gsl-ref.texi

开放gsl矩阵运算

\input texinfo @c -*-texinfo-*-
@c This will be for the printing version of the manual
@tex
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@c @cropmarks
@c @afourpaper
@c @paperbackbook
@c @set publish
@raggedbottom
@c %**start of header
@setfilename gsl-ref.info
@settitle GNU Scientific Library -- Reference Manual
@finalout
@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$\mathxxx}
\gdef\mathxxx#1{#1$\Etex}
\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\Etex\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\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}}
@end tex

@include version-ref.texi
@set GSL @i{GNU Scientific Library}

@ifinfo
This file documents the @value{GSL}.

Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001 The GSL Team.

Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.1
or any later version published by the Free Software Foundation;
with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
A copy of the license is included in the section entitled ``GNU
Free Documentation License''.

@ignore
Permission is granted to make and distribute verbatim copies of
this manual provided the copyright notice and this permission notice
are preserved on all copies.
@end ignore

@ignore
Permission is granted to process this file through TeX and print the
results, provided the printed document carries copying permission
notice identical to this one except for the removal of this paragraph
(this paragraph not being relevant to the printed manual).

@end ignore

@ignore
Permission is granted to copy and distribute modified versions of this
manual under the conditions for verbatim copying, provided that the entire
resulting derived work is distributed under the terms of a permission
notice identical to this one.

Permission is granted to copy and distribute translations of this manual
into another language, under the above conditions for modified versions,
except that this permission notice may be stated in a translation approved
by the GSL Team.
@end ignore
@end ifinfo

@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 Fluid Dynamics 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
@ifset publish
Published by Network Theory Limited.

15 Royal Park,
Clifton,
Bristol BS8 3AL,
United Kingdom.

@end ifset
Copyright @copyright{} 1996, 1997, 1998, 1999, 2000, 2001 The GSL Team.

Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.1
or any later version published by the Free Software Foundation;
with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
A copy of the license is included in the section entitled ``GNU
Free Documentation License''.

@ignore
Permission is granted to make and distribute verbatim copies of
this manual provided the copyright notice and this permission notice
are preserved on all copies.

Permission is granted to copy and distribute modified versions of this
manual under the conditions for verbatim copying, provided that the entire
resulting derived work is distributed under the terms of a permission
notice identical to this one.

Permission is granted to copy and distribute translations of this manual
into another language, under the above conditions for modified versions,
except that this permission notice may be stated in a translation approved
by the GSL Team.
@end ignore
@end titlepage

@ifset publish
@contents
@end ifset

@ifinfo
@node Top, Introduction, (dir), (dir)
@top GSL
@end ifinfo

@ifinfo
This file documents the @value{GSL}, a collection of numerical routines
for scientific computing.  The documentation corresponds to version
@value{VERSION}.

@comment As of @value{UPDATED} the library is in beta-test release only and is
@comment not recommended for general use.

More information about GSL can be found at the project homepage,
@url{http://sources.redhat.com/gsl/}.
@end ifinfo

@menu
* Introduction::                
* Using the library::           
* Error Handling::              
* Mathematical Functions::      
* Complex Numbers::             
* Roots of Polynomials::        
* Special Functions::           
* Vectors and Matrices::        
* Permutations::                
* 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::         
* Discrete Hankel Transforms::  
* One dimensional Root-Finding::  
* One dimensional Minimization::  
* Multidimensional Root-Finding::  
* Multidimensional Minimization::