliptic Integrals134611
Node: Legendre Form of Incomplete Elliptic Integrals136179
Node: Carlson Forms138367
Node: Elliptic Functions (Jacobi)139914
Node: Error Functions140495
Node: Error Function140946
Node: Complementary Error Function141319
Node: Log Complementary Error Function141779
Node: Probability functions142231
Node: Exponential Functions143484
Node: Exponential Function143867
Node: Relative Exponential Functions145090
Node: Exponentiation With Error Estimate146762
Node: Exponential Integrals147971
Node: Exponential Integral148453
Node: Ei(x)149380
Node: Hyperbolic Integrals149828
Node: Ei_3(x)150484
Node: Trigonometric Integrals150876
Node: Arctangent Integral151475
Node: Fermi-Dirac Function151875
Node: Complete Fermi-Dirac Integrals152245
Node: Incomplete Fermi-Dirac Integrals154813
Node: Gamma and Beta Functions155456
Node: Gamma Functions156029
Node: Factorials159138
Node: Pochhammer Symbol161691
Node: Incomplete Gamma Functions163197
Node: Beta Functions164446
Node: Incomplete Beta Function165198
Node: Gegenbauer Functions165909
Node: Hypergeometric Functions167559
Node: Laguerre Functions171822
Node: Lambert W Functions173385
Node: Legendre Functions and Spherical Harmonics174423
Node: Legendre Polynomials175012
Node: Associated Legendre Polynomials and Spherical Harmonics177067
Node: Conical Functions179900
Node: Radial Functions for Hyperbolic Space182023
Node: Logarithm and Related Functions184200
Node: Mathieu Functions185824
Node: Mathieu Function Workspace187173
Node: Mathieu Function Characteristic Values187987
Node: Angular Mathieu Functions189059
Node: Radial Mathieu Functions190095
Node: Power Function191337
Node: Psi (Digamma) Function192264
Node: Digamma Function192784
Node: Trigamma Function193614
Node: Polygamma Function194191
Node: Synchrotron Functions194575
Node: Transport Functions195338
Node: Trigonometric Functions196485
Node: Circular Trigonometric Functions197108
Node: Trigonometric Functions for Complex Arguments198117
Node: Hyperbolic Trigonometric Functions199153
Node: Conversion Functions199756
Node: Restriction Functions200539
Node: Trigonometric Functions With Error Estimates201471
Node: Zeta Functions202381
Node: Riemann Zeta Function202839
Node: Riemann Zeta Function Minus One203518
Node: Hurwitz Zeta Function204289
Node: Eta Function204794
Node: Special Functions Examples205353
Node: Special Functions References and Further Reading207047
Node: Vectors and Matrices208317
Node: Data types209076
Node: Blocks210279
Node: Block allocation211195
Node: Reading and writing blocks212679
Node: Example programs for blocks214743
Node: Vectors215370
Node: Vector allocation217256
Node: Accessing vector elements218874
Ref: Accessing vector elements-Footnote-1222016
Node: Initializing vector elements222255
Node: Reading and writing vectors222949
Node: Vector views225039
Node: Copying vectors232481
Node: Exchanging elements233341
Node: Vector operations233899
Node: Finding maximum and minimum elements of vectors235352
Node: Vector properties236938
Node: Example programs for vectors237703
Node: Matrices239992
Node: Matrix allocation242850
Node: Accessing matrix elements244517
Node: Initializing matrix elements246466
Node: Reading and writing matrices247262
Node: Matrix views249365
Node: Creating row and column views256505
Node: Copying matrices260975
Node: Copying rows and columns261571
Node: Exchanging rows and columns263248
Node: Matrix operations264726
Node: Finding maximum and minimum elements of matrices266366
Node: Matrix properties268270
Node: Example programs for matrices269162
Node: Vector and Matrix References and Further Reading273233
Node: Permutations273719
Node: The Permutation struct275007
Node: Permutation allocation275511
Node: Accessing permutation elements276945
Node: Permutation properties277788
Node: Permutation functions278493
Node: Applying Permutations279750
Node: Reading and writing permutations281676
Ref: Reading and writing permutations-Footnote-1283891
