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16<h1><img src="../../../../boost.png" align="middle" />Container Concepts</h1>
17<div class="toc" id="toc"></div>
18<h2><a name="vector"></a>Vector</h2>
19<h4>Description</h4>
20<p>A Vector describes common aspects of dense, packed and sparse
21vectors.</p>
22<h4>Refinement of</h4>
23<p><a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>,
24<a href="expression_concept.html#vector_expression">Vector Expression</a>
25<a href="#vector_expression_note">[1]</a>.</p>
26<h4>Associated types</h4>
27<p>In addition to the types defined by <a href="expression_concept.html#vector_expression">Vector Expression</a></p>
28<table border="1" summary="types">
29<tbody>
30<tr>
31<td>Public base</td>
32<td>vector_container&lt;V&gt;</td>
33<td>V must be derived from this public base type.</td>
34</tr>
35<tr>
36<td>Storage array</td>
37<td>V::array_type</td>
38<td>
39Dense Vector ONLY. The type of underlying storage array used to store the elements. The array_type must model the
40<a href="storage_concept.html"><b>Storage</b></a> concept.</td>
41</tr>
42</tbody>
43</table>
44<h4>Notation</h4>
45<table border="0" summary="notation">
46<tbody>
47<tr>
48<td><code>V</code></td>
49<td>A type that is a model of Vector</td>
50</tr>
51<tr>
52<td><code>v</code></td>
53<td>Objects of type <code>V</code></td>
54</tr>
55<tr>
56<td><code>n, i</code></td>
57<td>Objects of a type convertible to <code>size_type</code></td>
58</tr>
59<tr>
60<td><code>t</code></td>
61<td>Object of a type convertible to <code>value_type</code></td>
62</tr>
63<tr>
64<td><code>p</code></td>
65<td>Object of a type convertible to <code>bool</code></td>
66</tr>
67</tbody>
68</table>
69<h4>Definitions</h4>
70<h4>Valid expressions</h4>
71<p>In addition to the expressions defined in <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>,
72<a href="expression_concept.html#vector_expression">Vector Expression</a> the following expressions must be valid.</p>
73<table border="1" summary="expressions">
74<tbody>
75<tr>
76<th>Name</th>
77<th>Expression</th>
78<th>Type requirements</th>
79<th>Return type</th>
80</tr>
81<tr>
82<td>Sizing constructor</td>
83<td><code>V v (n)</code></td>
84<td>&nbsp;</td>
85<td><code>V</code></td>
86</tr>
87<tr>
88<td>Insert</td>
89<td><code>v.insert_element (i, t)</code></td>
90<td><code>v</code> is mutable.</td>
91<td><code>void</code></td>
92</tr>
93<tr>
94<td>Erase</td>
95<td><code>v.erase_element (i)</code></td>
96<td><code>v</code> is mutable.</td>
97<td><code>void</code></td>
98</tr>
99<tr>
100<td>Clear</td>
101<td><code>v.clear ()</code></td>
102<td><code>v</code> is mutable.</td>
103<td><code>void</code></td>
104</tr>
105<tr>
106<td>Resize</td>
107<td><code>v.resize (n)</code><br />
108<code>v.resize (n, p)</code></td>
109<td><code>v</code> is mutable.</td>
110<td><code>void</code></td>
111</tr>
112<tr>
113<td>Storage</td>
114<td><code>v.data()</code></td>
115<td><code>v</code> is mutable and Dense.</td>
116<td><code>array_type&amp;</code> if <code>v</code> is mutable, <code>const array_type&amp;</code> otherwise</td>
117</tr>
118</tbody>
119</table>
120<h4>Expression semantics</h4>
121<p>Semantics of an expression is defined only where it differs
122from, or is not defined in <a href=
123"expression_concept.html#vector_expression">Vector Expression</a> .</p>
124<table border="1" summary="semantics">
125<tr>
126<th>Name</th>
127<th>Expression</th>
128<th>Precondition</th>
129<th>Semantics</th>
130<th>Postcondition</th>
131</tr>
132<tr>
133<td>Sizing constructor</td>
134<td><code>V v (n)</code></td>
135<td><code>n &gt;= 0</code></td>
136<td>Allocates a vector of<code>n</code> elements.</td>
137<td><code>v.size () == n</code>.</td>
138</tr>
139<tr>
140<td>Element access <a href="#element_access_note">[2]</a></td>
141<td><code>v[n]</code></td>
142<td><code>0&lt;n&gt;v.size()</code></td>
143<td>returns the n-th element in v</td>
144<td>&nbsp;</td>
145</tr>
146<tr>
147<td>Insert</td>
148<td><code>v.insert_element (i, t)</code></td>
149<td><code>0 &lt;= i &lt; v.size ()</code>.</td>
150<td>Inserts an element at <code>v (i)</code> with value <code>t</code>.
