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diff --git a/gsl-1.9/doc/gsl-ref.info b/gsl-1.9/doc/gsl-ref.info new file mode 100644 index 0000000..0423ca6 --- /dev/null +++ b/gsl-1.9/doc/gsl-ref.info @@ -0,0 +1,596 @@ +This is gsl-ref.info, produced by makeinfo version 4.8 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 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: 939 +gsl-ref.info-2: 298842 +gsl-ref.info-3: 596860 +gsl-ref.info-4: 895867 +gsl-ref.info-5: 1072596 +gsl-ref.info-6: 1311271 + +Tag Table: +(Indirect) +Node: Top939 +Node: Introduction3646 +Node: Routines available in GSL4298 +Node: GSL is Free Software6213 +Node: Obtaining GSL8605 +Node: No Warranty9746 +Node: Reporting Bugs10252 +Node: Further Information11136 +Node: Conventions used in this manual12149 +Node: Using the library12913 +Node: An Example Program13499 +Node: Compiling and Linking14203 +Node: Linking programs with the library15273 +Node: Linking with an alternative BLAS library16418 +Node: Shared Libraries17348 +Node: ANSI C Compliance18764 +Node: Inline functions19857 +Node: Long double20900 +Node: Portability functions22298 +Node: Alternative optimized functions23695 +Node: Support for different numeric types25153 +Node: Compatibility with C++28216 +Node: Aliasing of arrays28788 +Node: Thread-safety29539 +Node: Deprecated Functions30626 +Node: Code Reuse31251 +Node: Error Handling31895 +Node: Error Reporting32645 +Node: Error Codes34537 +Node: Error Handlers36393 +Node: Using GSL error reporting in your own functions40028 +Node: Error Reporting Examples41986 +Node: Mathematical Functions43190 +Node: Mathematical Constants43951 +Node: Infinities and Not-a-number45081 +Node: Elementary Functions46149 +Node: Small integer powers48404 +Node: Testing the Sign of Numbers49966 +Node: Testing for Odd and Even Numbers50397 +Node: Maximum and Minimum functions50953 +Node: Approximate Comparison of Floating Point Numbers53035 +Node: Complex Numbers54241 +Ref: Complex Numbers-Footnote-155549 +Node: Complex numbers55613 +Node: Properties of complex numbers57416 +Node: Complex arithmetic operators58403 +Node: Elementary Complex Functions61149 +Node: Complex Trigonometric Functions62969 +Node: Inverse Complex Trigonometric Functions64190 +Node: Complex Hyperbolic Functions66796 +Node: Inverse Complex Hyperbolic Functions68092 +Node: Complex Number References and Further Reading70080 +Node: Polynomials71476 +Node: Polynomial Evaluation72243 +Node: Divided Difference Representation of Polynomials72703 +Node: Quadratic Equations74372 +Node: Cubic Equations76312 +Node: General Polynomial Equations77683 +Node: Roots of Polynomials Examples80028 +Node: Roots of Polynomials References and Further Reading81417 +Node: Special Functions82362 +Node: Special Function Usage84356 +Node: The gsl_sf_result struct85539 +Node: Special Function Modes86803 +Node: Airy Functions and Derivatives87739 +Node: Airy Functions88435 +Node: Derivatives of Airy Functions89795 +Node: Zeros of Airy Functions91307 +Node: Zeros of Derivatives of Airy Functions92026 +Node: Bessel Functions92785 +Node: Regular Cylindrical Bessel Functions93977 +Node: Irregular Cylindrical Bessel Functions95301 +Node: Regular Modified Cylindrical Bessel Functions96757 +Node: Irregular Modified Cylindrical Bessel Functions99584 +Node: Regular Spherical Bessel Functions102552 +Node: Irregular Spherical Bessel Functions104764 +Node: Regular Modified Spherical Bessel Functions106451 +Node: Irregular Modified Spherical Bessel Functions108454 +Node: Regular Bessel Function - Fractional Order110517 +Node: Irregular Bessel Functions - Fractional Order111515 +Node: Regular Modified Bessel Functions - Fractional Order112097 +Node: Irregular Modified Bessel Functions - Fractional Order113022 +Node: Zeros of Regular Bessel Functions114258 +Node: Clausen Functions115361 +Node: Coulomb Functions115965 +Node: Normalized