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13<title>Symmetric Matrix</title>
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15<body>
16<h1><img src="../../../../boost.png" align="middle" />Symmetric Matrix</h1>
17<div class="toc" id="toc"></div>
18<h2><a name="symmetric_matrix"></a>Symmetric Matrix</h2>
19<h4>Description</h4>
20<p>The templated class <code>symmetric_matrix&lt;T, F1, F2,
21A&gt;</code> is the base container adaptor for symmetric matrices.
22For a <em>(n x n</em> )-dimensional symmetric matrix and <em>0
23&lt;= i &lt; n</em>, <em>0 &lt;= j &lt; n</em> holds
24<em>s</em><sub><em>i, j</em></sub> <em>= s</em><sub><em>j,
25i</em></sub>. The storage of symmetric matrices is packed.</p>
26<h4>Example</h4>
27<pre>
28#include &lt;boost/numeric/ublas/symmetric.hpp&gt;
29#include &lt;boost/numeric/ublas/io.hpp&gt;
30
31int main () {
32 using namespace boost::numeric::ublas;
33 symmetric_matrix&lt;double, lower&gt; ml (3, 3);
34 for (unsigned i = 0; i &lt; ml.size1 (); ++ i)
35 for (unsigned j = 0; j &lt;= i; ++ j)
36 ml (i, j) = 3 * i + j;
37 std::cout &lt;&lt; ml &lt;&lt; std::endl;
38 symmetric_matrix&lt;double, upper&gt; mu (3, 3);
39 for (unsigned i = 0; i &lt; mu.size1 (); ++ i)
40 for (unsigned j = i; j &lt; mu.size2 (); ++ j)
41 mu (i, j) = 3 * i + j;
42 std::cout &lt;&lt; mu &lt;&lt; std::endl;
43}
44</pre>
45<h4>Definition</h4>
46<p>Defined in the header symmetric.hpp.</p>
47<h4>Template parameters</h4>
48<table border="1" summary="parameters">
49<tbody>
50<tr>
51<th>Parameter</th>
52<th>Description</th>
53<th>Default</th>
54</tr>
55<tr>
56<td><code>T</code></td>
57<td>The type of object stored in the matrix.</td>
58<td></td>
59</tr>
60<tr>
61<td><code>F1</code></td>
62<td>Functor describing the type of the symmetric matrix. <a name=
63"#symmetric_matrix_1">[1]</a></td>
64<td><code>lower</code></td>
65</tr>
66<tr>
67<td><code>F2</code></td>
68<td>Functor describing the storage organization. <a name=
69"#symmetric_matrix_2">[2]</a></td>
70<td><code>row_major</code></td>
71</tr>
72<tr>
73<td><code>A</code></td>
74<td>The type of the adapted array. <a name="#symmetric_matrix_3"
75>[3]</a></td>
76<td><code>unbounded_array&lt;T&gt;</code></td>
77</tr>
78</tbody>
79</table>
80<h4>Model of</h4>
81<p><a href="container_concept.html#matrix">Matrix</a> .</p>
82<h4>Type requirements</h4>
83<p>None, except for those imposed by the requirements of <a href=
84"container_concept.html#matrix">Matrix</a> .</p>
85<h4>Public base classes</h4>
86<p><code>matrix_container&lt;symmetric_matrix&lt;T, F1, F2, A&gt;
87&gt;</code></p>
88<h4>Members</h4>
89<table border="1" summary="members">
90<tbody>
91<tr>
92<th>Member</th>
93<th>Description</th>
94</tr>
95<tr>
96<td><code>symmetric_matrix (size_type size)</code></td>
97<td>Allocates an uninitialized <code>symmetric_matrix</code> that
98holds <code>size</code> rows of <code>size</code> elements.</td>
99</tr>
100<tr>
101<td><code>symmetric_matrix (const symmetric_matrix
102&amp;m)</code></td>
103<td>The copy constructor.</td>
104</tr>
105<tr>
106<td><code>template&lt;class AE&gt;<br />
107symmetric_matrix (const matrix_expression&lt;AE&gt;
108&amp;ae)</code></td>
109<td>The extended copy constructor.</td>
110</tr>
111<tr>
112<td><code>void resize (size_type size, bool preserve =
113true)</code></td>
114<td>Reallocates a <code>symmetric_matrix</code> to hold
