Gitiles
Code Review Sign In
realtimeroboticsgroup.org / RealtimeRoboticsGroup / test / dc6866bfe21cff39c0481df3fb8a37d6f44f3e4d / . / doc / banded.html
blob: 6ce82f2df474d9ecabb7152ac8324fc5dc93763c [file] [log] [blame]
Brian Silvermandc6866b2018-08-05 00:18:23 -0700[diff] [blame^]1<!DOCTYPE html PUBLIC "-//W3C/utf-8XHTML 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 rel="stylesheet" href="../../../../boost.css" type="text/css"/>
10<link rel="stylesheet" href="ublas.css" type="text/css" />
11<script type="text/javascript" src="js/jquery-1.3.2.min.js" async="async" ></script>
12<script type="text/javascript" src="js/jquery.toc-gw.js" async="async" ></script>
13<title>Banded Matrix</title>
14</head>
15<body>
16<h1><img src="../../../../boost.png" align="middle" />Banded Matrix</h1>
17<div class="toc" id="toc"></div>
18<h2><a name="banded_matrix"></a>Banded Matrix</h2>
19<h4>Description</h4>
20<p>The templated class <code>banded_matrix&lt;T, F, A&gt;</code> is
21the base container adaptor for banded matrices. For a <em>(m x
22n</em>)-dimensional banded matrix with <em>l</em> lower and
23<em>u</em> upper diagonals and <em>0 &lt;= i &lt; m</em>, <em>0
24&lt;= j &lt; n</em> holds <em>b</em><sub><em>i, j</em></sub> <em>=
250</em>, if <em>i &gt; j + l</em> or <em>i &lt; j - u</em>. The
26storage of banded matrices is packed.</p>
27<h4>Example</h4>
28<pre>
29#include &lt;boost/numeric/ublas/banded.hpp&gt;
30#include &lt;boost/numeric/ublas/io.hpp&gt;
31
32int main () {
33 using namespace boost::numeric::ublas;
34 banded_matrix&lt;double&gt; m (3, 3, 1, 1);
35 for (signed i = 0; i &lt; signed (m.size1 ()); ++ i)
36 for (signed j = std::max (i - 1, 0); j &lt; std::min (i + 2, signed (m.size2 ())); ++ j)
37 m (i, j) = 3 * i + j;
38 std::cout &lt;&lt; m &lt;&lt; std::endl;
39}
40</pre>
41<h4>Definition</h4>
42<p>Defined in the header banded.hpp.</p>
43<h4>Template parameters</h4>
44<table border="1" summary="parameters">
45<tbody>
46<tr>
47<th>Parameter</th>
48<th>Description</th>
49<th>Default</th>
50</tr>
51<tr>
52<td><code>T</code></td>
53<td>The type of object stored in the matrix.</td>
54<td></td>
55</tr>
56<tr>
57<td><code>F</code></td>
58<td>Functor describing the storage organization. <a href=
59"#banded_matrix_1">[1]</a></td>
60<td><code>row_major</code></td>
61</tr>
62<tr>
63<td><code>A</code></td>
64<td>The type of the adapted array. <a href=
65"#banded_matrix_2">[2]</a></td>
66<td><code>unbounded_array&lt;T&gt;</code></td>
67</tr>
68</tbody>
69</table>
70<h4>Model of</h4>
71<p><a href="container_concept.html#matrix">Matrix</a> .</p>
72<h4>Type requirements</h4>
73<p>None, except for those imposed by the requirements of <a href=
74"container_concept.html#matrix">Matrix</a> .</p>
75<h4>Public base classes</h4>
76<p><code>matrix_container&lt;banded_matrix&lt;T, F, A&gt;
77&gt;</code></p>
78<h4>Members</h4>
79<table border="1" summary="members">
80<tbody>
81<tr>
82<th>Member</th>
83<th>Description</th>
84</tr>
85<tr>
86<td><code>banded_matrix ()</code></td>
87<td>Allocates an uninitialized <code>banded_matrix</code> that
88holds zero rows of zero elements.</td>
89</tr>
90<tr>
91<td><code>banded_matrix (size_type size1, size_type size2,
92size_type lower = 0, size_type upper = 0)</code></td>
93<td>Allocates an uninitialized <code>banded_matrix</code> that
94holds <code>(lower + 1 + upper)</code> diagonals around the main
95diagonal of a matrix with <code>size1</code> rows of
