This is gsl-ref.info, produced by makeinfo version 4.6 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


Indirect:
gsl-ref.info-1: 228
gsl-ref.info-2: 299155
gsl-ref.info-3: 598821
gsl-ref.info-4: 898452

Tag Table:
(Indirect)
Node: Top228
Node: Introduction2225
Node: Routines available in GSL2873
Node: GSL is Free Software4585
Node: Obtaining GSL6914
Node: No Warranty8029
Node: Reporting Bugs8527
Node: Further Information9403
Node: Conventions used in this manual10105
Node: Using the library10861
Node: An Example Program11443
Node: Compiling and Linking12144
Node: Shared Libraries14882
Node: ANSI C Compliance16290
Node: Inline functions17375
Node: Long double18410
Node: Portability functions19800
Node: Alternative optimized functions21194
Node: Support for different numeric types22644
Node: Compatibility with C++25699
Node: Aliasing of arrays26261
Node: Thread-safety27002
Node: Deprecated Functions28079
Node: Code Reuse28694
Node: Error Handling29328
Node: Error Reporting30074
Node: Error Codes31963
Node: Error Handlers33719
Node: Using GSL error reporting in your own functions37365
Node: Error Reporting Examples39313
Node: Mathematical Functions40531
Node: Mathematical Constants41288
Node: Infinities and Not-a-number42410
Node: Elementary Functions43464
Node: Small integer powers45703
Node: Testing the Sign of Numbers47245
Node: Testing for Odd and Even Numbers47667
Node: Maximum and Minimum functions48213
Node: Approximate Comparison of Floating Point Numbers50279
Node: Complex Numbers51478
Ref: Complex Numbers-Footnote-152782
Node: Complex numbers52846
Node: Properties of complex numbers54634
Node: Complex arithmetic operators55609
Node: Elementary Complex Functions58332
Node: Complex Trigonometric Functions60136
Node: Inverse Complex Trigonometric Functions61343
Node: Complex Hyperbolic Functions63931
Node: Inverse Complex Hyperbolic Functions65213
Node: Complex Number References and Further Reading67037
Node: Polynomials68425
Node: Polynomial Evaluation69188
Node: Divided Difference Representation of Polynomials69639
Node: Quadratic Equations71297
Node: Cubic Equations73227
Node: General Polynomial Equations74588
Node: Roots of Polynomials Examples76868
Node: Roots of Polynomials References and Further Reading78286
Node: Special Functions79223
Node: Special Function Usage81191
Node: The gsl_sf_result struct82366
Node: Special Function Modes83622
Node: Airy Functions and Derivatives84550
Node: Airy Functions85238
Node: Derivatives of Airy Functions86578
Node: Zeros of Airy Functions88070
Node: Zeros of Derivatives of Airy Functions88773
Node: Bessel Functions89516
Node: Regular Cylindrical Bessel Functions90700
Node: Irregular Cylindrical Bessel Functions92005
Node: Regular Modified Cylindrical Bessel Functions93442
Node: Irregular Modified Cylindrical Bessel Functions96243
Node: Regular Spherical Bessel Functions99185
Node: Irregular Spherical Bessel Functions101375
Node: Regular Modified Spherical Bessel Functions103041
Node: Irregular Modified Spherical Bessel Functions105023
Node: Regular Bessel Function - Fractional Order107065
Node: Irregular Bessel Functions - Fractional Order108048
Node: Regular Modified Bessel Functions - Fractional Order108614
Node: Irregular Modified Bessel Functions - Fractional Order109521
Node: Zeros of Regular Bessel Functions110737
Node: Clausen Functions111820
Node: Coulomb Functions112414
Node: Normalized Hydrogenic Bound States112855
Node: Coulomb Wave Functions113862
Node: Coulomb Wave Function Normalization Constant117259
Node: Coupling Coefficients117998
Node: 3-j Symbols118713
Node: 6-j Symbols119303
Node: 9-j Symbols119913
Node: Dawson Function120605
Node: Debye Functions121162
Node: Dilogarithm122462
Node: Real Argument122747
Node: Complex Argument123300
Node: Elementary Operations123754
Node: Elliptic Integrals124566
Node: Definition of Legendre Forms125029
Node: Definition of Carlson Forms125864
Node: Legendre Form of Complete Elliptic Integrals126562
Node: Legendre Form of Incomplete Elliptic Integrals127428
Node: Carlson Forms129146
Node: Elliptic Functions (Jacobi)130671
Node: Error Functions131241
Node: Error Function131682
Node: Complementary Error Function132039
Node: Log Complementary Error Function132483
Node: Probability functions132919