Hydrogenic Bound States116414 +Node: Coulomb Wave Functions117527 +Node: Coulomb Wave Function Normalization Constant120937 +Node: Coupling Coefficients121690 +Node: 3-j Symbols122413 +Node: 6-j Symbols123017 +Node: 9-j Symbols123641 +Node: Dawson Function124347 +Node: Debye Functions124914 +Node: Dilogarithm126688 +Node: Real Argument126983 +Node: Complex Argument127552 +Node: Elementary Operations128021 +Node: Elliptic Integrals128845 +Node: Definition of Legendre Forms129417 +Node: Definition of Carlson Forms130237 +Node: Legendre Form of Complete Elliptic Integrals130934 +Node: Legendre Form of Incomplete Elliptic Integrals132502 +Node: Carlson Forms134690 +Node: Elliptic Functions (Jacobi)136237 +Node: Error Functions136818 +Node: Error Function137269 +Node: Complementary Error Function137642 +Node: Log Complementary Error Function138102 +Node: Probability functions138554 +Node: Exponential Functions139807 +Node: Exponential Function140190 +Node: Relative Exponential Functions141413 +Node: Exponentiation With Error Estimate143084 +Node: Exponential Integrals144293 +Node: Exponential Integral144775 +Node: Ei(x)145425 +Node: Hyperbolic Integrals145873 +Node: Ei_3(x)146529 +Node: Trigonometric Integrals146921 +Node: Arctangent Integral147520 +Node: Fermi-Dirac Function147920 +Node: Complete Fermi-Dirac Integrals148290 +Node: Incomplete Fermi-Dirac Integrals150751 +Node: Gamma and Beta Functions151394 +Node: Gamma Functions151830 +Node: Factorials154951 +Node: Pochhammer Symbol157504 +Node: Incomplete Gamma Functions159016 +Node: Beta Functions160265 +Node: Incomplete Beta Function161017 +Node: Gegenbauer Functions161548 +Node: Hypergeometric Functions163198 +Node: Laguerre Functions167465 +Node: Lambert W Functions169028 +Node: Legendre Functions and Spherical Harmonics170066 +Node: Legendre Polynomials170655 +Node: Associated Legendre Polynomials and Spherical Harmonics172735 +Node: Conical Functions175536 +Node: Radial Functions for Hyperbolic Space177659 +Node: Logarithm and Related Functions179836 +Node: Mathieu Functions181460 +Node: Mathieu Function Workspace182809 +Node: Mathieu Function Characteristic Values183622 +Node: Angular Mathieu Functions184690 +Node: Radial Mathieu Functions185722 +Node: Power Function186960 +Node: Psi (Digamma) Function187887 +Node: Digamma Function188407 +Node: Trigamma Function189237 +Node: Polygamma Function189814 +Node: Synchrotron Functions190198 +Node: Transport Functions190961 +Node: Trigonometric Functions192108 +Node: Circular Trigonometric Functions192731 +Node: Trigonometric Functions for Complex Arguments193740 +Node: Hyperbolic Trigonometric Functions194774 +Node: Conversion Functions195377 +Node: Restriction Functions196160 +Node: Trigonometric Functions With Error Estimates197092 +Node: Zeta Functions198002 +Node: Riemann Zeta Function198460 +Node: Riemann Zeta Function Minus One199139 +Node: Hurwitz Zeta Function199910 +Node: Eta Function200415 +Node: Special Functions Examples200974 +Node: Special Functions References and Further Reading202668 +Node: Vectors and Matrices203775 +Node: Data types204534 +Node: Blocks205737 +Node: Block allocation206653 +Node: Reading and writing blocks208137 +Node: Example programs for blocks210201 +Node: Vectors210828 +Node: Vector allocation212714 +Node: Accessing vector elements214332 +Node: Initializing vector elements216574 +Node: Reading and writing vectors217268 +Node: Vector views219358 +Node: Copying vectors226800 +Node: Exchanging elements227660 +Node: Vector operations228218 +Node: Finding maximum and minimum elements of vectors229732 +Node: Vector properties231257 +Node: Example programs for vectors231880 +Node: Matrices234169 +Node: Matrix allocation237027 +Node: Accessing matrix elements238694 +Node: Initializing matrix elements240402 +Node: Reading and writing matrices241198 +Node: Matrix views243301 +Node: Creating row and column