96<code>size2</code> elements.</td>
97</tr>
98<tr>
99<td><code>banded_matrix (const banded_matrix &amp;m)</code></td>
100<td>The copy constructor.</td>
101</tr>
102<tr>
103<td><code>template&lt;class AE&gt;<br />
104banded_matrix (const matrix_expression&lt;AE&gt;
105&amp;ae)</code></td>
106<td>The extended copy constructor.</td>
107</tr>
108<tr>
109<td><code>void resize (size_type size1, size_type size2, size_type
110lower = 0, size_type upper = 0, bool preserve = true)</code></td>
111<td>Reallocates a <code>banded_matrix</code> to hold <code>(lower +
1121 + upper)</code> diagonals around the main diagonal of a matrix
113with <code>size1</code> rows of <code>size2</code> elements. The
114existing elements of the <code>banded_matrix</code> are preseved
115when specified.</td>
116</tr>
117<tr>
118<td><code>size_type size1 () const</code></td>
119<td>Returns the number of rows.</td>
120</tr>
121<tr>
122<td><code>size_type size2 () const</code></td>
123<td>Returns the number of columns.</td>
124</tr>
125<tr>
126<td><code>size_type lower () const</code></td>
127<td>Returns the number of diagonals below the main diagonal.</td>
128</tr>
129<tr>
130<td><code>size_type upper () const</code></td>
131<td>Returns the number of diagonals above the main diagonal.</td>
132</tr>
133<tr>
134<td><code>const_reference operator () (size_type i, size_type j)
135const</code></td>
136<td>Returns a <code>const</code> reference of the <code>j</code>
137-th element in the <code>i</code>-th row.</td>
138</tr>
139<tr>
140<td><code>reference operator () (size_type i, size_type
141j)</code></td>
142<td>Returns a reference of the <code>j</code>-th element in the
143<code>i</code>-th row.</td>
144</tr>
145<tr>
146<td><code>banded_matrix &amp;operator = (const banded_matrix
147&amp;m)</code></td>
148<td>The assignment operator.</td>
149</tr>
150<tr>
151<td><code>banded_matrix &amp;assign_temporary (banded_matrix
152&amp;m)</code></td>
153<td>Assigns a temporary. May change the banded matrix
154<code>m</code> .</td>
155</tr>
156<tr>
157<td><code>template&lt;class AE&gt;<br />
158banded_matrix &amp;operator = (const matrix_expression&lt;AE&gt;
159&amp;ae)</code></td>
160<td>The extended assignment operator.</td>
161</tr>
162<tr>
163<td><code>template&lt;class AE&gt;<br />
164banded_matrix &amp;assign (const matrix_expression&lt;AE&gt;
165&amp;ae)</code></td>
166<td>Assigns a matrix expression to the banded matrix. Left and
167right hand side of the assignment should be independent.</td>
168</tr>
169<tr>
170<td><code>template&lt;class AE&gt;<br />
171banded_matrix &amp;operator += (const matrix_expression&lt;AE&gt;
172&amp;ae)</code></td>
173<td>A computed assignment operator. Adds the matrix expression to
174the banded matrix.</td>
175</tr>
176<tr>
177<td><code>template&lt;class AE&gt;<br />
178banded_matrix &amp;plus_assign (const matrix_expression&lt;AE&gt;
179&amp;ae)</code></td>
180<td>Adds a matrix expression to the banded matrix. Left and right
181hand side of the assignment should be independent.</td>
182</tr>
183<tr>
184<td><code>template&lt;class AE&gt;<br />
185banded_matrix &amp;operator -= (const matrix_expression&lt;AE&gt;
186&amp;ae)</code></td>
187<td>A computed assignment operator. Subtracts the matrix expression
188from the banded matrix.</td>
189</tr>
190<tr>
191<td><code>template&lt;class AE&gt;<br />
192banded_matrix &amp;minus_assign (const matrix_expression&lt;AE&gt;
