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13 | <title>Iterator Concepts</title> | |
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15 | <body> | |
16 | <h1><img src="../../../../boost.png" align="middle" />Iterator Concepts</h1> | |
17 | <div class="toc" id="toc"></div> | |
18 | <p>An Iterator is a restricted pointer-like object pointing into a | |
19 | vector or matrix container.</p> | |
20 | <h2><a name="indexed_bidirectional_iterator" | |
21 | ></a>Indexed Bidirectional Iterator</h2> | |
22 | <h4>Description</h4> | |
23 | <p>An Indexed Bidirectional Iterator is an iterator of a container | |
24 | that can be dereferenced, incremented, decremented and carries | |
25 | index information.</p> | |
26 | <h4>Refinement of</h4> | |
27 | <p>Assignable, Equality Comparable, Default Constructible.</p> | |
28 | <h4>Associated types</h4> | |
29 | <table border="1" summary="associated types"> | |
30 | <tbody> | |
31 | <tr> | |
32 | <td>Value type</td> | |
33 | <td>The type of the value obtained by dereferencing a Indexed | |
34 | Bidirectional Iterator</td> | |
35 | </tr> | |
36 | <tr> | |
37 | <td>Container type</td> | |
38 | <td>The type of the container a Indexed Bidirectional Iterator | |
39 | points into.</td> | |
40 | </tr> | |
41 | </tbody> | |
42 | </table> | |
43 | <h4>Notation</h4> | |
44 | <table border="0" summary="notation"> | |
45 | <tbody> | |
46 | <tr> | |
47 | <td><code>I</code></td> | |
48 | <td>A type that is a model of Indexed Bidirectional Iterator</td> | |
49 | </tr> | |
50 | <tr> | |
51 | <td><code>T</code></td> | |
52 | <td>The value type of <code>I</code></td> | |
53 | </tr> | |
54 | <tr> | |
55 | <td><code>C</code></td> | |
56 | <td>The container type of <code>I</code></td> | |
57 | </tr> | |
58 | <tr> | |
59 | <td><code>it</code>, <code>itt, it1</code>, <code>it2</code></td> | |
60 | <td>Objects of type <code>I</code></td> | |
61 | </tr> | |
62 | <tr> | |
63 | <td><code>t</code></td> | |
64 | <td>Object of type <code>T</code></td> | |
65 | </tr> | |
66 | <tr> | |
67 | <td><code>c</code></td> | |
68 | <td>Object of type <code>C</code></td> | |
69 | </tr> | |
70 | </tbody> | |
71 | </table> | |
72 | <h4>Definitions</h4> | |
73 | <p>A Indexed Bidirectional Iterator may be <i>mutable</i>, meaning | |
74 | that the values referred to by objects of that type may be | |
75 | modified, or <i>constant</i> , meaning that they may not. If an | |
76 | iterator type is mutable, this implies that its value type is a | |
77 | model of Assignable; the converse, though, is not necessarily | |
78 | true.</p> | |
79 | <p>A Indexed Bidirectional Iterator may have a <i>singular</i> | |
80 | value, meaning that the results of most operations, including | |
81 | comparison for equality, are undefined. The only operation that is | |
82 | guaranteed to be supported is assigning a nonsingular iterator to a | |
83 | singular iterator.</p> | |
84 | <p>A Indexed Bidirectional Iterator may have a | |
85 | <i>dereferenceable</i> value, meaning that dereferencing it yields | |
86 | a well-defined value. Dereferenceable iterators are always | |
87 | nonsingular, but the converse is not true.</p> | |
88 | <p>An Indexed Bidirectional Iterator is <i>past-the-end</i> if it | |
89 | points beyond the last element of a container. Past-the-end values | |
90 | are nonsingular and nondereferenceable.</p> | |
91 | <h4>Valid expressions</h4> | |
92 | <p>In addition to the expressions defined for Assignable, Equality | |
