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1<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
2    "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
3<html xmlns="http://www.w3.org/1999/xhtml">
4<head>
5<meta name="generator" content=
6"HTML Tidy for Linux/x86 (vers 1st March 2004), see www.w3.org" />
7<meta http-equiv="Content-Type" content=
8"text/html; charset=us-ascii" />
9<link href="ublas.css" type="text/css" />
10<title>Boost Basic Linear Algebra</title>
11</head>
12<body>
13<h1><img src="../../../../boost.png" align="middle" />
14Basic Linear Algebra</h1>
15<p>uBLAS is a C++ template class library that provides <a href=
16"http://www.netlib.org/blas">BLAS</a> level 1, 2, 3 functionality
17for dense, packed and sparse matrices. The design and
18implementation unify mathematical notation via operator overloading
19and efficient code generation via expression templates.</p>
20<h2>Functionality</h2>
21<p>uBLAS provides templated C++ classes for dense, unit and sparse
22vectors, dense, identity, triangular, banded, symmetric, hermitian
23and sparse matrices. Views into vectors and matrices can be
24constructed via ranges or slices and adaptor classes. The library
25covers the usual basic linear algebra operations on vectors and
26matrices: reductions like different norms, addition and subtraction
27of vectors and matrices and multiplication with a scalar, inner and
28outer products of vectors, matrix vector and matrix matrix products
29and triangular solver. The glue between containers, views and
30expression templated operations is a mostly <a href=
31"http://www.sgi.com/tech/stl">STL</a> conforming iterator
32interface.</p>
33<h2>Documentation</h2>
34<ul>
35<li><big><a href="overview.htm">Overview</a></big>
36<ul>
37<li><a href="overview.htm#rationale">Rationale</a>
38<li><a href="overview.htm#functionality">Functionality</a>
39<li><a href="types_overview.htm">Overview of Matrix- and Vector-Types</a></li>
40<li><a href="operations_overview.htm">Overview of Matrix and Vector Operations</a></li>
41<li><a href="#further_information">Effective uBLAS and further information</a></li>
42</ul>
43</li>
44<li><a href="vector.htm">Vector</a>
45<ul>
46<li><a href="vector.htm#vector">Vector</a></li>
47<li><a href="vector.htm#unit_vector">Unit Vector</a></li>
48<li><a href="vector.htm#zero_vector">Zero Vector</a></li>
49<li><a href="vector.htm#scalar_vector">Scalar Vector</a></li>
50</ul>
51</li>
52<li><a href="vector_sparse.htm">Sparse Vector</a>
53<ul>
54<li><a href="vector_sparse.htm#mapped_vector">Sparse
55Vector</a></li>
56<li><a href="vector_sparse.htm#compressed_vector">Compressed
57Vector</a></li>
58<li><a href="vector_sparse.htm#coordinate_vector">Coordinate
59Vector</a></li>
60</ul>
61</li>
62<li><a href="vector_proxy.htm">Vector Proxies</a>
63<ul>
64<li><a href="vector_proxy.htm#vector_range">Vector Range</a></li>
65<li><a href="vector_proxy.htm#vector_slice">Vector Slice</a></li>
66</ul>
67</li>
68<li><a href="vector_expression.htm">Vector Expressions</a>
69<ul>
70<li><a href="vector_expression.htm#vector_expression">Vector
71Expression</a></li>
72<li><a href="vector_expression.htm#vector_references">Vector
73References</a></li>
74<li><a href="vector_expression.htm#vector_operations">Vector
75Operations</a></li>
76<li><a href="vector_expression.htm#vector_reductions">Vector
77Reductions</a></li>
78</ul>
79</li>
80<li><a href="matrix.htm">Matrix</a>
81<ul>
82<li><a href="matrix.htm#matrix">Matrix</a></li>
83<li><a href="matrix.htm#identity_matrix">Identity Matrix</a></li>
84<li><a href="matrix.htm#zero_matrix">Zero Matrix</a></li>
85<li><a href="matrix.htm#scalar_matrix">Scalar Matrix</a></li>
86</ul>
87</li>
88<li><a href="triangular.htm">Triangular Matrix</a>
89<ul>
90<li><a href="triangular.htm#triangular_matrix">Triangular
91Matrix</a></li>
92<li><a href="triangular.htm#triangular_adaptor">Triangular
93Adaptor</a></li>
94</ul>
95</li>
96<li><a href="symmetric.htm">Symmetric Matrix</a>
97<ul>
98<li><a href="symmetric.htm#symmetric_matrix">Symmetric
99Matrix</a></li>
100<li><a href="symmetric.htm#symmetric_adaptor">Symmetric
101Adaptor</a></li>
102</ul>
103</li>
104<li><a href="hermitian.htm">Hermitian Matrix</a>
105<ul>
106<li><a href="hermitian.htm#hermitian_matrix">Hermitian
107Matrix</a></li>
108<li><a href="hermitian.htm#hermitian_adaptor">Hermitian