193&amp;ae)</code></td>
194<td>Subtracts a matrix expression from the banded matrix. Left and
195right hand side of the assignment should be independent.</td>
196</tr>
197<tr>
198<td><code>template&lt;class AT&gt;<br />
199banded_matrix &amp;operator *= (const AT &amp;at)</code></td>
200<td>A computed assignment operator. Multiplies the banded matrix
201with a scalar.</td>
202</tr>
203<tr>
204<td><code>template&lt;class AT&gt;<br />
205banded_matrix &amp;operator /= (const AT &amp;at)</code></td>
206<td>A computed assignment operator. Divides the banded matrix
207through a scalar.</td>
208</tr>
209<tr>
210<td><code>void swap (banded_matrix &amp;m)</code></td>
211<td>Swaps the contents of the banded matrices.</td>
212</tr>
213<tr>
214<td><code>void insert (size_type i, size_type j, const_reference
215t)</code></td>
216<td>Inserts the value <code>t</code> at the <code>j</code>-th
217element of the <code>i</code>-th row.</td>
218</tr>
219<tr>
220<td><code>void erase (size_type i, size_type j)</code></td>
221<td>Erases the value at the <code>j</code>-th elemenst of the
222<code>i</code>-th row.</td>
223</tr>
224<tr>
225<td><code>void clear ()</code></td>
226<td>Clears the matrix.</td>
227</tr>
228<tr>
229<td><code>const_iterator1 begin1 () const</code></td>
230<td>Returns a <code>const_iterator1</code> pointing to the
231beginning of the <code>banded_matrix</code>.</td>
232</tr>
233<tr>
234<td><code>const_iterator1 end1 () const</code></td>
235<td>Returns a <code>const_iterator1</code> pointing to the end of
236the <code>banded_matrix</code>.</td>
237</tr>
238<tr>
239<td><code>iterator1 begin1 ()</code></td>
240<td>Returns a <code>iterator1</code> pointing to the beginning of
241the <code>banded_matrix</code>.</td>
242</tr>
243<tr>
244<td><code>iterator1 end1 ()</code></td>
245<td>Returns a <code>iterator1</code> pointing to the end of the
246<code>banded_matrix</code>.</td>
247</tr>
248<tr>
249<td><code>const_iterator2 begin2 () const</code></td>
250<td>Returns a <code>const_iterator2</code> pointing to the
251beginning of the <code>banded_matrix</code>.</td>
252</tr>
253<tr>
254<td><code>const_iterator2 end2 () const</code></td>
255<td>Returns a <code>const_iterator2</code> pointing to the end of
256the <code>banded_matrix</code>.</td>
257</tr>
258<tr>
259<td><code>iterator2 begin2 ()</code></td>
260<td>Returns a <code>iterator2</code> pointing to the beginning of
261the <code>banded_matrix</code>.</td>
262</tr>
263<tr>
264<td><code>iterator2 end2 ()</code></td>
265<td>Returns a <code>iterator2</code> pointing to the end of the
266<code>banded_matrix</code>.</td>
267</tr>
268<tr>
269<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
270<td>Returns a <code>const_reverse_iterator1</code> pointing to the
271beginning of the reversed <code>banded_matrix</code>.</td>
272</tr>
273<tr>
274<td><code>const_reverse_iterator1 rend1 () const</code></td>
275<td>Returns a <code>const_reverse_iterator1</code> pointing to the
276end of the reversed <code>banded_matrix</code>.</td>
277</tr>
278<tr>
279<td><code>reverse_iterator1 rbegin1 ()</code></td>
280<td>Returns a <code>reverse_iterator1</code> pointing to the
281beginning of the reversed <code>banded_matrix</code>.</td>
282</tr>
283<tr>
284<td><code>reverse_iterator1 rend1 ()</code></td>
285<td>Returns a <code>reverse_iterator1</code> pointing to the end of
286the reversed <code>banded_matrix</code>.</td>
287</tr>
288<tr>
