This is gsl-ref.info, produced by makeinfo version 4.6 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 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: 929
gsl-ref.info-2: 297420
gsl-ref.info-3: 595737
gsl-ref.info-4: 895442
gsl-ref.info-5: 1158865

Tag Table:
(Indirect)
Node: Top929
Node: Introduction3495
Node: Routines available in GSL4143
Node: GSL is Free Software6050
Node: Obtaining GSL8434
Node: No Warranty9567
Node: Reporting Bugs10065
Node: Further Information10941
Node: Conventions used in this manual11946
Node: Using the library12702
Node: An Example Program13284
Node: Compiling and Linking13985
Node: Linking programs with the library15047
Node: Linking with an alternative BLAS library16180
Node: Shared Libraries17098
Node: ANSI C Compliance18506
Node: Inline functions19591
Node: Long double20626
Node: Portability functions22016
Node: Alternative optimized functions23410
Node: Support for different numeric types24860
Node: Compatibility with C++27915
Node: Aliasing of arrays28477
Node: Thread-safety29218
Node: Deprecated Functions30295
Node: Code Reuse30910
Node: Error Handling31544
Node: Error Reporting32290
Node: Error Codes34179
Node: Error Handlers35935
Node: Using GSL error reporting in your own functions39581
Node: Error Reporting Examples41529
Node: Mathematical Functions42747
Node: Mathematical Constants43504
Node: Infinities and Not-a-number44626
Node: Elementary Functions45680
Node: Small integer powers47919
Node: Testing the Sign of Numbers49461
Node: Testing for Odd and Even Numbers49883
Node: Maximum and Minimum functions50429
Node: Approximate Comparison of Floating Point Numbers52495
Node: Complex Numbers53694
Ref: Complex Numbers-Footnote-154998
Node: Complex numbers55062
Node: Properties of complex numbers56850
Node: Complex arithmetic operators57825
Node: Elementary Complex Functions60548
Node: Complex Trigonometric Functions62352
Node: Inverse Complex Trigonometric Functions63559
Node: Complex Hyperbolic Functions66147
Node: Inverse Complex Hyperbolic Functions67429
Node: Complex Number References and Further Reading69253
Node: Polynomials70641
Node: Polynomial Evaluation71404
Node: Divided Difference Representation of Polynomials71855
Node: Quadratic Equations73513
Node: Cubic Equations75443
Node: General Polynomial Equations76804
Node: Roots of Polynomials Examples79084
Node: Roots of Polynomials References and Further Reading80502
Node: Special Functions81439
Node: Special Function Usage83407
Node: The gsl_sf_result struct84582
Node: Special Function Modes85838
Node: Airy Functions and Derivatives86766
Node: Airy Functions87454
Node: Derivatives of Airy Functions88794
Node: Zeros of Airy Functions90286
Node: Zeros of Derivatives of Airy Functions90989
Node: Bessel Functions91732
Node: Regular Cylindrical Bessel Functions92916
Node: Irregular Cylindrical Bessel Functions94221
Node: Regular Modified Cylindrical Bessel Functions95658
Node: Irregular Modified Cylindrical Bessel Functions98459
Node: Regular Spherical Bessel Functions101401
Node: Irregular Spherical Bessel Functions103591
Node: Regular Modified Spherical Bessel Functions105257
Node: Irregular Modified Spherical Bessel Functions107239
Node: Regular Bessel Function - Fractional Order109281
Node: Irregular Bessel Functions - Fractional Order110264
Node: Regular Modified Bessel Functions - Fractional Order110830
Node: Irregular Modified Bessel Functions - Fractional Order111737
Node: Zeros of Regular Bessel Functions112953
Node: Clausen Functions114036
Node: Coulomb Functions114630
Node: Normalized Hydrogenic Bound States115071
Node: Coulomb Wave Functions116168
Node: Coulomb Wave Function Normalization Constant119565
Node: Coupling Coefficients120304
Node: 3-j Symbols121019
Node: 6-j Symbols121609
Node: 9-j Symbols122219
Node: Dawson Function122911
Node: Debye Functions123468
Node: Dilogarithm125221
Node: Real Argument125506
Node: Complex Argument126059
Node: Elementary Operations126513
Node: Elliptic Integrals127325
Node: Definition of Legendre Forms127788
Node: Definition of Carlson Forms128623
Node: Legendre Form of Complete Elliptic Integrals129321
Node: Legendre Form of Incomplete Elliptic Integrals130187
Node: Carlson Forms131905
Node: Elliptic Functions (Jacobi)133430
Node: Error Functions134000
Node: Error Function134441
Node: Complementary Error Function134798
Node: Log Complementary Error Function135242
