This is gsl-ref.info, produced by makeinfo version 4.8 from
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INFO-DIR-SECTION Scientific software
START-INFO-DIR-ENTRY
* gsl-ref: (gsl-ref).                   GNU Scientific Library - Reference
END-INFO-DIR-ENTRY

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

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

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


Indirect:
gsl-ref.info-1: 924
gsl-ref.info-2: 300894
gsl-ref.info-3: 599483
gsl-ref.info-4: 896610
gsl-ref.info-5: 1119386
gsl-ref.info-6: 1365699

Tag Table:
(Indirect)
Node: Top924
Node: Introduction3617
Node: Routines available in GSL4269
Node: GSL is Free Software6184
Node: Obtaining GSL8576
Node: No Warranty9717
Node: Reporting Bugs10223
Node: Further Information11107
Node: Conventions used in this manual12120
Node: Using the library12884
Node: An Example Program13470
Ref: An Example Program-Footnote-114213
Node: Compiling and Linking14320
Node: Linking programs with the library15390
Node: Linking with an alternative BLAS library16535
Node: Shared Libraries17465
Node: ANSI C Compliance18881
Node: Inline functions19974
Node: Long double21017
Node: Portability functions22605
Node: Alternative optimized functions24002
Node: Support for different numeric types25460
Node: Compatibility with C++28523
Node: Aliasing of arrays29095
Node: Thread-safety29846
Node: Deprecated Functions30933
Node: Code Reuse31558
Node: Error Handling32202
Node: Error Reporting32952
Node: Error Codes34844
Node: Error Handlers36700
Node: Using GSL error reporting in your own functions40337
Node: Error Reporting Examples42295
Node: Mathematical Functions43507
Node: Mathematical Constants44268
Node: Infinities and Not-a-number45398
Node: Elementary Functions46466
Node: Small integer powers48913
Node: Testing the Sign of Numbers50497
Node: Testing for Odd and Even Numbers50928
Node: Maximum and Minimum functions51484
Node: Approximate Comparison of Floating Point Numbers53566
Node: Complex Numbers54925
Ref: Complex Numbers-Footnote-156233
Node: Complex numbers56297
Node: Properties of complex numbers58180
Node: Complex arithmetic operators59167
Node: Elementary Complex Functions61913
Node: Complex Trigonometric Functions63733
Node: Inverse Complex Trigonometric Functions64954
Node: Complex Hyperbolic Functions67560
Node: Inverse Complex Hyperbolic Functions68856
Node: Complex Number References and Further Reading70844
Node: Polynomials72240
Node: Polynomial Evaluation73007
Node: Divided Difference Representation of Polynomials74038
Node: Quadratic Equations75787
Node: Cubic Equations77727
Node: General Polynomial Equations79309
Node: Roots of Polynomials Examples81654
Node: Roots of Polynomials References and Further Reading83043
Node: Special Functions83988
Node: Special Function Usage85982
Node: The gsl_sf_result struct87165
Node: Special Function Modes88429
Node: Airy Functions and Derivatives89365
Node: Airy Functions90061
Node: Derivatives of Airy Functions91421
Node: Zeros of Airy Functions92933
Node: Zeros of Derivatives of Airy Functions93652
Node: Bessel Functions94411
Node: Regular Cylindrical Bessel Functions95603
Node: Irregular Cylindrical Bessel Functions96927
Node: Regular Modified Cylindrical Bessel Functions98383
Node: Irregular Modified Cylindrical Bessel Functions101210
Node: Regular Spherical Bessel Functions104178
Node: Irregular Spherical Bessel Functions106390
Node: Regular Modified Spherical Bessel Functions108077
Node: Irregular Modified Spherical Bessel Functions110080
Node: Regular Bessel Function - Fractional Order112143
Node: Irregular Bessel Functions - Fractional Order113141
Node: Regular Modified Bessel Functions - Fractional Order113723
Node: Irregular Modified Bessel Functions - Fractional Order114648
Node: Zeros of Regular Bessel Functions115884
Node: Clausen Functions116987
Node: Coulomb Functions117591