289<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
290<td>Returns a <code>const_reverse_iterator2</code> pointing to the
291beginning of the reversed <code>banded_matrix</code>.</td>
292</tr>
293<tr>
294<td><code>const_reverse_iterator2 rend2 () const</code></td>
295<td>Returns a <code>const_reverse_iterator2</code> pointing to the
296end of the reversed <code>banded_matrix</code>.</td>
297</tr>
298<tr>
299<td><code>reverse_iterator2 rbegin2 ()</code></td>
300<td>Returns a <code>reverse_iterator2</code> pointing to the
301beginning of the reversed <code>banded_matrix</code>.</td>
302</tr>
303<tr>
304<td><code>reverse_iterator2 rend2 ()</code></td>
305<td>Returns a <code>reverse_iterator2</code> pointing to the end of
306the reversed <code>banded_matrix</code>.</td>
307</tr>
308</tbody>
309</table>
310<h4>Notes</h4>
311<p><a name="banded_matrix_1" id="banded_matrix_1">[1]</a> Supported
312parameters for the storage organization are <code>row_major</code>
313and <code>column_major</code>.</p>
314<p><a name="banded_matrix_2" id="banded_matrix_2">[2]</a> Supported
315parameters for the adapted array are
316<code>unbounded_array&lt;T&gt;</code> ,
317<code>bounded_array&lt;T&gt;</code> and
318<code>std::vector&lt;T&gt;</code> .</p>
319<h2><a name="banded_adaptor"></a>Banded Adaptor</h2>
320<h4>Description</h4>
321<p>The templated class <code>banded_adaptor&lt;M&gt;</code> is a
322banded matrix adaptor for other matrices.</p>
323<h4>Example</h4>
324<pre>
325#include &lt;boost/numeric/ublas/banded.hpp&gt;
326#include &lt;boost/numeric/ublas/io.hpp&gt;
327
328int main () {
329 using namespace boost::numeric::ublas;
330 matrix&lt;double&gt; m (3, 3);
331 banded_adaptor&lt;matrix&lt;double&gt; &gt; ba (m, 1, 1);
332 for (signed i = 0; i &lt; signed (ba.size1 ()); ++ i)
333 for (signed j = std::max (i - 1, 0); j &lt; std::min (i + 2, signed (ba.size2 ())); ++ j)
334 ba (i, j) = 3 * i + j;
335 std::cout &lt;&lt; ba &lt;&lt; std::endl;
336}
337</pre>
338<h4>Definition</h4>
339<p>Defined in the header banded.hpp.</p>
340<h4>Template parameters</h4>
341<table border="1" summary="parameters">
342<tbody>
343<tr>
344<th>Parameter</th>
345<th>Description</th>
346<th>Default</th>
347</tr>
348<tr>
349<td><code>M</code></td>
350<td>The type of the adapted matrix.</td>
351<td></td>
352</tr>
353</tbody>
354</table>
355<h4>Model of</h4>
356<p><a href="expression_concept.html#matrix_expression">Matrix Expression</a>
357.</p>
358<h4>Type requirements</h4>
359<p>None, except for those imposed by the requirements of <a href=
360"expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
361<h4>Public base classes</h4>
362<p><code>matrix_expression&lt;banded_adaptor&lt;M&gt;
363&gt;</code></p>
364<h4>Members</h4>
365<table border="1" summary="members">
366<tbody>
367<tr>
368<th>Member</th>
369<th>Description</th>
370</tr>
371<tr>
372<td><code>banded_adaptor (matrix_type &amp;data, size_type lower =
3730, size_type upper = 0)</code></td>
374<td>Constructs a <code>banded_adaptor</code> that holds
375<code>(lower + 1 + upper)</code> diagonals around the main diagonal
376of a matrix.</td>
377</tr>
378<tr>
379<td><code>banded_adaptor (const banded_adaptor &amp;m)</code></td>
380<td>The copy constructor.</td>
381</tr>
382<tr>
383<td><code>template&lt;class AE&gt;<br />
384banded_adaptor (const matrix_expression&lt;AE&gt;
385&amp;ae)</code></td>
386<td>The extended copy constructor.</td>
387</tr>
388<tr>