Node: Permutations in cyclic form284003
Node: Permutation Examples287428
Node: Permutation References and Further Reading289971
Node: Combinations290645
Node: The Combination struct291492
Node: Combination allocation292044
Node: Accessing combination elements293829
Node: Combination properties294488
Node: Combination functions295374
Node: Reading and writing combinations296314
Ref: Reading and writing combinations-Footnote-1298548
Node: Combination Examples298660
Node: Combination References and Further Reading299968
Node: Multisets300372
Node: The Multiset struct301298
Node: Multiset allocation301820
Node: Accessing multiset elements303511
Node: Multiset properties304140
Node: Multiset functions304953
Node: Reading and writing multisets305863
Ref: Reading and writing multisets-Footnote-1308014
Node: Multiset Examples308126
Node: Sorting310234
Node: Sorting objects311181
Node: Sorting vectors314092
Node: Selecting the k smallest or largest elements316668
Node: Computing the rank320002
Node: Sorting Examples321203
Node: Sorting References and Further Reading322847
Node: BLAS Support323393
Ref: BLAS Support-Footnote-1326772
Node: GSL BLAS Interface326940
Node: Level 1 GSL BLAS Interface327427
Node: Level 2 GSL BLAS Interface334166
Node: Level 3 GSL BLAS Interface343460
Node: BLAS Examples354600
Node: BLAS References and Further Reading356021
Node: Linear Algebra357368
Node: LU Decomposition358493
Node: QR Decomposition363738
Node: QR Decomposition with Column Pivoting370047
Node: Singular Value Decomposition374502
Node: Cholesky Decomposition378498
Node: Tridiagonal Decomposition of Real Symmetric Matrices381583
Node: Tridiagonal Decomposition of Hermitian Matrices383431
Node: Hessenberg Decomposition of Real Matrices385383
Node: Hessenberg-Triangular Decomposition of Real Matrices387793
Node: Bidiagonalization388913
Node: Householder Transformations391338
Node: Householder solver for linear systems393690
Node: Tridiagonal Systems394595
Node: Balancing397467
Node: Linear Algebra Examples398268
Node: Linear Algebra References and Further Reading400256
Node: Eigensystems401901
Node: Real Symmetric Matrices403115
Node: Complex Hermitian Matrices405629
Node: Real Nonsymmetric Matrices408256
Node: Real Generalized Symmetric-Definite Eigensystems413469
Node: Complex Generalized Hermitian-Definite Eigensystems416341
Node: Real Generalized Nonsymmetric Eigensystems419048
Node: Sorting Eigenvalues and Eigenvectors425632
Node: Eigenvalue and Eigenvector Examples428909
Node: Eigenvalue and Eigenvector References434299
Node: Fast Fourier Transforms435324
Node: Mathematical Definitions436533
Node: Overview of complex data FFTs438938
Node: Radix-2 FFT routines for complex data441881
Node: Mixed-radix FFT routines for complex data446093
Node: Overview of real data FFTs455422
Node: Radix-2 FFT routines for real data457856
Node: Mixed-radix FFT routines for real data462285
Node: FFT References and Further Reading472959
Node: Numerical Integration475828
Node: Numerical Integration Introduction477552
Node: Integrands without weight functions479821
Node: Integrands with weight functions480650
Node: Integrands with singular weight functions481361
Node: QNG non-adaptive Gauss-Kronrod integration482279
Node: QAG adaptive integration483560
Node: QAGS adaptive integration with singularities486191
Node: QAGP adaptive integration with known singular points487991
Node: QAGI adaptive integration on infinite intervals489305
Node: QAWC adaptive integration for Cauchy principal values491598
Node: QAWS adaptive integration for singular functions492773
Node: QAWO adaptive integration for oscillatory functions495995
Node: QAWF adaptive integration for Fourier integrals499774
Node: Fixed order Gauss-Legendre integration502404
Node: Numerical integration error codes503949
Node: Numerical integration examples504708
Node: Numerical integration References and Further Reading506754
Node: Random Number Generation507483
