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16<h1><img src="../../../../boost.png" align="middle" />Matrix Proxies</h1>
17<div class="toc" id="toc"></div>
18<h2><a name="matrix_row"></a>Matrix Row</h2>
19<h4>Description</h4>
20<p>The templated class <code>matrix_row&lt;M&gt;</code> allows
21addressing a row of a matrix.</p>
22<h4>Example</h4>
23<pre>
24#include &lt;boost/numeric/ublas/matrix.hpp&gt;
25#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
26#include &lt;boost/numeric/ublas/io.hpp&gt;
27
28int main () {
29 using namespace boost::numeric::ublas;
30 matrix&lt;double&gt; m (3, 3);
31 for (unsigned i = 0; i &lt; m.size1 (); ++ i) {
32 matrix_row&lt;matrix&lt;double&gt; &gt; mr (m, i);
33 for (unsigned j = 0; j &lt; mr.size (); ++ j)
34 mr (j) = 3 * i + j;
35 std::cout &lt;&lt; mr &lt;&lt; std::endl;
36 }
37}
38</pre>
39<h4>Definition</h4>
40<p>Defined in the header matrix_proxy.hpp.</p>
41<h4>Template parameters</h4>
42<table border="1" summary="parameters">
43<tbody>
44<tr>
45<th>Parameter</th>
46<th>Description</th>
47<th>Default</th>
48</tr>
49<tr>
50<td><code>M</code></td>
51<td>The type of matrix referenced.</td>
52<td></td>
53</tr>
54</tbody>
55</table>
56<h4>Model of</h4>
57<p><a href="expression_concept.html#vector_expression">Vector Expression</a>
58.</p>
59<p>If the specified row falls outside that of the row index range
60of the matrix, then the <code>matrix_row</code> is not a well
61formed Vector Expression. That is, access to an element which is
62outside of the matrix is <i>undefined</i>.</p>
63<h4>Type requirements</h4>
64<p>None, except for those imposed by the requirements of <a href=
65"expression_concept.html#vector_expression">Vector Expression</a> .</p>
66<h4>Public base classes</h4>
67<p><code>vector_expression&lt;matrix_row&lt;M&gt; &gt;</code></p>
68<h4>Members</h4>
69<table border="1" summary="members">
70<tbody>
71<tr>
72<th>Member</th>
73<th>Description</th>
74</tr>
75<tr>
76<td><code>matrix_row (matrix_type &amp;data, size_type
77i)</code></td>
78<td>Constructs a sub vector.</td>
79</tr>
80<tr>
81<td><code>size_type size () const</code></td>
82<td>Returns the size of the sub vector.</td>
83</tr>
84<tr>
85<td><code>const_reference operator () (size_type i)
86const</code></td>
87<td>Returns the value of the <code>i</code>-th element.</td>
88</tr>
89<tr>
90<td><code>reference operator () (size_type i)</code></td>
91<td>Returns a reference of the <code>i</code>-th element.</td>
92</tr>
93<tr>
94<td><code>matrix_row &amp;operator = (const matrix_row
95&amp;mr)</code></td>
96<td>The assignment operator.</td>
97</tr>
98<tr>
99<td><code>matrix_row &amp;assign_temporary (matrix_row
100&amp;mr)</code></td>
101<td>Assigns a temporary. May change the matrix row <code>mr</code>
102.</td>
103</tr>
104<tr>
105<td><code>template&lt;class AE&gt;<br />
106matrix_row &amp;operator = (const vector_expression&lt;AE&gt;
107&amp;ae)</code></td>
108<td>The extended assignment operator.</td>
109</tr>
110<tr>
111<td><code>template&lt;class AE&gt;<br />
112matrix_row &amp;assign (const vector_expression&lt;AE&gt;
113&amp;ae)</code></td>
114<td>Assigns a vector expression to the sub vector. Left and right
115hand side of the assignment should be independent.</td>
116</tr>
117<tr>
118<td><code>template&lt;class AE&gt;<br />
119matrix_row &amp;operator += (const vector_expression&lt;AE&gt;
120&amp;ae)</code></td>
121<td>A computed assignment operator. Adds the vector expression to
122the sub vector.</td>
123</tr>
124<tr>
125<td><code>template&lt;class AE&gt;<br />
126matrix_row &amp;plus_assign (const vector_expression&lt;AE&gt;
127&amp;ae)</code></td>
128<td>Adds a vector expression to the sub vector. Left and right hand
129side of the assignment should be independent.</td>
130</tr>
131<tr>
132<td><code>template&lt;class AE&gt;<br />
133matrix_row &amp;operator -= (const vector_expression&lt;AE&gt;
134&amp;ae)</code></td>
135<td>A computed assignment operator. Subtracts the vector expression
136from the sub vector.</td>
137</tr>
138<tr>
139<td><code>template&lt;class AE&gt;<br />
140matrix_row &amp;minus_assign (const vector_expression&lt;AE&gt;
141&amp;ae)</code></td>
142<td>Subtracts a vector expression from the sub vector. Left and
143right hand side of the assignment should be independent.</td>
144</tr>
145<tr>
146<td><code>template&lt;class AT&gt;<br />
147matrix_row &amp;operator *= (const AT &amp;at)</code></td>
148<td>A computed assignment operator. Multiplies the sub vector with
149a scalar.</td>
150</tr>
151<tr>
152<td><code>template&lt;class AT&gt;<br />
153matrix_row &amp;operator /= (const AT &amp;at)</code></td>
154<td>A computed assignment operator. Divides the sub vector through
155a scalar.</td>
156</tr>
157<tr>
158<td><code>void swap (matrix_row &amp;mr)</code></td>
159<td>Swaps the contents of the sub vectors.</td>
160</tr>
161<tr>
162<td><code>const_iterator begin () const</code></td>
163<td>Returns a <code>const_iterator</code> pointing to the beginning
164of the <code>matrix_row</code>.</td>
165</tr>
166<tr>
167<td><code>const_iterator end () const</code></td>
168<td>Returns a <code>const_iterator</code> pointing to the end of
169the <code>matrix_row</code>.</td>
170</tr>
171<tr>
172<td><code>iterator begin ()</code></td>
173<td>Returns a <code>iterator</code> pointing to the beginning of
174the <code>matrix_row</code>.</td>
175</tr>
176<tr>
177<td><code>iterator end ()</code></td>
178<td>Returns a <code>iterator</code> pointing to the end of the
179<code>matrix_row</code>.</td>
180</tr>
181<tr>
182<td><code>const_reverse_iterator rbegin () const</code></td>
183<td>Returns a <code>const_reverse_iterator</code> pointing to the
184beginning of the reversed <code>matrix_row</code>.</td>
185</tr>
186<tr>
187<td><code>const_reverse_iterator rend () const</code></td>
188<td>Returns a <code>const_reverse_iterator</code> pointing to the
189end of the reversed <code>matrix_row</code>.</td>
190</tr>
191<tr>
192<td><code>reverse_iterator rbegin ()</code></td>
193<td>Returns a <code>reverse_iterator</code> pointing to the
194beginning of the reversed <code>matrix_row</code>.</td>
195</tr>
196<tr>
197<td><code>reverse_iterator rend ()</code></td>
198<td>Returns a <code>reverse_iterator</code> pointing to the end of
199the reversed <code>matrix_row</code>.</td>
200</tr>
201</tbody>