views250441 +Node: Copying matrices253612 +Node: Copying rows and columns254208 +Node: Exchanging rows and columns255885 +Node: Matrix operations257363 +Node: Finding maximum and minimum elements of matrices259003 +Node: Matrix properties260907 +Node: Example programs for matrices261655 +Node: Vector and Matrix References and Further Reading265726 +Node: Permutations266212 +Node: The Permutation struct267500 +Node: Permutation allocation268004 +Node: Accessing permutation elements269438 +Node: Permutation properties270201 +Node: Permutation functions270900 +Node: Applying Permutations272157 +Node: Reading and writing permutations274082 +Node: Permutations in cyclic form276264 +Node: Permutation Examples279689 +Node: Permutation References and Further Reading282232 +Node: Combinations282906 +Node: The Combination struct283751 +Node: Combination allocation284303 +Node: Accessing combination elements286088 +Node: Combination properties286667 +Node: Combination functions287553 +Node: Reading and writing combinations288493 +Node: Combination Examples290693 +Node: Combination References and Further Reading292001 +Node: Sorting292405 +Node: Sorting objects293355 +Node: Sorting vectors296266 +Node: Selecting the k smallest or largest elements298842 +Node: Computing the rank302176 +Node: Sorting Examples303377 +Node: Sorting References and Further Reading305021 +Node: BLAS Support305567 +Node: GSL BLAS Interface308542 +Node: Level 1 GSL BLAS Interface309029 +Node: Level 2 GSL BLAS Interface315772 +Node: Level 3 GSL BLAS Interface325066 +Node: BLAS Examples336202 +Node: BLAS References and Further Reading337623 +Node: Linear Algebra338982 +Node: LU Decomposition340164 +Node: QR Decomposition345372 +Node: QR Decomposition with Column Pivoting351174 +Node: Singular Value Decomposition355584 +Node: Cholesky Decomposition359174 +Node: Tridiagonal Decomposition of Real Symmetric Matrices361181 +Node: Tridiagonal Decomposition of Hermitian Matrices363029 +Node: Hessenberg Decomposition of Real Matrices364984 +Node: Bidiagonalization367329 +Node: Householder Transformations369739 +Node: Householder solver for linear systems371587 +Node: Tridiagonal Systems372492 +Node: Balancing375145 +Node: Linear Algebra Examples375946 +Node: Linear Algebra References and Further Reading377934 +Node: Eigensystems379424 +Node: Real Symmetric Matrices380603 +Node: Complex Hermitian Matrices382835 +Node: Real Nonsymmetric Matrices385343 +Node: Sorting Eigenvalues and Eigenvectors390537 +Node: Eigenvalue and Eigenvector Examples392404 +Node: Eigenvalue and Eigenvector References397790 +Node: Fast Fourier Transforms398498 +Node: Mathematical Definitions399707 +Node: Overview of complex data FFTs402112 +Node: Radix-2 FFT routines for complex data405055 +Node: Mixed-radix FFT routines for complex data409267 +Node: Overview of real data FFTs418596 +Node: Radix-2 FFT routines for real data421030 +Node: Mixed-radix FFT routines for real data424037 +Node: FFT References and Further Reading434617 +Node: Numerical Integration437486 +Node: Numerical Integration Introduction439031 +Node: Integrands without weight functions440965 +Node: Integrands with weight functions441794 +Node: Integrands with singular weight functions442505 +Node: QNG non-adaptive Gauss-Kronrod integration443423 +Node: QAG adaptive integration444694 +Node: QAGS adaptive integration with singularities447325 +Node: QAGP adaptive integration with known singular points449125 +Node: QAGI adaptive integration on infinite intervals450439 +Node: QAWC adaptive integration for Cauchy principal values452732 +Node: QAWS adaptive integration for singular functions453907 +Node: QAWO adaptive integration for oscillatory functions457129 +Node: QAWF adaptive integration for Fourier integrals460908 +Node: Numerical integration error codes463533 +Node: Numerical integration examples464301 +Node: Numerical integration References and