Node: Exponential Functions134152
Node: Exponential Function134525
Node: Relative Exponential Functions135718
Node: Exponentiation With Error Estimate137367
Node: Exponential Integrals138558
Node: Exponential Integral139030
Node: Ei(x)139660
Node: Hyperbolic Integrals140092
Node: Ei_3(x)140730
Node: Trigonometric Integrals141106
Node: Arctangent Integral141687
Node: Fermi-Dirac Function142071
Node: Complete Fermi-Dirac Integrals142431
Node: Incomplete Fermi-Dirac Integrals144862
Node: Gamma and Beta Functions145489
Node: Gegenbauer Functions153671
Node: Hypergeometric Functions155302
Node: Laguerre Functions159503
Node: Lambert W Functions160755
Node: Legendre Functions and Spherical Harmonics161769
Node: Legendre Polynomials162348
Node: Associated Legendre Polynomials and Spherical Harmonics164348
Node: Conical Functions167128
Node: Radial Functions for Hyperbolic Space169225
Node: Logarithm and Related Functions171381
Node: Power Function172983
Node: Psi (Digamma) Function173912
Node: Digamma Function174422
Node: Trigamma Function175232
Node: Polygamma Function175791
Node: Synchrotron Functions176159
Node: Transport Functions176908
Node: Trigonometric Functions177997
Node: Circular Trigonometric Functions178610
Node: Trigonometric Functions for Complex Arguments179597
Node: Hyperbolic Trigonometric Functions180614
Node: Conversion Functions181199
Node: Restriction Functions181966
Node: Trigonometric Functions With Error Estimates182577
Node: Zeta Functions183321
Node: Riemann Zeta Function183769
Node: Riemann Zeta Function Minus One184430
Node: Hurwitz Zeta Function185183
Node: Eta Function185672
Node: Special Functions Examples186213
Node: Special Functions References and Further Reading187940
Node: Vectors and Matrices189036
Node: Data types189791
Node: Blocks190986
Node: Block allocation191894
Node: Reading and writing blocks193283
Node: Example programs for blocks195331
Node: Vectors195963
Node: Vector allocation197841
Node: Accessing vector elements199362
Node: Initializing vector elements201588
Node: Reading and writing vectors202267
Node: Vector views204331
Node: Copying vectors211749
Node: Exchanging elements212595
Node: Vector operations213139
Node: Finding maximum and minimum elements of vectors214635
Node: Vector properties216142
Node: Example programs for vectors216490
Node: Matrices218722
Node: Matrix allocation221572
Node: Accessing matrix elements223142
Node: Initializing matrix elements224834
Node: Reading and writing matrices225615
Node: Matrix views227692
Node: Creating row and column views234810
Node: Copying matrices237959
Node: Copying rows and columns238541
Node: Exchanging rows and columns240202
Node: Matrix operations241663
Node: Finding maximum and minimum elements of matrices243283
Node: Matrix properties245137
Node: Example programs for matrices245488
Node: Vector and Matrix References and Further Reading249537
Node: Permutations250015
Node: The Permutation struct251299
Node: Permutation allocation251794
Node: Accessing permutation elements253215
Node: Permutation properties253968
Node: Permutation functions254656
Node: Applying Permutations255901
Node: Reading and writing permutations257813
Node: Permutations in cyclic form259983
Node: Permutation Examples263395
Node: Permutation References and Further Reading265868
Node: Combinations266532
Node: The Combination struct267371
Node: Combination allocation267912
Node: Accessing combination elements269681
Node: Combination properties270249
Node: Combination functions271121
Node: Reading and writing combinations272049
Node: Combination Examples274235
Node: Combination References and Further Reading275551
Node: Sorting275944
Node: Sorting objects276888
Node: Sorting vectors279787
Node: Selecting the k smallest or largest elements282348
Node: Computing the rank285672
Node: Sorting Examples286878
Node: Sorting References and Further Reading288499
Node: BLAS Support289035
Node: GSL BLAS Interface292004
Node: Level 1 GSL BLAS Interface292481
Node: Level 2 GSL BLAS Interface299155
Node: Level 3 GSL BLAS Interface308410
Node: BLAS Examples319495
Node: BLAS References and Further Reading320949
Node: Linear Algebra322298
Node: LU Decomposition323546
Node: QR Decomposition328718
Node: QR Decomposition with Column Pivoting334477
Node: Singular Value Decomposition338869