389<td><code>size_type size1 () const</code></td>
390<td>Returns the number of rows.</td>
391</tr>
392<tr>
393<td><code>size_type size2 () const</code></td>
394<td>Returns the number of columns.</td>
395</tr>
396<tr>
397<td><code>size_type lower () const</code></td>
398<td>Returns the number of diagonals below the main diagonal.</td>
399</tr>
400<tr>
401<td><code>size_type upper () const</code></td>
402<td>Returns the number of diagonals above the main diagonal.</td>
403</tr>
404<tr>
405<td><code>const_reference operator () (size_type i, size_type j)
406const</code></td>
407<td>Returns a <code>const</code> reference of the <code>j</code>
408-th element in the <code>i</code>-th row.</td>
409</tr>
410<tr>
411<td><code>reference operator () (size_type i, size_type
412j)</code></td>
413<td>Returns a reference of the <code>j</code>-th element in the
414<code>i</code>-th row.</td>
415</tr>
416<tr>
417<td><code>banded_adaptor &amp;operator = (const banded_adaptor
418&amp;m)</code></td>
419<td>The assignment operator.</td>
420</tr>
421<tr>
422<td><code>banded_adaptor &amp;assign_temporary (banded_adaptor
423&amp;m)</code></td>
424<td>Assigns a temporary. May change the banded adaptor
425<code>m</code> .</td>
426</tr>
427<tr>
428<td><code>template&lt;class AE&gt;<br />
429banded_adaptor &amp;operator = (const matrix_expression&lt;AE&gt;
430&amp;ae)</code></td>
431<td>The extended assignment operator.</td>
432</tr>
433<tr>
434<td><code>template&lt;class AE&gt;<br />
435banded_adaptor &amp;assign (const matrix_expression&lt;AE&gt;
436&amp;ae)</code></td>
437<td>Assigns a matrix expression to the banded adaptor. Left and
438right hand side of the assignment should be independent.</td>
439</tr>
440<tr>
441<td><code>template&lt;class AE&gt;<br />
442banded_adaptor &amp;operator += (const matrix_expression&lt;AE&gt;
443&amp;ae)</code></td>
444<td>A computed assignment operator. Adds the matrix expression to
445the banded adaptor.</td>
446</tr>
447<tr>
448<td><code>template&lt;class AE&gt;<br />
449banded_adaptor &amp;plus_assign (const matrix_expression&lt;AE&gt;
450&amp;ae)</code></td>
451<td>Adds a matrix expression to the banded adaptor. Left and right
452hand side of the assignment should be independent.</td>
453</tr>
454<tr>
455<td><code>template&lt;class AE&gt;<br />
456banded_adaptor &amp;operator -= (const matrix_expression&lt;AE&gt;
457&amp;ae)</code></td>
458<td>A computed assignment operator. Subtracts the matrix expression
459from the banded adaptor.</td>
460</tr>
461<tr>
462<td><code>template&lt;class AE&gt;<br />
463banded_adaptor &amp;minus_assign (const matrix_expression&lt;AE&gt;
464&amp;ae)</code></td>
465<td>Subtracts a matrix expression from the banded adaptor. Left and
466right hand side of the assignment should be independent.</td>
467</tr>
468<tr>
469<td><code>template&lt;class AT&gt;<br />
470banded_adaptor &amp;operator *= (const AT &amp;at)</code></td>
471<td>A computed assignment operator. Multiplies the banded adaptor
472with a scalar.</td>
473</tr>
474<tr>
475<td><code>template&lt;class AT&gt;<br />
476banded_adaptor &amp;operator /= (const AT &amp;at)</code></td>
477<td>A computed assignment operator. Divides the banded adaptor
478through a scalar.</td>
479</tr>
480<tr>
481<td><code>void swap (banded_adaptor &amp;m)</code></td>
482<td>Swaps the contents of the banded adaptors.</td>
483</tr>
484<tr>
485<td><code>const_iterator1 begin1 () const</code></td>