202</table>
203<h3>Projections</h3>
204<h4>Description</h4>
205<p>The free <code>row</code> functions support the construction of
206matrix rows.</p>
207<h4>Prototypes</h4>
208<pre><code>
209 template&lt;class M&gt;
210 matrix_row&lt;M&gt; row (M &amp;data, std::size_t i);
211 template&lt;class M&gt;
212 const matrix_row&lt;const M&gt; row (const M &amp;data, std::size_t i);
213</code></pre>
214<h4>Definition</h4>
215<p>Defined in the header matrix_proxy.hpp.</p>
216<h4>Type requirements</h4>
217<ul>
218<li><code>M</code> is a model of <a href=
219"expression_concept.html#matrix_expression">Matrix Expression</a> .</li>
220</ul>
221<h4>Complexity</h4>
222<p>Linear depending from the size of the row.</p>
223<h4>Examples</h4>
224<pre>
225#include &lt;boost/numeric/ublas/matrix.hpp&gt;
226#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
227#include &lt;boost/numeric/ublas/io.hpp&gt;
228
229int main () {
230 using namespace boost::numeric::ublas;
231 matrix&lt;double&gt; m (3, 3);
232 for (unsigned i = 0; i &lt; m.size1 (); ++ i) {
233 for (unsigned j = 0; j &lt; m.size2 (); ++ j)
234 row (m, i) (j) = 3 * i + j;
235 std::cout &lt;&lt; row (m, i) &lt;&lt; std::endl;
236 }
237}
238</pre>
239<h2><a name="matrix_column"></a>Matrix Column</h2>
240<h4>Description</h4>
241<p>The templated class <code>matrix_column&lt;M&gt;</code> allows
242addressing a column of a matrix.</p>
243<h4>Example</h4>
244<pre>
245#include &lt;boost/numeric/ublas/matrix.hpp&gt;
246#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
247#include &lt;boost/numeric/ublas/io.hpp&gt;
248
249int main () {
250 using namespace boost::numeric::ublas;
251 matrix&lt;double&gt; m (3, 3);
252 for (unsigned j = 0; j &lt; m.size2 (); ++ j) {
253 matrix_column&lt;matrix&lt;double&gt; &gt; mc (m, j);
254 for (unsigned i = 0; i &lt; mc.size (); ++ i)
255 mc (i) = 3 * i + j;
256 std::cout &lt;&lt; mc &lt;&lt; std::endl;
257 }
258}
259</pre>
260<h4>Definition</h4>
261<p>Defined in the header matrix_proxy.hpp.</p>
262<h4>Template parameters</h4>
263<table border="1" summary="parameters">
264<tbody>
265<tr>
266<th>Parameter</th>
267<th>Description</th>
268<th>Default</th>
269</tr>
270<tr>
271<td><code>M</code></td>
272<td>The type of matrix referenced.</td>
273<td></td>
274</tr>
275</tbody>
276</table>
277<h4>Model of</h4>
278<p><a href="expression_concept.html#vector_expression">Vector Expression</a>
279.</p>
280<p>If the specified column falls outside that of the column index
281range of the matrix, then the <code>matrix_column</code> is not a
282well formed Vector Expression. That is, access to an element which
283is outside of the matrix is <i>undefined</i>.</p>
284<h4>Type requirements</h4>
285<p>None, except for those imposed by the requirements of <a href=
286"expression_concept.html#vector_expression">Vector Expression</a> .</p>
287<h4>Public base classes</h4>
288<p><code>vector_expression&lt;matrix_column&lt;M&gt;
289&gt;</code></p>
290<h4>Members</h4>
291<table border="1" summary="members">
292<tbody>
293<tr>
294<th>Member</th>
295<th>Description</th>
296</tr>
297<tr>
298<td><code>matrix_column (matrix_type &amp;data, size_type
299j)</code></td>
300<td>Constructs a sub vector.</td>
301</tr>
302<tr>
303<td><code>size_type size () const</code></td>
304<td>Returns the size of the sub vector.</td>
305</tr>
306<tr>
307<td><code>const_reference operator () (size_type i)
308const</code></td>
309<td>Returns the value of the <code>i</code>-th element.</td>
310</tr>
311<tr>
312<td><code>reference operator () (size_type i)</code></td>
313<td>Returns a reference of the <code>i</code>-th element.</td>
314</tr>
315<tr>
316<td><code>matrix_column &amp;operator = (const matrix_column
317&amp;mc)</code></td>
318<td>The assignment operator.</td>
319</tr>
320<tr>
321<td><code>matrix_column &amp;assign_temporary (matrix_column
322&amp;mc)</code></td>
323<td>Assigns a temporary. May change the matrix column
324<code>mc</code> .</td>
325</tr>
326<tr>
327<td><code>template&lt;class AE&gt;<br />
328matrix_column &amp;operator = (const vector_expression&lt;AE&gt;
329&amp;ae)</code></td>
330<td>The extended assignment operator.</td>
331</tr>
332<tr>
333<td><code>template&lt;class AE&gt;<br />
334matrix_column &amp;assign (const vector_expression&lt;AE&gt;
335&amp;ae)</code></td>
336<td>Assigns a vector expression to the sub vector. Left and right
337hand side of the assignment should be independent.</td>
338</tr>
339<tr>
340<td><code>template&lt;class AE&gt;<br />
341matrix_column &amp;operator += (const vector_expression&lt;AE&gt;
342&amp;ae)</code></td>
343<td>A computed assignment operator. Adds the vector expression to
344the sub vector.</td>
345</tr>
346<tr>
347<td><code>template&lt;class AE&gt;<br />
348matrix_column &amp;plus_assign (const vector_expression&lt;AE&gt;
349&amp;ae)</code></td>
350<td>Adds a vector expression to the sub vector. Left and right hand
351side of the assignment should be independent.</td>
352</tr>
353<tr>
354<td><code>template&lt;class AE&gt;<br />
355matrix_column &amp;operator -= (const vector_expression&lt;AE&gt;
356&amp;ae)</code></td>
357<td>A computed assignment operator. Subtracts the vector expression
358from the sub vector.</td>
359</tr>
360<tr>
361<td><code>template&lt;class AE&gt;<br />
362matrix_column &amp;minus_assign (const vector_expression&lt;AE&gt;
363&amp;ae)</code></td>
364<td>Subtracts a vector expression from the sub vector. Left and
365right hand side of the assignment should be independent.</td>
366</tr>
367<tr>
368<td><code>template&lt;class AT&gt;<br />
369matrix_column &amp;operator *= (const AT &amp;at)</code></td>
370<td>A computed assignment operator. Multiplies the sub vector with
371a scalar.</td>
372</tr>
373<tr>
374<td><code>template&lt;class AT&gt;<br />
375matrix_column &amp;operator /= (const AT &amp;at)</code></td>
376<td>A computed assignment operator. Divides the sub vector through
377a scalar.</td>
378</tr>
379<tr>
380<td><code>void swap (matrix_column &amp;mc)</code></td>
381<td>Swaps the contents of the sub vectors.</td>
382</tr>
383<tr>
384<td><code>const_iterator begin () const</code></td>
385<td>Returns a <code>const_iterator</code> pointing to the beginning
386of the <code>matrix_column</code>.</td>
387</tr>
388<tr>
389<td><code>const_iterator end () const</code></td>
