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

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

   Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,
2005, 2006, 2007, 2008 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: 931
gsl-ref.info-2: 299527
gsl-ref.info-3: 598896
gsl-ref.info-4: 898337
gsl-ref.info-5: 1131697
gsl-ref.info-6: 1380540

Tag Table:
(Indirect)
Node: Top931
Node: Introduction3630
Node: Routines available in GSL4282
Node: GSL is Free Software6197
Node: Obtaining GSL8589
Node: No Warranty9730
Node: Reporting Bugs10236
Node: Further Information11120
Node: Conventions used in this manual12133
Node: Using the library12897
Node: An Example Program13483
Ref: An Example Program-Footnote-114226
Node: Compiling and Linking14333
Node: Linking programs with the library15403
Node: Linking with an alternative BLAS library16548
Node: Shared Libraries17478
Node: ANSI C Compliance18894
Node: Inline functions19987
Node: Long double21525
Node: Portability functions23113
Node: Alternative optimized functions24510
Node: Support for different numeric types25968
Node: Compatibility with C++29031
Node: Aliasing of arrays29603
Node: Thread-safety30354
Node: Deprecated Functions31441
Node: Code Reuse32066
Node: Error Handling32710
Node: Error Reporting33460
Node: Error Codes35352
Node: Error Handlers37208
Node: Using GSL error reporting in your own functions40845
Node: Error Reporting Examples42803
Node: Mathematical Functions44015
Node: Mathematical Constants44776
Node: Infinities and Not-a-number45906
Ref: Infinities and Not-a-number-Footnote-147013
Node: Elementary Functions47423
Node: Small integer powers49870
Node: Testing the Sign of Numbers51454
Node: Testing for Odd and Even Numbers51885
Node: Maximum and Minimum functions52441
Node: Approximate Comparison of Floating Point Numbers54716
Node: Complex Numbers56075
Ref: Complex Numbers-Footnote-157401
Node: Representation of complex numbers57465
Node: Properties of complex numbers59402
Node: Complex arithmetic operators60407
Node: Elementary Complex Functions63153
Node: Complex Trigonometric Functions64973
Node: Inverse Complex Trigonometric Functions66194
Node: Complex Hyperbolic Functions68800
Node: Inverse Complex Hyperbolic Functions70096
Node: Complex Number References and Further Reading72084
Node: Polynomials73480
Node: Polynomial Evaluation74247
Node: Divided Difference Representation of Polynomials75278
Node: Quadratic Equations77027
Node: Cubic Equations78967
Node: General Polynomial Equations80549
Node: Roots of Polynomials Examples82894
Node: Roots of Polynomials References and Further Reading84283
Node: Special Functions85228
Node: Special Function Usage87222
Node: The gsl_sf_result struct88405
Node: Special Function Modes89669
Node: Airy Functions and Derivatives90605
Node: Airy Functions91301
Node: Derivatives of Airy Functions92661
Node: Zeros of Airy Functions94173
Node: Zeros of Derivatives of Airy Functions94892
Node: Bessel Functions95651
Node: Regular Cylindrical Bessel Functions96843
Node: Irregular Cylindrical Bessel Functions98167
Node: Regular Modified Cylindrical Bessel Functions99623
Node: Irregular Modified Cylindrical Bessel Functions102450
Node: Regular Spherical Bessel Functions105418
Node: Irregular Spherical Bessel Functions107630
Node: Regular Modified Spherical Bessel Functions109317
Node: Irregular Modified Spherical Bessel Functions111320
Node: Regular Bessel Function - Fractional Order113383
Node: Irregular Bessel Functions - Fractional Order114381
Node: Regular Modified Bessel Functions - Fractional Order114963
Node: Irregular Modified Bessel Functions - Fractional Order115888
Node: Zeros of Regular Bessel Functions117124
Node: Clausen Functions118227
Node: Coulomb Functions118831
Node: Normalized Hydrogenic Bound States119280
Node: Coulomb Wave Functions120393
Node: Coulomb Wave Function Normalization Constant123803