Node: Normalized Hydrogenic Bound States118040
Node: Coulomb Wave Functions119153
Node: Coulomb Wave Function Normalization Constant122563
Node: Coupling Coefficients123316
Node: 3-j Symbols124039
Node: 6-j Symbols124643
Node: 9-j Symbols125267
Node: Dawson Function125973
Node: Debye Functions126540
Node: Dilogarithm128314
Node: Real Argument128609
Node: Complex Argument129302
Node: Elementary Operations129771
Node: Elliptic Integrals130595
Node: Definition of Legendre Forms131167
Node: Definition of Carlson Forms131987
Node: Legendre Form of Complete Elliptic Integrals132684
Node: Legendre Form of Incomplete Elliptic Integrals134252
Node: Carlson Forms136440
Node: Elliptic Functions (Jacobi)137987
Node: Error Functions138568
Node: Error Function139019
Node: Complementary Error Function139392
Node: Log Complementary Error Function139852
Node: Probability functions140304
Node: Exponential Functions141557
Node: Exponential Function141940
Node: Relative Exponential Functions143163
Node: Exponentiation With Error Estimate144834
Node: Exponential Integrals146043
Node: Exponential Integral146525
Node: Ei(x)147452
Node: Hyperbolic Integrals147900
Node: Ei_3(x)148556
Node: Trigonometric Integrals148948
Node: Arctangent Integral149547
Node: Fermi-Dirac Function149947
Node: Complete Fermi-Dirac Integrals150317
Node: Incomplete Fermi-Dirac Integrals152885
Node: Gamma and Beta Functions153528
Node: Gamma Functions153964
Node: Factorials157085
Node: Pochhammer Symbol159638
Node: Incomplete Gamma Functions161150
Node: Beta Functions162399
Node: Incomplete Beta Function163151
Node: Gegenbauer Functions163862
Node: Hypergeometric Functions165512
Node: Laguerre Functions169792
Node: Lambert W Functions171355
Node: Legendre Functions and Spherical Harmonics172393
Node: Legendre Polynomials172982
Node: Associated Legendre Polynomials and Spherical Harmonics175062
Node: Conical Functions177943
Node: Radial Functions for Hyperbolic Space180066
Node: Logarithm and Related Functions182243
Node: Mathieu Functions183867
Node: Mathieu Function Workspace185216
Node: Mathieu Function Characteristic Values186029
Node: Angular Mathieu Functions187097
Node: Radial Mathieu Functions188129
Node: Power Function189367
Node: Psi (Digamma) Function190294
Node: Digamma Function190814
Node: Trigamma Function191644
Node: Polygamma Function192221
Node: Synchrotron Functions192605
Node: Transport Functions193368
Node: Trigonometric Functions194515
Node: Circular Trigonometric Functions195138
Node: Trigonometric Functions for Complex Arguments196147
Node: Hyperbolic Trigonometric Functions197181
Node: Conversion Functions197784
Node: Restriction Functions198567
Node: Trigonometric Functions With Error Estimates199499
Node: Zeta Functions200409
Node: Riemann Zeta Function200867
Node: Riemann Zeta Function Minus One201546
Node: Hurwitz Zeta Function202317
Node: Eta Function202822
Node: Special Functions Examples203381
Node: Special Functions References and Further Reading205075
Node: Vectors and Matrices206182
Node: Data types206941
Node: Blocks208144
Node: Block allocation209060
Node: Reading and writing blocks210544
Node: Example programs for blocks212608
Node: Vectors213235
Node: Vector allocation215121
Node: Accessing vector elements216739
Node: Initializing vector elements219222
Node: Reading and writing vectors219916
Node: Vector views222006
Node: Copying vectors229448
Node: Exchanging elements230308
Node: Vector operations230866
Node: Finding maximum and minimum elements of vectors232380
Node: Vector properties233905
Node: Example programs for vectors234519
Node: Matrices236808
Node: Matrix allocation239666
Node: Accessing matrix elements241333
Node: Initializing matrix elements243282
Node: Reading and writing matrices244078
Node: Matrix views246181
Node: Creating row and column views253321
Node: Copying matrices257792
Node: Copying rows and columns258388