Node: Cholesky Decomposition342221
Node: Tridiagonal Decomposition of Real Symmetric Matrices344119
Node: Tridiagonal Decomposition of Hermitian Matrices345954
Node: Bidiagonalization347872
Node: Householder Transformations350274
Node: Householder solver for linear systems352106
Node: Tridiagonal Systems352997
Node: Linear Algebra Examples355492
Node: Linear Algebra References and Further Reading357518
Node: Eigensystems358996
Node: Real Symmetric Matrices360047
Node: Complex Hermitian Matrices362263
Node: Sorting Eigenvalues and Eigenvectors364765
Node: Eigenvalue and Eigenvector Examples366084
Node: Eigenvalue and Eigenvector References368449
Node: Fast Fourier Transforms369147
Node: Mathematical Definitions370350
Node: Overview of complex data FFTs372745
Node: Radix-2 FFT routines for complex data375683
Node: Mixed-radix FFT routines for complex data379925
Node: Overview of real data FFTs389319
Node: Radix-2 FFT routines for real data391743
Node: Mixed-radix FFT routines for real data394569
Node: FFT References and Further Reading405218
Node: Numerical Integration408077
Node: Numerical Integration Introduction409616
Node: QNG non-adaptive Gauss-Kronrod integration413338
Node: QAG adaptive integration414598
Node: QAGS adaptive integration with singularities417226
Node: QAGP adaptive integration with known singular points419015
Node: QAGI adaptive integration on infinite intervals420318
Node: QAWC adaptive integration for Cauchy principal values422588
Node: QAWS adaptive integration for singular functions423752
Node: QAWO adaptive integration for oscillatory functions426979
Node: QAWF adaptive integration for Fourier integrals430743
Node: Numerical integration error codes433355
Node: Numerical integration examples434111
Node: Numerical integration References and Further Reading436140
Node: Random Number Generation436856
Node: General comments on random numbers438352
Node: The Random Number Generator Interface440292
Node: Random number generator initialization441640
Node: Sampling from a random number generator443643
Node: Auxiliary random number generator functions446123
Node: Random number environment variables448457
Node: Copying random number generator state450974
Node: Reading and writing random number generator state451937
Node: Random number generator algorithms453337
Node: Unix random number generators462725
Node: Other random number generators466439
Node: Random Number Generator Performance475747
Node: Random Number Generator Examples477058
Node: Random Number References and Further Reading478640
Node: Random Number Acknowledgements479925
Node: Quasi-Random Sequences480399
Node: Quasi-random number generator initialization481500
Node: Sampling from a quasi-random number generator482502
Node: Auxiliary quasi-random number generator functions483108
Node: Saving and resorting quasi-random number generator state484041
Node: Quasi-random number generator algorithms484827
Node: Quasi-random number generator examples485590
Node: Quasi-random number references486580
Node: Random Number Distributions487096
Node: Random Number Distribution Introduction489941
Node: The Gaussian Distribution491035
Node: The Gaussian Tail Distribution493451
Node: The Bivariate Gaussian Distribution495096
Node: The Exponential Distribution496397
Node: The Laplace Distribution497520
Node: The Exponential Power Distribution498601
Node: The Cauchy Distribution499565
Node: The Rayleigh Distribution500799
Node: The Rayleigh Tail Distribution501955
Node: The Landau Distribution502813
Node: The Levy alpha-Stable Distributions503754
Node: The Levy skew alpha-Stable Distribution504799
Node: The Gamma Distribution506398
Node: The Flat (Uniform) Distribution507654
Node: The Lognormal Distribution508778
Node: The Chi-squared Distribution510108
Node: The F-distribution511494
Node: The t-distribution512918
Node: The Beta Distribution514294
Node: The Logistic Distribution515266
Node: The Pareto Distribution516377
Node: Spherical Vector Distributions517529
Node: The Weibull Distribution520347
Node: The Type-1 Gumbel Distribution521523
Node: The Type-2 Gumbel Distribution522742
Node: The Dirichlet Distribution523955
Node: General Discrete Distributions525608
Node: The Poisson Distribution529457
Node: The Bernoulli Distribution530174