Node: General comments on random numbers508985
Node: The Random Number Generator Interface510935
Node: Random number generator initialization512293
Node: Sampling from a random number generator514666
Node: Auxiliary random number generator functions517907
Node: Random number environment variables520227
Node: Copying random number generator state522753
Node: Reading and writing random number generator state523728
Node: Random number generator algorithms525122
Node: Unix random number generators534931
Node: Other random number generators538649
Node: Random Number Generator Performance547282
Node: Random Number Generator Examples548403
Node: Random Number References and Further Reading549959
Node: Random Number Acknowledgements551256
Node: Quasi-Random Sequences551742
Node: Quasi-random number generator initialization552849
Node: Sampling from a quasi-random number generator553864
Node: Auxiliary quasi-random number generator functions554561
Node: Saving and resorting quasi-random number generator state555507
Node: Quasi-random number generator algorithms556315
Node: Quasi-random number generator examples557451
Node: Quasi-random number references558436
Node: Random Number Distributions558962
Node: Random Number Distribution Introduction562161
Node: The Gaussian Distribution563956
Node: The Gaussian Tail Distribution566617
Node: The Bivariate Gaussian Distribution568286
Node: The Exponential Distribution569609
Node: The Laplace Distribution570748
Node: The Exponential Power Distribution571845
Node: The Cauchy Distribution573113
Node: The Rayleigh Distribution574362
Node: The Rayleigh Tail Distribution575534
Node: The Landau Distribution576406
Node: The Levy alpha-Stable Distributions577361
Node: The Levy skew alpha-Stable Distribution578419
Node: The Gamma Distribution580031
Node: The Flat (Uniform) Distribution581688
Node: The Lognormal Distribution582840
Node: The Chi-squared Distribution584188
Node: The F-distribution585592
Node: The t-distribution587228
Node: The Beta Distribution588622
Node: The Logistic Distribution589781
Node: The Pareto Distribution590910
Node: Spherical Vector Distributions592080
Node: The Weibull Distribution594914
Node: The Type-1 Gumbel Distribution596108
Node: The Type-2 Gumbel Distribution597345
Node: The Dirichlet Distribution598576
Node: General Discrete Distributions600243
Node: The Poisson Distribution604110
Node: The Bernoulli Distribution605118
Node: The Binomial Distribution605869
Node: The Multinomial Distribution607074
Node: The Negative Binomial Distribution608843
Node: The Pascal Distribution610208
Node: The Geometric Distribution611366
Node: The Hypergeometric Distribution612614
Node: The Logarithmic Distribution614267
Node: Shuffling and Sampling615058
Node: Random Number Distribution Examples617877
Node: Random Number Distribution References and Further Reading621073
Node: Statistics623216
Node: Mean and standard deviation and variance624616
Node: Absolute deviation628124
Node: Higher moments (skewness and kurtosis)629416
Node: Autocorrelation631549
Node: Covariance632363
Node: Correlation633339
Node: Weighted Samples634048
Node: Maximum and Minimum values639898
Node: Median and Percentiles642637
Node: Example statistical programs645052
Node: Statistics References and Further Reading647713
Node: Histograms648921
Node: The histogram struct650681
Node: Histogram allocation652484
Node: Copying Histograms655445
Node: Updating and accessing histogram elements656121
Node: Searching histogram ranges659388
Node: Histogram Statistics660387
Node: Histogram Operations662247
Node: Reading and writing histograms664319
Node: Resampling from histograms667361
Node: The histogram probability distribution struct668159
Node: Example programs for histograms671190
Node: Two dimensional histograms673253
Node: The 2D histogram struct673974
Node: 2D Histogram allocation675782
Node: Copying 2D Histograms677853
Node: Updating and accessing 2D histogram elements678558
