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diff --git a/gsl-1.9/doc/gsl-ref.texi b/gsl-1.9/doc/gsl-ref.texi new file mode 100644 index 0000000..c2ba564 --- /dev/null +++ b/gsl-1.9/doc/gsl-ref.texi @@ -0,0 +1,647 @@ +\input texinfo @c -*-texinfo-*- +@c This will be for the printing version of the manual +@c @input config-local.texi +@c %**start of header +@setfilename gsl-ref.info +@settitle GNU Scientific Library -- Reference Manual +@finalout +@set frontcontents +@ifset publish +@setchapternewpage odd +@end ifset +@c %**end of header + +@dircategory Scientific software +@direntry +* gsl-ref: (gsl-ref). GNU Scientific Library -- Reference +@end direntry + +@c How to use the math macros +@c ========================== +@c +@c For simple expressions, simply use the @math{} command, e.g. +@c +@c @math{\exp(x)/(1+x^2)} +@c +@c but if the expression includes characters that need to be 'escaped' +@c in texinfo, like '{' or '}', or needs different output for TeX and info, +@c then use the following form, +@c +@c blah blah blah @c{$y^{1+b} \le \pi$} +@c @math{y^@{1+b@} <= \pi} +@c +@c The first part using @c{} must appear at the end of a line (it reads +@c up to the line end -- as far as texinfo is concerned it's actually +@c a 'comment'). The comment command @c has been modified to capture +@c a TeX expression which is output by the next @math. +@c +@c For ordinary comments use the @comment command. + +@tex +% Mathematical macros taken from the GNU Calc Manual +% ================================================== +% +% Some special kludges to make TeX formatting prettier. +% Because makeinfo.c exists, we can't just define new commands. +% So instead, we take over little-used existing commands. +% +% Redefine @cite{text} to act like $text$ in regular TeX. +% Info will typeset this same as @samp{text}. +\gdef\goodtex{\tex \let\rm\goodrm \let\t\ttfont \turnoffactive} +\gdef\goodrm{\fam0\tenrm} +\gdef\math{\goodtex$\mathxxx} +\gdef\mathxxx#1{#1$\endgroup} +\global\let\oldxrefX=\xrefX +\gdef\xrefX[#1]{\begingroup\let\math=\dfn\oldxrefX[#1]\endgroup} +% +% Redefine @i{text} to be equivalent to @cite{text}, i.e., to use math mode. +% This looks the same in TeX but omits the surrounding ` ' in Info. +%\global\let\i=\cite +%\global\let\math=\cite +% +% Redefine @c{tex-stuff} \n @whatever{info-stuff}. +\gdef\c{\futurelet\next\mycxxx} +\gdef\mycxxx{% + \ifx\next\bgroup \goodtex\let\next\mycxxy + \else\ifx\next\mindex \let\next\relax + \else\ifx\next\kindex \let\next\relax + \else\ifx\next\starindex \let\next\relax \else \let\next\comment + \fi\fi\fi\fi \next +} +\gdef\mycxxy#1#2{#1\endgroup\mycxxz} +\gdef\mycxxz#1{} +% +% Define \Hat to take over from \hat as an accent +\gdef\Hat{\mathaccent "705E} +% +%\gdef\beforedisplay{\vskip-10pt} +%\gdef\afterdisplay{\vskip-5pt} +\gdef\beforedisplay{} +\gdef\afterdisplay{} +{\globaldefs = 1 +\abovedisplayskip=7pt plus 2pt minus 1pt +\belowdisplayskip=7pt plus 2pt minus 1pt +\abovedisplayshortskip=7pt plus 2pt minus 1pt +\belowdisplayshortskip=7pt plus 2pt minus 1pt} +%\abovedisplayskip=12pt plus 3pt minus 3pt +%\belowdisplayskip=12pt plus 3pt minus 3pt +%\abovedisplayshortskip=7pt plus 1pt minus 1pt +%\belowdisplayshortskip=7pt plus 1pt minus 1pt +%\gdef\beforedisplayh{\vskip-25pt} +%\gdef\afterdisplayh{\vskip-10pt} +% +\gdef\arcsec{\hbox{\rm arcsec}} +\gdef\arccsc{\hbox{\rm arccsc}} +\gdef\arccot{\hbox{\rm arccot}} +\gdef\sech{\hbox{\rm sech}} +\gdef\csch{\hbox{\rm csch}} +\gdef\coth{\hbox{\rm coth}} +\gdef\arcsinh{\hbox{\rm arcsinh}} +\gdef\arccosh{\hbox{\rm arccosh}} +\gdef\arctanh{\hbox{\rm arctanh}} +\gdef\arcsech{\hbox{\rm arcsech}} +\gdef\arccsch{\hbox{\rm arccsch}} +\gdef\arccoth{\hbox{\rm arccoth}} +% +\gdef\Re{\hbox{\rm Re}} +\gdef\Im{\hbox{\rm