Node: Probability functions135678
Node: Exponential Functions136911
Node: Exponential Function137284
Node: Relative Exponential Functions138477
Node: Exponentiation With Error Estimate140126
Node: Exponential Integrals141317
Node: Exponential Integral141789
Node: Ei(x)142419
Node: Hyperbolic Integrals142851
Node: Ei_3(x)143489
Node: Trigonometric Integrals143865
Node: Arctangent Integral144446
Node: Fermi-Dirac Function144830
Node: Complete Fermi-Dirac Integrals145190
Node: Incomplete Fermi-Dirac Integrals147621
Node: Gamma and Beta Functions148248
Node: Gamma Functions148674
Node: Factorials151738
Node: Pochhammer Symbol154263
Node: Incomplete Gamma Functions155733
Node: Beta Functions156962
Node: Incomplete Beta Function157631
Node: Gegenbauer Functions158137
Node: Hypergeometric Functions159768
Node: Laguerre Functions163969
Node: Lambert W Functions165514
Node: Legendre Functions and Spherical Harmonics166528
Node: Legendre Polynomials167107
Node: Associated Legendre Polynomials and Spherical Harmonics169107
Node: Conical Functions171887
Node: Radial Functions for Hyperbolic Space173984
Node: Logarithm and Related Functions176140
Node: Power Function177742
Node: Psi (Digamma) Function178671
Node: Digamma Function179181
Node: Trigamma Function179991
Node: Polygamma Function180550
Node: Synchrotron Functions180918
Node: Transport Functions181667
Node: Trigonometric Functions182756
Node: Circular Trigonometric Functions183369
Node: Trigonometric Functions for Complex Arguments184356
Node: Hyperbolic Trigonometric Functions185373
Node: Conversion Functions185958
Node: Restriction Functions186725
Node: Trigonometric Functions With Error Estimates187336
Node: Zeta Functions188230
Node: Riemann Zeta Function188678
Node: Riemann Zeta Function Minus One189339
Node: Hurwitz Zeta Function190092
Node: Eta Function190581
Node: Special Functions Examples191122
Node: Special Functions References and Further Reading192849
Node: Vectors and Matrices193945
Node: Data types194700
Node: Blocks195895
Node: Block allocation196803
Node: Reading and writing blocks198192
Node: Example programs for blocks200240
Node: Vectors200872
Node: Vector allocation202750
Node: Accessing vector elements204271
Node: Initializing vector elements206497
Node: Reading and writing vectors207176
Node: Vector views209240
Node: Copying vectors216658
Node: Exchanging elements217504
Node: Vector operations218048
Node: Finding maximum and minimum elements of vectors219544
Node: Vector properties221051
Node: Example programs for vectors221399
Node: Matrices223631
Node: Matrix allocation226481
Node: Accessing matrix elements228051
Node: Initializing matrix elements229743
Node: Reading and writing matrices230524
Node: Matrix views232601
Node: Creating row and column views239719
Node: Copying matrices242868
Node: Copying rows and columns243450
Node: Exchanging rows and columns245111
Node: Matrix operations246572
Node: Finding maximum and minimum elements of matrices248192
Node: Matrix properties250076
Node: Example programs for matrices250427
Node: Vector and Matrix References and Further Reading254476
Node: Permutations254954
Node: The Permutation struct256238
Node: Permutation allocation256733
Node: Accessing permutation elements258154
Node: Permutation properties258907
Node: Permutation functions259595
Node: Applying Permutations260840
Node: Reading and writing permutations262752
Node: Permutations in cyclic form264922
Node: Permutation Examples268334
Node: Permutation References and Further Reading270807
Node: Combinations271471
Node: The Combination struct272310
Node: Combination allocation272851
Node: Accessing combination elements274620
Node: Combination properties275188
Node: Combination functions276060
Node: Reading and writing combinations276988
Node: Combination Examples279174
Node: Combination References and Further Reading280490
Node: Sorting280883
Node: Sorting objects281827
Node: Sorting vectors284726
Node: Selecting the k smallest or largest elements287287
Node: Computing the rank290611
Node: Sorting Examples291817
Node: Sorting References and Further Reading293438
Node: BLAS Support293974
Node: GSL BLAS Interface296943
Node: Level 1 GSL BLAS Interface297420
Node: Level 2 GSL BLAS Interface304093
Node: Level 3 GSL BLAS Interface313348
Node: BLAS Examples324433
Node: BLAS References and Further Reading325887
Node: Linear Algebra327236
Node: LU Decomposition328484