109Adaptor</a></li>
110</ul>
111</li>
112<li><a href="banded.htm">Banded Matrix</a>
113<ul>
114<li><a href="banded.htm#banded_matrix">Banded Matrix</a></li>
115<li><a href="banded.htm#banded_adaptor">Banded Adaptor</a></li>
116</ul>
117</li>
118<li><a href="matrix_sparse.htm">Sparse Matrix</a>
119<ul>
120<li><a href="matrix_sparse.htm#mapped_matrix">Sparse
121Matrix</a></li>
122<li><a href="matrix_sparse.htm#compressed_matrix">Compressed
123Matrix</a></li>
124<li><a href="matrix_sparse.htm#coordinate_matrix">Coordinate
125Matrix</a></li>
126</ul>
127</li>
128<li><a href="matrix_proxy.htm">Matrix Proxies</a>
129<ul>
130<li><a href="matrix_proxy.htm#matrix_row">Matrix Row</a></li>
131<li><a href="matrix_proxy.htm#matrix_column">Matrix Column</a></li>
132<li><a href="matrix_proxy.htm#vector_range">Vector Range</a></li>
133<li><a href="matrix_proxy.htm#vector_slice">Vector Slice</a></li>
134<li><a href="matrix_proxy.htm#matrix_range">Matrix Range</a></li>
135<li><a href="matrix_proxy.htm#matrix_slice">Matrix Slice</a></li>
136</ul>
137</li>
138<li><a href="matrix_expression.htm">Matrix Expressions</a>
139<ul>
140<li><a href="matrix_expression.htm#matrix_expression">Matrix
141Expression</a></li>
142<li><a href="matrix_expression.htm#matrix_references">Matrix
143References</a></li>
144<li><a href="matrix_expression.htm#matrix_operations">Matrix
145Operations</a></li>
146<li><a href="matrix_expression.htm#matrix_vector_operations">Matrix
147Vector Operations</a></li>
148<li><a href="matrix_expression.htm#matrix_matrix_operations">Matrix
149Matrix Operations</a></li>
150</ul>
151</li>
152<li>Storage and special containers
153<ul>
154<li><a href="unbounded_array.htm">Unbounded Array</a></li>
155<li><a href="bounded_array.htm">Bounded Array</a></li>
156<li><a href="range.htm#range">Range</a></li>
157<li><a href="range.htm#slice">Slice</a></li>
158</ul>
159</li>
160<li><a href="storage_sparse.htm">Sparse Storage</a>
161<ul>
162<li><a href="storage_sparse.htm#map_std">Default Standard
163Map</a></li>
164<li><a href="storage_sparse.htm#map_array">Map Array</a></li>
165</ul>
166</li>
167<li>Operations &amp; Functions
168<ul>
169<li><a href="products.htm">Special Products</a></li>
170<li><a href="blas.htm">BLAS</a></li>
171</ul>
172<li>uBLAS Concept definitions
173<ul>
174<li><a href="container_concept.htm">Container Concepts</a>
175<ul>
176<li><a href="container_concept.htm#vector">Vector</a></li>
177<li><a href="container_concept.htm#matrix">Matrix</a></li>
178</ul>
179<li><a href="expression_concept.htm">Expression Concepts</a>
180<ul>
181<li><a href="expression_concept.htm#scalar_expression">Scalar
182Expression</a></li>
183<li><a href="expression_concept.htm#vector_expression">Vector
184Expression</a></li>
185<li><a href="expression_concept.htm#matrix_expression">Matrix
186Expression</a></li>
187</ul>
188<li><a href="storage_concept.htm">Storage Concept</a>
189<li><a href="iterator_concept.htm">Iterator Concepts</a>
190<ul>
191<li><a href="iterator_concept.htm#indexed_bidirectional_iterator">Indexed
192Bidirectional Iterator</a></li>
193<li><a href="iterator_concept.htm#indexed_random_access_iterator">Indexed
194Random Access Iterator</a></li>
195<li><a href=
196"iterator_concept.htm#indexed_bidirectional_cr_iterator">Indexed
197Bidirectional Column/Row Iterator</a></li>
198<li><a href=
199"iterator_concept.htm#indexed_random_access_cr_iterator">Indexed Random
200Access Column/Row Iterator</a></li>
201</ul>
202</li>
203</ul>
204</li>
205</ul>
206<h2>Supported Platforms</h2>
207<p>The current version of uBLAS expects a modern (ISO standard compliant) compiler. Compilers targeted and tested
208with this release are:</p>
209<ul>
210<li>GCC 3.2.3, 3.3.x, 3.4.x, 4.0.x</li>
211<li>MSVC 7.1, 8.0</li>
212<li>ICC 8.0, 8.1</li>
213<li>Visual age 6</li>
214<li>Codewarrior 9.4, 9.5</li>
215</ul>
216<p>The version of uBLAS in Boost 1.32.0 (and earlier) support many older compilers. If you are
217using such a compiler please use this version of uBLAS. Compilers known to accept this older library
218are:</p>
219<ul>
220<li>MSVC 6.0 with STLPort-4.5.3, 7.0, 7.1</li>
221<li>GCC 2.95.x, 3.0.x, 3.1.x, 3.2.x, 3.3.x, 3.4.x</li>
222<li>ICC 7.0, 7.1 8.0</li>
223<li>Comeau 4.2.x</li>
224<li>Codewarrior 8.3</li>
225</ul>
226<p>For possible problems please consider to consult the Boost