Node: Coupling Coefficients124556
Node: 3-j Symbols125279
Node: 6-j Symbols125883
Node: 9-j Symbols126507
Node: Dawson Function127213
Node: Debye Functions127780
Node: Dilogarithm129554
Node: Real Argument129849
Node: Complex Argument130542
Node: Elementary Operations131011
Node: Elliptic Integrals131835
Node: Definition of Legendre Forms132407
Node: Definition of Carlson Forms133227
Node: Legendre Form of Complete Elliptic Integrals133924
Node: Legendre Form of Incomplete Elliptic Integrals135492
Node: Carlson Forms137680
Node: Elliptic Functions (Jacobi)139227
Node: Error Functions139808
Node: Error Function140259
Node: Complementary Error Function140632
Node: Log Complementary Error Function141092
Node: Probability functions141544
Node: Exponential Functions142797
Node: Exponential Function143180
Node: Relative Exponential Functions144403
Node: Exponentiation With Error Estimate146074
Node: Exponential Integrals147283
Node: Exponential Integral147765
Node: Ei(x)148692
Node: Hyperbolic Integrals149140
Node: Ei_3(x)149796
Node: Trigonometric Integrals150188
Node: Arctangent Integral150787
Node: Fermi-Dirac Function151187
Node: Complete Fermi-Dirac Integrals151557
Node: Incomplete Fermi-Dirac Integrals154125
Node: Gamma and Beta Functions154768
Node: Gamma Functions155204
Node: Factorials158325
Node: Pochhammer Symbol160878
Node: Incomplete Gamma Functions162390
Node: Beta Functions163639
Node: Incomplete Beta Function164391
Node: Gegenbauer Functions165102
Node: Hypergeometric Functions166752
Node: Laguerre Functions171032
Node: Lambert W Functions172595
Node: Legendre Functions and Spherical Harmonics173633
Node: Legendre Polynomials174222
Node: Associated Legendre Polynomials and Spherical Harmonics176302
Node: Conical Functions179183
Node: Radial Functions for Hyperbolic Space181306
Node: Logarithm and Related Functions183483
Node: Mathieu Functions185107
Node: Mathieu Function Workspace186456
Node: Mathieu Function Characteristic Values187269
Node: Angular Mathieu Functions188337
Node: Radial Mathieu Functions189369
Node: Power Function190607
Node: Psi (Digamma) Function191534
Node: Digamma Function192054
Node: Trigamma Function192884
Node: Polygamma Function193461
Node: Synchrotron Functions193845
Node: Transport Functions194608
Node: Trigonometric Functions195755
Node: Circular Trigonometric Functions196378
Node: Trigonometric Functions for Complex Arguments197387
Node: Hyperbolic Trigonometric Functions198421
Node: Conversion Functions199024
Node: Restriction Functions199807
Node: Trigonometric Functions With Error Estimates200739
Node: Zeta Functions201649
Node: Riemann Zeta Function202107
Node: Riemann Zeta Function Minus One202786
Node: Hurwitz Zeta Function203557
Node: Eta Function204062
Node: Special Functions Examples204621
Node: Special Functions References and Further Reading206315
Node: Vectors and Matrices207422
Node: Data types208181
Node: Blocks209384
Node: Block allocation210300
Node: Reading and writing blocks211784
Node: Example programs for blocks213848
Node: Vectors214475
Node: Vector allocation216361
Node: Accessing vector elements217979
Node: Initializing vector elements220462
Node: Reading and writing vectors221156
Node: Vector views223246
Node: Copying vectors230688
Node: Exchanging elements231548
Node: Vector operations232106
Node: Finding maximum and minimum elements of vectors233559
Node: Vector properties235145
Node: Example programs for vectors235910
Node: Matrices238199
Node: Matrix allocation241057
Node: Accessing matrix elements242724
Node: Initializing matrix elements244673
Node: Reading and writing matrices245469
Node: Matrix views247572
Node: Creating row and column views254712
Node: Copying matrices259183
Node: Copying rows and columns259779
Node: Exchanging rows and columns261456
Node: Matrix operations262934
Node: Finding maximum and minimum elements of matrices264574
Node: Matrix properties266478