93 | Comparable and Default Constructible, the following expressions | |
94 | must be valid.</p> | |
95 | <table border="1" summary="expressions"> | |
96 | <tbody> | |
97 | <tr> | |
98 | <th>Name</th> | |
99 | <th>Expression</th> | |
100 | <th>Type requirements</th> | |
101 | <th>Return type</th> | |
102 | </tr> | |
103 | <tr> | |
104 | <td>Default constructor</td> | |
105 | <td><code>I it</code></td> | |
106 | <td> </td> | |
107 | <td> </td> | |
108 | </tr> | |
109 | <tr> | |
110 | <td>Dereference</td> | |
111 | <td><code>*it</code></td> | |
112 | <td> </td> | |
113 | <td>Convertible to <code>T</code>.</td> | |
114 | </tr> | |
115 | <tr> | |
116 | <td>Dereference assignment</td> | |
117 | <td><code>*it = t</code></td> | |
118 | <td><code>I</code> is mutable.</td> | |
119 | <td> </td> | |
120 | </tr> | |
121 | <tr> | |
122 | <td>Member access</td> | |
123 | <td><code>it->m</code></td> | |
124 | <td><code>T</code> is a type for which <code>t.m</code> is | |
125 | defined.</td> | |
126 | <td> </td> | |
127 | </tr> | |
128 | <tr> | |
129 | <td>Preincrement</td> | |
130 | <td><code>++ it</code></td> | |
131 | <td> </td> | |
132 | <td><code>I &</code></td> | |
133 | </tr> | |
134 | <tr> | |
135 | <td>Postincrement</td> | |
136 | <td><code>it ++</code></td> | |
137 | <td> </td> | |
138 | <td><code>I</code></td> | |
139 | </tr> | |
140 | <tr> | |
141 | <td>Predecrement</td> | |
142 | <td><code>-- it</code></td> | |
143 | <td> </td> | |
144 | <td><code>I &</code></td> | |
145 | </tr> | |
146 | <tr> | |
147 | <td>Postdecrement</td> | |
148 | <td><code>it --</code></td> | |
149 | <td> </td> | |
150 | <td><code>I</code></td> | |
151 | </tr> | |
152 | <tr> | |
153 | <td>Index</td> | |
154 | <td><code>it.index ()</code></td> | |
155 | <td> </td> | |
156 | <td><code>C::size_type</code></td> | |
157 | </tr> | |
158 | </tbody> | |
159 | </table> | |
160 | <h4>Expression Semantics</h4> | |
161 | <p>Semantics of an expression is defined only where it differs | |
162 | from, or is not defined in, Assignable, Equality Comparable and | |
163 | Default Constructible.</p> | |
164 | <table border="1" summary="semantics"> | |
165 | <tbody> | |
166 | <tr> | |
167 | <th>Name</th> | |
168 | <th>Expression</th> | |
169 | <th>Precondition</th> | |
170 | <th>Semantics</th> | |
171 | <th>Postcondition</th> | |
172 | </tr> | |
173 | <tr> | |
174 | <td>Default constructor</td> | |
175 | <td><code>I it</code></td> | |
176 | <td> </td> | |
177 | <td> </td> | |
178 | <td><code>it</code> is singular.</td> | |
179 | </tr> | |
180 | <tr> | |
181 | <td>Dereference</td> | |
182 | <td><code>*it</code></td> | |
183 | <td><code>it</code> is dereferenceable.</td> | |
184 | <td> </td> | |
185 | <td> </td> | |
186 | </tr> | |
187 | <tr> | |
188 | <td>Dereference assignment</td> | |
189 | <td><code>*it = t</code></td> | |
190 | <td>Same as for <code>*it</code>.</td> | |
191 | <td> </td> | |
192 | <td><code>*it</code> is a copy of t.</td> | |
193 | </tr> | |
194 | <tr> | |
195 | <td>Member access</td> | |
196 | <td><code>it->m</code></td> | |
197 | <td><code>it</code> is dereferenceable.</td> | |
198 | <td>Equivalent to <code>(*it).m</code></td> | |
199 | <td> </td> | |
200 | </tr> | |
201 | <tr> | |
202 | <td>Preincrement</td> | |
203 | <td><code>++ it</code></td> | |
204 | <td><code>it</code> is dereferenceable.</td> | |
205 | <td><code>it</code> is modified to point to the next element.</td> | |
206 | <td><code>it</code> is dereferenceable or past-the-end. | |
207 | <code><br /> | |