227regression tests.</p>
228<a name="further_information"></a>
229<h2>Known limitations:</h2>
230<ul type="Disc">
231<li>The implementation assumes a linear memory address model.</li>
232<li>Tuning was focussed on dense matrices.</li>
233</ul>
234<h2>Further Information</h2>
235<h3>Project Location and Download</h3>
236<p>The latest stable release of uBLAS is part of the <a href=
237"http://www.boost.org">Boost</a> libraries.</p>
238<h3>Documentation and Discussion</h3>
239<p>Visit the <a href=
240"http://www.crystalclearsoftware.com/cgi-bin/boost_wiki/wiki.pl?Effective_UBLAS">
241Effective uBLAS</a> wiki for up to date information and
242contributions.</p>
243<p>There is also an active uBLAS <a href=
244"http://lists.boost.org/">mailing list</a> where uBLAS specific
245user and development questions are answered.</p>
246<h3>uBLAS and Boost Project</h3>
247<p>There is also an active uBLAS <a href=
248"http://lists.boost.org/">mailing list</a> where uBLAS specific
249from the latest uBLAS project code. You can <a href=
250"http://cvs.sourceforge.net/cgi-bin/viewcvs.cgi/boost">view</a> the
251Boost CVS archive directly. You will find the library <a href=
252"http://cvs.sourceforge.net/cgi-bin/viewcvs.cgi/boost/boost/boost/numeric/ublas/">
253here</a>. Documentation and test programs reside <a href=
254"http://cvs.sourceforge.net/cgi-bin/viewcvs.cgi/boost/boost/libs/numeric/ublas/">
255here</a>.</p>
256<h2>Authors and Credits</h2>
257<p>uBLAS initially was written by Joerg Walter and Mathias Koch. We
258would like to thank all, which supported and contributed to the
259development of this library: David Abrahams, Ed Brey, Fernando
260Cacciola, Juan Jose Gomez Cadenas, Beman Dawes, Matt Davies, Bob
261Fletcher, Kresimir Fresl, Joachim Kessel, Patrick Kowalzick, Toon
262Knapen, Hendrik Kueck, John Maddock, Jens Maurer, Alexei Novakov,
263Gary Powell, Joachim Pyras, Peter Schmitteckert, Jeremy Siek,
264Markus Steffl, Michael Stevens, Benedikt Weber, Martin Weiser,
265Gunter Winkler, Marc Zimmermann and the members of <a href=
266"http://www.boost.org">Boost</a></p>
267<h2>Frequently Asked Questions</h2>
268<p>Q: I'm running the uBLAS dense vector and matrix benchmarks. Why
269do I see a significant performance difference between the native C
270and library implementations?<br />
271A: uBLAS distinguishes debug mode (size and type conformance checks
272enabled, expression templates disabled) and release mode (size and
273type conformance checks disabled, expression templates enabled).
274Please check, if the preprocessor symbol <code>NDEBUG</code> of
275<code>cassert</code> is defined. <code>NDEBUG</code> enables
276release mode, which in turn uses expression templates.</p>
277<p>Q: I've written some uBLAS tests, which try to incorrectly
278assign different matrix types or overrun vector and matrix
279dimensions. Why don't I get a compile time or runtime
280diagnostic?<br />
281A: uBLAS distinguishes debug mode (size and type conformance checks
282enabled, expression templates disabled) and release mode (size and
283type conformance checks disabled, expression templates enabled).
284Please check, if the preprocessor symbol <code>NDEBUG</code> of
285<code>cassert</code> is defined. <code>NDEBUG</code> disables debug
286mode, which is needed to get size and type conformance checks.</p>
287<p>Q: I've written some uBLAS benchmarks to measure the performance
288of matrix chain multiplications like <code>prod (A, prod (B,
289C))</code> and see a significant performance penalty due to the use
290of expression templates. How can I disable expression
291templates?<br />
292A: You do not need to disable expression templates. Please try
293reintroducing temporaries using either <code>prod (A,</code>
294<code><em>matrix_type</em></code> <code>(prod (B, C)))</code> or
295<code>prod (A, prod&lt;</code><code><em>matrix_type</em></code>
296<code>&gt; (B, C))</code>.</p>
297<hr />
298<p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
299Permission to copy, use, modify, sell and distribute this document
300is granted provided this copyright notice appears in all copies.
301This document is provided ``as is'' without express or implied
302warranty, and with no claim as to its suitability for any
303purpose.</p>
304</body>
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