Im}} +\gdef\Sin{\hbox{\rm Sin}} +\gdef\Cos{\hbox{\rm Cos}} +\gdef\Log{\hbox{\rm Log}} +% +\gdef\erf{\hbox{\rm erf}} +\gdef\erfc{\hbox{\rm erfc}} +\gdef\sinc{\hbox{\rm sinc}} +\gdef\sgn{\hbox{\rm sgn}} +\gdef\sign{\hbox{\rm sign}} +\gdef\det{\hbox{\rm det}} +\gdef\Var{\hbox{\rm Var}} +\gdef\arg{\hbox{\rm arg}} % avoid temporary clobbering of arg in texinfo-4.8 +@end tex + +@include version-ref.texi +@set GSL @i{GNU Scientific Library} + +@copying +Copyright @copyright{} 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.'' +@end copying + +@titlepage +@title GNU Scientific Library +@subtitle Reference Manual +@subtitle Edition @value{EDITION}, for GSL Version @value{VERSION} +@subtitle @value{UPDATED} + +@author Mark Galassi +Los Alamos National Laboratory +@comment @email{rosalia@@lanl.gov} +@sp 1 + +@author Jim Davies +Department of Computer Science, Georgia Institute of Technology +@comment @email{jimmyd@@nis.lanl.gov} +@sp 1 + +@author James Theiler +Astrophysics and Radiation Measurements Group, Los Alamos National Laboratory +@comment @email{jt@@nis.lanl.gov} +@sp 1 + +@author Brian Gough +Network Theory Limited +@comment @email{bjg@@network-theory.co.uk} +@sp 1 + +@comment Asked to be moved to 'contributors' appendix +@comment @author Reid Priedhorsky +@comment Mathematical Modeling and Analysis Group, Los Alamos National Laboratory +@comment @email{rp@@lanl.gov} +@comment @sp 1 + +@author Gerard Jungman +Theoretical Astrophysics Group, Los Alamos National Laboratory +@comment @email{jungman@@lanl.gov} +@sp 1 + +@author Michael Booth +Department of Physics and Astronomy, The Johns Hopkins University +@comment @email{booth@@planck.pha.jhu.edu} or @email{booth@@debian.org} +@sp 1 + +@author Fabrice Rossi +University of Paris-Dauphine +@comment @email{rossi@@ufrmd.dauphine.fr} +@sp 1 +@page +@vskip 0pt plus 1filll +@insertcopying +@ifclear publish +Printed copies of this manual can be purchased from Network Theory Ltd +at @uref{http://www.network-theory.co.uk/gsl/manual/}. + +The money raised from sales of the manual helps support the +development of GSL. +@end ifclear +@end titlepage + +@iftex +@ifset frontcontents +@contents +@end ifset +@end iftex + +@ifnottex +@node Top, Introduction, (dir), (dir) +@top GSL + +This file documents the @value{GSL} (GSL), a collection of numerical +routines for scientific computing. It corresponds to release +@value{VERSION} of the library. Please report any errors in this +manual to @email{bug-gsl@@gnu.org}. + +More information about GSL can be found at the project homepage, +@uref{http://www.gnu.org/software/gsl/}. + +Printed copies of this manual can be purchased from Network Theory Ltd +at @uref{http://www.network-theory.co.uk/gsl/manual/}. The money +raised from sales of the manual helps support the development of GSL. + +A Japanese translation of this manual is available from the GSL +project homepage thanks to Daisuke Tominaga. + +@insertcopying +@sp 1 +@end ifnottex + +@menu +* Introduction:: +* Using the library:: +* Error Handling:: +* Mathematical Functions:: +* Complex Numbers:: +* Polynomials:: +* Special Functions:: +* Vectors and Matrices:: +* Permutations:: +* Combinations:: +* Sorting:: +* BLAS Support:: +* Linear Algebra:: +* Eigensystems:: +* Fast Fourier Transforms:: +* Numerical Integration:: +* Random Number Generation:: +* Quasi-Random Sequences:: +* Random Number Distributions:: +* Statistics:: +* Histograms:: +* N-tuples:: +* Monte Carlo Integration:: +* Simulated Annealing:: +* Ordinary Differential Equations:: +* Interpolation:: +* Numerical Differentiation:: +* Chebyshev Approximations:: +* Series Acceleration:: +* Wavelet Transforms:: +* Discrete Hankel Transforms:: +* One dimensional Root-Finding:: +* One