1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
|
// Copyright (C) 2005 David Saunders, 2010 LinBox. This file is part of LinBox,
// GNU LGPL, see COPYING for license information.
/*
* Coypright (c) LinBox
* ========LICENCE========
* This file is part of the library LinBox.
*
* LinBox is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*
*/
/** \mainpage LinBox Symbolic Linear Algebra Software Library.
*
* \section intro Introduction
*
* %LinBox is a C++ template library of routines for solution of linear algebra
* problems including linear system solution, rank, determinant, minimal
* polynomial, characteristic polynomial, and Smith normal form.
*
* Algorithms are provided for matrices with integer entries or entries in a
* finite field. A number of matrix storage types is provided, especially for
* blackbox representation of sparse or structured matrix classes.
* A few algorithms for rational matrices are available. %LinBox also uses
* underlying data structures and algorithms for integer, rational, polynomial,
* finite fields and rings, as well as dense and sparse matrix formats coming
* from the %Givaro (https://casys.gricad-pages.univ-grenoble-alpes.fr/givaro)
* and FFLAS-FFPACK (http://linbox-team.github.io/fflas-ffpack) libraries.
*
* \section goals Goals
*
* Project %LinBox (http://linalg.org) is a collaborative effort among
* researchers at a number of locations around the world. Some of the most
* active participants are listed \subpage AUTHORS "here". The goals are to
* produce algorithms and software for symbolic linear algebra, particularly
* using \ref blackbox matrix methods, i.e. iterative methods requiring only
* the linear transform property of the matrix (that, given A and x, one can
* compute \f$y \gets Ax\f$). Such methods are especially effective with
* sparse or structured matrices for which the matrix-vector product can be
* computed cheaply. %LinBox also provides elimination based methods
* for dense matrices exploiting the numeric BLAS routines via FFLAS-FFPACK.
*
* A good collection of finite field implementations is available. Some
* algorithms are probabilistic, but their results are extremely reliable
* except over very small fields (less than 1000 elements, say).
*
* \section desig Design
*
* %LinBox depends on other packages for some of its functionality. It is a
* design goal of %LinBox to be a kind of \e middleware, providing a common
* interface for use in projects needing linear algebra and providing access to
* other systems and programs through wrappers whenever their capabilities may
* contribute to the linear algebra. Thus, to gain full advangage of %LinBox
* it will be desirable to have certain other packages installed. In
* particular GMP and a BLAS implementation are required. GMP provides the
* basic large integer system used throughout. We have been using ATLAS for
* the BLAS implementation. The remaining dependencies are optional, but two
* packages stand out as contributing substantially to %LinBox. They are %NTL
* and Givaro. %NTL is used for some finite field and ring representations,
* particularly in the case of \c GF(q), where \c q is a prime power or a prime
* greater than word size. %NTL is also used by algorithms that need
* polynomial operations such as factorization. Givaro is another source of
* field representations and polynomial operations. Importantly, Givaro
* provides our best representation of small non-prime fields, say <code>q =
* p<sup>e</sup> < 10<sup>6</sup></code>. Functionality from some other
* systems has been wrapped also but is currently less widely used in %LinBox.
*
* \e Genericity and \e high \e performance are the twin goals of %LinBox. The
* genericity is achieved by use of a small set of interfaces. Algorithms are
* implemented with C++ template parameters which may be instantiated with any
* class adhering to the specified interface. High performance is achieved by
* judicious specializations of the generic algorithms. It is entirely within
* the spirit of the project to introduce new implementations. Thus a user of
* the library may invoke a %LinBox algorithm, say for determinant or rank of a
* matrix, but providing a blackbox class of her own design and perhaps even
* providing the underlying field (or commutative ring) representation.
* Conversely, the %LinBox field and ring interfaces and the many specific
* representations can be used for purposes other than linear algebra
* computation or with algorithms not provided by %LinBox.
*
* \section using Using LinBox
*
* - \subpage copy.
* - \subpage tuto. This is a brief introduction to %LinBox capabilities.
* - \subpage inst. Explains how to install from sources or from the latest svn
* version.
* - \subpage arch. Describes how %LinBox is organized
* \internal
* - \subpage upgr. Explains how to make new versions of %LinBox \endinternal
* .
*
* \section docu Documentation
* - <a href="index.html" style="color: blue ; font-weight:
* bold"> Documentation for Users</a>. If everything around is blue, then you
* are reading the lighter, user-oriented, documentation.