Node: Example programs for matrices267370
Node: Vector and Matrix References and Further Reading271441
Node: Permutations271927
Node: The Permutation struct273215
Node: Permutation allocation273719
Node: Accessing permutation elements275153
Node: Permutation properties275996
Node: Permutation functions276701
Node: Applying Permutations277958
Node: Reading and writing permutations279883
Ref: Reading and writing permutations-Footnote-1282098
Node: Permutations in cyclic form282210
Node: Permutation Examples285635
Node: Permutation References and Further Reading288178
Node: Combinations288852
Node: The Combination struct289697
Node: Combination allocation290249
Node: Accessing combination elements292034
Node: Combination properties292693
Node: Combination functions293579
Node: Reading and writing combinations294519
Ref: Reading and writing combinations-Footnote-1296753
Node: Combination Examples296865
Node: Combination References and Further Reading298173
Node: Sorting298577
Node: Sorting objects299527
Node: Sorting vectors302438
Node: Selecting the k smallest or largest elements305014
Node: Computing the rank308348
Node: Sorting Examples309549
Node: Sorting References and Further Reading311193
Node: BLAS Support311739
Node: GSL BLAS Interface314893
Node: Level 1 GSL BLAS Interface315380
Node: Level 2 GSL BLAS Interface322123
Node: Level 3 GSL BLAS Interface331417
Node: BLAS Examples342557
Node: BLAS References and Further Reading343978
Node: Linear Algebra345337
Node: LU Decomposition346462
Node: QR Decomposition351707
Node: QR Decomposition with Column Pivoting358016
Node: Singular Value Decomposition362471
Node: Cholesky Decomposition366442
Node: Tridiagonal Decomposition of Real Symmetric Matrices369527
Node: Tridiagonal Decomposition of Hermitian Matrices371375
Node: Hessenberg Decomposition of Real Matrices373330
Node: Hessenberg-Triangular Decomposition of Real Matrices375740
Node: Bidiagonalization376860
Node: Householder Transformations379285
Node: Householder solver for linear systems381637
Node: Tridiagonal Systems382542
Node: Balancing385414
Node: Linear Algebra Examples386215
Node: Linear Algebra References and Further Reading388203
Node: Eigensystems389848
Node: Real Symmetric Matrices391062
Node: Complex Hermitian Matrices393576
Node: Real Nonsymmetric Matrices396084
Node: Real Generalized Symmetric-Definite Eigensystems401287
Node: Complex Generalized Hermitian-Definite Eigensystems404159
Node: Real Generalized Nonsymmetric Eigensystems406866
Node: Sorting Eigenvalues and Eigenvectors413440
Node: Eigenvalue and Eigenvector Examples416717
Node: Eigenvalue and Eigenvector References422105
Node: Fast Fourier Transforms423130
Node: Mathematical Definitions424339
Node: Overview of complex data FFTs426744
Node: Radix-2 FFT routines for complex data429687
Node: Mixed-radix FFT routines for complex data433899
Node: Overview of real data FFTs443228
Node: Radix-2 FFT routines for real data445662
Node: Mixed-radix FFT routines for real data450091
Node: FFT References and Further Reading460765
Node: Numerical Integration463634
Node: Numerical Integration Introduction465179
Node: Integrands without weight functions467448
Node: Integrands with weight functions468277
Node: Integrands with singular weight functions468988
Node: QNG non-adaptive Gauss-Kronrod integration469906
Node: QAG adaptive integration471187
Node: QAGS adaptive integration with singularities473818
Node: QAGP adaptive integration with known singular points475618
Node: QAGI adaptive integration on infinite intervals476932
Node: QAWC adaptive integration for Cauchy principal values479225
Node: QAWS adaptive integration for singular functions480400
Node: QAWO adaptive integration for oscillatory functions483622
Node: QAWF adaptive integration for Fourier integrals487401
Node: Numerical integration error codes490026
Node: Numerical integration examples490794