dimensional Minimization:: +* Multidimensional Root-Finding:: +* Multidimensional Minimization:: +* Least-Squares Fitting:: +* Nonlinear Least-Squares Fitting:: +* Basis Splines:: +* Physical Constants:: +* IEEE floating-point arithmetic:: +* Debugging Numerical Programs:: +* Contributors to GSL:: +* Autoconf Macros:: +* GSL CBLAS Library:: +* Free Software Needs Free Documentation:: +* GNU General Public License:: +* GNU Free Documentation License:: +* Function Index:: +* Variable Index:: +* Type Index:: +* Concept Index:: +@end menu + +@node Introduction, Using the library, Top, Top +@chapter Introduction +@include intro.texi + +@node Using the library, Error Handling, Introduction, Top +@chapter Using the library +@cindex usage, compiling application programs +@include usage.texi + +@node Error Handling, Mathematical Functions, Using the library, Top +@chapter Error Handling +@cindex Errors +@include err.texi + +@node Mathematical Functions, Complex Numbers, Error Handling, Top +@chapter Mathematical Functions +@include math.texi + +@node Complex Numbers, Polynomials, Mathematical Functions, Top +@chapter Complex Numbers +@include complex.texi + +@node Polynomials, Special Functions, Complex Numbers, Top +@chapter Polynomials +@include poly.texi + +@node Special Functions, Vectors and Matrices, Polynomials, Top +@chapter Special Functions +@include specfunc.texi + +@node Vectors and Matrices, Permutations, Special Functions, Top +@chapter Vectors and Matrices +@include vectors.texi + +@node Permutations, Combinations, Vectors and Matrices, Top +@chapter Permutations +@include permutation.texi + +@node Combinations, Sorting, Permutations, Top +@chapter Combinations +@include combination.texi + +@node Sorting, BLAS Support, Combinations, Top +@chapter Sorting +@include sort.texi + +@node BLAS Support, Linear Algebra, Sorting, Top +@chapter BLAS Support +@include blas.texi + +@node Linear Algebra, Eigensystems, BLAS Support, Top +@chapter Linear Algebra +@include linalg.texi + +@node Eigensystems, Fast Fourier Transforms, Linear Algebra, Top +@chapter Eigensystems +@include eigen.texi + +@node Fast Fourier Transforms, Numerical Integration, Eigensystems, Top +@chapter Fast Fourier Transforms (FFTs) +@include fft.texi + +@node Numerical Integration, Random Number Generation, Fast Fourier Transforms, Top +@chapter Numerical Integration +@include integration.texi + +@node Random Number Generation, Quasi-Random Sequences, Numerical Integration, Top +@chapter Random Number Generation +@include rng.texi + +@node Quasi-Random Sequences, Random Number Distributions, Random Number Generation, Top +@chapter Quasi-Random Sequences +@include qrng.texi + +@node Random Number Distributions, Statistics, Quasi-Random Sequences, Top +@chapter Random Number Distributions +@include randist.texi + +@node Statistics, Histograms, Random Number Distributions, Top +@chapter Statistics +@include statistics.texi + +@node Histograms, N-tuples, Statistics, Top +@chapter Histograms +@include histogram.texi + +@node N-tuples, Monte Carlo Integration, Histograms, Top +@chapter N-tuples +@include ntuple.texi + +@node Monte Carlo Integration, Simulated Annealing, N-tuples, Top +@chapter Monte Carlo Integration +@include montecarlo.texi + +@node Simulated Annealing, Ordinary Differential Equations, Monte Carlo Integration, Top +@chapter Simulated Annealing +@include siman.texi + +@node Ordinary Differential Equations, Interpolation, Simulated Annealing, Top +@chapter Ordinary Differential Equations +@include ode-initval.texi + +@node Interpolation, Numerical Differentiation, Ordinary Differential Equations, Top +@chapter Interpolation +@include interp.texi + +@node Numerical Differentiation, Chebyshev Approximations, Interpolation, Top +@chapter Numerical Differentiation +@include diff.texi + +@node Chebyshev Approximations, Series Acceleration, Numerical Differentiation, Top +@chapter Chebyshev Approximations +@include cheb.texi + +@node Series Acceleration, Wavelet Transforms, Chebyshev Approximations, Top +@chapter Series Acceleration +@include sum.texi + +@node Wavelet Transforms, Discrete Hankel Transforms, Series Acceleration, Top +@chapter Wavelet Transforms +@include dwt.texi + +@node Discrete Hankel Transforms, One dimensional Root-Finding, Wavelet Transforms, Top +@chapter Discrete Hankel Transforms +@include dht.texi + +@node One dimensional Root-Finding, One dimensional Minimization, Discrete Hankel Transforms, Top +@chapter One dimensional Root-Finding +@include roots.texi + +@node One dimensional Minimization, Multidimensional Root-Finding, One dimensional Root-Finding, Top +@chapter One dimensional Minimization +@include min.texi + +@node Multidimensional Root-Finding, Multidimensional Minimization, One dimensional Minimization, Top +@chapter Multidimensional Root-Finding +@include multiroots.texi + +@node Multidimensional Minimization, Least-Squares Fitting, Multidimensional Root-Finding, Top +@chapter Multidimensional Minimization +@include multimin.texi + +@node Least-Squares Fitting, Nonlinear Least-Squares Fitting, Multidimensional Minimization, Top +@chapter Least-Squares Fitting +@include fitting.texi + +@node Nonlinear Least-Squares Fitting, Basis Splines, Least-Squares Fitting, Top +@chapter Nonlinear Least-Squares Fitting +@include multifit.texi + +@node Basis Splines, Physical Constants, Nonlinear Least-Squares Fitting, Top +@chapter Basis Splines +@include bspline.texi + +@node Physical Constants, IEEE floating-point arithmetic, Basis Splines, Top +@chapter Physical Constants +@include const.texi + +@node IEEE floating-point arithmetic, Debugging Numerical Programs, Physical Constants, Top +@chapter IEEE floating-point arithmetic +@include ieee754.texi + +@node Debugging Numerical Programs, Contributors to GSL, IEEE floating-point arithmetic, Top +@appendix Debugging Numerical Programs +@include debug.texi + +@node Contributors to GSL, Autoconf Macros, Debugging Numerical Programs, Top +@appendix Contributors to GSL + +(See the AUTHORS file in the distribution for up-to-date information.) + +@table @strong +@item Mark Galassi +Conceived GSL (with James Theiler) and wrote the design document. Wrote +the simulated annealing package and the relevant chapter in the manual. + +@item James Theiler +Conceived GSL (with Mark Galassi). Wrote the random number generators +and the relevant chapter in this manual. + +@item Jim Davies +Wrote the statistical routines and the relevant chapter in this +manual. + +@item Brian Gough +FFTs, numerical integration, random number generators and distributions, +root finding, minimization and fitting, polynomial solvers, complex +numbers, physical constants, permutations, vector and matrix functions, +histograms, statistics, ieee-utils, revised @sc{cblas} Level 2 & 3, +matrix decompositions, eigensystems, cumulative distribution functions, +testing, documentation and releases. + +@item Reid Priedhorsky +Wrote and documented the initial version of the root finding routines +while at Los Alamos National Laboratory, Mathematical Modeling and +Analysis Group. +@comment email: reid@reidster.net + +@item Gerard Jungman +Special Functions, Series acceleration, ODEs, BLAS, Linear Algebra, +Eigensystems, Hankel Transforms. + +@item Mike Booth +Wrote the Monte Carlo library. + +@item Jorma Olavi T@"ahtinen +Wrote the initial complex arithmetic functions. + +@item Thomas Walter +Wrote the initial heapsort routines and cholesky decomposition. + +@item Fabrice