208 | &it == &++ it</code>.<br /> | |
209 | If <code>it1 == it2</code>,<br /> | |
210 | then <code>++ it1 == ++ it2</code>.</td> | |
211 | </tr> | |
212 | <tr> | |
213 | <td>Postincrement</td> | |
214 | <td><code>it ++</code></td> | |
215 | <td>Same as for <code>++ it</code>.</td> | |
216 | <td>Equivalent to<br /> | |
217 | <code>{<br /> | |
218 | I itt = it;<br /> | |
219 | ++ it;<br /> | |
220 | return itt;<br /> | |
221 | }</code></td> | |
222 | <td><code>it</code> is dereferenceable or past-the-end.</td> | |
223 | </tr> | |
224 | <tr> | |
225 | <td>Predecrement</td> | |
226 | <td><code>-- it</code></td> | |
227 | <td><code>it</code> is dereferenceable or past-the-end.<br /> | |
228 | There exists a dereferenceable iterator <code>itt</code> such that | |
229 | <code>it == ++ itt</code>.</td> | |
230 | <td><code>it</code> is modified to point to the previous | |
231 | element.</td> | |
232 | <td><code>it</code> is dereferenceable.<br /> | |
233 | <code>&it = &-- it</code>.<br /> | |
234 | If <code>it1 == it2</code>,<br /> | |
235 | then <code>-- it1 == -- it2</code>.<br /> | |
236 | If <code>it2</code> is dereferenceable and <code>it1 == | |
237 | ++it2</code>,<br /> | |
238 | then <code>--it1 == it2</code>.</td> | |
239 | </tr> | |
240 | <tr> | |
241 | <td>Postdecrement</td> | |
242 | <td><code>it --</code></td> | |
243 | <td>Same as for -- <code>it</code>.</td> | |
244 | <td>Equivalent to<br /> | |
245 | <code>{<br /> | |
246 | I itt = it;<br /> | |
247 | -- it;<br /> | |
248 | return itt;<br /> | |
249 | }</code></td> | |
250 | <td><code>it</code> is dereferenceable. </td> | |
251 | </tr> | |
252 | <tr> | |
253 | <td>Index</td> | |
254 | <td><code>it.index ()</code></td> | |
255 | <td><code>it</code> is dereferenceable.</td> | |
256 | <td><code>it.index () >= 0</code><br /> | |
257 | and<br /> | |
258 | <code>it.index () < it ().size ()</code></td> | |
259 | <td>If <code>it1 == it2</code>,<br /> | |
260 | then <code>it1.index () == it2.index ()</code>.<br /> | |
261 | If <code>it1 == it2</code>,<br /> | |
262 | then <code>it1.index () < (++ it2).index | |
263 | ()</code>.<br /> | |
264 | If <code>it1 == it2</code>,<br /> | |
265 | then <code>it1.index () > (-- it2).index | |
266 | ()</code>.</td> | |
267 | </tr> | |
268 | </tbody> | |
269 | </table> | |
270 | <h4>Complexity guarantees</h4> | |
271 | <p>The complexity of operations on indexed bidirectional iterators | |
272 | is guaranteed to be amortized constant time.</p> | |
273 | <h4>Invariants</h4> | |
274 | <table border="1" summary="invariants"> | |
275 | <tbody> | |
276 | <tr> | |
277 | <td>Identity</td> | |
278 | <td><code>it1 == it2</code> if and only if <code>&*it1 == | |
279 | &*it2</code>.</td> | |
280 | </tr> | |
281 | <tr> | |
282 | <td>Symmetry of increment and decrement</td> | |
283 | <td>If <code>it</code> is dereferenceable, then <code>++ it; | |
284 | --it;</code> is a null operation. Similarly, <code>-- it; ++ | |
285 | it;</code> is a null operation.</td> | |
286 | </tr> | |
287 | <tr> | |
288 | <td>Relation between iterator index and container element | |
289 | operator</td> | |
290 | <td>If <code>it</code> is dereferenceable, <code>*it == it () | |
291 | (it.index ())</code>.</td> | |
292 | </tr> | |
293 | </tbody> | |
294 | </table> | |
295 | <h4>Models</h4> | |
296 | <ul> | |
297 | <li><code>sparse_vector::iterator</code></li> | |
298 | </ul> | |
299 | <h2><a name="indexed_random_access_iterator" | |
300 | ></a>Indexed Random Access Iterator</h2> | |