Node: Numerical integration References and Further Reading492839
Node: Random Number Generation493568
Node: General comments on random numbers495070
Node: The Random Number Generator Interface497020
Node: Random number generator initialization498378
Node: Sampling from a random number generator500751
Node: Auxiliary random number generator functions503992
Node: Random number environment variables506312
Node: Copying random number generator state508838
Node: Reading and writing random number generator state509813
Node: Random number generator algorithms511207
Node: Unix random number generators521016
Node: Other random number generators524734
Node: Random Number Generator Performance533367
Node: Random Number Generator Examples534685
Node: Random Number References and Further Reading536241
Node: Random Number Acknowledgements537538
Node: Quasi-Random Sequences538024
Node: Quasi-random number generator initialization539131
Node: Sampling from a quasi-random number generator540146
Node: Auxiliary quasi-random number generator functions540843
Node: Saving and resorting quasi-random number generator state541789
Node: Quasi-random number generator algorithms542597
Node: Quasi-random number generator examples543733
Node: Quasi-random number references544718
Node: Random Number Distributions545244
Node: Random Number Distribution Introduction548443
Node: The Gaussian Distribution550238
Node: The Gaussian Tail Distribution552900
Node: The Bivariate Gaussian Distribution554569
Node: The Exponential Distribution555892
Node: The Laplace Distribution557031
Node: The Exponential Power Distribution558128
Node: The Cauchy Distribution559396
Node: The Rayleigh Distribution560645
Node: The Rayleigh Tail Distribution561817
Node: The Landau Distribution562689
Node: The Levy alpha-Stable Distributions563644
Node: The Levy skew alpha-Stable Distribution564702
Node: The Gamma Distribution566314
Node: The Flat (Uniform) Distribution567971
Node: The Lognormal Distribution569123
Node: The Chi-squared Distribution570471
Node: The F-distribution571875
Node: The t-distribution573511
Node: The Beta Distribution574905
Node: The Logistic Distribution576064
Node: The Pareto Distribution577193
Node: Spherical Vector Distributions578363
Node: The Weibull Distribution581197
Node: The Type-1 Gumbel Distribution582391
Node: The Type-2 Gumbel Distribution583628
Node: The Dirichlet Distribution584859
Node: General Discrete Distributions586527
Node: The Poisson Distribution590392
Node: The Bernoulli Distribution591400
Node: The Binomial Distribution592151
Node: The Multinomial Distribution593356
Node: The Negative Binomial Distribution595125
Node: The Pascal Distribution596490
Node: The Geometric Distribution597648
Node: The Hypergeometric Distribution598896
Node: The Logarithmic Distribution600549
Node: Shuffling and Sampling601340
Node: Random Number Distribution Examples604159
Node: Random Number Distribution References and Further Reading607355
Node: Statistics609421
Node: Mean and standard deviation and variance610716
Node: Absolute deviation614224
Node: Higher moments (skewness and kurtosis)615516
Node: Autocorrelation617649
Node: Covariance618463
Node: Correlation619439
Node: Weighted Samples620148
Node: Maximum and Minimum values625976
Node: Median and Percentiles628715
Node: Example statistical programs631130
Node: Statistics References and Further Reading633791
Node: Histograms634999
Node: The histogram struct636759
Node: Histogram allocation638562
Node: Copying Histograms641523
Node: Updating and accessing histogram elements642199
Node: Searching histogram ranges645466
Node: Histogram Statistics646465
Node: Histogram Operations648325
Node: Reading and writing histograms650397
Node: Resampling from histograms653439
Node: The histogram probability distribution struct654237
Node: Example programs for histograms657268
Node: Two dimensional histograms659331