Node: The Binomial Distribution530912
Node: The Multinomial Distribution531776
Node: The Negative Binomial Distribution533414
Node: The Pascal Distribution534419
Node: The Geometric Distribution535244
Node: The Hypergeometric Distribution536060
Node: The Logarithmic Distribution537049
Node: Shuffling and Sampling537827
Node: Random Number Distribution Examples540671
Node: Random Number Distribution References and Further Reading543906
Node: Statistics545960
Node: Mean and standard deviation and variance547233
Node: Absolute deviation550261
Node: Higher moments (skewness and kurtosis)551541
Node: Autocorrelation553660
Node: Covariance554462
Node: Weighted Samples555399
Node: Maximum and Minimum values560620
Node: Median and Percentiles563044
Node: Example statistical programs565447
Node: Statistics References and Further Reading568157
Node: Histograms569353
Node: The histogram struct571107
Node: Histogram allocation572899
Node: Copying Histograms575876
Node: Updating and accessing histogram elements576540
Node: Searching histogram ranges579789
Node: Histogram Statistics580777
Node: Histogram Operations582620
Node: Reading and writing histograms584675
Node: Resampling from histograms587693
Node: The histogram probability distribution struct588481
Node: Example programs for histograms591495
Node: Two dimensional histograms593571
Node: The 2D histogram struct594280
Node: 2D Histogram allocation596075
Node: Copying 2D Histograms598130
Node: Updating and accessing 2D histogram elements598821
Node: Searching 2D histogram ranges602452
Node: 2D Histogram Statistics603458
Node: 2D Histogram Operations606295
Node: Reading and writing 2D histograms608450
Node: Resampling from 2D histograms612091
Node: Example programs for 2D histograms615093
Node: N-tuples617158
Node: The ntuple struct618408
Node: Creating ntuples618876
Node: Opening an existing ntuple file619532
Node: Writing ntuples620149
Node: Reading ntuples620598
Node: Closing an ntuple file620918
Node: Histogramming ntuple values621247
Node: Example ntuple programs623242
Node: Ntuple References and Further Reading626683
Node: Monte Carlo Integration626994
Node: Monte Carlo Interface628233
Node: PLAIN Monte Carlo630870
Node: MISER633294
Node: VEGAS639113
Node: Monte Carlo Examples647425
Node: Monte Carlo Integration References and Further Reading653453
Node: Simulated Annealing654225
Node: Simulated Annealing algorithm655371
Node: Simulated Annealing functions656541
Node: Examples with Simulated Annealing661048
Node: Trivial example661533
Node: Traveling Salesman Problem664303
Node: Ordinary Differential Equations667891
Node: Defining the ODE System668706
Node: Stepping Functions670887
Node: Adaptive Step-size Control674819
Node: Evolution680259
Node: ODE Example programs682806
Node: ODE References and Further Reading687844
Node: Interpolation688473
Node: Introduction to Interpolation689480
Node: Interpolation Functions689911
Node: Interpolation Types691074
Node: Index Look-up and Acceleration693041
Node: Evaluation of Interpolating Functions694657
Node: Higher-level Interface697023
Node: Interpolation Example programs698883
Node: Interpolation References and Further Reading700588
Node: Numerical Differentiation701018
Node: Numerical Differentiation functions701601
Node: Numerical Differentiation Examples704444
Node: Numerical Differentiation References705888
Node: Chebyshev Approximations706429
Node: Chebyshev Definitions707439
Node: Creation and Calculation of Chebyshev Series708208
Node: Chebyshev Series Evaluation709167
Node: Derivatives and Integrals710527
Node: Chebyshev Approximation examples711757
Node: Chebyshev Approximation References and Further Reading713290
Node: Series Acceleration713729
Node: Acceleration functions714488
Node: Acceleration functions without error estimation716717
Node: Example of accelerating a series719323
Node: Series Acceleration References721731
Node: Wavelet Transforms722609
Node: DWT Definitions723144
Node: DWT Initialization724086
Node: DWT Transform Functions726644
Node: DWT in one dimension727169
Node: DWT in two dimension729167
Node: DWT Examples733742
Node: DWT References735445
Node: Discrete Hankel Transforms737598
Node: Discrete Hankel Transform Definition738060
Node: Discrete Hankel Transform Functions739896