301 | <h4>Description</h4> | |
302 | <p>An Indexed Random Access Iterator is an iterator of a container | |
303 | that can be dereferenced, moved forward, moved backward and carries | |
304 | index information.</p> | |
305 | <h4>Refinement of</h4> | |
306 | <p>LessThanComparable, <a href= | |
307 | "#indexed_bidirectional_iterator">Indexed Bidirectional | |
308 | Iterator</a> .</p> | |
309 | <h4>Associated types</h4> | |
310 | <table border="1" summary="associated types"> | |
311 | <tbody> | |
312 | <tr> | |
313 | <td>Value type</td> | |
314 | <td>The type of the value obtained by dereferencing a Indexed | |
315 | Random Access Iterator</td> | |
316 | </tr> | |
317 | <tr> | |
318 | <td>Container type</td> | |
319 | <td>The type of the container a Indexed Random Access Iterator | |
320 | points into.</td> | |
321 | </tr> | |
322 | </tbody> | |
323 | </table> | |
324 | <h4>Notation</h4> | |
325 | <table border="0" summary="notation"> | |
326 | <tbody> | |
327 | <tr> | |
328 | <td><code>I</code></td> | |
329 | <td>A type that is a model of Indexed Random Access Iterator</td> | |
330 | </tr> | |
331 | <tr> | |
332 | <td><code>T</code></td> | |
333 | <td>The value type of <code>I</code></td> | |
334 | </tr> | |
335 | <tr> | |
336 | <td><code>C</code></td> | |
337 | <td>The container type of <code>I</code></td> | |
338 | </tr> | |
339 | <tr> | |
340 | <td><code>it</code>, <code>itt, it1</code>, <code>it2</code></td> | |
341 | <td>Objects of type <code>I</code></td> | |
342 | </tr> | |
343 | <tr> | |
344 | <td><code>t</code></td> | |
345 | <td>Object of type <code>T</code></td> | |
346 | </tr> | |
347 | <tr> | |
348 | <td><code>n</code></td> | |
349 | <td>Object of type <code>C::difference_type</code></td> | |
350 | </tr> | |
351 | </tbody> | |
352 | </table> | |
353 | <h4>Definitions</h4> | |
354 | <p>An Indexed Random Access Iterator <code>it1</code> is | |
355 | <i>reachable</i> from an Indexed Random Access Iterator | |
356 | <code>it2</code> if, after applying <code>operator ++</code> to | |
357 | <code>it2</code> a finite number of times, <code>it1 == | |
358 | it2</code>.</p> | |
359 | <h4>Valid expressions</h4> | |
360 | <p>In addition to the expressions defined for <a href= | |
361 | "#indexed_bidirectional_iterator">Indexed Bidirectional | |
362 | Iterator</a> , the following expressions must be valid.</p> | |
363 | <table border="1" summary="expressions"> | |
364 | <tbody> | |
365 | <tr> | |
366 | <th>Name</th> | |
367 | <th>Expression</th> | |
368 | <th>Type requirements</th> | |
369 | <th>Return type</th> | |
370 | </tr> | |
371 | <tr> | |
372 | <td>Forward motion</td> | |
373 | <td><code>it += n</code></td> | |
374 | <td> </td> | |
375 | <td><code>I &</code></td> | |
376 | </tr> | |
377 | <tr> | |
378 | <td>Iterator addition</td> | |
379 | <td><code>it + n</code></td> | |
380 | <td> </td> | |
381 | <td><code>I</code></td> | |
382 | </tr> | |
383 | <tr> | |
384 | <td>Backward motion</td> | |
385 | <td><code>i -= n</code></td> | |
386 | <td> </td> | |
387 | <td><code>I &</code></td> | |
388 | </tr> | |
389 | <tr> | |
390 | <td>Iterator subtraction</td> | |
391 | <td><code>it - n</code></td> | |
392 | <td> </td> | |
393 | <td><code>I</code> </td> | |
394 | </tr> | |
395 | <tr> | |
396 | <td>Difference</td> | |
397 | <td><code>it1 - it2</code></td> | |
398 | <td> </td> | |
399 | <td><code>C::difference_type</code></td> | |
400 | </tr> | |
401 | <tr> | |
402 | <td>Element operator</td> | |
403 | <td><code>it [n]</code></td> | |