390<td>Returns a <code>const_iterator</code> pointing to the end of
391the <code>matrix_column</code>.</td>
392</tr>
393<tr>
394<td><code>iterator begin ()</code></td>
395<td>Returns a <code>iterator</code> pointing to the beginning of
396the <code>matrix_column</code>.</td>
397</tr>
398<tr>
399<td><code>iterator end ()</code></td>
400<td>Returns a <code>iterator</code> pointing to the end of the
401<code>matrix_column</code>.</td>
402</tr>
403<tr>
404<td><code>const_reverse_iterator rbegin () const</code></td>
405<td>Returns a <code>const_reverse_iterator</code> pointing to the
406beginning of the reversed <code>matrix_column</code>.</td>
407</tr>
408<tr>
409<td><code>const_reverse_iterator rend () const</code></td>
410<td>Returns a <code>const_reverse_iterator</code> pointing to the
411end of the reversed <code>matrix_column</code>.</td>
412</tr>
413<tr>
414<td><code>reverse_iterator rbegin ()</code></td>
415<td>Returns a <code>reverse_iterator</code> pointing to the
416beginning of the reversed <code>matrix_column</code>.</td>
417</tr>
418<tr>
419<td><code>reverse_iterator rend ()</code></td>
420<td>Returns a <code>reverse_iterator</code> pointing to the end of
421the reversed <code>matrix_column</code>.</td>
422</tr>
423</tbody>
424</table>
425<h3>Projections</h3>
426<h4>Description</h4>
427<p>The free <code>column</code> functions support the construction
428of matrix columns.</p>
429<h4>Prototypes</h4>
430<pre><code>
431 template&lt;class M&gt;
432 matrix_column&lt;M&gt; column (M &amp;data, std::size_t j);
433 template&lt;class M&gt;
434 const matrix_column&lt;const M&gt; column (const M &amp;data, std::size_t j);
435</code></pre>
436<h4>Definition</h4>
437<p>Defined in the header matrix_proxy.hpp.</p>
438<h4>Type requirements</h4>
439<ul>
440<li><code>M</code> is a model of <a href=
441"expression_concept.html#matrix_expression">Matrix Expression</a> .</li>
442</ul>
443<h4>Complexity</h4>
444<p>Linear depending from the size of the column.</p>
445<h4>Examples</h4>
446<pre>
447#include &lt;boost/numeric/ublas/matrix.hpp&gt;
448#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
449#include &lt;boost/numeric/ublas/io.hpp&gt;
450
451int main () {
452 using namespace boost::numeric::ublas;
453 matrix&lt;double&gt; m (3, 3);
454 for (unsigned j = 0; j &lt; m.size2 (); ++ j) {
455 for (unsigned i = 0; i &lt; m.size1 (); ++ i)
456 column (m, j) (i) = 3 * i + j;
457 std::cout &lt;&lt; column (m, j) &lt;&lt; std::endl;
458 }
459}
460</pre>
461<h2><a name="vector_range"></a>Vector Range</h2>
462<h4>Description</h4>
463<p>The templated class <code>matrix_vector_range&lt;M&gt;</code>
464allows addressing a sub vector of a matrix.</p>
465<h4>Example</h4>
466<pre>
467#include &lt;boost/numeric/ublas/matrix.hpp&gt;
468#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
469#include &lt;boost/numeric/ublas/io.hpp&gt;
470
471int main () {
472 using namespace boost::numeric::ublas;
473 matrix&lt;double&gt; m (3, 3);
474 for (unsigned i = 0; i &lt; m.size1 (); ++ i)
475 for (unsigned j = 0; j &lt; m.size2 (); ++ j)
476 m (i, j) = 3 * i + j;
477
478 matrix_vector_range&lt;matrix&lt;double&gt; &gt; mvr (m, range (0, 3), range (0, 3));
479 std::cout &lt;&lt; mvr &lt;&lt; std::endl;
480}
481</pre>
482<h4>Definition</h4>
483<p>Defined in the header matrix_proxy.hpp.</p>
484<h4>Template parameters</h4>
485<table border="1" summary="parameters">
486<tbody>
487<tr>
488<th>Parameter</th>
489<th>Description</th>
490<th>Default</th>
491</tr>
492<tr>
493<td><code>M</code></td>
494<td>The type of matrix referenced.</td>
495<td></td>
496</tr>
497</tbody>
498</table>
499<h4>Model of</h4>
500<p><a href="expression_concept.html#vector_expression">Vector Expression</a>
501.</p>
502<p>If the specified ranges fall outside that of the index range of
503the matrix, then the <code>matrix_vector_range</code> is not a well
504formed Vector Expression. That is, access to an element which is
505outside of the matrix is <i>undefined</i>.</p>
506<h4>Type requirements</h4>
507<p>None, except for those imposed by the requirements of <a href=
508"expression_concept.html#vector_expression">Vector Expression</a> .</p>
509<h4>Public base classes</h4>
510<p><code>vector_expression&lt;matrix_vector_range&lt;M&gt;
511&gt;</code></p>
512<h4>Members</h4>
513<table border="1" summary="members">
514<tbody>
515<tr>
516<th>Member</th>
517<th>Description</th>
518</tr>
519<tr>
520<td><code>matrix_vector_range (matrix_type &amp;data,<br />
521const range &amp;r1, const range &amp;r2)</code></td>
522<td>Constructs a sub vector.</td>
523</tr>
524<tr>
525<td><code>size_type size () const</code></td>
526<td>Returns the size of the sub vector.</td>
527</tr>
528<tr>
529<td><code>const_reference operator () (size_type i)
530const</code></td>
531<td>Returns the value of the <code>i</code>-th element.</td>
532</tr>
533<tr>
534<td><code>reference operator () (size_type i)</code></td>
535<td>Returns a reference of the <code>i</code>-th element.</td>
536</tr>
537<tr>
538<td><code>matrix_vector_range &amp;operator = (const
539matrix_vector_range &amp;mvr)</code></td>
540<td>The assignment operator.</td>
541</tr>
542<tr>
543<td><code>matrix_vector_range &amp;assign_temporary
544(matrix_vector_range &amp;mvr)</code></td>
545<td>Assigns a temporary. May change the matrix vector range
546<code>mvr</code>.</td>
547</tr>
548<tr>
549<td><code>template&lt;class AE&gt;<br />
550matrix_vector_range &amp;operator = (const
551vector_expression&lt;AE&gt; &amp;ae)</code></td>
552<td>The extended assignment operator.</td>
553</tr>
554<tr>
555<td><code>template&lt;class AE&gt;<br />
556matrix_vector_range &amp;assign (const vector_expression&lt;AE&gt;
557&amp;ae)</code></td>
558<td>Assigns a vector expression to the sub vector. Left and right
559hand side of the assignment should be independent.</td>
560</tr>
561<tr>
562<td><code>template&lt;class AE&gt;<br />
563matrix_vector_range &amp;operator += (const
564vector_expression&lt;AE&gt; &amp;ae)</code></td>
565<td>A computed assignment operator. Adds the vector expression to
566the sub vector.</td>
567</tr>
568<tr>
569<td><code>template&lt;class AE&gt;<br />
570matrix_vector_range &amp;plus_assign (const
571vector_expression&lt;AE&gt; &amp;ae)</code></td>
572<td>Adds a vector expression to the sub vector. Left and right hand
573side of the assignment should be independent.</td>