Node: Discrete Hankel Transform References741400
Node: One dimensional Root-Finding741794
Node: Root Finding Overview743048
Node: Root Finding Caveats744896
Node: Initializing the Solver746653
Node: Providing the function to solve749268
Node: Search Bounds and Guesses753067
Node: Root Finding Iteration753918
Node: Search Stopping Parameters755751
Node: Root Bracketing Algorithms758252
Node: Root Finding Algorithms using Derivatives761537
Node: Root Finding Examples765027
Node: Root Finding References and Further Reading772369
Node: One dimensional Minimization772996
Node: Minimization Overview774292
Node: Minimization Caveats775988
Node: Initializing the Minimizer777315
Node: Providing the function to minimize779541
Node: Minimization Iteration780009
Node: Minimization Stopping Parameters782128
Node: Minimization Algorithms783726
Node: Minimization Examples786153
Node: Minimization References and Further Reading789145
Node: Multidimensional Root-Finding789591
Node: Overview of Multidimensional Root Finding791074
Node: Initializing the Multidimensional Solver793251
Node: Providing the multidimensional system of equations to solve796421
Node: Iteration of the multidimensional solver801364
Node: Search Stopping Parameters for the multidimensional solver803531
Node: Algorithms using Derivatives805256
Node: Algorithms without Derivatives809988
Node: Example programs for Multidimensional Root finding812992
Node: References and Further Reading for Multidimensional Root Finding821780
Node: Multidimensional Minimization823009
Node: Multimin Overview824295
Node: Multimin Caveats826257
Node: Initializing the Multidimensional Minimizer826996
Node: Providing a function to minimize829901
Node: Multimin Iteration833599
Node: Multimin Stopping Criteria835571
Node: Multimin Algorithms837111
Node: Multimin Examples841424
Node: Multimin References and Further Reading848181
Node: Least-Squares Fitting848849
Node: Linear regression849781
Node: Linear fitting without a constant term852383
Node: Multi-parameter fitting854773
Node: Fitting Examples859484
Node: Fitting References and Further Reading866314
Node: Nonlinear Least-Squares Fitting867127
Node: Overview of Nonlinear Least-Squares Fitting868575
Node: Initializing the Nonlinear Least-Squares Solver869455
Node: Providing the Function to be Minimized872114
Node: Iteration of the Minimization Algorithm874755
Node: Search Stopping Parameters for Minimization Algorithms876581
Node: Minimization Algorithms using Derivatives878663
Node: Minimization Algorithms without Derivatives881899
Node: Computing the covariance matrix of best fit parameters882281
Node: Example programs for Nonlinear Least-Squares Fitting883339
Node: References and Further Reading for Nonlinear Least-Squares Fitting890631
Node: Physical Constants891355
Node: Fundamental Constants892777
Node: Astronomy and Astrophysics893906
Node: Atomic and Nuclear Physics894561
Node: Measurement of Time896117
Node: Imperial Units896537
Node: Speed and Nautical Units896969
Node: Printers Units897463
Node: Volume Area and Length897776
Node: Mass and Weight898452
Node: Thermal Energy and Power899261
Node: Pressure899672
Node: Viscosity900273
Node: Light and Illumination900537
Node: Radioactivity901117
Node: Force and Energy901440
Node: Prefixes901832
Node: Physical Constant Examples902563
Node: Physical Constant References and Further Reading904372
Node: IEEE floating-point arithmetic905071
Node: Representation of floating point numbers905651
Node: Setting up your IEEE environment910164
Node: IEEE References and Further Reading916813
Node: Debugging Numerical Programs917957
Node: Using gdb918419
Node: Examining floating point registers921769
Node: Handling floating point exceptions923046
Node: GCC warning options for numerical programs924452
Node: Debugging References928637
Node: Contributors to GSL929341
Node: Autoconf Macros931547
Node: GSL CBLAS Library935525
Node: Level 1 CBLAS Functions936030
Node: Level 2 CBLAS Functions941278
Node: Level 3 CBLAS Functions957874
Node: GSL CBLAS Examples967497
Node: Free Software Needs Free Documentation969107
Node: GNU General Public License974176
Node: GNU Free Documentation License993474
Node: Function Index1015910
Node: Variable Index1136473
Node: Type Index1137283
Node: Concept Index1139212

End Tag Table