404 | <td> </td> | |
405 | <td>Convertible to <code>T</code>.</td> | |
406 | </tr> | |
407 | <tr> | |
408 | <td>Element assignment</td> | |
409 | <td><code>it [n] = t</code></td> | |
410 | <td><code>I</code> is mutable</td> | |
411 | <td>Convertible to <code>T</code>.</td> | |
412 | </tr> | |
413 | </tbody> | |
414 | </table> | |
415 | <h4>Expression Semantics</h4> | |
416 | <p>Semantics of an expression is defined only where it differs | |
417 | from, or is not defined in, <a href= | |
418 | "#indexed_bidirectional_iterator">Indexed Bidirectional | |
419 | Iterator</a> .</p> | |
420 | <table border="1" summary="semantics"> | |
421 | <tbody> | |
422 | <tr> | |
423 | <th>Name</th> | |
424 | <th>Expression</th> | |
425 | <th>Precondition</th> | |
426 | <th>Semantics</th> | |
427 | <th>Postcondition</th> | |
428 | </tr> | |
429 | <tr> | |
430 | <td>Forward motion</td> | |
431 | <td><code>it += n</code></td> | |
432 | <td>Including <code>it</code> itself, there must be <code>n</code> | |
433 | dereferenceable or past-the-end iterators following or preceding | |
434 | <code>it</code>, depending on whether <code>n</code> is positive or | |
435 | negative.</td> | |
436 | <td>If <code>n > 0</code>, equivalent to executing <code>++ | |
437 | it</code> <code>n</code> times. If <code>n < 0</code>, | |
438 | equivalent to executing <code>-- it</code> <code>n</code> times. If | |
439 | <code>n == 0</code>, this is a null operation.</td> | |
440 | <td><code>it</code> is dereferenceable or past-the-end.</td> | |
441 | </tr> | |
442 | <tr> | |
443 | <td>Iterator addition</td> | |
444 | <td><code>it + n</code></td> | |
445 | <td>Same as for <code>i += n</code>.</td> | |
446 | <td>Equivalent to<br /> | |
447 | <code>{<br /> | |
448 | I itt = it;<br /> | |
449 | return itt += n;<br /> | |
450 | }</code></td> | |
451 | <td>Result is dereferenceable or past-the-end.</td> | |
452 | </tr> | |
453 | <tr> | |
454 | <td>Backward motion</td> | |
455 | <td><code>it -= n</code></td> | |
456 | <td>Including <code>it</code> itself, there must be <code>n</code> | |
457 | dereferenceable or past-the-end iterators preceding or following | |
458 | <code>it</code>, depending on whether <code>n</code> is positive or | |
459 | negative.</td> | |
460 | <td>Equivalent to <code>it += (-n)</code>.</td> | |
461 | <td><code>it</code> is dereferenceable or past-the-end.</td> | |
462 | </tr> | |
463 | <tr> | |
464 | <td>Iterator subtraction</td> | |
465 | <td><code>it - n</code></td> | |
466 | <td>Same as for <code>i -= n</code>.</td> | |
467 | <td>Equivalent to<br /> | |
468 | <code>{<br /> | |
469 | I itt = it;<br /> | |
470 | return itt -= n;<br /> | |
471 | }</code></td> | |
472 | <td>Result is dereferenceable or past-the-end.</td> | |
473 | </tr> | |
474 | <tr> | |
475 | <td>Difference</td> | |
476 | <td><code>it1 - it2</code></td> | |
477 | <td>Either <code>it1</code> is reachable from <code>it2</code> or | |
478 | <code>it2</code> is reachable from <code>it1</code>, or both.</td> | |
479 | <td>Returns a number <code>n</code> such that <code>it1 == it2 + | |
480 | n</code></td> | |
481 | <td> </td> | |
482 | </tr> | |
483 | <tr> | |
484 | <td>Element operator</td> | |
485 | <td><code>it [n]</code></td> | |
486 | <td><code>it + n</code> exists and is dereferenceable.</td> | |
487 | <td>Equivalent to <code>*(it + n)</code></td> | |
488 | <td> </td> | |
489 | </tr> | |
490 | <tr> | |
491 | <td>Element assignment</td> | |
492 | <td><code>i[n] = t</code></td> | |