Node: The 2D histogram struct660052
Node: 2D Histogram allocation661860
Node: Copying 2D Histograms663931
Node: Updating and accessing 2D histogram elements664636
Node: Searching 2D histogram ranges668292
Node: 2D Histogram Statistics669311
Node: 2D Histogram Operations672170
Node: Reading and writing 2D histograms674344
Node: Resampling from 2D histograms677973
Node: Example programs for 2D histograms680992
Node: N-tuples682820
Node: The ntuple struct684076
Node: Creating ntuples684554
Node: Opening an existing ntuple file685221
Node: Writing ntuples685849
Node: Reading ntuples686310
Node: Closing an ntuple file686641
Node: Histogramming ntuple values686981
Node: Example ntuple programs688987
Node: Ntuple References and Further Reading692316
Node: Monte Carlo Integration692637
Node: Monte Carlo Interface693882
Node: PLAIN Monte Carlo696505
Node: MISER698943
Node: VEGAS704781
Node: Monte Carlo Examples713116
Node: Monte Carlo Integration References and Further Reading719059
Node: Simulated Annealing719841
Node: Simulated Annealing algorithm721048
Node: Simulated Annealing functions722202
Node: Examples with Simulated Annealing726737
Node: Trivial example727291
Node: Traveling Salesman Problem729942
Node: Simulated Annealing References and Further Reading733255
Node: Ordinary Differential Equations733666
Node: Defining the ODE System734487
Node: Stepping Functions736679
Node: Adaptive Step-size Control741024
Node: Evolution746482
Node: ODE Example programs750099
Node: ODE References and Further Reading755338
Node: Interpolation755977
Node: Introduction to Interpolation756990
Node: Interpolation Functions757431
Node: Interpolation Types758638
Node: Index Look-up and Acceleration761248
Node: Evaluation of Interpolating Functions763043
Node: Higher-level Interface765427
Node: Interpolation Example programs767466
Node: Interpolation References and Further Reading770716
Node: Numerical Differentiation771289
Node: Numerical Differentiation functions771878
Node: Numerical Differentiation Examples774736
Node: Numerical Differentiation References776149
Node: Chebyshev Approximations776700
Node: Chebyshev Definitions777761
Node: Creation and Calculation of Chebyshev Series778551
Node: Auxiliary Functions for Chebyshev Series779536
Node: Chebyshev Series Evaluation780276
Node: Derivatives and Integrals781656
Node: Chebyshev Approximation Examples782898
Node: Chebyshev Approximation References and Further Reading784394
Node: Series Acceleration784843
Node: Acceleration functions785608
Node: Acceleration functions without error estimation787933
Node: Example of accelerating a series790543
Node: Series Acceleration References792889
Node: Wavelet Transforms793777
Node: DWT Definitions794318
Node: DWT Initialization795270
Node: DWT Transform Functions797849
Node: DWT in one dimension798384
Node: DWT in two dimension800403
Node: DWT Examples805004
Node: DWT References806821
Node: Discrete Hankel Transforms808984
Node: Discrete Hankel Transform Definition809452
Node: Discrete Hankel Transform Functions811591
Node: Discrete Hankel Transform References813122
Node: One dimensional Root-Finding813526
Node: Root Finding Overview814786
Node: Root Finding Caveats816644
Node: Initializing the Solver818411
Node: Providing the function to solve821044
Node: Search Bounds and Guesses824810
Node: Root Finding Iteration825671
Node: Search Stopping Parameters827520
Node: Root Bracketing Algorithms830034
Node: Root Finding Algorithms using Derivatives833332
Node: Root Finding Examples836835
Node: Root Finding References and Further Reading844123
Node: One dimensional Minimization844762
Node: Minimization Overview846064
Node: Minimization Caveats847770
Node: Initializing the Minimizer849107
Node: Providing the function to minimize851348
Node: Minimization Iteration851826
Node: Minimization Stopping Parameters853962
Node: Minimization Algorithms855571
Node: Minimization Examples858010