574</tr>
575<tr>
576<td><code>template&lt;class AE&gt;<br />
577matrix_vector_range &amp;operator -= (const
578vector_expression&lt;AE&gt; &amp;ae)</code></td>
579<td>A computed assignment operator. Subtracts the vector expression
580from the sub vector.</td>
581</tr>
582<tr>
583<td><code>template&lt;class AE&gt;<br />
584matrix_vector_range &amp;minus_assign (const
585vector_expression&lt;AE&gt; &amp;ae)</code></td>
586<td>Subtracts a vector expression from the sub vector. Left and
587right hand side of the assignment should be independent.</td>
588</tr>
589<tr>
590<td><code>template&lt;class AT&gt;<br />
591matrix_vector_range &amp;operator *= (const AT &amp;at)</code></td>
592<td>A computed assignment operator. Multiplies the sub vector with
593a scalar.</td>
594</tr>
595<tr>
596<td><code>template&lt;class AT&gt;<br />
597matrix_vector_range &amp;operator /= (const AT &amp;at)</code></td>
598<td>A computed assignment operator. Divides the sub vector through
599a scalar.</td>
600</tr>
601<tr>
602<td><code>void swap (matrix_vector_range &amp;mvr)</code></td>
603<td>Swaps the contents of the sub vectors.</td>
604</tr>
605<tr>
606<td><code>const_iterator begin () const</code></td>
607<td>Returns a <code>const_iterator</code> pointing to the beginning
608of the <code>matrix_vector_range</code>.</td>
609</tr>
610<tr>
611<td><code>const_iterator end () const</code></td>
612<td>Returns a <code>const_iterator</code> pointing to the end of
613the <code>matrix_vector_range</code>.</td>
614</tr>
615<tr>
616<td><code>iterator begin ()</code></td>
617<td>Returns a <code>iterator</code> pointing to the beginning of
618the <code>matrix_vector_range</code>.</td>
619</tr>
620<tr>
621<td><code>iterator end ()</code></td>
622<td>Returns a <code>iterator</code> pointing to the end of the
623<code>matrix_vector_range</code>.</td>
624</tr>
625<tr>
626<td><code>const_reverse_iterator rbegin () const</code></td>
627<td>Returns a <code>const_reverse_iterator</code> pointing to the
628beginning of the <code>matrix_vector_range</code>.</td>
629</tr>
630<tr>
631<td><code>const_reverse_iterator rend () const</code></td>
632<td>Returns a <code>const_reverse_iterator</code> pointing to the
633end of the reversed <code>matrix_vector_range</code>.</td>
634</tr>
635<tr>
636<td><code>reverse_iterator rbegin ()</code></td>
637<td>Returns a <code>reverse_iterator</code> pointing to the
638beginning of the reversed <code>matrix_vector_range</code>.</td>
639</tr>
640<tr>
641<td><code>reverse_iterator rend ()</code></td>
642<td>Returns a <code>reverse_iterator</code> pointing to the end of
643the reversed <code>matrix_vector_range</code>.</td>
644</tr>
645</tbody>
646</table>
647<h2><a name="vector_slice"></a>Vector Slice</h2>
648<h4>Description</h4>
649<p>The templated class <code>matrix_vector_slice&lt;M&gt;</code>
650allows addressing a sliced sub vector of a matrix.</p>
651<h4>Example</h4>
652<pre>
653#include &lt;boost/numeric/ublas/matrix.hpp&gt;
654#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
655#include &lt;boost/numeric/ublas/io.hpp&gt;
656
657int main () {
658 using namespace boost::numeric::ublas;
659 matrix&lt;double&gt; m (3, 3);
660 for (unsigned i = 0; i &lt; m.size1 (); ++ i)
661 for (unsigned j = 0; j &lt; m.size2 (); ++ j)
662 m (i, j) = 3 * i + j;
663
664 matrix_vector_slice&lt;matrix&lt;double&gt; &gt; mvs (m, slice (0, 1, 3), slice (0, 1, 3));
665 std::cout &lt;&lt; mvs &lt;&lt; std::endl;
666}
667</pre>
668<h4>Definition</h4>
669<p>Defined in the header matrix_proxy.hpp.</p>
670<h4>Template parameters</h4>
671<table border="1" summary="parameters">
672<tbody>
673<tr>
674<th>Parameter</th>
675<th>Description</th>
676<th>Default</th>
677</tr>
678<tr>
679<td><code>M</code></td>
680<td>The type of matrix referenced.</td>
681<td></td>
682</tr>
683</tbody>
684</table>
685<h4>Model of</h4>
686<p><a href="expression_concept.html#vector_expression">Vector Expression</a>
687.</p>
688<p>If the specified slices fall outside that of the index range of
689the matrix, then the <code>matrix_vector_slice</code> is not a well
690formed Vector Expression. That is, access to an element which is
691outside of the matrix is <i>undefined</i>.</p>
692<h4>Type requirements</h4>
693<p>None, except for those imposed by the requirements of <a href=
694"expression_concept.html#vector_expression">Vector Expression</a> .</p>
695<h4>Public base classes</h4>
696<p><code>vector_expression&lt;matrix_vector_slice&lt;M&gt;
697&gt;</code></p>
698<h4>Members</h4>
699<table border="1" summary="members">
700<tbody>
701<tr>
702<th>Member</th>
703<th>Description</th>
704</tr>
705<tr>
706<td><code>matrix_vector_slice (matrix_type &amp;data,<br />
707const slice &amp;s1, const slice &amp;s2)</code></td>
708<td>Constructs a sub vector.</td>
709</tr>
710<tr>
711<td><code>size_type size () const</code></td>
712<td>Returns the size of the sub vector.</td>
713</tr>
714<tr>
715<td><code>const_reference operator () (size_type i)
716const</code></td>
717<td>Returns the value of the <code>i</code>-th element.</td>
718</tr>
719<tr>
720<td><code>reference operator () (size_type i)</code></td>
721<td>Returns a reference of the <code>i</code>-th element.</td>
722</tr>
723<tr>
724<td><code>matrix_vector_slice &amp;operator = (const
725matrix_vector_slice &amp;mvs)</code></td>
726<td>The assignment operator.</td>
727</tr>
728<tr>
729<td><code>matrix_vector_slice &amp;assign_temporary
730(matrix_vector_slice &amp;mvs)</code></td>
731<td>Assigns a temporary. May change the matrix vector slice
732<code>vs</code>.</td>
733</tr>
734<tr>
735<td><code>template&lt;class AE&gt;<br />
736matrix_vector_slice &amp;operator = (const
737vector_expression&lt;AE&gt; &amp;ae)</code></td>
738<td>The extended assignment operator.</td>
739</tr>
740<tr>
741<td><code>template&lt;class AE&gt;<br />
742matrix_vector_slice &amp;assign (const vector_expression&lt;AE&gt;
743&amp;ae)</code></td>
744<td>Assigns a vector expression to the sub vector. Left and right
745hand side of the assignment should be independent.</td>
746</tr>
747<tr>
748<td><code>template&lt;class AE&gt;<br />
749matrix_vector_slice &amp;operator += (const
750vector_expression&lt;AE&gt; &amp;ae)</code></td>
751<td>A computed assignment operator. Adds the vector expression to
752the sub vector.</td>
753</tr>