115<code>size</code> rows of <code>size</code> elements. The existing
116elements of the <code>symmetric_matrix</code> are preseved when
117specified.</td>
118</tr>
119<tr>
120<td><code>size_type size1 () const</code></td>
121<td>Returns the number of rows.</td>
122</tr>
123<tr>
124<td><code>size_type size2 () const</code></td>
125<td>Returns the number of columns.</td>
126</tr>
127<tr>
128<td><code>const_reference operator () (size_type i, size_type j)
129const</code></td>
130<td>Returns a <code>const</code> reference of the <code>j</code>
131-th element in the <code>i</code>-th row.</td>
132</tr>
133<tr>
134<td><code>reference operator () (size_type i, size_type
135j)</code></td>
136<td>Returns a reference of the <code>j</code>-th element in the
137<code>i</code>-th row.</td>
138</tr>
139<tr>
140<td><code>symmetric_matrix &amp;operator = (const symmetric_matrix
141&amp;m)</code></td>
142<td>The assignment operator.</td>
143</tr>
144<tr>
145<td><code>symmetric_matrix &amp;assign_temporary (symmetric_matrix
146&amp;m)</code></td>
147<td>Assigns a temporary. May change the symmetric matrix
148<code>m</code> .</td>
149</tr>
150<tr>
151<td><code>template&lt;class AE&gt;<br />
152symmetric_matrix &amp;operator = (const matrix_expression&lt;AE&gt;
153&amp;ae)</code></td>
154<td>The extended assignment operator.</td>
155</tr>
156<tr>
157<td><code>template&lt;class AE&gt;<br />
158symmetric_matrix &amp;assign (const matrix_expression&lt;AE&gt;
159&amp;ae)</code></td>
160<td>Assigns a matrix expression to the symmetric matrix. Left and
161right hand side of the assignment should be independent.</td>
162</tr>
163<tr>
164<td><code>template&lt;class AE&gt;<br />
165symmetric_matrix &amp;operator += (const
166matrix_expression&lt;AE&gt; &amp;ae)</code></td>
167<td>A computed assignment operator. Adds the matrix expression to
168the symmetric matrix.</td>
169</tr>
170<tr>
171<td><code>template&lt;class AE&gt;<br />
172symmetric_matrix &amp;plus_assign (const
173matrix_expression&lt;AE&gt; &amp;ae)</code></td>
174<td>Adds a matrix expression to the symmetric matrix. Left and
175right hand side of the assignment should be independent.</td>
176</tr>
177<tr>
178<td><code>template&lt;class AE&gt;<br />
179symmetric_matrix &amp;operator -= (const
180matrix_expression&lt;AE&gt; &amp;ae)</code></td>
181<td>A computed assignment operator. Subtracts the matrix expression
182from the symmetric matrix.</td>
183</tr>
184<tr>
185<td><code>template&lt;class AE&gt;<br />
186symmetric_matrix &amp;minus_assign (const
187matrix_expression&lt;AE&gt; &amp;ae)</code></td>
188<td>Subtracts a matrix expression from the symmetric matrix. Left
189and right hand side of the assignment should be independent.</td>
190</tr>
191<tr>
192<td><code>template&lt;class AT&gt;<br />
193symmetric_matrix &amp;operator *= (const AT &amp;at)</code></td>
194<td>A computed assignment operator. Multiplies the symmetric matrix
195with a scalar.</td>
196</tr>
197<tr>
198<td><code>template&lt;class AT&gt;<br />
199symmetric_matrix &amp;operator /= (const AT &amp;at)</code></td>
200<td>A computed assignment operator. Divides the symmetric matrix
201through a scalar.</td>
202</tr>
203<tr>
204<td><code>void swap (symmetric_matrix &amp;m)</code></td>
205<td>Swaps the contents of the symmetric matrices.</td>
206</tr>
207<tr>
208<td><code>void insert (size_type i, size_type j, const_reference
