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13<title>Hermitian Matrix</title>
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15<body>
16<h1><img src="../../../../boost.png" align="middle" />Hermitian Matrix</h1>
17<div class="toc" id="toc"></div>
18<h2><a name="hermitian_matrix"></a>Hermitian Matrix</h2>
19<h4>Description</h4>
20<p>The templated class <code>hermitian_matrix&lt;T, F1, F2,
21A&gt;</code> is the base container adaptor for hermitian matrices.
22For a <em>(n x n</em> )-dimensional hermitian matrix and <em>0
23&lt;= i &lt; n</em>, <em>0 &lt;= j &lt; n</em> holds
24<em>h</em><sub><em>i, j</em></sub> <em>= h</em><sub><em>j,
25i</em></sub><sup><em>-</em></sup>. The storage of hermitian
26matrices is packed.</p>
27<h4>Example</h4>
28<pre>
29#include &lt;boost/numeric/ublas/hermitian.hpp&gt;
30#include &lt;boost/numeric/ublas/io.hpp&gt;
31
32int main () {
33 using namespace boost::numeric::ublas;
34 hermitian_matrix&lt;std::complex&lt;double&gt;, lower&gt; ml (3, 3);
35 for (unsigned i = 0; i &lt; ml.size1 (); ++ i) {
36 for (unsigned j = 0; j &lt; i; ++ j)
37 ml (i, j) = std::complex&lt;double&gt; (3 * i + j, 3 * i + j);
38 ml (i, i) = std::complex&lt;double&gt; (4 * i, 0);
39 }
40 std::cout &lt;&lt; ml &lt;&lt; std::endl;
41 hermitian_matrix&lt;std::complex&lt;double&gt;, upper&gt; mu (3, 3);
42 for (unsigned i = 0; i &lt; mu.size1 (); ++ i) {
43 mu (i, i) = std::complex&lt;double&gt; (4 * i, 0);
44 for (unsigned j = i + 1; j &lt; mu.size2 (); ++ j)
45 mu (i, j) = std::complex&lt;double&gt; (3 * i + j, 3 * i + j);
46 }
47 std::cout &lt;&lt; mu &lt;&lt; std::endl;
48}
49</pre>
50<h4>Definition</h4>
51<p>Defined in the header hermitian.hpp.</p>
52<h4>Template parameters</h4>
53<table border="1" summary="parameters">
54<tbody>
55<tr>
56<th>Parameter</th>
57<th>Description</th>
58<th>Default</th>
59</tr>
60<tr>
61<td><code>T</code></td>
62<td>The type of object stored in the matrix.</td>
63<td></td>
64</tr>
65<tr>
66<td><code>F1</code></td>
67<td>Functor describing the type of the hermitian matrix. <a href=
68"#hermitian_matrix_1">[1]</a></td>
69<td><code>lower</code></td>
70</tr>
71<tr>
72<td><code>F2</code></td>
73<td>Functor describing the storage organization. <a href=
74"#hermitian_matrix_2">[2]</a></td>
75<td><code>row_major</code></td>
76</tr>
77<tr>
78<td><code>A</code></td>
79<td>The type of the adapted array. <a href=
80"#hermitian_matrix_3">[3]</a></td>
81<td><code>unbounded_array&lt;T&gt;</code></td>
82</tr>
83</tbody>
84</table>
85<h4>Model of</h4>
86<p><a href="container_concept.html#matrix">Matrix</a> .</p>
87<h4>Type requirements</h4>
88<p>None, except for those imposed by the requirements of <a href=
89"container_concept.html#matrix">Matrix</a> .</p>
90<h4>Public base classes</h4>
91<p><code>matrix_container&lt;hermitian_matrix&lt;T, F1, F2, A&gt;
92&gt;</code></p>
93<h4>Members</h4>
94<table border="1" summary="members">
95<tbody>
96<tr>
97<th>Member</th>
98<th>Description</th>
99</tr>
100<tr>
101<td><code>hermitian_matrix ()</code></td>
102<td>Allocates an uninitialized <code>hermitian_matrix</code> that
103holds zero rows of zero elements.</td>
104</tr>
105<tr>
106<td><code>hermitian_matrix (size_type size)</code></td>
107<td>Allocates an uninitialized <code>hermitian_matrix</code> that
108holds <code>size</code> rows of <code>size</code> elements.</td>
109</tr>
110<tr>
111<td><code>hermitian_matrix (const hermitian_matrix
112&amp;m)</code></td>
113<td>The copy constructor.</td>