754<tr>
755<td><code>template&lt;class AE&gt;<br />
756matrix_vector_slice &amp;plus_assign (const
757vector_expression&lt;AE&gt; &amp;ae)</code></td>
758<td>Adds a vector expression to the sub vector. Left and right hand
759side of the assignment should be independent.</td>
760</tr>
761<tr>
762<td><code>template&lt;class AE&gt;<br />
763matrix_vector_slice &amp;operator -= (const
764vector_expression&lt;AE&gt; &amp;ae)</code></td>
765<td>A computed assignment operator. Subtracts the vector expression
766from the sub vector.</td>
767</tr>
768<tr>
769<td><code>template&lt;class AE&gt;<br />
770matrix_vector_slice &amp;minus_assign (const
771vector_expression&lt;AE&gt; &amp;ae)</code></td>
772<td>Subtracts a vector expression from the sub vector. Left and
773right hand side of the assignment should be independent.</td>
774</tr>
775<tr>
776<td><code>template&lt;class AT&gt;<br />
777matrix_vector_slice &amp;operator *= (const AT &amp;at)</code></td>
778<td>A computed assignment operator. Multiplies the sub vector with
779a scalar.</td>
780</tr>
781<tr>
782<td><code>template&lt;class AT&gt;<br />
783matrix_vector_slice &amp;operator /= (const AT &amp;at)</code></td>
784<td>A computed assignment operator. Divides the sub vector through
785a scalar.</td>
786</tr>
787<tr>
788<td><code>void swap (matrix_vector_slice &amp;mvs)</code></td>
789<td>Swaps the contents of the sub vectors.</td>
790</tr>
791<tr>
792<td><code>const_iterator begin () const</code></td>
793<td>Returns a <code>const_iterator</code> pointing to the beginning
794of the <code>matrix_vector_slice</code>.</td>
795</tr>
796<tr>
797<td><code>const_iterator end () const</code></td>
798<td>Returns a <code>const_iterator</code> pointing to the end of
799the <code>matrix_vector_slice</code>.</td>
800</tr>
801<tr>
802<td><code>iterator begin ()</code></td>
803<td>Returns a <code>iterator</code> pointing to the beginning of
804the <code>matrix_vector_slice</code>.</td>
805</tr>
806<tr>
807<td><code>iterator end ()</code></td>
808<td>Returns a <code>iterator</code> pointing to the end of the
809<code>matrix_vector_slice</code>.</td>
810</tr>
811<tr>
812<td><code>const_reverse_iterator rbegin () const</code></td>
813<td>Returns a <code>const_reverse_iterator</code> pointing to the
814beginning of the reversed <code>matrix_vector_slice</code>.</td>
815</tr>
816<tr>
817<td><code>const_reverse_iterator rend () const</code></td>
818<td>Returns a <code>const_reverse_iterator</code> pointing to the
819end of the reversed <code>matrix_vector_slice</code>.</td>
820</tr>
821<tr>
822<td><code>reverse_iterator rbegin ()</code></td>
823<td>Returns a <code>reverse_iterator</code> pointing to the
824beginning of the reversed <code>matrix_vector_slice</code>.</td>
825</tr>
826<tr>
827<td><code>reverse_iterator rend ()</code></td>
828<td>Returns a <code>reverse_iterator</code> pointing to the end of
829the reversed <code>matrix_vector_slice</code>.</td>
830</tr>
831</tbody>
832</table>
833<h2><a name="matrix_range"></a>Matrix Range</h2>
834<h4>Description</h4>
835<p>The templated class <code>matrix_range&lt;M&gt;</code> allows
836addressing a sub matrix of a matrix.</p>
837<h4>Example</h4>
838<pre>
839#include &lt;boost/numeric/ublas/matrix.hpp&gt;
840#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
841#include &lt;boost/numeric/ublas/io.hpp&gt;
842
843int main () {
844 using namespace boost::numeric::ublas;
845 matrix&lt;double&gt; m (3, 3);
846 matrix_range&lt;matrix&lt;double&gt; &gt; mr (m, range (0, 3), range (0, 3));
847 for (unsigned i = 0; i &lt; mr.size1 (); ++ i)
848 for (unsigned j = 0; j &lt; mr.size2 (); ++ j)
849 mr (i, j) = 3 * i + j;
850 std::cout &lt;&lt; mr &lt;&lt; std::endl;
851}
852</pre>
853<h4>Definition</h4>
854<p>Defined in the header matrix_proxy.hpp.</p>
855<h4>Template parameters</h4>
856<table border="1" summary="parameters">
857<tbody>
858<tr>
859<th>Parameter</th>
860<th>Description</th>
861<th>Default</th>
862</tr>
863<tr>
864<td><code>M</code></td>
865<td>The type of matrix referenced.</td>
866<td></td>
867</tr>
868</tbody>
869</table>
870<h4>Model of</h4>
871<p><a href="expression_concept.html#matrix_expression">Matrix Expression</a>
872.</p>
873<p>If the specified ranges fall outside that of the index range of
874the matrix, then the <code>matrix_range</code> is not a well formed
875Matrix Expression. That is, access to an element which is outside
876of the matrix is <i>undefined</i>.</p>
877<h4>Type requirements</h4>
878<p>None, except for those imposed by the requirements of <a href=
879"expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
880<h4>Public base classes</h4>
881<p><code>matrix_expression&lt;matrix_range&lt;M&gt; &gt;</code></p>
882<h4>Members</h4>
883<table border="1" summary="members">
884<tbody>
885<tr>
886<th>Member</th>
887<th>Description</th>
888</tr>
889<tr>
890<td><code>matrix_range (matrix_type &amp;data,<br />
891const range &amp;r1, const range &amp;r2)</code></td>
892<td>Constructs a sub matrix.</td>
893</tr>
894<tr>
895<td><code>size_type start1 () const</code></td>
896<td>Returns the index of the first row.</td>
897</tr>
898<tr>
899<td><code>size_type size1 () const</code></td>
900<td>Returns the number of rows.</td>
901</tr>
902<tr>
903<td><code>size_type start2 () const</code></td>
904<td>Returns the index of the first column.</td>
905</tr>
906<tr>
907<td><code>size_type size2 () const</code></td>
908<td>Returns the number of columns.</td>
909</tr>
910<tr>
911<td><code>const_reference operator () (size_type i, size_type j)
912const</code></td>
913<td>Returns the value of the <code>j</code>-th element in the
914<code>i</code>-th row.</td>
915</tr>
916<tr>
917<td><code>reference operator () (size_type i, size_type
918j)</code></td>
919<td>Returns a reference of the <code>j</code>-th element in the
920<code>i</code>-th row.</td>
921</tr>
922<tr>
923<td><code>matrix_range &amp;operator = (const matrix_range
924&amp;mr)</code></td>
925<td>The assignment operator.</td>
926</tr>
927<tr>
928<td><code>matrix_range &amp;assign_temporary (matrix_range
929&amp;mr)</code></td>
930<td>Assigns a temporary. May change the matrix range
931<code>mr</code> .</td>
932</tr>
933<tr>
934<td><code>template&lt;class AE&gt;<br />
935matrix_range &amp;operator = (const matrix_expression&lt;AE&gt;
936&amp;ae)</code></td>