* - <a href="../liblinbox-dev-doc/index.html" style="color: green ; font-weight:
* bold"> Documentation for Developers</a>. If everything around is green, then
* you can get to everything (not necessarily yet) documented. Note: The Debian
* package does not ship this documentation, for details please see
* /usr/share/doc/liblinbox-doc/README.Debian.
* .
*
* \section contrib Contributing to LinBox, getting assistance.
* We warmly welcome contributors ! Contributing can rhyme with providing
* documentation, pointing out bugs, requesting more features, giving
* test-cases, making comments about the code,...<br>
* You can contact the LinBox team at \f$\mathtt{linbox}\!-\!\mathtt{use}
* \mathtt{@} \mathtt{googlegroups}\!\cdot\!\mathtt{com}\f$ (user oriented
* discussions) or \f$\mathtt{linbox}\!-\!\mathtt{use} \mathtt{@}
* \mathtt{googlegroups}\!\cdot\!\mathtt{com}\f$ (development oriented
* discussions).
*
* \authors Members of the \link AUTHORS %LinBox group\endlink. The most
* prolific documenters have been William J Turner, Bradford Hovinen,
* David Saunders, Brice Boyer.
*
* \version 1.7.0
*
* \par Support.
* The project is supported by the National Science Foundation
* (http://www.nsf.gov/) in the USA and by CNRS in France.
*/
/*! \page copy Copyright and Licencing
* The copyright and licensing (GNU LGPL) info of %LinBox is in \c COPYING.LESSER (and below).
* It gives permissions in addition to those of the GPL, see \c COPYING.
* \verbinclude "COPYING.LESSER".
*/
/*! \page inst Installing LinBox
* To install from a distribution, the usual <em> configure, make</em> sequence
* applies. See \subpage dist "configuring and installing" for more details.
* To install a development version from the SVN repository see the \subpage dev
* "developer info". The generic Free Software Foundation \subpage INSTALL
* "INSTALL" may also be of use.
*/
/*! \page arch Architecture of the library
*
* The distribution contains subdirectories (documented as `modules' <a
* href=modules.html>here</a>)
*
* - <a href="group__linbox.html">linbox</a>. This contains the library
* sources. The defined objects are in the namespace LinBox.
* - linbox/<a href="group__field.html">field</a>, linbox/<a
* href="group__ring.html">ring</a>, field and ring representations.
* - linbox/<a href="group__randiter.html">randiter</a>, random element
* generation for fields and rings.
* - linbox/<a href="group__blackbox.html">blackbox</a>, generally
* immutable matrix representations for blackbox methods (based on
* matrix-vector products).
* - linbox/<a href="group__matrix.html">matrix</a>, mutable sparse and
* dense matrices.
* - linbox/<a href="group__algorithms.html">algorithms</a>, the core
* algorithms of %LinBox
* - linbox/<a href="group__solutions.html">solutions</a>, convenience
* wrappers of algorithms
* - linbox/<a href="group__element.html">element</a>, details of field
* and ring element representation.
* - linbox/<a href="group__fflas.html">fflas</a>, wrapper of BLAS for
* exact finite prime field linear algebra.
* - linbox/<a href="group__ffpack.html">ffpack</a>, .
* - linbox/<a href="group__util.html">util</a>, basic integers, timing
* clocks, commentator.
* .
* - <a href="group__examples.html">examples</a>, programs meant to be
* directly useful or be guides
* for the progammer using %LinBox.
* - <a href="group__doc.html">doc</a>, the browsable \c html documentation is
* generated with Doxygen,
* - <a href="group__interfaces.html">interfaces</a>, interfaces to other
* systems, such as Maple, gap, web servers,
* - <a href="group__tests.html">tests</a>, primarily correctness tests to aid
* development.
* - <a href="group__benchmarks.html">benchmarks</a>, where you can benchmark
* and compare your LinBox installation.
* .
*/
/*! \page AUTHORS LinBox Authors
* \verbinclude "AUTHORS"
*/
/*! \page INSTALL The INSTALL in LinBox
* \verbinclude "INSTALL"
*/
/*! \page dist Configuring and Installing LinBox
* \htmlinclude "doc/install-dist.html"
*/
/*! \page dev Developer info for LinBox
* \htmlinclude "doc/install-dev.html"
*
* \par HACKING LinBox.
* \verbinclude "HACKING"
*/
// vim:syn=doxygen
|