Node: Exchanging rows and columns260065
Node: Matrix operations261543
Node: Finding maximum and minimum elements of matrices263183
Node: Matrix properties265087
Node: Example programs for matrices265826
Node: Vector and Matrix References and Further Reading269897
Node: Permutations270383
Node: The Permutation struct271671
Node: Permutation allocation272175
Node: Accessing permutation elements273609
Node: Permutation properties274452
Node: Permutation functions275157
Node: Applying Permutations276414
Node: Reading and writing permutations278339
Ref: Reading and writing permutations-Footnote-1280554
Node: Permutations in cyclic form280666
Node: Permutation Examples284091
Node: Permutation References and Further Reading286634
Node: Combinations287308
Node: The Combination struct288153
Node: Combination allocation288705
Node: Accessing combination elements290490
Node: Combination properties291149
Node: Combination functions292035
Node: Reading and writing combinations292975
Ref: Reading and writing combinations-Footnote-1295209
Node: Combination Examples295321
Node: Combination References and Further Reading296629
Node: Sorting297033
Node: Sorting objects297983
Node: Sorting vectors300894
Node: Selecting the k smallest or largest elements303470
Node: Computing the rank306804
Node: Sorting Examples308005
Node: Sorting References and Further Reading309649
Node: BLAS Support310195
Node: GSL BLAS Interface313170
Node: Level 1 GSL BLAS Interface313657
Node: Level 2 GSL BLAS Interface320400
Node: Level 3 GSL BLAS Interface329694
Node: BLAS Examples340830
Node: BLAS References and Further Reading342251
Node: Linear Algebra343610
Node: LU Decomposition344735
Node: QR Decomposition349943
Node: QR Decomposition with Column Pivoting356148
Node: Singular Value Decomposition360558
Node: Cholesky Decomposition364148
Node: Tridiagonal Decomposition of Real Symmetric Matrices366862
Node: Tridiagonal Decomposition of Hermitian Matrices368710
Node: Hessenberg Decomposition of Real Matrices370665
Node: Hessenberg-Triangular Decomposition of Real Matrices373075
Node: Bidiagonalization374195
Node: Householder Transformations376618
Node: Householder solver for linear systems378970
Node: Tridiagonal Systems379875
Node: Balancing382747
Node: Linear Algebra Examples383548
Node: Linear Algebra References and Further Reading385536
Node: Eigensystems387026
Node: Real Symmetric Matrices388240
Node: Complex Hermitian Matrices390754
Node: Real Nonsymmetric Matrices393262
Node: Real Generalized Symmetric-Definite Eigensystems398465
Node: Complex Generalized Hermitian-Definite Eigensystems401337
Node: Real Generalized Nonsymmetric Eigensystems404044
Node: Sorting Eigenvalues and Eigenvectors410618
Node: Eigenvalue and Eigenvector Examples413895
Node: Eigenvalue and Eigenvector References419283
Node: Fast Fourier Transforms420308
Node: Mathematical Definitions421517
Node: Overview of complex data FFTs423922
Node: Radix-2 FFT routines for complex data426865
Node: Mixed-radix FFT routines for complex data431077
Node: Overview of real data FFTs440406
Node: Radix-2 FFT routines for real data442840
Node: Mixed-radix FFT routines for real data445847
Node: FFT References and Further Reading456427
Node: Numerical Integration459296
Node: Numerical Integration Introduction460841
Node: Integrands without weight functions463110
Node: Integrands with weight functions463939
Node: Integrands with singular weight functions464650
Node: QNG non-adaptive Gauss-Kronrod integration465568
Node: QAG adaptive integration466849
Node: QAGS adaptive integration with singularities469480
Node: QAGP adaptive integration with known singular points471280
Node: QAGI adaptive integration on infinite intervals472594
Node: QAWC adaptive integration for Cauchy principal values474887
Node: QAWS adaptive integration for singular functions476062
Node: QAWO adaptive integration for oscillatory functions479284