Node: QR Decomposition333656
Node: QR Decomposition with Column Pivoting339415
Node: Singular Value Decomposition343807
Node: Cholesky Decomposition347159
Node: Tridiagonal Decomposition of Real Symmetric Matrices349067
Node: Tridiagonal Decomposition of Hermitian Matrices350902
Node: Bidiagonalization352820
Node: Householder Transformations355222
Node: Householder solver for linear systems357054
Node: Tridiagonal Systems357945
Node: Linear Algebra Examples360440
Node: Linear Algebra References and Further Reading362466
Node: Eigensystems363944
Node: Real Symmetric Matrices364995
Node: Complex Hermitian Matrices367211
Node: Sorting Eigenvalues and Eigenvectors369713
Node: Eigenvalue and Eigenvector Examples371032
Node: Eigenvalue and Eigenvector References373397
Node: Fast Fourier Transforms374095
Node: Mathematical Definitions375298
Node: Overview of complex data FFTs377693
Node: Radix-2 FFT routines for complex data380631
Node: Mixed-radix FFT routines for complex data384873
Node: Overview of real data FFTs394267
Node: Radix-2 FFT routines for real data396691
Node: Mixed-radix FFT routines for real data399517
Node: FFT References and Further Reading410166
Node: Numerical Integration413025
Node: Numerical Integration Introduction414564
Node: Integrands without weight functions416503
Node: Integrands with weight functions417318
Node: Integrands with singular weight functions418015
Node: QNG non-adaptive Gauss-Kronrod integration418919
Node: QAG adaptive integration420179
Node: QAGS adaptive integration with singularities422807
Node: QAGP adaptive integration with known singular points424596
Node: QAGI adaptive integration on infinite intervals425899
Node: QAWC adaptive integration for Cauchy principal values428169
Node: QAWS adaptive integration for singular functions429333
Node: QAWO adaptive integration for oscillatory functions432560
Node: QAWF adaptive integration for Fourier integrals436324
Node: Numerical integration error codes438936
Node: Numerical integration examples439692
Node: Numerical integration References and Further Reading441721
Node: Random Number Generation442437
Node: General comments on random numbers443933
Node: The Random Number Generator Interface445873
Node: Random number generator initialization447221
Node: Sampling from a random number generator449224
Node: Auxiliary random number generator functions452377
Node: Random number environment variables454711
Node: Copying random number generator state457228
Node: Reading and writing random number generator state458191
Node: Random number generator algorithms459591
Node: Unix random number generators469030
Node: Other random number generators472744
Node: Random Number Generator Performance482052
Node: Random Number Generator Examples483363
Node: Random Number References and Further Reading484945
Node: Random Number Acknowledgements486230
Node: Quasi-Random Sequences486704
Node: Quasi-random number generator initialization487805
Node: Sampling from a quasi-random number generator488807
Node: Auxiliary quasi-random number generator functions489413
Node: Saving and resorting quasi-random number generator state490346
Node: Quasi-random number generator algorithms491132
Node: Quasi-random number generator examples491895
Node: Quasi-random number references492885
Node: Random Number Distributions493401
Node: Random Number Distribution Introduction496594
Node: The Gaussian Distribution498379
Node: The Gaussian Tail Distribution501016
Node: The Bivariate Gaussian Distribution502661
Node: The Exponential Distribution503962
Node: The Laplace Distribution505085
Node: The Exponential Power Distribution506166
Node: The Cauchy Distribution507420
Node: The Rayleigh Distribution508653
Node: The Rayleigh Tail Distribution509809
Node: The Landau Distribution510667
Node: The Levy alpha-Stable Distributions511608
Node: The Levy skew alpha-Stable Distribution512653
Node: The Gamma Distribution514252
Node: The Flat (Uniform) Distribution515762
Node: The Lognormal Distribution516886
Node: The Chi-squared Distribution518216
Node: The F-distribution519602
Node: The t-distribution521210
Node: The Beta Distribution522586
Node: The Logistic Distribution523717
Node: The Pareto Distribution524828
Node: Spherical Vector Distributions525980
Node: The Weibull Distribution528798
Node: The Type-1 Gumbel Distribution529974
Node: The Type-2 Gumbel Distribution531193
Node: The Dirichlet Distribution532406