209t)</code></td>
210<td>Inserts the value <code>t</code> at the <code>j</code>-th
211element of the <code>i</code>-th row.</td>
212</tr>
213<tr>
214<td><code>void erase (size_type i, size_type j)</code></td>
215<td>Erases the value at the <code>j</code>-th elemenst of the
216<code>i</code>-th row.</td>
217</tr>
218<tr>
219<td><code>void clear ()</code></td>
220<td>Clears the matrix.</td>
221</tr>
222<tr>
223<td><code>const_iterator1 begin1 () const</code></td>
224<td>Returns a <code>const_iterator1</code> pointing to the
225beginning of the <code>symmetric_matrix</code>.</td>
226</tr>
227<tr>
228<td><code>const_iterator1 end1 () const</code></td>
229<td>Returns a <code>const_iterator1</code> pointing to the end of
230the <code>symmetric_matrix</code>.</td>
231</tr>
232<tr>
233<td><code>iterator1 begin1 ()</code></td>
234<td>Returns a <code>iterator1</code> pointing to the beginning of
235the <code>symmetric_matrix</code>.</td>
236</tr>
237<tr>
238<td><code>iterator1 end1 ()</code></td>
239<td>Returns a <code>iterator1</code> pointing to the end of the
240<code>symmetric_matrix</code>.</td>
241</tr>
242<tr>
243<td><code>const_iterator2 begin2 () const</code></td>
244<td>Returns a <code>const_iterator2</code> pointing to the
245beginning of the <code>symmetric_matrix</code>.</td>
246</tr>
247<tr>
248<td><code>const_iterator2 end2 () const</code></td>
249<td>Returns a <code>const_iterator2</code> pointing to the end of
250the <code>symmetric_matrix</code>.</td>
251</tr>
252<tr>
253<td><code>iterator2 begin2 ()</code></td>
254<td>Returns a <code>iterator2</code> pointing to the beginning of
255the <code>symmetric_matrix</code>.</td>
256</tr>
257<tr>
258<td><code>iterator2 end2 ()</code></td>
259<td>Returns a <code>iterator2</code> pointing to the end of the
260<code>symmetric_matrix</code>.</td>
261</tr>
262<tr>
263<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
264<td>Returns a <code>const_reverse_iterator1</code> pointing to the
265beginning of the reversed <code>symmetric_matrix</code>.</td>
266</tr>
267<tr>
268<td><code>const_reverse_iterator1 rend1 () const</code></td>
269<td>Returns a <code>const_reverse_iterator1</code> pointing to the
270end of the reversed <code>symmetric_matrix</code>.</td>
271</tr>
272<tr>
273<td><code>reverse_iterator1 rbegin1 ()</code></td>
274<td>Returns a <code>reverse_iterator1</code> pointing to the
275beginning of the reversed <code>symmetric_matrix</code>.</td>
276</tr>
277<tr>
278<td><code>reverse_iterator1 rend1 ()</code></td>
279<td>Returns a <code>reverse_iterator1</code> pointing to the end of
280the reversed <code>symmetric_matrix</code>.</td>
281</tr>
282<tr>
283<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
284<td>Returns a <code>const_reverse_iterator2</code> pointing to the
285beginning of the reversed <code>symmetric_matrix</code>.</td>
286</tr>
287<tr>
288<td><code>const_reverse_iterator2 rend2 () const</code></td>
289<td>Returns a <code>const_reverse_iterator2</code> pointing to the
290end of the reversed <code>symmetric_matrix</code>.</td>
291</tr>
292<tr>
293<td><code>reverse_iterator2 rbegin2 ()</code></td>
294<td>Returns a <code>reverse_iterator2</code> pointing to the
295beginning of the reversed <code>symmetric_matrix</code>.</td>
296</tr>
297<tr>
298<td><code>reverse_iterator2 rend2 ()</code></td>
299<td>Returns a <code>reverse_iterator2</code> pointing to the end of