Node: QAWF adaptive integration for Fourier integrals483063
Node: Numerical integration error codes485688
Node: Numerical integration examples486456
Node: Numerical integration References and Further Reading488501
Node: Random Number Generation489230
Node: General comments on random numbers490732
Node: The Random Number Generator Interface492682
Node: Random number generator initialization494040
Node: Sampling from a random number generator496056
Node: Auxiliary random number generator functions499297
Node: Random number environment variables501617
Node: Copying random number generator state504143
Node: Reading and writing random number generator state505118
Node: Random number generator algorithms506530
Node: Unix random number generators516339
Node: Other random number generators520057
Node: Random Number Generator Performance528690
Node: Random Number Generator Examples530008
Node: Random Number References and Further Reading531564
Node: Random Number Acknowledgements532861
Node: Quasi-Random Sequences533347
Node: Quasi-random number generator initialization534454
Node: Sampling from a quasi-random number generator535469
Node: Auxiliary quasi-random number generator functions536166
Node: Saving and resorting quasi-random number generator state537112
Node: Quasi-random number generator algorithms537920
Node: Quasi-random number generator examples539057
Node: Quasi-random number references540042
Node: Random Number Distributions540568
Node: Random Number Distribution Introduction543767
Node: The Gaussian Distribution545562
Node: The Gaussian Tail Distribution548224
Node: The Bivariate Gaussian Distribution549893
Node: The Exponential Distribution551216
Node: The Laplace Distribution552355
Node: The Exponential Power Distribution553452
Node: The Cauchy Distribution554720
Node: The Rayleigh Distribution555969
Node: The Rayleigh Tail Distribution557141
Node: The Landau Distribution558013
Node: The Levy alpha-Stable Distributions558968
Node: The Levy skew alpha-Stable Distribution560026
Node: The Gamma Distribution561638
Node: The Flat (Uniform) Distribution563295
Node: The Lognormal Distribution564447
Node: The Chi-squared Distribution565795
Node: The F-distribution567199
Node: The t-distribution568835
Node: The Beta Distribution570229
Node: The Logistic Distribution571388
Node: The Pareto Distribution572517
Node: Spherical Vector Distributions573687
Node: The Weibull Distribution576521
Node: The Type-1 Gumbel Distribution577715
Node: The Type-2 Gumbel Distribution578952
Node: The Dirichlet Distribution580183
Node: General Discrete Distributions581851
Node: The Poisson Distribution585716
Node: The Bernoulli Distribution586724
Node: The Binomial Distribution587475
Node: The Multinomial Distribution588680
Node: The Negative Binomial Distribution590449
Node: The Pascal Distribution591814
Node: The Geometric Distribution592972
Node: The Hypergeometric Distribution594220
Node: The Logarithmic Distribution595873
Node: Shuffling and Sampling596664
Node: Random Number Distribution Examples599483
Node: Random Number Distribution References and Further Reading602679
Node: Statistics604745
Node: Mean and standard deviation and variance606040
Node: Absolute deviation609548
Node: Higher moments (skewness and kurtosis)610840
Node: Autocorrelation612973
Node: Covariance613787
Node: Correlation614763
Node: Weighted Samples615472
Node: Maximum and Minimum values621300
Node: Median and Percentiles624039
Node: Example statistical programs626454
Node: Statistics References and Further Reading629115
Node: Histograms630323
Node: The histogram struct632083
Node: Histogram allocation633886
Node: Copying Histograms636847
Node: Updating and accessing histogram elements637523
Node: Searching histogram ranges640790
Node: Histogram Statistics641789
Node: Histogram Operations643649
Node: Reading and writing histograms645721