151The storage requirement of the Vector may be increased.</td>
152<td><code>v (i)</code> is equal to <code>t</code>.</td>
153</tr>
154<tr>
155<td>Erase</td>
156<td><code>v.erase_element (i)</code></td>
157<td><code>0 &lt;= i &lt; v.size ()</code></td>
158<td>Destroys the element as <code>v (i)</code> and replaces it with the default
159<code>value_type ()</code>.
160The storage requirement of the Vector may be decreased.</td>
161<td><code>v (i)</code> is equal to <code>value_type ()</code>.</td>
162</tr>
163<tr>
164<td>Clear</td>
165<td><code>v.clear ()</code></td>
166<td>&nbsp;</td>
167<td>Equivalent to<br />
168<code>for (i = 0; i &lt; v.size (); ++ i)</code><br />
169&nbsp; <code>v.erase_element (i);</code></td>
170<td>&nbsp;</td>
171</tr>
172<tr>
173<td>Resize</td>
174<td><code>v.resize (n)
175<br />v.resize (n, p)</code></td>
176<td>&nbsp;</td>
177<td>Reallocates the vector so that it can hold <code>n</code>
178elements.<br />
179Erases or appends elements in order to bring the vector to the prescribed size. Appended elements copies of <code>value_type()</code>.
180<br />
181When <code>p == false</code> then existing elements are not preserved and elements will not appended as normal. Instead the vector is in the same state as that after an equivalent sizing constructor.</td>
182<td><code>v.size () == n</code>.</td>
183</tr>
184<tr>
185<td>Storage</td>
186<td><code>v.data()</code></td>
187<td></td>
188<td>Returns a reference to the underlying dense storage.</td>
189<td>&nbsp;</td>
190</tr>
191</table>
192<h4>Complexity guarantees</h4>
193<p>The run-time complexity of the sizing constructor is linear in
194the vector's size.</p>
195<p>The run-time complexity of insert_element and erase_element is specific for the
196Vector model and it depends on increases/decreases in storage requirements.</p>
197<p>The run-time complexity of resize is linear in the vector's
198size.</p>
199<h4>Invariants</h4>
200<h4>Models</h4>
201<ul>
202<li><code>vector</code>, <code>bounded_vector</code>, <code>c_vector</code></li>
203<li><code>unit_vector</code>, <code>zero_vector</code>, <code>scalar_vector</code></li>
204<li><code>mapped_vector;</code>, <code>compressed_vector</code>, <code>coordinate_vector</code></li>
205</ul>
206<h4>Notes</h4>
207<p><a name="vector_expression_note">[1]</a>
208As a user you need not care about <tt>Vector</tt> being a refinement of the VectorExpression. Being a refinement of the VectorExpression is only important for the template-expression engine but not the user.</p>
209<p><a name="element_access_note">[2]</a>
210The <code>operator[]</code> is added purely for convenience
211and compatibility with the <code>std::vector</code>. In uBLAS however,
212generally <code>operator()</code> is used for indexing because this can be
213used for both vectors and matrices.</p>
214<h2><a name="matrix"></a>Matrix</h2>
215<h4>Description</h4>
216<p>A Matrix describes common aspects of dense, packed and sparse
217matrices.</p>
218<h4>Refinement of</h4>
219<p><a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>,
220<a href="expression_concept.html#matrix_expression">Matrix Expression</a>
221<a href="#matrix_expression_note">[1]</a>
222.</p>
223<h4>Associated types</h4>
224<p>In addition to the types defined by <a href="expression_concept.html#matrix_expression">Matrix Expression</a></p>
225<table border="1" summary="types">
226<tbody>
227<tr>