114</tr>
115<tr>
116<td><code>template&lt;class AE&gt;<br />
117hermitian_matrix (const matrix_expression&lt;AE&gt;
118&amp;ae)</code></td>
119<td>The extended copy constructor.</td>
120</tr>
121<tr>
122<td><code>void resize (size_type size, bool preserve =
123true)</code></td>
124<td>Reallocates a <code>hermitian_matrix</code> to hold
125<code>size</code> rows of <code>size</code> elements. The existing
126elements of the <code>hermitian_matrix</code> are preseved when
127specified.</td>
128</tr>
129<tr>
130<td><code>size_type size1 () const</code></td>
131<td>Returns the number of rows.</td>
132</tr>
133<tr>
134<td><code>size_type size2 () const</code></td>
135<td>Returns the number of columns.</td>
136</tr>
137<tr>
138<td><code>const_reference operator () (size_type i, size_type j)
139const</code></td>
140<td>Returns a <code>const</code> reference of the <code>j</code>
141-th element in the <code>i</code>-th row.</td>
142</tr>
143<tr>
144<td><code>reference operator () (size_type i, size_type
145j)</code></td>
146<td>Returns a reference of the <code>j</code>-th element in the
147<code>i</code>-th row.</td>
148</tr>
149<tr>
150<td><code>hermitian_matrix &amp;operator = (const hermitian_matrix
151&amp;m)</code></td>
152<td>The assignment operator.</td>
153</tr>
154<tr>
155<td><code>hermitian_matrix &amp;assign_temporary (hermitian_matrix
156&amp;m)</code></td>
157<td>Assigns a temporary. May change the hermitian matrix
158<code>m</code> .</td>
159</tr>
160<tr>
161<td><code>template&lt;class AE&gt;<br />
162hermitian_matrix &amp;operator = (const matrix_expression&lt;AE&gt;
163&amp;ae)</code></td>
164<td>The extended assignment operator.</td>
165</tr>
166<tr>
167<td><code>template&lt;class AE&gt;<br />
168hermitian_matrix &amp;assign (const matrix_expression&lt;AE&gt;
169&amp;ae)</code></td>
170<td>Assigns a matrix expression to the hermitian matrix. Left and
171right hand side of the assignment should be independent.</td>
172</tr>
173<tr>
174<td><code>template&lt;class AE&gt;<br />
175hermitian_matrix &amp;operator += (const
176matrix_expression&lt;AE&gt; &amp;ae)</code></td>
177<td>A computed assignment operator. Adds the matrix expression to
178the hermitian matrix.</td>
179</tr>
180<tr>
181<td><code>template&lt;class AE&gt;<br />
182hermitian_matrix &amp;plus_assign (const
183matrix_expression&lt;AE&gt; &amp;ae)</code></td>
184<td>Adds a matrix expression to the hermitian matrix. Left and
185right hand side of the assignment should be independent.</td>
186</tr>
187<tr>
188<td><code>template&lt;class AE&gt;<br />
189hermitian_matrix &amp;operator -= (const
190matrix_expression&lt;AE&gt; &amp;ae)</code></td>
191<td>A computed assignment operator. Subtracts the matrix expression
192from the hermitian matrix.</td>
193</tr>
194<tr>
195<td><code>template&lt;class AE&gt;<br />
196hermitian_matrix &amp;minus_assign (const
197matrix_expression&lt;AE&gt; &amp;ae)</code></td>
198<td>Subtracts a matrix expression from the hermitian matrix. Left
199and right hand side of the assignment should be independent.</td>
200</tr>
201<tr>
202<td><code>template&lt;class AT&gt;<br />
203hermitian_matrix &amp;operator *= (const AT &amp;at)</code></td>
204<td>A computed assignment operator. Multiplies the hermitian matrix
205with a scalar.</td>
206</tr>
207<tr>
208<td><code>template&lt;class AT&gt;<br />
209hermitian_matrix &amp;operator /= (const AT &amp;at)</code></td>
210<td>A computed assignment operator. Divides the hermitian matrix