Node: Minimization References and Further Reading860937
Node: Multidimensional Root-Finding861393
Node: Overview of Multidimensional Root Finding862882
Node: Initializing the Multidimensional Solver865069
Node: Providing the multidimensional system of equations to solve868300
Node: Iteration of the multidimensional solver873205
Node: Search Stopping Parameters for the multidimensional solver875484
Node: Algorithms using Derivatives877221
Node: Algorithms without Derivatives881967
Node: Example programs for Multidimensional Root finding885055
Node: References and Further Reading for Multidimensional Root Finding893668
Node: Multidimensional Minimization894907
Node: Multimin Overview896260
Node: Multimin Caveats898337
Node: Initializing the Multidimensional Minimizer899086
Node: Providing a function to minimize902247
Node: Multimin Iteration906299
Node: Multimin Stopping Criteria908290
Node: Multimin Algorithms with Derivatives909859
Node: Multimin Algorithms without Derivatives913387
Node: Multimin Examples915562
Node: Multimin References and Further Reading922142
Node: Least-Squares Fitting923007
Node: Fitting Overview924006
Node: Linear regression926340
Node: Linear fitting without a constant term928942
Node: Multi-parameter fitting931135
Node: Fitting Examples936785
Node: Fitting References and Further Reading943610
Node: Nonlinear Least-Squares Fitting944432
Node: Overview of Nonlinear Least-Squares Fitting945882
Node: Initializing the Nonlinear Least-Squares Solver947349
Node: Providing the Function to be Minimized950202
Node: Iteration of the Minimization Algorithm953139
Node: Search Stopping Parameters for Minimization Algorithms954989
Node: Minimization Algorithms using Derivatives957084
Node: Minimization Algorithms without Derivatives960332
Node: Computing the covariance matrix of best fit parameters960724
Node: Example programs for Nonlinear Least-Squares Fitting962758
Node: References and Further Reading for Nonlinear Least-Squares Fitting970486
Node: Basis Splines971222
Node: Overview of B-splines971851
Node: Initializing the B-splines solver973134
Node: Constructing the knots vector974466
Node: Evaluation of B-spline basis functions975253
Node: Evaluation of B-spline basis function derivatives976812
Node: Example programs for B-splines978731
Node: References and Further Reading982747
Node: Physical Constants983291
Node: Fundamental Constants984701
Node: Astronomy and Astrophysics985840
Node: Atomic and Nuclear Physics986505
Node: Measurement of Time988142
Node: Imperial Units988572
Node: Speed and Nautical Units989014
Node: Printers Units989518
Node: Volume Area and Length989841
Node: Mass and Weight990527
Node: Thermal Energy and Power991346
Node: Pressure991769
Node: Viscosity992382
Node: Light and Illumination992658
Node: Radioactivity993250
Node: Force and Energy993585
Node: Prefixes993989
Node: Physical Constant Examples994732
Node: Physical Constant References and Further Reading996521
Node: IEEE floating-point arithmetic997232
Node: Representation of floating point numbers997818
Node: Setting up your IEEE environment1002299
Node: IEEE References and Further Reading1009291
Node: Debugging Numerical Programs1010446
Node: Using gdb1010930
Node: Examining floating point registers1014273
Node: Handling floating point exceptions1015558
Node: GCC warning options for numerical programs1016970
Node: Debugging References1021149
Node: Contributors to GSL1021861
Node: Autoconf Macros1026096
Node: GSL CBLAS Library1030125
Node: Level 1 CBLAS Functions1030652
Node: Level 2 CBLAS Functions1035954
Node: Level 3 CBLAS Functions1052624
Node: GSL CBLAS Examples1062286
Node: Free Software Needs Free Documentation1063848
Node: GNU General Public License1068917
Node: GNU Free Documentation License1106529
Node: Function Index1131697
Node: Variable Index1375646
Node: Type Index1376818
Node: Concept Index1380540

End Tag Table