Further Reading466346 +Node: Random Number Generation467075 +Node: General comments on random numbers468577 +Node: The Random Number Generator Interface470527 +Node: Random number generator initialization471885 +Node: Sampling from a random number generator473901 +Node: Auxiliary random number generator functions477066 +Node: Random number environment variables479386 +Node: Copying random number generator state481912 +Node: Reading and writing random number generator state482887 +Node: Random number generator algorithms484299 +Node: Unix random number generators494108 +Node: Other random number generators497826 +Node: Random Number Generator Performance506459 +Node: Random Number Generator Examples507777 +Node: Random Number References and Further Reading509333 +Node: Random Number Acknowledgements510630 +Node: Quasi-Random Sequences511116 +Node: Quasi-random number generator initialization512223 +Node: Sampling from a quasi-random number generator513238 +Node: Auxiliary quasi-random number generator functions513855 +Node: Saving and resorting quasi-random number generator state514801 +Node: Quasi-random number generator algorithms515609 +Node: Quasi-random number generator examples516384 +Node: Quasi-random number references517369 +Node: Random Number Distributions517895 +Node: Random Number Distribution Introduction521094 +Node: The Gaussian Distribution522889 +Node: The Gaussian Tail Distribution525551 +Node: The Bivariate Gaussian Distribution527220 +Node: The Exponential Distribution528543 +Node: The Laplace Distribution529682 +Node: The Exponential Power Distribution530779 +Node: The Cauchy Distribution532047 +Node: The Rayleigh Distribution533296 +Node: The Rayleigh Tail Distribution534468 +Node: The Landau Distribution535340 +Node: The Levy alpha-Stable Distributions536295 +Node: The Levy skew alpha-Stable Distribution537353 +Node: The Gamma Distribution538965 +Node: The Flat (Uniform) Distribution540622 +Node: The Lognormal Distribution541774 +Node: The Chi-squared Distribution543122 +Node: The F-distribution544526 +Node: The t-distribution546162 +Node: The Beta Distribution547556 +Node: The Logistic Distribution548715 +Node: The Pareto Distribution549844 +Node: Spherical Vector Distributions551014 +Node: The Weibull Distribution553848 +Node: The Type-1 Gumbel Distribution555042 +Node: The Type-2 Gumbel Distribution556279 +Node: The Dirichlet Distribution557510 +Node: General Discrete Distributions559178 +Node: The Poisson Distribution563043 +Node: The Bernoulli Distribution564051 +Node: The Binomial Distribution564802 +Node: The Multinomial Distribution566007 +Node: The Negative Binomial Distribution567776 +Node: The Pascal Distribution569141 +Node: The Geometric Distribution570299 +Node: The Hypergeometric Distribution571547 +Node: The Logarithmic Distribution573200 +Node: Shuffling and Sampling573991 +Node: Random Number Distribution Examples576810 +Node: Random Number Distribution References and Further Reading580006 +Node: Statistics582072 +Node: Mean and standard deviation and variance583351 +Node: Absolute deviation586396 +Node: Higher moments (skewness and kurtosis)587688 +Node: Autocorrelation589821 +Node: Covariance590635 +Node: Weighted Samples591616 +Node: Maximum and Minimum values596860 +Node: Median and Percentiles599599 +Node: Example statistical programs602014 +Node: Statistics References and Further Reading604673 +Node: Histograms605881 +Node: The histogram struct607641 +Node: Histogram allocation609444 +Node: Copying Histograms612405 +Node: Updating and accessing histogram elements613081 +Node: Searching histogram ranges616348 +Node: Histogram Statistics617347 +Node: Histogram Operations619207 +Node: Reading and writing histograms621279 +Node: Resampling from histograms624321 +Node: The histogram probability distribution struct625119 +Node: Example programs for histograms628150 +Node: Two dimensional histograms630213 +Node: The 2D histogram struct630934 +Node: 2D Histogram allocation632742 +Node: Copying 2D Histograms634813 +Node: Updating and accessing 2D histogram elements635518 +Node: Searching 2D histogram ranges639173 +Node: 2D Histogram Statistics640192 +Node: 2D Histogram Operations643051 +Node: Reading and writing 2D histograms645225 +Node: Resampling from 2D histograms648852 +Node: Example programs for 2D histograms651871 +Node: N-tuples653699 +Node: The ntuple struct654955 +Node: Creating ntuples655433 +Node: Opening an existing ntuple file656100 +Node: Writing ntuples656728 +Node: Reading ntuples657189 +Node: Closing an ntuple file657520 +Node: Histogramming ntuple values657860 +Node: Example ntuple programs659866 +Node: Ntuple References and Further Reading663195 +Node: Monte Carlo Integration663516 +Node: Monte Carlo Interface664761 +Node: PLAIN Monte Carlo667384 +Node: MISER669822 +Node: VEGAS675660 +Node: Monte Carlo Examples683995 +Node: Monte Carlo Integration References and Further Reading689938 +Node: Simulated Annealing690720 +Node: Simulated Annealing algorithm691927 +Node: Simulated Annealing functions693081 +Node: Examples with Simulated Annealing697607 +Node: Trivial example698161 +Node: Traveling Salesman Problem700812 +Node: Simulated Annealing References and Further Reading704125 +Node: Ordinary Differential Equations704536 +Node: Defining the ODE System705357 +Node: Stepping Functions707549 +Node: Adaptive Step-size Control711728 +Node: Evolution717186 +Node: ODE Example programs719864 +Node: ODE References and Further Reading724934 +Node: Interpolation725573 +Node: Introduction to Interpolation726586 +Node: Interpolation Functions727027 +Node: Interpolation Types728203 +Node: Index Look-up and Acceleration730813 +Node: Evaluation of Interpolating Functions732443 +Node: Higher-level Interface734827 +Node: Interpolation Example programs736866 +Node: Interpolation References and Further Reading740113 +Node: Numerical Differentiation740686 +Node: Numerical Differentiation functions741275 +Node: Numerical Differentiation Examples744133 +Node: Numerical Differentiation References745546 +Node: Chebyshev Approximations746097 +Node: Chebyshev Definitions747113 +Node: Creation and Calculation of Chebyshev Series747903 +Node: Chebyshev Series Evaluation748875 +Node: Derivatives and Integrals750259 +Node: Chebyshev Approximation examples751501 +Node: Chebyshev Approximation References and Further Reading752997 +Node: Series Acceleration753446 +Node: Acceleration functions754211 +Node: Acceleration functions without error estimation756536 +Node: Example of accelerating a series759146 +Node: Series Acceleration References761492 +Node: Wavelet Transforms762380 +Node: DWT Definitions762921 +Node: DWT Initialization763873 +Node: DWT Transform Functions766452 +Node: DWT in one dimension766987 +Node: DWT in two dimension769006 +Node: DWT Examples773607 +Node: DWT References775424 +Node: Discrete Hankel Transforms777587 +Node: Discrete Hankel Transform Definition778055 +Node: Discrete Hankel Transform Functions780194 +Node: Discrete Hankel Transform References781725 +Node: One dimensional Root-Finding782129 +Node: Root Finding Overview783389 +Node: Root Finding Caveats785247 +Node: Initializing the Solver787014 +Node: Providing the function to solve789647 +Node: Search Bounds and Guesses793413 +Node: Root Finding Iteration794274 +Node: Search Stopping Parameters796123 +Node: Root Bracketing Algorithms798637 +Node: Root Finding Algorithms using Derivatives801935 +Node: Root Finding Examples805438 +Node: Root Finding References and Further Reading812726 +Node: One dimensional Minimization813365 +Node: Minimization Overview814667 +Node: Minimization Caveats816373 +Node: Initializing the Minimizer817710 +Node: Providing the function to minimize819951 +Node: Minimization Iteration820429 +Node: Minimization Stopping Parameters822565 +Node: Minimization Algorithms824174 +Node: Minimization Examples826613 +Node: Minimization References and Further Reading829557 +Node: Multidimensional Root-Finding830013 +Node: Overview of Multidimensional Root Finding831502 +Node: Initializing the Multidimensional Solver833689 +Node: Providing the multidimensional system of equations to solve836887 +Node: Iteration of the multidimensional solver841792 +Node: Search Stopping Parameters for the multidimensional solver843977 +Node: Algorithms using Derivatives845714 +Node: Algorithms without Derivatives850460 +Node: Example programs for Multidimensional Root finding853548 +Node: References and Further Reading for Multidimensional Root Finding862161 +Node: Multidimensional Minimization863400 +Node: Multimin Overview864692 +Node: Multimin Caveats866664 +Node: Initializing the Multidimensional Minimizer867413 +Node: Providing a function to minimize870574 +Node: Multimin Iteration874239 +Node: Multimin Stopping Criteria876230 +Node: Multimin Algorithms877782 +Node: Multimin Examples882741 +Node: Multimin References and Further Reading889358 +Node: Least-Squares Fitting890221 +Node: Fitting Overview891220 +Node: Linear regression893436 +Node: Linear fitting without a constant term895867 +Node: Multi-parameter fitting898058 +Node: Fitting Examples902963 +Node: Fitting References and Further Reading909788 +Node: Nonlinear Least-Squares Fitting910610 +Node: Overview of Nonlinear Least-Squares Fitting912060 +Node: Initializing the Nonlinear Least-Squares Solver913527 +Node: Providing the Function to be Minimized916380 +Node: Iteration of the Minimization Algorithm919317 +Node: Search Stopping Parameters for Minimization Algorithms921167 +Node: Minimization Algorithms using Derivatives923262 +Node: Minimization Algorithms without Derivatives926510 +Node: Computing the covariance matrix of best fit parameters926902 +Node: Example programs for Nonlinear Least-Squares Fitting928936 +Node: References and Further Reading for Nonlinear Least-Squares Fitting936664 +Node: Basis Splines937400 +Node: Overview of B-splines937975 +Node: Initializing the B-splines solver939260 +Node: Constructing the knots vector940003 +Node: Evaluation of B-spline basis functions940790 +Node: Example programs for B-splines941523 +Node: References and Further Reading945220 +Node: Physical Constants945734 +Node: Fundamental Constants947144 +Node: Astronomy and Astrophysics948283 +Node: Atomic and Nuclear Physics948948 +Node: Measurement of Time950585 +Node: Imperial Units951015 +Node: Speed and Nautical Units951457 +Node: Printers Units951961 +Node: Volume Area and Length952284 +Node: Mass and Weight952970 +Node: Thermal Energy and Power953789 +Node: Pressure954212 +Node: Viscosity954825 +Node: Light and Illumination955101 +Node: Radioactivity955693 +Node: Force and Energy956028 +Node: Prefixes956432 +Node: Physical Constant Examples957175 +Node: Physical Constant References and Further Reading958964 +Node: IEEE floating-point arithmetic959675 +Node: Representation of floating point numbers960261 +Node: Setting up your IEEE environment964742 +Node: IEEE References and Further Reading971351 +Node: Debugging Numerical Programs972506 +Node: Using gdb972990 +Node: Examining floating point registers976333 +Node: Handling floating point exceptions977618 +Node: GCC warning options for numerical programs979030 +Node: Debugging References983223 +Node: Contributors to GSL983935 +Node: Autoconf Macros988118 +Node: GSL CBLAS Library992103 +Node: Level 1 CBLAS Functions992630 +Node: Level 2 CBLAS Functions997932 +Node: Level 3 CBLAS Functions1014602 +Node: GSL CBLAS Examples1024264 +Node: Free Software Needs Free Documentation1025826 +Node: GNU General Public License1030895 +Node: GNU Free Documentation License1050165 +Node: Function Index1072596 +Node: Variable Index1306453 +Node: Type Index1307625 +Node: Concept Index1311271 + +End Tag Table |