300the reversed <code>symmetric_matrix</code>.</td>
301</tr>
302</tbody>
303</table>
304<h4>Notes</h4>
305<p><a name="symmetric_matrix_1">[1]</a>
306Supported parameters for the type of the symmetric matrix are
307<code>lower</code> and <code>upper</code>.</p>
308<p><a name="symmetric_matrix_2">[2]</a>
309Supported parameters for the storage organization are
310<code>row_major</code> and <code>column_major</code>.</p>
311<p><a name="symmetric_matrix_3">[3]</a>
312Supported parameters for the adapted array are
313<code>unbounded_array&lt;T&gt;</code> ,
314<code>bounded_array&lt;T&gt;</code> and
315<code>std::vector&lt;T&gt;</code> .</p>
316<h2><a name="symmetric_adaptor"></a>Symmetric Adaptor</h2>
317<h4>Description</h4>
318<p>The templated class <code>symmetric_adaptor&lt;M, F&gt;</code>
319is a symmetric matrix adaptor for other matrices.</p>
320<h4>Example</h4>
321<pre>
322#include &lt;boost/numeric/ublas/symmetric.hpp&gt;
323#include &lt;boost/numeric/ublas/io.hpp&gt;
324
325int main () {
326 using namespace boost::numeric::ublas;
327 matrix&lt;double&gt; m (3, 3);
328 symmetric_adaptor&lt;matrix&lt;double&gt;, lower&gt; sal (m);
329 for (unsigned i = 0; i &lt; sal.size1 (); ++ i)
330 for (unsigned j = 0; j &lt;= i; ++ j)
331 sal (i, j) = 3 * i + j;
332 std::cout &lt;&lt; sal &lt;&lt; std::endl;
333 symmetric_adaptor&lt;matrix&lt;double&gt;, upper&gt; sau (m);
334 for (unsigned i = 0; i &lt; sau.size1 (); ++ i)
335 for (unsigned j = i; j &lt; sau.size2 (); ++ j)
336 sau (i, j) = 3 * i + j;
337 std::cout &lt;&lt; sau &lt;&lt; std::endl;
338}
339</pre>
340<h4>Definition</h4>
341<p>Defined in the header symmetric.hpp.</p>
342<h4>Template parameters</h4>
343<table border="1" summary="parameters">
344<tbody>
345<tr>
346<th>Parameter</th>
347<th>Description</th>
348<th>Default</th>
349</tr>
350<tr>
351<td><code>M</code></td>
352<td>The type of the adapted matrix.</td>
353<td></td>
354</tr>
355<tr>
356<td><code>F</code></td>
357<td>Functor describing the type of the symmetric adaptor. <a href=
358"#symmetric_adaptor_1">[1]</a></td>
359<td><code>lower</code></td>
360</tr>
361</tbody>
362</table>
363<h4>Model of</h4>
364<p><a href="expression_concept.html#matrix_expression">Matrix Expression</a>
365.</p>
366<h4>Type requirements</h4>
367<p>None, except for those imposed by the requirements of <a href=
368"expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
369<h4>Public base classes</h4>
370<p><code>matrix_expression&lt;symmetric_adaptor&lt;M, F&gt;
371&gt;</code></p>
372<h4>Members</h4>
373<table border="1" summary="members">
374<tbody>
375<tr>
376<th>Member</th>
377<th>Description</th>
378</tr>
379<tr>
380<td><code>symmetric_adaptor ()</code></td>
381<td>Constructs a <code>symmetric_adaptor</code> that holds zero
382rows of zero elements.</td>
383</tr>
384<tr>
385<td><code>symmetric_adaptor (matrix_type &amp;data)</code></td>
386<td>Constructs a <code>symmetric_adaptor</code> of a matrix.</td>
387</tr>
388<tr>
389<td><code>symmetric_adaptor (const symmetric_adaptor
390&amp;m)</code></td>
391<td>The copy constructor.</td>
392</tr>
393<tr>
394<td><code>template&lt;class AE&gt;<br />
395symmetric_adaptor (const matrix_expression&lt;AE&gt;
396&amp;ae)</code></td>
397<td>The extended copy constructor.</td>
398</tr>
399<tr>
400<td><code>size_type size1 () const</code></td>