937<td>The extended assignment operator.</td>
938</tr>
939<tr>
940<td><code>template&lt;class AE&gt;<br />
941matrix_range &amp;assign (const matrix_expression&lt;AE&gt;
942&amp;ae)</code></td>
943<td>Assigns a matrix expression to the sub matrix. Left and right
944hand side of the assignment should be independent.</td>
945</tr>
946<tr>
947<td><code>template&lt;class AE&gt;<br />
948matrix_range &amp;operator += (const matrix_expression&lt;AE&gt;
949&amp;ae)</code></td>
950<td>A computed assignment operator. Adds the matrix expression to
951the sub matrix.</td>
952</tr>
953<tr>
954<td><code>template&lt;class AE&gt;<br />
955matrix_range &amp;plus_assign (const matrix_expression&lt;AE&gt;
956&amp;ae)</code></td>
957<td>Adds a matrix expression to the sub matrix. Left and right hand
958side of the assignment should be independent.</td>
959</tr>
960<tr>
961<td><code>template&lt;class AE&gt;<br />
962matrix_range &amp;operator -= (const matrix_expression&lt;AE&gt;
963&amp;ae)</code></td>
964<td>A computed assignment operator. Subtracts the matrix expression
965from the sub matrix.</td>
966</tr>
967<tr>
968<td><code>template&lt;class AE&gt;<br />
969matrix_range &amp;minus_assign (const matrix_expression&lt;AE&gt;
970&amp;ae)</code></td>
971<td>Subtracts a matrix expression from the sub matrix. Left and
972right hand side of the assignment should be independent.</td>
973</tr>
974<tr>
975<td><code>template&lt;class AT&gt;<br />
976matrix_range &amp;operator *= (const AT &amp;at)</code></td>
977<td>A computed assignment operator. Multiplies the sub matrix with
978a scalar.</td>
979</tr>
980<tr>
981<td><code>template&lt;class AT&gt;<br />
982matrix_range &amp;operator /= (const AT &amp;at)</code></td>
983<td>A computed assignment operator. Divides the sub matrix through
984a scalar.</td>
985</tr>
986<tr>
987<td><code>void swap (matrix_range &amp;mr)</code></td>
988<td>Swaps the contents of the sub matrices.</td>
989</tr>
990<tr>
991<td><code>const_iterator1 begin1 () const</code></td>
992<td>Returns a <code>const_iterator1</code> pointing to the
993beginning of the <code>matrix_range</code>.</td>
994</tr>
995<tr>
996<td><code>const_iterator1 end1 () const</code></td>
997<td>Returns a <code>const_iterator1</code> pointing to the end of
998the <code>matrix_range</code>.</td>
999</tr>
1000<tr>
1001<td><code>iterator1 begin1 ()</code></td>
1002<td>Returns a <code>iterator1</code> pointing to the beginning of
1003the <code>matrix_range</code>.</td>
1004</tr>
1005<tr>
1006<td><code>iterator1 end1 ()</code></td>
1007<td>Returns a <code>iterator1</code> pointing to the end of the
1008<code>matrix_range</code>.</td>
1009</tr>
1010<tr>
1011<td><code>const_iterator2 begin2 () const</code></td>
1012<td>Returns a <code>const_iterator2</code> pointing to the
1013beginning of the <code>matrix_range</code>.</td>
1014</tr>
1015<tr>
1016<td><code>const_iterator2 end2 () const</code></td>
1017<td>Returns a <code>const_iterator2</code> pointing to the end of
1018the <code>matrix_range</code>.</td>
1019</tr>
1020<tr>
1021<td><code>iterator2 begin2 ()</code></td>
1022<td>Returns a <code>iterator2</code> pointing to the beginning of
1023the <code>matrix_range</code>.</td>
1024</tr>
1025<tr>
1026<td><code>iterator2 end2 ()</code></td>
1027<td>Returns a <code>iterator2</code> pointing to the end of the
1028<code>matrix_range</code>.</td>
1029</tr>
1030<tr>
1031<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
1032<td>Returns a <code>const_reverse_iterator1</code> pointing to the
1033beginning of the reversed <code>matrix_range</code>.</td>
1034</tr>
1035<tr>
1036<td><code>const_reverse_iterator1 rend1 () const</code></td>
1037<td>Returns a <code>const_reverse_iterator1</code> pointing to the
1038end of the reversed <code>matrix_range</code>.</td>
1039</tr>
1040<tr>
1041<td><code>reverse_iterator1 rbegin1 ()</code></td>
1042<td>Returns a <code>reverse_iterator1</code> pointing to the
1043beginning of the reversed <code>matrix_range</code>.</td>
1044</tr>
1045<tr>
1046<td><code>reverse_iterator1 rend1 ()</code></td>
1047<td>Returns a <code>reverse_iterator1</code> pointing to the end of
1048the reversed <code>matrix_range</code>.</td>
1049</tr>
1050<tr>
1051<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
1052<td>Returns a <code>const_reverse_iterator2</code> pointing to the
1053beginning of the reversed <code>matrix_range</code>.</td>
1054</tr>
1055<tr>
1056<td><code>const_reverse_iterator2 rend2 () const</code></td>
1057<td>Returns a <code>const_reverse_iterator2</code> pointing to the
1058end of the reversed <code>matrix_range</code>.</td>
1059</tr>
1060<tr>
1061<td><code>reverse_iterator2 rbegin2 ()</code></td>
1062<td>Returns a <code>reverse_iterator2</code> pointing to the
1063beginning of the reversed <code>matrix_range</code>.</td>
1064</tr>
1065<tr>
1066<td><code>reverse_iterator2 rend2 ()</code></td>
1067<td>Returns a <code>reverse_iterator2</code> pointing to the end of
1068reversed the <code>matrix_range</code>.</td>
1069</tr>
1070</tbody>
1071</table>
1072<h3>Simple Projections</h3>
1073<h4>Description</h4>
1074<p>The free <code>subrange</code> functions support the construction
1075of matrix ranges.</p>
1076<h4>Prototypes</h4>
1077<pre><code>
1078 template&lt;class M&gt;
1079 matrix_range&lt;M&gt; subrange (M &amp;data,
1080 M::size_type start1, M::size_type stop1, M::size_type start2, M::size_type, stop2);
1081 template&lt;class M&gt;
1082 const matrix_range&lt;const M&gt; subrange (const M &amp;data,
1083 M::size_type start1, M::size_type stop1, M::size_type start2, M::size_type, stop2);
1084</code></pre>
1085<h3>Generic Projections</h3>
1086<h4>Description</h4>
1087<p>The free <code>project</code> functions support the construction
1088of matrix ranges. Existing <code>matrix_range</code>'s can be composed with further ranges. The resulting ranges are computed using this existing ranges' <code>compose</code> function.</p>
1089<h4>Prototypes</h4>
1090<pre><code>
1091 template&lt;class M&gt;
1092 matrix_range&lt;M&gt; project (M &amp;data, const range &amp;r1, const range &amp;r2);
1093 template&lt;class M&gt;
1094 const matrix_range&lt;const M&gt; project (const M &amp;data, const range &amp;r1, const range &amp;r2);
1095 template&lt;class M&gt;
1096 matrix_range&lt;M&gt; project (matrix_range&lt;M&gt; &amp;data, const range &amp;r1, const range &amp;r2);