Node: Searching 2D histogram ranges682214
Node: 2D Histogram Statistics683233
Node: 2D Histogram Operations686092
Node: Reading and writing 2D histograms688266
Node: Resampling from 2D histograms691895
Node: Example programs for 2D histograms694914
Node: N-tuples696742
Node: The ntuple struct697998
Node: Creating ntuples698476
Node: Opening an existing ntuple file699143
Node: Writing ntuples699771
Node: Reading ntuples700232
Node: Closing an ntuple file700563
Node: Histogramming ntuple values700903
Node: Example ntuple programs702911
Node: Ntuple References and Further Reading706240
Node: Monte Carlo Integration706561
Node: Monte Carlo Interface707806
Node: PLAIN Monte Carlo710429
Node: MISER712879
Ref: MISER-Footnote-1719555
Node: VEGAS719680
Node: Monte Carlo Examples729231
Node: Monte Carlo Integration References and Further Reading735216
Node: Simulated Annealing735998
Node: Simulated Annealing algorithm737205
Node: Simulated Annealing functions738359
Node: Examples with Simulated Annealing742894
Node: Trivial example743448
Node: Traveling Salesman Problem746099
Node: Simulated Annealing References and Further Reading749412
Node: Ordinary Differential Equations749823
Node: Defining the ODE System750644
Node: Stepping Functions752836
Node: Adaptive Step-size Control757181
Node: Evolution762639
Node: ODE Example programs766256
Node: ODE References and Further Reading771495
Node: Interpolation772134
Node: Introduction to Interpolation773305
Node: Interpolation Functions773746
Node: Interpolation Types774953
Node: Index Look-up and Acceleration777562
Node: Evaluation of Interpolating Functions779614
Node: Higher-level Interface781998
Node: Interpolation Example programs784037
Node: Interpolation References and Further Reading787253
Node: Numerical Differentiation787826
Node: Numerical Differentiation functions788415
Node: Numerical Differentiation Examples791273
Node: Numerical Differentiation References792686
Node: Chebyshev Approximations793237
Node: Chebyshev Definitions794298
Node: Creation and Calculation of Chebyshev Series795088
Node: Auxiliary Functions for Chebyshev Series796073
Node: Chebyshev Series Evaluation796813
Node: Derivatives and Integrals798193
Node: Chebyshev Approximation Examples799435
Node: Chebyshev Approximation References and Further Reading800931
Node: Series Acceleration801380
Node: Acceleration functions802145
Node: Acceleration functions without error estimation804470
Node: Example of accelerating a series807080
Node: Series Acceleration References809426
Node: Wavelet Transforms810314
Node: DWT Definitions810855
Node: DWT Initialization811807
Node: DWT Transform Functions814456
Node: DWT in one dimension814991
Node: DWT in two dimension817010
Node: DWT Examples821588
Node: DWT References823405
Node: Discrete Hankel Transforms825568
Node: Discrete Hankel Transform Definition826036
Node: Discrete Hankel Transform Functions828235
Node: Discrete Hankel Transform References829899
Node: One dimensional Root-Finding830303
Node: Root Finding Overview831563
Node: Root Finding Caveats833421
Node: Initializing the Solver835188
Node: Providing the function to solve837821
Node: Search Bounds and Guesses841587
Node: Root Finding Iteration842450
Node: Search Stopping Parameters844299
Node: Root Bracketing Algorithms846813
Node: Root Finding Algorithms using Derivatives850111
Ref: Root Finding Algorithms using Derivatives-Footnote-1853653
Node: Root Finding Examples853808
Node: Root Finding References and Further Reading861096
Node: One dimensional Minimization861735
Node: Minimization Overview863037
Node: Minimization Caveats864743
Node: Initializing the Minimizer866080
Node: Providing the function to minimize868321
Node: Minimization Iteration868799
Node: Minimization Stopping Parameters870935
Node: Minimization Algorithms872544
Node: Minimization Examples875148
Node: Minimization References and Further Reading878075
Node: Multidimensional Root-Finding878531