401<td>Returns the number of rows.</td>
402</tr>
403<tr>
404<td><code>size_type size2 () const</code></td>
405<td>Returns the number of columns.</td>
406</tr>
407<tr>
408<td><code>const_reference operator () (size_type i, size_type j)
409const</code></td>
410<td>Returns a <code>const</code> reference of the <code>j</code>
411-th element in the <code>i</code>-th row.</td>
412</tr>
413<tr>
414<td><code>reference operator () (size_type i, size_type
415j)</code></td>
416<td>Returns a reference of the <code>j</code>-th element in the
417<code>i</code>-th row.</td>
418</tr>
419<tr>
420<td><code>symmetric_adaptor &amp;operator = (const
421symmetric_adaptor &amp;m)</code></td>
422<td>The assignment operator.</td>
423</tr>
424<tr>
425<td><code>symmetric_adaptor &amp;assign_temporary
426(symmetric_adaptor &amp;m)</code></td>
427<td>Assigns a temporary. May change the symmetric adaptor
428<code>m</code>.</td>
429</tr>
430<tr>
431<td><code>template&lt;class AE&gt;<br />
432symmetric_adaptor &amp;operator = (const
433matrix_expression&lt;AE&gt; &amp;ae)</code></td>
434<td>The extended assignment operator.</td>
435</tr>
436<tr>
437<td><code>template&lt;class AE&gt;<br />
438symmetric_adaptor &amp;assign (const matrix_expression&lt;AE&gt;
439&amp;ae)</code></td>
440<td>Assigns a matrix expression to the symmetric adaptor. Left and
441right hand side of the assignment should be independent.</td>
442</tr>
443<tr>
444<td><code>template&lt;class AE&gt;<br />
445symmetric_adaptor &amp;operator += (const
446matrix_expression&lt;AE&gt; &amp;ae)</code></td>
447<td>A computed assignment operator. Adds the matrix expression to
448the symmetric adaptor.</td>
449</tr>
450<tr>
451<td><code>template&lt;class AE&gt;<br />
452symmetric_adaptor &amp;plus_assign (const
453matrix_expression&lt;AE&gt; &amp;ae)</code></td>
454<td>Adds a matrix expression to the symmetric adaptor. Left and
455right hand side of the assignment should be independent.</td>
456</tr>
457<tr>
458<td><code>template&lt;class AE&gt;<br />
459symmetric_adaptor &amp;operator -= (const
460matrix_expression&lt;AE&gt; &amp;ae)</code></td>
461<td>A computed assignment operator. Subtracts the matrix expression
462from the symmetric adaptor.</td>
463</tr>
464<tr>
465<td><code>template&lt;class AE&gt;<br />
466symmetric_adaptor &amp;minus_assign (const
467matrix_expression&lt;AE&gt; &amp;ae)</code></td>
468<td>Subtracts a matrix expression from the symmetric adaptor. Left
469and right hand side of the assignment should be independent.</td>
470</tr>
471<tr>
472<td><code>template&lt;class AT&gt;<br />
473symmetric_adaptor &amp;operator *= (const AT &amp;at)</code></td>
474<td>A computed assignment operator. Multiplies the symmetric
475adaptor with a scalar.</td>
476</tr>
477<tr>
478<td><code>template&lt;class AT&gt;<br />
479symmetric_adaptor &amp;operator /= (const AT &amp;at)</code></td>
480<td>A computed assignment operator. Divides the symmetric adaptor
481through a scalar.</td>
482</tr>
483<tr>
484<td><code>void swap (symmetric_adaptor &amp;m)</code></td>
485<td>Swaps the contents of the symmetric adaptors.</td>
486</tr>
487<tr>
488<td><code>const_iterator1 begin1 () const</code></td>
489<td>Returns a <code>const_iterator1</code> pointing to the
490beginning of the <code>symmetric_adaptor</code>.</td>
491</tr>
492<tr>
493<td><code>const_iterator1 end1 () const</code></td>