Node: General Discrete Distributions534059
Node: The Poisson Distribution537908
Node: The Bernoulli Distribution538890
Node: The Binomial Distribution539627
Node: The Multinomial Distribution540816
Node: The Negative Binomial Distribution542453
Node: The Pascal Distribution543802
Node: The Geometric Distribution544944
Node: The Hypergeometric Distribution546176
Node: The Logarithmic Distribution547813
Node: Shuffling and Sampling548590
Node: Random Number Distribution Examples551434
Node: Random Number Distribution References and Further Reading554669
Node: Statistics556723
Node: Mean and standard deviation and variance557996
Node: Absolute deviation561024
Node: Higher moments (skewness and kurtosis)562304
Node: Autocorrelation564423
Node: Covariance565225
Node: Weighted Samples566162
Node: Maximum and Minimum values571383
Node: Median and Percentiles574106
Node: Example statistical programs576509
Node: Statistics References and Further Reading579219
Node: Histograms580415
Node: The histogram struct582169
Node: Histogram allocation583961
Node: Copying Histograms586938
Node: Updating and accessing histogram elements587602
Node: Searching histogram ranges590851
Node: Histogram Statistics591839
Node: Histogram Operations593682
Node: Reading and writing histograms595737
Node: Resampling from histograms598755
Node: The histogram probability distribution struct599543
Node: Example programs for histograms602557
Node: Two dimensional histograms604633
Node: The 2D histogram struct605342
Node: 2D Histogram allocation607137
Node: Copying 2D Histograms609192
Node: Updating and accessing 2D histogram elements609883
Node: Searching 2D histogram ranges613514
Node: 2D Histogram Statistics614520
Node: 2D Histogram Operations617357
Node: Reading and writing 2D histograms619512
Node: Resampling from 2D histograms623153
Node: Example programs for 2D histograms626155
Node: N-tuples627953
Node: The ntuple struct629203
Node: Creating ntuples629671
Node: Opening an existing ntuple file630327
Node: Writing ntuples630944
Node: Reading ntuples631393
Node: Closing an ntuple file631713
Node: Histogramming ntuple values632042
Node: Example ntuple programs634037
Node: Ntuple References and Further Reading637478
Node: Monte Carlo Integration637789
Node: Monte Carlo Interface639028
Node: PLAIN Monte Carlo641665
Node: MISER644089
Node: VEGAS649908
Node: Monte Carlo Examples658220
Node: Monte Carlo Integration References and Further Reading664248
Node: Simulated Annealing665020
Node: Simulated Annealing algorithm666221
Node: Simulated Annealing functions667363
Node: Examples with Simulated Annealing671870
Node: Trivial example672414
Node: Traveling Salesman Problem675142
Node: Simulated Annealing References and Further Reading678478
Node: Ordinary Differential Equations678879
Node: Defining the ODE System679694
Node: Stepping Functions681875
Node: Adaptive Step-size Control685807
Node: Evolution691247
Node: ODE Example programs693794
Node: ODE References and Further Reading698978
Node: Interpolation699607
Node: Introduction to Interpolation700614
Node: Interpolation Functions701045
Node: Interpolation Types702208
Node: Index Look-up and Acceleration704800
Node: Evaluation of Interpolating Functions706416
Node: Higher-level Interface708782
Node: Interpolation Example programs710798
Node: Interpolation References and Further Reading714111
Node: Numerical Differentiation714673
Node: Numerical Differentiation functions715256
Node: Numerical Differentiation Examples718099
Node: Numerical Differentiation References719543
Node: Chebyshev Approximations720084
Node: Chebyshev Definitions721094
Node: Creation and Calculation of Chebyshev Series721874
Node: Chebyshev Series Evaluation722833
Node: Derivatives and Integrals724193
Node: Chebyshev Approximation examples725423
Node: Chebyshev Approximation References and Further Reading726956
Node: Series Acceleration727395
Node: Acceleration functions728154
Node: Acceleration functions without error estimation730383
Node: Example of accelerating a series732989
Node: Series Acceleration References735397
Node: Wavelet Transforms736275
Node: DWT Definitions736810
Node: DWT Initialization737752
Node: DWT Transform Functions740310
Node: DWT in one dimension740835
Node: DWT in two dimension742837
Node: DWT Examples747412
Node: DWT References749115
Node: Discrete Hankel Transforms751268
Node: Discrete Hankel Transform Definition751730