1097 template&lt;class M&gt;
1098 const matrix_range&lt;M&gt; project (const matrix_range&lt;M&gt; &amp;data, const range &amp;r1, const range &amp;r2);
1099</code></pre>
1100<h4>Definition</h4>
1101<p>Defined in the header matrix_proxy.hpp.</p>
1102<h4>Type requirements</h4>
1103<ul>
1104<li><code>M</code> is a model of <a href=
1105"expression_concept.html#matrix_expression">Matrix Expression</a> .</li>
1106</ul>
1107<h4>Complexity</h4>
1108<p>Quadratic depending from the size of the ranges.</p>
1109<h4>Examples</h4>
1110<pre>
1111#include &lt;boost/numeric/ublas/matrix.hpp&gt;
1112#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
1113#include &lt;boost/numeric/ublas/io.hpp&gt;
1114
1115int main () {
1116 using namespace boost::numeric::ublas;
1117 matrix&lt;double&gt; m (3, 3);
1118 for (unsigned i = 0; i &lt; m.size1 (); ++ i)
1119 for (unsigned j = 0; j &lt; m.size2 (); ++ j)
1120 project (m, range (0, 3), range (0, 3)) (i, j) = 3 * i + j;
1121 std::cout &lt;&lt; project (m, range (0, 3), range (0, 3)) &lt;&lt; std::endl;
1122}
1123</pre>
1124<h2><a name="matrix_slice"></a>Matrix Slice</h2>
1125<h4>Description</h4>
1126<p>The templated class <code>matrix_slice&lt;M&gt;</code> allows
1127addressing a sliced sub matrix of a matrix.</p>
1128<h4>Example</h4>
1129<pre>
1130#include &lt;boost/numeric/ublas/matrix.hpp&gt;
1131#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
1132#include &lt;boost/numeric/ublas/io.hpp&gt;
1133
1134int main () {
1135 using namespace boost::numeric::ublas;
1136 matrix&lt;double&gt; m (3, 3);
1137 matrix_slice&lt;matrix&lt;double&gt; &gt; ms (m, slice (0, 1, 3), slice (0, 1, 3));
1138 for (unsigned i = 0; i &lt; ms.size1 (); ++ i)
1139 for (unsigned j = 0; j &lt; ms.size2 (); ++ j)
1140 ms (i, j) = 3 * i + j;
1141 std::cout &lt;&lt; ms &lt;&lt; std::endl;
1142}
1143</pre>
1144<h4>Definition</h4>
1145<p>Defined in the header matrix_proxy.hpp.</p>
1146<h4>Template parameters</h4>
1147<table border="1" summary="parameters">
1148<tbody>
1149<tr>
1150<th>Parameter</th>
1151<th>Description</th>
1152<th>Default</th>
1153</tr>
1154<tr>
1155<td><code>M</code></td>
1156<td>The type of matrix referenced.</td>
1157<td></td>
1158</tr>
1159</tbody>
1160</table>
1161<h4>Model of</h4>
1162<p><a href="expression_concept.html#matrix_expression">Matrix Expression</a>
1163.</p>
1164<p>If the specified slices fall outside that of the index range of
1165the matrix, then the <code>matrix_slice</code> is not a well formed
1166Matrix Expression. That is, access to an element which is outside
1167of the matrix is <i>undefined</i>.</p>
1168<h4>Type requirements</h4>
1169<p>None, except for those imposed by the requirements of <a href=
1170"expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
1171<h4>Public base classes</h4>
1172<p><code>matrix_expression&lt;matrix_slice&lt;M&gt; &gt;</code></p>
1173<h4>Members</h4>
1174<table border="1" summary="members">
1175<tbody>
1176<tr>
1177<th>Member</th>
1178<th>Description</th>
1179</tr>
1180<tr>
1181<td><code>matrix_slice (matrix_type &amp;data,<br />
1182const slice &amp;s1, const slice &amp;s2)</code></td>
1183<td>Constructs a sub matrix.</td>
1184</tr>
1185<tr>
1186<td><code>size_type size1 () const</code></td>
1187<td>Returns the number of rows.</td>
1188</tr>
1189<tr>
1190<td><code>size_type size2 () const</code></td>
1191<td>Returns the number of columns.</td>
1192</tr>
1193<tr>
1194<td><code>const_reference operator () (size_type i, size_type j)
1195const</code></td>
1196<td>Returns the value of the <code>j</code>-th element in the
1197<code>i</code>-th row.</td>
1198</tr>
1199<tr>
1200<td><code>reference operator () (size_type i, size_type
1201j)</code></td>
1202<td>Returns a reference of the <code>j</code>-th element in the
1203<code>i</code>-th row.</td>
1204</tr>
1205<tr>
1206<td><code>matrix_slice &amp;operator = (const matrix_slice
1207&amp;ms)</code></td>
1208<td>The assignment operator.</td>
1209</tr>
1210<tr>
1211<td><code>matrix_slice &amp;assign_temporary (matrix_slice
1212&amp;ms)</code></td>
1213<td>Assigns a temporary. May change the matrix slice
1214<code>ms</code> .</td>
1215</tr>
1216<tr>
1217<td><code>template&lt;class AE&gt;<br />
1218matrix_slice &amp;operator = (const matrix_expression&lt;AE&gt;
1219&amp;ae)</code></td>
1220<td>The extended assignment operator.</td>
1221</tr>
1222<tr>
1223<td><code>template&lt;class AE&gt;<br />
1224matrix_slice &amp;assign (const matrix_expression&lt;AE&gt;
1225&amp;ae)</code></td>
1226<td>Assigns a matrix expression to the sub matrix. Left and right
1227hand side of the assignment should be independent.</td>
1228</tr>
1229<tr>
1230<td><code>template&lt;class AE&gt;<br />
1231matrix_slice &amp;operator += (const matrix_expression&lt;AE&gt;
1232&amp;ae)</code></td>
1233<td>A computed assignment operator. Adds the matrix expression to
1234the sub matrix.</td>
1235</tr>
1236<tr>
1237<td><code>template&lt;class AE&gt;<br />
1238matrix_slice &amp;plus_assign (const matrix_expression&lt;AE&gt;
1239&amp;ae)</code></td>
1240<td>Adds a matrix expression to the sub matrix. Left and right hand
1241side of the assignment should be independent.</td>
1242</tr>
1243<tr>
1244<td><code>template&lt;class AE&gt;<br />
1245matrix_slice &amp;operator -= (const matrix_expression&lt;AE&gt;
1246&amp;ae)</code></td>
1247<td>A computed assignment operator. Subtracts the matrix expression
1248from the sub matrix.</td>
1249</tr>
1250<tr>
1251<td><code>template&lt;class AE&gt;<br />
1252matrix_slice &amp;minus_assign (const matrix_expression&lt;AE&gt;
1253&amp;ae)</code></td>
1254<td>Subtracts a matrix expression from the sub matrix. Left and
1255right hand side of the assignment should be independent.</td>
1256</tr>
1257<tr>
1258<td><code>template&lt;class AT&gt;<br />
1259matrix_slice &amp;operator *= (const AT &amp;at)</code></td>
1260<td>A computed assignment operator. Multiplies the sub matrix with
1261a scalar.</td>
1262</tr>
1263<tr>
1264<td><code>template&lt;class AT&gt;<br />
1265matrix_slice &amp;operator /= (const AT &amp;at)</code></td>
1266<td>A computed assignment operator. Multiplies the sub matrix
1267through a scalar.</td>
1268</tr>
1269<tr>
1270<td><code>void swap (matrix_slice &amp;ms)</code></td>
1271<td>Swaps the contents of the sub matrices.</td>
1272</tr>