Rossi +Multidimensional minimization. + +@item Carlo Perassi +Implementation of the random number generators in Knuth's +@cite{Seminumerical Algorithms}, 3rd Ed. + +@item Szymon Jaroszewicz +@comment <sj@cs.umb.edu> +Wrote the routines for generating combinations. + +@item Nicolas Darnis +Wrote the initial routines for canonical permutations. + +@item Jason H. Stover +@comment (jason@sakla.net) +Wrote the major cumulative distribution functions. + +@item Ivo Alxneit +Wrote the routines for wavelet transforms. + +@item Tuomo Keskitalo +Improved the implementation of the ODE solvers. + +@item Lowell Johnson +Implementation of the Mathieu functions. + +@item Patrick Alken +Implementation of non-symmetric eigensystems and B-splines. + +@end table + +Thanks to Nigel Lowry for help in proofreading the manual. + +The non-symmetric eigensystems routines contain code based on the +LAPACK linear algebra library. LAPACK is distributed under the +following license: + +@iftex +@smallerfonts @rm +@end iftex +@sp 1 +@quotation +Copyright (c) 1992-2006 The University of Tennessee. All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + +@bullet{} Redistributions of source code must retain the above copyright +notice, this list of conditions and the following disclaimer. + +@bullet{} Redistributions in binary form must reproduce the above copyright +notice, this list of conditions and the following disclaimer listed +in this license in the documentation and/or other materials +provided with the distribution. + +@bullet{} Neither the name of the copyright holders nor the names of its +contributors may be used to endorse or promote products derived from +this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +@end quotation + +@iftex +@textfonts @rm +@end iftex + + + +@node Autoconf Macros, GSL CBLAS Library, Contributors to GSL, Top +@appendix Autoconf Macros +@include autoconf.texi + +@node GSL CBLAS Library, Free Software Needs Free Documentation, Autoconf Macros, Top +@appendix GSL CBLAS Library +@include cblas.texi + +@comment @node Copyright, GNU General Public License, Contributors to GSL, Top +@comment @unnumbered Copyright +@comment @include science.texi + +@node Free Software Needs Free Documentation, GNU General Public License, GSL CBLAS Library, Top +@unnumbered Free Software Needs Free Documentation +@include freemanuals.texi + +@node GNU General Public License, GNU Free Documentation License, Free Software Needs Free Documentation, Top +@unnumbered GNU General Public License +@include gpl.texi + +@node GNU Free Documentation License, Function Index, GNU General Public License, Top +@unnumbered GNU Free Documentation License +@include fdl.texi + +@comment htmlhelp: @printindex fn +@comment htmlhelp: @printindex vr +@comment htmlhelp: @printindex tp +@comment htmlhelp: @printindex cp +@comment htmlhelp: @bye + +@iftex +@normalbottom +@end iftex + +@node Function Index, Variable Index, GNU Free Documentation License, Top +@unnumbered Function Index + +@printindex fn + +@node Variable Index, Type Index, Function Index, Top +@unnumbered Variable Index + +@printindex vr + +@node Type Index, Concept Index, Variable Index, Top +@unnumbered Type Index + +@printindex tp + +@node Concept Index, , Type Index, Top +@unnumbered Concept Index + +@printindex cp + +@ifclear frontcontents +@comment Use @setchapternewpage odd to ensure that the contents starts +@comment on an odd page so that it can always be moved to the front when +@comment printing two-up. +@setchapternewpage odd +@contents +@end ifclear + +@ifset extrablankpages +@comment final page must be blank for printed version +@page +@headings off +@* +@page +@* +@comment @page +@comment @* +@comment @page +@comment @* +@end ifset +@bye |