Node: Discrete Hankel Transform Functions753859
Node: Discrete Hankel Transform References755363
Node: One dimensional Root-Finding755757
Node: Root Finding Overview757011
Node: Root Finding Caveats758859
Node: Initializing the Solver760616
Node: Providing the function to solve763231
Node: Search Bounds and Guesses767030
Node: Root Finding Iteration767881
Node: Search Stopping Parameters769714
Node: Root Bracketing Algorithms772215
Node: Root Finding Algorithms using Derivatives775500
Node: Root Finding Examples778990
Node: Root Finding References and Further Reading786332
Node: One dimensional Minimization786959
Node: Minimization Overview788255
Node: Minimization Caveats789951
Node: Initializing the Minimizer791278
Node: Providing the function to minimize793504
Node: Minimization Iteration793972
Node: Minimization Stopping Parameters796091
Node: Minimization Algorithms797689
Node: Minimization Examples800116
Node: Minimization References and Further Reading803108
Node: Multidimensional Root-Finding803554
Node: Overview of Multidimensional Root Finding805037
Node: Initializing the Multidimensional Solver807214
Node: Providing the multidimensional system of equations to solve810384
Node: Iteration of the multidimensional solver815327
Node: Search Stopping Parameters for the multidimensional solver817494
Node: Algorithms using Derivatives819219
Node: Algorithms without Derivatives823951
Node: Example programs for Multidimensional Root finding826955
Node: References and Further Reading for Multidimensional Root Finding835743
Node: Multidimensional Minimization836972
Node: Multimin Overview838258
Node: Multimin Caveats840220
Node: Initializing the Multidimensional Minimizer840959
Node: Providing a function to minimize843864
Node: Multimin Iteration847562
Node: Multimin Stopping Criteria849534
Node: Multimin Algorithms851074
Node: Multimin Examples855387
Node: Multimin References and Further Reading862144
Node: Least-Squares Fitting862812
Node: Fitting Overview863805
Node: Linear regression865846
Node: Linear fitting without a constant term868264
Node: Multi-parameter fitting870442
Node: Fitting Examples875246
Node: Fitting References and Further Reading882063
Node: Nonlinear Least-Squares Fitting882876
Node: Overview of Nonlinear Least-Squares Fitting884324
Node: Initializing the Nonlinear Least-Squares Solver885781
Node: Providing the Function to be Minimized888609
Node: Iteration of the Minimization Algorithm891534
Node: Search Stopping Parameters for Minimization Algorithms893360
Node: Minimization Algorithms using Derivatives895442
Node: Minimization Algorithms without Derivatives898678
Node: Computing the covariance matrix of best fit parameters899060
Node: Example programs for Nonlinear Least-Squares Fitting901083
Node: References and Further Reading for Nonlinear Least-Squares Fitting908943
Node: Physical Constants909667
Node: Fundamental Constants911089
Node: Astronomy and Astrophysics912218
Node: Atomic and Nuclear Physics912873
Node: Measurement of Time914500
Node: Imperial Units914920
Node: Speed and Nautical Units915352
Node: Printers Units915846
Node: Volume Area and Length916159
Node: Mass and Weight916835
Node: Thermal Energy and Power917644
Node: Pressure918055
Node: Viscosity918656
Node: Light and Illumination918920
Node: Radioactivity919500
Node: Force and Energy919823
Node: Prefixes920215
Node: Physical Constant Examples920946
Node: Physical Constant References and Further Reading922755
Node: IEEE floating-point arithmetic923454
Node: Representation of floating point numbers924034
Node: Setting up your IEEE environment928547
Node: IEEE References and Further Reading935196
Node: Debugging Numerical Programs936340
Node: Using gdb936802
Node: Examining floating point registers940152
Node: Handling floating point exceptions941429
Node: GCC warning options for numerical programs942835
Node: Debugging References947020
Node: Contributors to GSL947724
Node: Autoconf Macros949930
Node: GSL CBLAS Library953908
Node: Level 1 CBLAS Functions954413
Node: Level 2 CBLAS Functions959661
Node: Level 3 CBLAS Functions976257
Node: GSL CBLAS Examples985880
Node: Free Software Needs Free Documentation987490
Node: GNU General Public License992559
Node: GNU Free Documentation License1011857
Node: Function Index1034293
Node: Variable Index1156126
Node: Type Index1156936
Node: Concept Index1158865

End Tag Table