211through a scalar.</td>
212</tr>
213<tr>
214<td><code>void swap (hermitian_matrix &amp;m)</code></td>
215<td>Swaps the contents of the hermitian matrices.</td>
216</tr>
217<tr>
218<td><code>void insert (size_type i, size_type j, const_reference
219t)</code></td>
220<td>Inserts the value <code>t</code> at the <code>j</code>-th
221element of the <code>i</code>-th row.</td>
222</tr>
223<tr>
224<td><code>void erase (size_type i, size_type j)</code></td>
225<td>Erases the value at the <code>j</code>-th elemenst of the
226<code>i</code>-th row.</td>
227</tr>
228<tr>
229<td><code>void clear ()</code></td>
230<td>Clears the matrix.</td>
231</tr>
232<tr>
233<td><code>const_iterator1 begin1 () const</code></td>
234<td>Returns a <code>const_iterator1</code> pointing to the
235beginning of the <code>hermitian_matrix</code>.</td>
236</tr>
237<tr>
238<td><code>const_iterator1 end1 () const</code></td>
239<td>Returns a <code>const_iterator1</code> pointing to the end of
240the <code>hermitian_matrix</code>.</td>
241</tr>
242<tr>
243<td><code>iterator1 begin1 ()</code></td>
244<td>Returns a <code>iterator1</code> pointing to the beginning of
245the <code>hermitian_matrix</code>.</td>
246</tr>
247<tr>
248<td><code>iterator1 end1 ()</code></td>
249<td>Returns a <code>iterator1</code> pointing to the end of the
250<code>hermitian_matrix</code>.</td>
251</tr>
252<tr>
253<td><code>const_iterator2 begin2 () const</code></td>
254<td>Returns a <code>const_iterator2</code> pointing to the
255beginning of the <code>hermitian_matrix</code>.</td>
256</tr>
257<tr>
258<td><code>const_iterator2 end2 () const</code></td>
259<td>Returns a <code>const_iterator2</code> pointing to the end of
260the <code>hermitian_matrix</code>.</td>
261</tr>
262<tr>
263<td><code>iterator2 begin2 ()</code></td>
264<td>Returns a <code>iterator2</code> pointing to the beginning of
265the <code>hermitian_matrix</code>.</td>
266</tr>
267<tr>
268<td><code>iterator2 end2 ()</code></td>
269<td>Returns a <code>iterator2</code> pointing to the end of the
270<code>hermitian_matrix</code>.</td>
271</tr>
272<tr>
273<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
274<td>Returns a <code>const_reverse_iterator1</code> pointing to the
275beginning of the reversed <code>hermitian_matrix</code>.</td>
276</tr>
277<tr>
278<td><code>const_reverse_iterator1 rend1 () const</code></td>
279<td>Returns a <code>const_reverse_iterator1</code> pointing to the
280end of the reversed <code>hermitian_matrix</code>.</td>
281</tr>
282<tr>
283<td><code>reverse_iterator1 rbegin1 ()</code></td>
284<td>Returns a <code>reverse_iterator1</code> pointing to the
285beginning of the reversed <code>hermitian_matrix</code>.</td>
286</tr>
287<tr>
288<td><code>reverse_iterator1 rend1 ()</code></td>
289<td>Returns a <code>reverse_iterator1</code> pointing to the end of
290the reversed <code>hermitian_matrix</code>.</td>
291</tr>
292<tr>
293<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
294<td>Returns a <code>const_reverse_iterator2</code> pointing to the
295beginning of the reversed <code>hermitian_matrix</code>.</td>
296</tr>
297<tr>
298<td><code>const_reverse_iterator2 rend2 () const</code></td>
299<td>Returns a <code>const_reverse_iterator2</code> pointing to the
300end of the reversed <code>hermitian_matrix</code>.</td>
301</tr>
302<tr>
303<td><code>reverse_iterator2 rbegin2 ()</code></td>
304<td>Returns a <code>reverse_iterator2</code> pointing to the
305beginning of the reversed <code>hermitian_matrix</code>.</td>