228<td>Public base</td>
229<td>matrix_container&lt;M&gt;</td>
230<td>M must be derived from this public base type.</td>
231</tr>
232<tr>
233<td>Storage array</td>
234<td>M::array_type</td>
235<td>Dense Matrix ONLY. The type of underlying storage array used to store the elements. The array_type must model
236the <a href="storage_concept.html"><b>Storage</b></a> concept.</td>
237</tr>
238</tbody>
239</table>
240<h4>Notation</h4>
241<table border="0" summary="notation">
242<tbody>
243<tr>
244<td><code>M</code></td>
245<td>A type that is a model of Matrix</td>
246</tr>
247<tr>
248<td><code>m</code></td>
249<td>Objects of type <code>M</code></td>
250</tr>
251<tr>
252<td><code>n1, n2, i, j</code></td>
253<td>Objects of a type convertible to <code>size_type</code></td>
254</tr>
255<tr>
256<td><code>t</code></td>
257<td>Object of a type convertible to <code>value_type</code></td>
258</tr>
259<tr>
260<td><code>p</code></td>
261<td>Object of a type convertible to <code>bool</code></td>
262</tr>
263</tbody>
264</table>
265<h4>Definitions</h4>
266<h4>Valid expressions</h4>
267<p>In addition to the expressions defined in <a href=
268"expression_concept.html#matrix_expression">Matrix Expression</a> the
269following expressions must be valid.</p>
270<table border="1" summary="expressions">
271<tbody>
272<tr>
273<th>Name</th>
274<th>Expression</th>
275<th>Type requirements</th>
276<th>Return type</th>
277</tr>
278<tr>
279<td>Sizing constructor</td>
280<td><code>M m (n1, n2)</code></td>
281<td>&nbsp;</td>
282<td><code>M</code></td>
283</tr>
284<tr>
285<td>Insert</td>
286<td><code>m.insert_element (i, j, t)</code></td>
287<td><code>m</code> is mutable.</td>
288<td><code>void</code></td>
289</tr>
290<tr>
291<td>Erase</td>
292<td><code>m.erase_element (i, j)</code></td>
293<td><code>m</code> is mutable.</td>
294<td><code>void</code></td>
295</tr>
296<tr>
297<td>Clear</td>
298<td><code>m.clear ()</code></td>
299<td><code>m</code> is mutable.</td>
300<td><code>void</code></td>
301</tr>
302<tr>
303<td>Resize</td>
304<td><code>m.resize (n1, n2)</code><br />
305<code>m.resize (n1, n2, p)</code></td>
306<td><code>m</code> is mutable.</td>
307<td><code>void</code></td>
308</tr>
309<tr>
310<td>Storage</td>
311<td><code>m.data()</code></td>
312<td><code>m</code> is mutable and Dense.</td>
313<td><code>array_type&amp;</code> if <code>m</code> is mutable, <code>const array_type&amp;</code> otherwise</td>
314</tr>
315</tbody>
316</table>
317<h4>Expression semantics</h4>
318<p>Semantics of an expression is defined only where it differs
319from, or is not defined in <a href=
320"expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
321<table border="1" summary="semantics">
322<tbody>
323<tr>
324<th>Name</th>
325<th>Expression</th>
326<th>Precondition</th>
327<th>Semantics</th>
328<th>Postcondition</th>
329</tr>
330<tr>
331<td>Sizing constructor</td>
332<td><code>M m (n1, n2)</code></td>
333<td><code>n1 &gt;= 0</code> and <code>n2 &gt;= 0</code></td>
334<td>Allocates a matrix of <code>n1</code> rows and <code>n2</code>
335columns.</td>
336<td><code>m.size1 () == n1</code> and <code>m.size2 () ==
337n2</code>.</td>
338</tr>
339<tr>
340<td>Insert</td>
341<td><code>m.insert_element (i, j, t)</code></td>
342<td><code>0 &lt;= i &lt; m.size1 ()</code>,<br />
343<code>0 &lt;= j &lt; m.size2 ()</code>.</td>
344<td>Inserts an element at <code>m (i, j)</code> with value <code>t</code>.