Node: Overview of Multidimensional Root Finding880020
Node: Initializing the Multidimensional Solver882207
Node: Providing the multidimensional system of equations to solve885438
Node: Iteration of the multidimensional solver890343
Node: Search Stopping Parameters for the multidimensional solver892622
Node: Algorithms using Derivatives894359
Node: Algorithms without Derivatives899105
Node: Example programs for Multidimensional Root finding902193
Node: References and Further Reading for Multidimensional Root Finding910806
Node: Multidimensional Minimization912045
Node: Multimin Overview913398
Node: Multimin Caveats915475
Node: Initializing the Multidimensional Minimizer916224
Node: Providing a function to minimize919385
Node: Multimin Iteration923437
Node: Multimin Stopping Criteria925428
Node: Multimin Algorithms with Derivatives926997
Node: Multimin Algorithms without Derivatives930525
Node: Multimin Examples933525
Node: Multimin References and Further Reading940091
Node: Least-Squares Fitting940956
Node: Fitting Overview941955
Node: Linear regression944289
Node: Linear fitting without a constant term946891
Node: Multi-parameter fitting949084
Node: Fitting Examples954898
Node: Fitting References and Further Reading961723
Node: Nonlinear Least-Squares Fitting962545
Node: Overview of Nonlinear Least-Squares Fitting963995
Node: Initializing the Nonlinear Least-Squares Solver965462
Node: Providing the Function to be Minimized968327
Node: Iteration of the Minimization Algorithm971264
Node: Search Stopping Parameters for Minimization Algorithms973114
Node: Minimization Algorithms using Derivatives975209
Ref: Minimization Algorithms using Derivatives-Footnote-1978690
Node: Minimization Algorithms without Derivatives978779
Node: Computing the covariance matrix of best fit parameters979171
Node: Example programs for Nonlinear Least-Squares Fitting981205
Node: References and Further Reading for Nonlinear Least-Squares Fitting988933
Node: Basis Splines989669
Node: Overview of B-splines990569
Node: Initializing the B-splines solver991878
Node: Constructing the knots vector993254
Node: Evaluation of B-spline basis functions994041
Node: Evaluation of B-spline basis function derivatives995698
Node: Obtaining Greville abscissae for B-spline basis functions997690
Node: Example programs for B-splines998728
Node: References and Further Reading1002740
Node: Physical Constants1003545
Node: Fundamental Constants1004955
Node: Astronomy and Astrophysics1006094
Node: Atomic and Nuclear Physics1006759
Node: Measurement of Time1008410
Node: Imperial Units1008840
Node: Speed and Nautical Units1009282
Node: Printers Units1009786
Node: Volume Area and Length1010109
Node: Mass and Weight1010795
Node: Thermal Energy and Power1011614
Node: Pressure1012037
Node: Viscosity1012650
Node: Light and Illumination1012926
Node: Radioactivity1013518
Node: Force and Energy1013853
Node: Prefixes1014257
Node: Physical Constant Examples1015000
Node: Physical Constant References and Further Reading1016789
Node: IEEE floating-point arithmetic1017519
Node: Representation of floating point numbers1018105
Node: Setting up your IEEE environment1022586
Node: IEEE References and Further Reading1029578
Node: Debugging Numerical Programs1030733
Node: Using gdb1031217
Node: Examining floating point registers1034560
Node: Handling floating point exceptions1035845
Node: GCC warning options for numerical programs1037257
Node: Debugging References1041219
Node: Contributors to GSL1041931
Node: Autoconf Macros1046166
Node: GSL CBLAS Library1050195
Node: Level 1 CBLAS Functions1050722
Node: Level 2 CBLAS Functions1056024
Node: Level 3 CBLAS Functions1072694
Node: GSL CBLAS Examples1082356
Node: Free Software Needs Free Documentation1083918
Node: GNU General Public License1088987
Node: GNU Free Documentation License1126599
Node: Function Index1151767
Node: Variable Index1398369
Node: Type Index1401672
Node: Concept Index1416298

End Tag Table