306</tr>
307<tr>
308<td><code>reverse_iterator2 rend2 ()</code></td>
309<td>Returns a <code>reverse_iterator2</code> pointing to the end of
310the reversed <code>hermitian_matrix</code>.</td>
311</tr>
312</tbody>
313</table>
314<h4>Notes</h4>
315<p><a name="hermitian_matrix_1" id="hermitian_matrix_1">[1]</a>
316Supported parameters for the type of the hermitian matrix are
317<code>lower</code> and <code>upper</code>.</p>
318<p><a name="hermitian_matrix_2" id="hermitian_matrix_2">[2]</a>
319Supported parameters for the storage organization are
320<code>row_major</code> and <code>column_major</code>.</p>
321<p><a name="hermitian_matrix_3" id="hermitian_matrix_3">[3]</a>
322Supported parameters for the adapted array are
323<code>unbounded_array&lt;T&gt;</code> ,
324<code>bounded_array&lt;T&gt;</code> and
325<code>std::vector&lt;T&gt;</code> .</p>
326<h2><a name="hermitian_adaptor"></a>Hermitian Adaptor</h2>
327<h4>Description</h4>
328<p>The templated class <code>hermitian_adaptor&lt;M, F&gt;</code>
329is a hermitian matrix adaptor for other matrices.</p>
330<h4>Example</h4>
331<pre>
332#include &lt;boost/numeric/ublas/hermitian.hpp&gt;
333#include &lt;boost/numeric/ublas/io.hpp&gt;
334
335int main () {
336 using namespace boost::numeric::ublas;
337 matrix&lt;std::complex&lt;double&gt; &gt; m (3, 3);
338 hermitian_adaptor&lt;matrix&lt;std::complex&lt;double&gt; &gt;, lower&gt; hal (m);
339 for (unsigned i = 0; i &lt; hal.size1 (); ++ i) {
340 for (unsigned j = 0; j &lt; i; ++ j)
341 hal (i, j) = std::complex&lt;double&gt; (3 * i + j, 3 * i + j);
342 hal (i, i) = std::complex&lt;double&gt; (4 * i, 0);
343 }
344 std::cout &lt;&lt; hal &lt;&lt; std::endl;
345 hermitian_adaptor&lt;matrix&lt;std::complex&lt;double&gt; &gt;, upper&gt; hau (m);
346 for (unsigned i = 0; i &lt; hau.size1 (); ++ i) {
347 hau (i, i) = std::complex&lt;double&gt; (4 * i, 0);
348 for (unsigned j = i + 1; j &lt; hau.size2 (); ++ j)
349 hau (i, j) = std::complex&lt;double&gt; (3 * i + j, 3 * i + j);
350 }
351 std::cout &lt;&lt; hau &lt;&lt; std::endl;
352}
353</pre>
354<h4>Definition</h4>
355<p>Defined in the header hermitian.hpp.</p>
356<h4>Template parameters</h4>
357<table border="1" summary="parameters">
358<tbody>
359<tr>
360<th>Parameter</th>
361<th>Description</th>
362<th>Default</th>
363</tr>
364<tr>
365<td><code>M</code></td>
366<td>The type of the adapted matrix.</td>
367<td></td>
368</tr>
369<tr>
370<td><code>F</code></td>
371<td>Functor describing the type of the hermitian adaptor. <a href=
372"#hermitian_adaptor_1">[1]</a></td>
373<td><code>lower</code></td>
374</tr>
375</tbody>
376</table>
377<h4>Model of</h4>
378<p><a href="expression_concept.html#matrix_expression">Matrix Expression</a>
379.</p>
380<h4>Type requirements</h4>
381<p>None, except for those imposed by the requirements of <a href=
382"expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
383<h4>Public base classes</h4>
384<p><code>matrix_expression&lt;hermitian_adaptor&lt;M, F&gt;
385&gt;</code></p>
386<h4>Members</h4>
387<table border="1" summary="members">
388<tbody>
389<tr>
390<th>Member</th>
391<th>Description</th>
392</tr>
393<tr>
394<td><code>hermitian_adaptor (matrix_type &amp;data)</code></td>
395<td>Constructs a <code>hermitian_adaptor</code> of a matrix.</td>
396</tr>
397<tr>
398<td><code>hermitian_adaptor (const hermitian_adaptor
399&amp;m)</code></td>
400<td>The copy constructor.</td>
401</tr>
402<tr>
403<td><code>template&lt;class AE&gt;<br />