345The storage requirement of the Matrix may be increased.</td>
346<td><code>m (i, j)</code> is equal to <code>t</code>.</td>
347</tr>
348<tr>
349<td>Erase</td>
350<td><code>m.erase_element (i, j)</code></td>
351<td><code>0 &lt;= i &lt; m.size1 ()</code>and <code><br />
3520 &lt;= j &lt; m.size2</code></td>
353<td>Destroys the element as <code>m (i, j)</code> and replaces it with the default
354<code>value_type ()</code>.
355The storage requirement of the Matrix may be decreased.</td>
356<td><code>m (i, j)</code> is equal to <code>value_type ()</code>.</td>
357</tr>
358<tr>
359<td>Clear</td>
360<td><code>m.clear ()</code></td>
361<td>&nbsp;</td>
362<td>Equivalent to<br />
363<code>for (i = 0; i &lt; m.size1 (); ++ i)</code><br />
364&nbsp; <code>for (j = 0; j &lt; m.size2 (); ++ j)</code><br />
365&nbsp; &nbsp; <code>m.erase_element (i, j);</code></td>
366<td>&nbsp;</td>
367</tr>
368<tr>
369<td>Resize</td>
370<td><code>m.resize (n1, n2)
371<br />
372m.resize (n1, n2, p)
373</code></td>
374<td>&nbsp;</td>
375<td>Reallocate the matrix so that it can hold <code>n1</code> rows
376and <code>n2</code> columns.<br />
377Erases or appends elements in order to bring the matrix to the
378prescribed size. Appended elements are <code>value_type()</code>
379copies.<br />
380When <code>p == false</code> then existing elements are not preserved and elements will not appended as normal. Instead the matrix is in the same state as that after an equivalent sizing constructor.</td>
381<td><code>m.size1 () == n1</code> and <code>m.size2 () == n2</code>.</td>
382</tr>
383<tr>
384<td>Storage</td>
385<td><code>m.data()</code></td>
386<td></td>
387<td>Returns a reference to the underlying dense storage.</td>
388<td>&nbsp;</td>
389</tbody>
390</table>
391<h4>Complexity guarantees</h4>
392<p>The run-time complexity of the sizing constructor is quadratic
393in the matrix's size.</p>
394<p>The run-time complexity of insert_element and erase_element is specific for the
395Matrix model and it depends on increases/decreases in storage requirements.</p>
396<p>The run-time complexity of resize is quadratic in the matrix's
397size.</p>
398<h4>Invariants</h4>
399<h4>Models</h4>
400<ul>
401<li><code>matrix</code>, <code>bounded_matrix</code>, <code>c_matrix</code></li>
402<li><code>identity_matrix</code> , <code>zero_matrix</code> , <code>scalar_matrix</code></li>
403<li><code>triangular_matrix</code> , <code>symmetric_matrix</code> , <code>banded_matrix</code></li>
404<li><code>mapped_matrix</code> , <code>compressed_matrix</code> , <code>coordinate_matrix</code></li>
405</ul>
406<h4>Notes</h4>
407<p><a name="matrix_expression_note">[1]</a>
408As a user you need not care about <tt>Matrix</tt> being a refinement of the MatrixExpression. Being a refinement of the MatrixExpression is only important for the template-expression engine but not the user.</p>
409<hr />
410<p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
411 Use, modification and distribution are subject to the
412 Boost Software License, Version 1.0.
413 (See accompanying file LICENSE_1_0.txt
414 or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
415 http://www.boost.org/LICENSE_1_0.txt
416 </a>).
417</p>
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