Node: Resampling from histograms648763
Node: The histogram probability distribution struct649561
Node: Example programs for histograms652592
Node: Two dimensional histograms654655
Node: The 2D histogram struct655376
Node: 2D Histogram allocation657184
Node: Copying 2D Histograms659255
Node: Updating and accessing 2D histogram elements659960
Node: Searching 2D histogram ranges663615
Node: 2D Histogram Statistics664634
Node: 2D Histogram Operations667493
Node: Reading and writing 2D histograms669667
Node: Resampling from 2D histograms673296
Node: Example programs for 2D histograms676315
Node: N-tuples678143
Node: The ntuple struct679399
Node: Creating ntuples679877
Node: Opening an existing ntuple file680544
Node: Writing ntuples681172
Node: Reading ntuples681633
Node: Closing an ntuple file681964
Node: Histogramming ntuple values682304
Node: Example ntuple programs684310
Node: Ntuple References and Further Reading687639
Node: Monte Carlo Integration687960
Node: Monte Carlo Interface689205
Node: PLAIN Monte Carlo691828
Node: MISER694266
Node: VEGAS700104
Node: Monte Carlo Examples708439
Node: Monte Carlo Integration References and Further Reading714382
Node: Simulated Annealing715164
Node: Simulated Annealing algorithm716371
Node: Simulated Annealing functions717525
Node: Examples with Simulated Annealing722060
Node: Trivial example722614
Node: Traveling Salesman Problem725265
Node: Simulated Annealing References and Further Reading728578
Node: Ordinary Differential Equations728989
Node: Defining the ODE System729810
Node: Stepping Functions732002
Node: Adaptive Step-size Control736347
Node: Evolution741805
Node: ODE Example programs745422
Node: ODE References and Further Reading750661
Node: Interpolation751300
Node: Introduction to Interpolation752313
Node: Interpolation Functions752754
Node: Interpolation Types753961
Node: Index Look-up and Acceleration756571
Node: Evaluation of Interpolating Functions758366
Node: Higher-level Interface760750
Node: Interpolation Example programs762789
Node: Interpolation References and Further Reading766039
Node: Numerical Differentiation766612
Node: Numerical Differentiation functions767201
Node: Numerical Differentiation Examples770059
Node: Numerical Differentiation References771472
Node: Chebyshev Approximations772023
Node: Chebyshev Definitions773039
Node: Creation and Calculation of Chebyshev Series773829
Node: Chebyshev Series Evaluation774801
Node: Derivatives and Integrals776185
Node: Chebyshev Approximation examples777427
Node: Chebyshev Approximation References and Further Reading778923
Node: Series Acceleration779372
Node: Acceleration functions780137
Node: Acceleration functions without error estimation782462
Node: Example of accelerating a series785072
Node: Series Acceleration References787418
Node: Wavelet Transforms788306
Node: DWT Definitions788847
Node: DWT Initialization789799
Node: DWT Transform Functions792378
Node: DWT in one dimension792913
Node: DWT in two dimension794932
Node: DWT Examples799533
Node: DWT References801350
Node: Discrete Hankel Transforms803513
Node: Discrete Hankel Transform Definition803981
Node: Discrete Hankel Transform Functions806120
Node: Discrete Hankel Transform References807651
Node: One dimensional Root-Finding808055
Node: Root Finding Overview809315
Node: Root Finding Caveats811173
Node: Initializing the Solver812940
Node: Providing the function to solve815573
Node: Search Bounds and Guesses819339
Node: Root Finding Iteration820200
Node: Search Stopping Parameters822049
Node: Root Bracketing Algorithms824563
Node: Root Finding Algorithms using Derivatives827861
Node: Root Finding Examples831364
Node: Root Finding References and Further Reading838652
Node: One dimensional Minimization839291
Node: Minimization Overview840593
Node: Minimization Caveats842299
Node: Initializing the Minimizer843636
Node: Providing the function to minimize845877