404hermitian_adaptor (const matrix_expression&lt;AE&gt;
405&amp;ae)</code></td>
406<td>The extended copy constructor.</td>
407</tr>
408<tr>
409<td><code>size_type size1 () const</code></td>
410<td>Returns the number of rows.</td>
411</tr>
412<tr>
413<td><code>size_type size2 () const</code></td>
414<td>Returns the number of columns.</td>
415</tr>
416<tr>
417<td><code>const_reference operator () (size_type i, size_type j)
418const</code></td>
419<td>Returns a <code>const</code> reference of the <code>j</code>
420-th element in the <code>i</code>-th row.</td>
421</tr>
422<tr>
423<td><code>reference operator () (size_type i, size_type
424j)</code></td>
425<td>Returns a reference of the <code>j</code>-th element in the
426<code>i</code>-th row.</td>
427</tr>
428<tr>
429<td><code>hermitian_adaptor &amp;operator = (const
430hermitian_adaptor &amp;m)</code></td>
431<td>The assignment operator.</td>
432</tr>
433<tr>
434<td><code>hermitian_adaptor &amp;assign_temporary
435(hermitian_adaptor &amp;m)</code></td>
436<td>Assigns a temporary. May change the hermitian adaptor
437<code>m</code>.</td>
438</tr>
439<tr>
440<td><code>template&lt;class AE&gt;<br />
441hermitian_adaptor &amp;operator = (const
442matrix_expression&lt;AE&gt; &amp;ae)</code></td>
443<td>The extended assignment operator.</td>
444</tr>
445<tr>
446<td><code>template&lt;class AE&gt;<br />
447hermitian_adaptor &amp;assign (const matrix_expression&lt;AE&gt;
448&amp;ae)</code></td>
449<td>Assigns a matrix expression to the hermitian adaptor. Left and
450right hand side of the assignment should be independent.</td>
451</tr>
452<tr>
453<td><code>template&lt;class AE&gt;<br />
454hermitian_adaptor &amp;operator += (const
455matrix_expression&lt;AE&gt; &amp;ae)</code></td>
456<td>A computed assignment operator. Adds the matrix expression to
457the hermitian adaptor.</td>
458</tr>
459<tr>
460<td><code>template&lt;class AE&gt;<br />
461hermitian_adaptor &amp;plus_assign (const
462matrix_expression&lt;AE&gt; &amp;ae)</code></td>
463<td>Adds a matrix expression to the hermitian adaptor. Left and
464right hand side of the assignment should be independent.</td>
465</tr>
466<tr>
467<td><code>template&lt;class AE&gt;<br />
468hermitian_adaptor &amp;operator -= (const
469matrix_expression&lt;AE&gt; &amp;ae)</code></td>
470<td>A computed assignment operator. Subtracts the matrix expression
471from the hermitian adaptor.</td>
472</tr>
473<tr>
474<td><code>template&lt;class AE&gt;<br />
475hermitian_adaptor &amp;minus_assign (const
476matrix_expression&lt;AE&gt; &amp;ae)</code></td>
477<td>Subtracts a matrix expression from the hermitian adaptor. Left
478and right hand side of the assignment should be independent.</td>
479</tr>
480<tr>
481<td><code>template&lt;class AT&gt;<br />
482hermitian_adaptor &amp;operator *= (const AT &amp;at)</code></td>
483<td>A computed assignment operator. Multiplies the hermitian
484adaptor with a scalar.</td>
485</tr>
486<tr>
487<td><code>template&lt;class AT&gt;<br />
488hermitian_adaptor &amp;operator /= (const AT &amp;at)</code></td>
489<td>A computed assignment operator. Divides the hermitian adaptor
490through a scalar.</td>
491</tr>
492<tr>
493<td><code>void swap (hermitian_adaptor &amp;m)</code></td>
494<td>Swaps the contents of the hermitian adaptors.</td>
495</tr>
496<tr>
497<td><code>const_iterator1 begin1 () const</code></td>
498<td>Returns a <code>const_iterator1</code> pointing to the
499beginning of the <code>hermitian_adaptor</code>.</td>
500</tr>
501<tr>