486<td>Returns a <code>const_iterator1</code> pointing to the
487beginning of the <code>banded_adaptor</code>.</td>
488</tr>
489<tr>
490<td><code>const_iterator1 end1 () const</code></td>
491<td>Returns a <code>const_iterator1</code> pointing to the end of
492the <code>banded_adaptor</code>.</td>
493</tr>
494<tr>
495<td><code>iterator1 begin1 ()</code></td>
496<td>Returns a <code>iterator1</code> pointing to the beginning of
497the <code>banded_adaptor</code>.</td>
498</tr>
499<tr>
500<td><code>iterator1 end1 ()</code></td>
501<td>Returns a <code>iterator1</code> pointing to the end of the
502<code>banded_adaptor</code>.</td>
503</tr>
504<tr>
505<td><code>const_iterator2 begin2 () const</code></td>
506<td>Returns a <code>const_iterator2</code> pointing to the
507beginning of the <code>banded_adaptor</code>.</td>
508</tr>
509<tr>
510<td><code>const_iterator2 end2 () const</code></td>
511<td>Returns a <code>const_iterator2</code> pointing to the end of
512the <code>banded_adaptor</code>.</td>
513</tr>
514<tr>
515<td><code>iterator2 begin2 ()</code></td>
516<td>Returns a <code>iterator2</code> pointing to the beginning of
517the <code>banded_adaptor</code>.</td>
518</tr>
519<tr>
520<td><code>iterator2 end2 ()</code></td>
521<td>Returns a <code>iterator2</code> pointing to the end of the
522<code>banded_adaptor</code>.</td>
523</tr>
524<tr>
525<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
526<td>Returns a <code>const_reverse_iterator1</code> pointing to the
527beginning of the reversed <code>banded_adaptor</code>.</td>
528</tr>
529<tr>
530<td><code>const_reverse_iterator1 rend1 () const</code></td>
531<td>Returns a <code>const_reverse_iterator1</code> pointing to the
532end of the reversed <code>banded_adaptor</code>.</td>
533</tr>
534<tr>
535<td><code>reverse_iterator1 rbegin1 ()</code></td>
536<td>Returns a <code>reverse_iterator1</code> pointing to the
537beginning of the reversed <code>banded_adaptor</code>.</td>
538</tr>
539<tr>
540<td><code>reverse_iterator1 rend1 ()</code></td>
541<td>Returns a <code>reverse_iterator1</code> pointing to the end of
542the reversed <code>banded_adaptor</code>.</td>
543</tr>
544<tr>
545<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
546<td>Returns a <code>const_reverse_iterator2</code> pointing to the
547beginning of the reversed <code>banded_adaptor</code>.</td>
548</tr>
549<tr>
550<td><code>const_reverse_iterator2 rend2 () const</code></td>
551<td>Returns a <code>const_reverse_iterator2</code> pointing to the
552end of the reversed <code>banded_adaptor</code>.</td>
553</tr>
554<tr>
555<td><code>reverse_iterator2 rbegin2 ()</code></td>
556<td>Returns a <code>reverse_iterator2</code> pointing to the
557beginning of the reversed <code>banded_adaptor</code>.</td>
558</tr>
559<tr>
560<td><code>reverse_iterator2 rend2 ()</code></td>
561<td>Returns a <code>reverse_iterator2</code> pointing to the end of
562the reversed <code>banded_adaptor</code>.</td>
563</tr>
564</tbody>
565</table>
566<hr />
567<p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
568 Use, modification and distribution are subject to the
569 Boost Software License, Version 1.0.
570 (See accompanying file LICENSE_1_0.txt
571 or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
572 http://www.boost.org/LICENSE_1_0.txt</a>).
573</p>
574<script type="text/javascript">
575(function($) {
576 $('#toc').toc();
577})(jQuery);
578</script>
579</body>
580</html>