Node: Minimization Iteration846355
Node: Minimization Stopping Parameters848491
Node: Minimization Algorithms850100
Node: Minimization Examples852539
Node: Minimization References and Further Reading855466
Node: Multidimensional Root-Finding855922
Node: Overview of Multidimensional Root Finding857411
Node: Initializing the Multidimensional Solver859598
Node: Providing the multidimensional system of equations to solve862829
Node: Iteration of the multidimensional solver867734
Node: Search Stopping Parameters for the multidimensional solver870013
Node: Algorithms using Derivatives871750
Node: Algorithms without Derivatives876496
Node: Example programs for Multidimensional Root finding879584
Node: References and Further Reading for Multidimensional Root Finding888197
Node: Multidimensional Minimization889436
Node: Multimin Overview890728
Node: Multimin Caveats892700
Node: Initializing the Multidimensional Minimizer893449
Node: Providing a function to minimize896610
Node: Multimin Iteration900662
Node: Multimin Stopping Criteria902653
Node: Multimin Algorithms904205
Node: Multimin Examples909164
Node: Multimin References and Further Reading915784
Node: Least-Squares Fitting916647
Node: Fitting Overview917646
Node: Linear regression919980
Node: Linear fitting without a constant term922582
Node: Multi-parameter fitting924775
Node: Fitting Examples930425
Node: Fitting References and Further Reading937250
Node: Nonlinear Least-Squares Fitting938072
Node: Overview of Nonlinear Least-Squares Fitting939522
Node: Initializing the Nonlinear Least-Squares Solver940989
Node: Providing the Function to be Minimized943842
Node: Iteration of the Minimization Algorithm946779
Node: Search Stopping Parameters for Minimization Algorithms948629
Node: Minimization Algorithms using Derivatives950724
Node: Minimization Algorithms without Derivatives953972
Node: Computing the covariance matrix of best fit parameters954364
Node: Example programs for Nonlinear Least-Squares Fitting956398
Node: References and Further Reading for Nonlinear Least-Squares Fitting964126
Node: Basis Splines964862
Node: Overview of B-splines965437
Node: Initializing the B-splines solver966720
Node: Constructing the knots vector967463
Node: Evaluation of B-spline basis functions968250
Node: Example programs for B-splines969184
Node: References and Further Reading973189
Node: Physical Constants973703
Node: Fundamental Constants975113
Node: Astronomy and Astrophysics976252
Node: Atomic and Nuclear Physics976917
Node: Measurement of Time978554
Node: Imperial Units978984
Node: Speed and Nautical Units979426
Node: Printers Units979930
Node: Volume Area and Length980253
Node: Mass and Weight980939
Node: Thermal Energy and Power981758
Node: Pressure982181
Node: Viscosity982794
Node: Light and Illumination983070
Node: Radioactivity983662
Node: Force and Energy983997
Node: Prefixes984401
Node: Physical Constant Examples985144
Node: Physical Constant References and Further Reading986933
Node: IEEE floating-point arithmetic987644
Node: Representation of floating point numbers988230
Node: Setting up your IEEE environment992711
Node: IEEE References and Further Reading999703
Node: Debugging Numerical Programs1000858
Node: Using gdb1001342
Node: Examining floating point registers1004685
Node: Handling floating point exceptions1005970
Node: GCC warning options for numerical programs1007382
Node: Debugging References1011575
Node: Contributors to GSL1012287
Node: Autoconf Macros1016522
Node: GSL CBLAS Library1020551
Node: Level 1 CBLAS Functions1021078
Node: Level 2 CBLAS Functions1026380
Node: Level 3 CBLAS Functions1043050
Node: GSL CBLAS Examples1052712
Node: Free Software Needs Free Documentation1054274
Node: GNU General Public License1059343
Node: GNU Free Documentation License1096955
Node: Function Index1119386
Node: Variable Index1360881
Node: Type Index1362053
Node: Concept Index1365699

End Tag Table