502<td><code>const_iterator1 end1 () const</code></td>
503<td>Returns a <code>const_iterator1</code> pointing to the end of
504the <code>hermitian_adaptor</code>.</td>
505</tr>
506<tr>
507<td><code>iterator1 begin1 ()</code></td>
508<td>Returns a <code>iterator1</code> pointing to the beginning of
509the <code>hermitian_adaptor</code>.</td>
510</tr>
511<tr>
512<td><code>iterator1 end1 ()</code></td>
513<td>Returns a <code>iterator1</code> pointing to the end of the
514<code>hermitian_adaptor</code>.</td>
515</tr>
516<tr>
517<td><code>const_iterator2 begin2 () const</code></td>
518<td>Returns a <code>const_iterator2</code> pointing to the
519beginning of the <code>hermitian_adaptor</code>.</td>
520</tr>
521<tr>
522<td><code>const_iterator2 end2 () const</code></td>
523<td>Returns a <code>const_iterator2</code> pointing to the end of
524the <code>hermitian_adaptor</code>.</td>
525</tr>
526<tr>
527<td><code>iterator2 begin2 ()</code></td>
528<td>Returns a <code>iterator2</code> pointing to the beginning of
529the <code>hermitian_adaptor</code>.</td>
530</tr>
531<tr>
532<td><code>iterator2 end2 ()</code></td>
533<td>Returns a <code>iterator2</code> pointing to the end of the
534<code>hermitian_adaptor</code>.</td>
535</tr>
536<tr>
537<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
538<td>Returns a <code>const_reverse_iterator1</code> pointing to the
539beginning of the reversed <code>hermitian_adaptor</code>.</td>
540</tr>
541<tr>
542<td><code>const_reverse_iterator1 rend1 () const</code></td>
543<td>Returns a <code>const_reverse_iterator1</code> pointing to the
544end of the reversed <code>hermitian_adaptor</code>.</td>
545</tr>
546<tr>
547<td><code>reverse_iterator1 rbegin1 ()</code></td>
548<td>Returns a <code>reverse_iterator1</code> pointing to the
549beginning of the reversed <code>hermitian_adaptor</code>.</td>
550</tr>
551<tr>
552<td><code>reverse_iterator1 rend1 ()</code></td>
553<td>Returns a <code>reverse_iterator1</code> pointing to the end of
554the reversed <code>hermitian_adaptor</code>.</td>
555</tr>
556<tr>
557<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
558<td>Returns a <code>const_reverse_iterator2</code> pointing to the
559beginning of the reversed <code>hermitian_adaptor</code>.</td>
560</tr>
561<tr>
562<td><code>const_reverse_iterator2 rend2 () const</code></td>
563<td>Returns a <code>const_reverse_iterator2</code> pointing to the
564end of the reversed <code>hermitian_adaptor</code>.</td>
565</tr>
566<tr>
567<td><code>reverse_iterator2 rbegin2 ()</code></td>
568<td>Returns a <code>reverse_iterator2</code> pointing to the
569beginning of the reversed <code>hermitian_adaptor</code>.</td>
570</tr>
571<tr>
572<td><code>reverse_iterator2 rend2 ()</code></td>
573<td>Returns a <code>reverse_iterator2</code> pointing to the end of
574the reversed <code>hermitian_adaptor</code>.</td>
575</tr>
576</tbody>
577</table>
578<h4>Notes</h4>
579<p><a name="hermitian_adaptor_1" id="hermitian_adaptor_1">[1]</a>
580Supported parameters for the type of the hermitian adaptor are
581<code>lower</code> and <code>upper</code>.</p>
582<hr />
583<p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
584 Use, modification and distribution are subject to the
585 Boost Software License, Version 1.0.
586 (See accompanying file LICENSE_1_0.txt
587 or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
588 http://www.boost.org/LICENSE_1_0.txt
589 </a>).
590</p>
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