494<td>Returns a <code>const_iterator1</code> pointing to the end of
495the <code>symmetric_adaptor</code>.</td>
496</tr>
497<tr>
498<td><code>iterator1 begin1 ()</code></td>
499<td>Returns a <code>iterator1</code> pointing to the beginning of
500the <code>symmetric_adaptor</code>.</td>
501</tr>
502<tr>
503<td><code>iterator1 end1 ()</code></td>
504<td>Returns a <code>iterator1</code> pointing to the end of the
505<code>symmetric_adaptor</code>.</td>
506</tr>
507<tr>
508<td><code>const_iterator2 begin2 () const</code></td>
509<td>Returns a <code>const_iterator2</code> pointing to the
510beginning of the <code>symmetric_adaptor</code>.</td>
511</tr>
512<tr>
513<td><code>const_iterator2 end2 () const</code></td>
514<td>Returns a <code>const_iterator2</code> pointing to the end of
515the <code>symmetric_adaptor</code>.</td>
516</tr>
517<tr>
518<td><code>iterator2 begin2 ()</code></td>
519<td>Returns a <code>iterator2</code> pointing to the beginning of
520the <code>symmetric_adaptor</code>.</td>
521</tr>
522<tr>
523<td><code>iterator2 end2 ()</code></td>
524<td>Returns a <code>iterator2</code> pointing to the end of the
525<code>symmetric_adaptor</code>.</td>
526</tr>
527<tr>
528<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
529<td>Returns a <code>const_reverse_iterator1</code> pointing to the
530beginning of the reversed <code>symmetric_adaptor</code>.</td>
531</tr>
532<tr>
533<td><code>const_reverse_iterator1 rend1 () const</code></td>
534<td>Returns a <code>const_reverse_iterator1</code> pointing to the
535end of the reversed <code>symmetric_adaptor</code>.</td>
536</tr>
537<tr>
538<td><code>reverse_iterator1 rbegin1 ()</code></td>
539<td>Returns a <code>reverse_iterator1</code> pointing to the
540beginning of the reversed <code>symmetric_adaptor</code>.</td>
541</tr>
542<tr>
543<td><code>reverse_iterator1 rend1 ()</code></td>
544<td>Returns a <code>reverse_iterator1</code> pointing to the end of
545the reversed <code>symmetric_adaptor</code>.</td>
546</tr>
547<tr>
548<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
549<td>Returns a <code>const_reverse_iterator2</code> pointing to the
550beginning of the reversed <code>symmetric_adaptor</code>.</td>
551</tr>
552<tr>
553<td><code>const_reverse_iterator2 rend2 () const</code></td>
554<td>Returns a <code>const_reverse_iterator2</code> pointing to the
555end of the reversed <code>symmetric_adaptor</code>.</td>
556</tr>
557<tr>
558<td><code>reverse_iterator2 rbegin2 ()</code></td>
559<td>Returns a <code>reverse_iterator2</code> pointing to the
560beginning of the reversed <code>symmetric_adaptor</code>.</td>
561</tr>
562<tr>
563<td><code>reverse_iterator2 rend2 ()</code></td>
564<td>Returns a <code>reverse_iterator2</code> pointing to the end of
565the reversed <code>symmetric_adaptor</code>.</td>
566</tr>
567</tbody>
568</table>
569<h4>Notes</h4>
570<p><a name="symmetric_adaptor_1">[1]</a>
571Supported parameters for the type of the symmetric adaptor are
572<code>lower</code> and <code>upper</code>.</p>
573<hr />
574<p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
575 Use, modification and distribution are subject to the
576 Boost Software License, Version 1.0.
577 (See accompanying file LICENSE_1_0.txt
578 or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
579 http://www.boost.org/LICENSE_1_0.txt
580 </a>).
581</p>
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