1273<tr>
1274<td><code>const_iterator1 begin1 () const</code></td>
1275<td>Returns a <code>const_iterator1</code> pointing to the
1276beginning of the <code>matrix_slice</code>.</td>
1277</tr>
1278<tr>
1279<td><code>const_iterator1 end1 () const</code></td>
1280<td>Returns a <code>const_iterator1</code> pointing to the end of
1281the <code>matrix_slice</code>.</td>
1282</tr>
1283<tr>
1284<td><code>iterator1 begin1 ()</code></td>
1285<td>Returns a <code>iterator1</code> pointing to the beginning of
1286the <code>matrix_slice</code>.</td>
1287</tr>
1288<tr>
1289<td><code>iterator1 end1 ()</code></td>
1290<td>Returns a <code>iterator1</code> pointing to the end of the
1291<code>matrix_slice</code>.</td>
1292</tr>
1293<tr>
1294<td><code>const_iterator2 begin2 () const</code></td>
1295<td>Returns a <code>const_iterator2</code> pointing to the
1296beginning of the <code>matrix_slice</code>.</td>
1297</tr>
1298<tr>
1299<td><code>const_iterator2 end2 () const</code></td>
1300<td>Returns a <code>const_iterator2</code> pointing to the end of
1301the <code>matrix_slice</code>.</td>
1302</tr>
1303<tr>
1304<td><code>iterator2 begin2 ()</code></td>
1305<td>Returns a <code>iterator2</code> pointing to the beginning of
1306the <code>matrix_slice</code>.</td>
1307</tr>
1308<tr>
1309<td><code>iterator2 end2 ()</code></td>
1310<td>Returns a <code>iterator2</code> pointing to the end of the
1311<code>matrix_slice</code>.</td>
1312</tr>
1313<tr>
1314<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
1315<td>Returns a <code>const_reverse_iterator1</code> pointing to the
1316beginning of the reversed <code>matrix_slice</code>.</td>
1317</tr>
1318<tr>
1319<td><code>const_reverse_iterator1 rend1 () const</code></td>
1320<td>Returns a <code>const_reverse_iterator1</code> pointing to the
1321end of the reversed <code>matrix_slice</code>.</td>
1322</tr>
1323<tr>
1324<td><code>reverse_iterator1 rbegin1 ()</code></td>
1325<td>Returns a <code>reverse_iterator1</code> pointing to the
1326beginning of the reversed <code>matrix_slice</code>.</td>
1327</tr>
1328<tr>
1329<td><code>reverse_iterator1 rend1 ()</code></td>
1330<td>Returns a <code>reverse_iterator1</code> pointing to the end of
1331the reversed <code>matrix_slice</code>.</td>
1332</tr>
1333<tr>
1334<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
1335<td>Returns a <code>const_reverse_iterator2</code> pointing to the
1336beginning of the reversed <code>matrix_slice</code>.</td>
1337</tr>
1338<tr>
1339<td><code>const_reverse_iterator2 rend2 () const</code></td>
1340<td>Returns a <code>const_reverse_iterator2</code> pointing to the
1341end of the reversed <code>matrix_slice</code>.</td>
1342</tr>
1343<tr>
1344<td><code>reverse_iterator2 rbegin2 ()</code></td>
1345<td>Returns a <code>reverse_iterator2</code> pointing to the
1346beginning of the reversed <code>matrix_slice</code>.</td>
1347</tr>
1348<tr>
1349<td><code>reverse_iterator2 rend2 ()</code></td>
1350<td>Returns a <code>reverse_iterator2</code> pointing to the end of
1351the reversed <code>matrix_slice</code>.</td>
1352</tr>
1353</tbody>
1354</table>
1355<h3>Simple Projections</h3>
1356<h4>Description</h4>
1357<p>The free <code>subslice</code> functions support the construction
1358of matrix slices.</p>
1359<h4>Prototypes</h4>
1360<pre><code>
1361 template&lt;class M&gt;
1362 matrix_slice&lt;M&gt; subslice (M &amp;data,
1363 M::size_type start1, M::difference_type stride1, M::size_type size1,
1364 M::size_type start2, M::difference_type stride2, M::size_type size2);
1365 template&lt;class M&gt;
1366 const matrix_slice&lt;const M&gt; subslice (const M &amp;data,
1367 M::size_type start1, M::difference_type stride1, M::size_type size1,
1368 M::size_type start2, M::difference_type stride2, M::size_type size2);
1369</code></pre>
1370<h3>Generic Projections</h3>
1371<h4>Description</h4>
1372<p>The free <code>project</code> functions support the construction
1373of matrix slices. Existing <code>matrix_slice</code>'s can be composed with further ranges or slices. The resulting slices are computed using this existing slices' <code>compose</code> function.</p>
1374<h4>Prototypes</h4>
1375<pre><code>
1376 template&lt;class M&gt;
1377 matrix_slice&lt;M&gt; project (M &amp;data, const slice &amp;s1, const slice &amp;s2);
1378 template&lt;class M&gt;
1379 const matrix_slice&lt;const M&gt; project (const M &amp;data, const slice &amp;s1, const slice &amp;s2);
1380 template&lt;class M&gt;
1381 matrix_slice&lt;M&gt; project (matrix_slice&lt;M&gt; &amp;data, const range &amp;r1, const range &amp;r2);
1382 template&lt;class M&gt;
1383 const matrix_slice&lt;M&gt; project (const matrix_slice&lt;M&gt; &amp;data, const range &amp;r1, const range &amp;r2);
1384 template&lt;class M&gt;
1385 matrix_slice&lt;M&gt; project (matrix_slice&lt;M&gt; &amp;data, const slice &amp;s1, const slice &amp;s2);
1386 template&lt;class M&gt;
1387 const matrix_slice&lt;M&gt; project (const matrix_slice&lt;M&gt; &amp;data, const slice &amp;s1, const slice &amp;s2);
1388</code></pre>
1389<h4>Definition</h4>
1390<p>Defined in the header matrix_proxy.hpp.</p>
1391<h4>Type requirements</h4>
1392<ul>
1393<li><code>M</code> is a model of <a href=
1394"expression_concept.html#matrix_expression">Matrix Expression</a> .</li>
1395</ul>
1396<h4>Complexity</h4>
1397<p>Quadratic depending from the size of the slices.</p>
1398<h4>Examples</h4>
1399<pre>
1400#include &lt;boost/numeric/ublas/matrix.hpp&gt;
1401#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
1402#include &lt;boost/numeric/ublas/io.hpp&gt;
1403
1404int main () {
1405 using namespace boost::numeric::ublas;
1406 matrix&lt;double&gt; m (3, 3);
1407 for (unsigned i = 0; i &lt; m.size1 (); ++ i)
1408 for (unsigned j = 0; j &lt; m.size2 (); ++ j)
1409 project (m, slice (0, 1, 3), slice (0, 1, 3)) (i, j) = 3 * i + j;
1410 std::cout &lt;&lt; project (m, slice (0, 1, 3), slice (0, 1, 3)) &lt;&lt; std::endl;
1411}
1412</pre>
1413<hr />
1414<p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
1415 Use, modification and distribution are subject to the
1416 Boost Software License, Version 1.0.
1417 (See accompanying file LICENSE_1_0.txt
1418 or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
1419 http://www.boost.org/LICENSE_1_0.txt
1420 </a>).
1421</p>
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