493 | <td>Same as for <code>it [n]</code>.</td> | |
494 | <td>Equivalent to <code>*(it + n) = t</code></td> | |
495 | <td> </td> | |
496 | </tr> | |
497 | </tbody> | |
498 | </table> | |
499 | <h4>Complexity guarantees</h4> | |
500 | <p>The complexity of operations on indexed random access iterators | |
501 | is guaranteed to be amortized constant time.</p> | |
502 | <h4>Invariants</h4> | |
503 | <table border="1" summary="invariants"> | |
504 | <tbody> | |
505 | <tr> | |
506 | <td>Symmetry of addition and subtraction</td> | |
507 | <td>If <code>it + n</code> is well-defined, then <code>it += n; it | |
508 | -= n;</code> and <code>(it + n) - n</code> are null operations. | |
509 | Similarly, if <code>it - n</code> is well-defined, then <code>it -= | |
510 | n; it += n;</code> and <code>(it - n) + n</code> are null | |
511 | operations.</td> | |
512 | </tr> | |
513 | <tr> | |
514 | <td>Relation between distance and addition</td> | |
515 | <td>If <code>it1 - it2</code> is well-defined, then <code>it1 == | |
516 | it2 + (it1 - it2)</code>.</td> | |
517 | </tr> | |
518 | <tr> | |
519 | <td>Reachability and distance</td> | |
520 | <td>If <code>it1</code> is reachable from <code>it2</code>, then | |
521 | <code>it1 - it2 >= 0</code>.</td> | |
522 | </tr> | |
523 | </tbody> | |
524 | </table> | |
525 | <h4>Models</h4> | |
526 | <ul> | |
527 | <li><code>vector::iterator</code></li> | |
528 | </ul> | |
529 | <h2><a name="indexed_bidirectional_cr_iterator" | |
530 | ></a>Indexed Bidirectional Column/Row Iterator</h2> | |
531 | <h4>Description</h4> | |
532 | <p>An Indexed Bidirectional Column/Row Iterator is an iterator of a | |
533 | container that can be dereferenced, incremented, decremented and | |
534 | carries index information.</p> | |
535 | <h4>Refinement of</h4> | |
536 | <p>Assignable, Equality Comparable, Default Constructible.</p> | |
537 | <h4>Associated types</h4> | |
538 | <table border="1" summary="associated types"> | |
539 | <tbody> | |
540 | <tr> | |
541 | <td>Value type</td> | |
542 | <td>The type of the value obtained by dereferencing a Indexed | |
543 | Bidirectional Column/Row Iterator</td> | |
544 | </tr> | |
545 | <tr> | |
546 | <td>Container type</td> | |
547 | <td>The type of the container a Indexed Bidirectional Column/Row | |
548 | Iterator points into.</td> | |
549 | </tr> | |
550 | </tbody> | |
551 | </table> | |
552 | <h4>Notation</h4> | |
553 | <table border="0" summary="notation"> | |
554 | <tbody> | |
555 | <tr> | |
556 | <td><code>I1</code></td> | |
557 | <td>A type that is a model of Indexed Bidirectional Column/Row | |
558 | Iterator</td> | |
559 | </tr> | |
560 | <tr> | |
561 | <td><code>I2</code></td> | |
562 | <td>A type that is a model of Indexed Bidirectional Row/Column | |
563 | Iterator</td> | |
564 | </tr> | |
565 | <tr> | |
566 | <td><code>T</code></td> | |
567 | <td>The value type of <code>I1</code> and <code>I2</code></td> | |
568 | </tr> | |
569 | <tr> | |
570 | <td><code>C</code></td> | |
571 | <td>The container type of <code>I1</code> and <code>I2</code></td> | |
572 | </tr> | |
573 | <tr> | |
574 | <td><code>it1</code>, <code>it1t, it11</code>, | |
575 | <code>it12</code></td> | |
576 | <td>Objects of type <code>I1</code></td> | |
577 | </tr> | |
578 | <tr> | |
579 | <td><code>it2</code>, <code>it2t</code></td> | |
580 | <td>Objects of type <code>I2</code></td> | |
581 | </tr> | |
582 | <tr> | |
583 | <td><code>t</code></td> | |
584 | <td>Object of type <code>T</code></td> | |
585 | </tr> | |
586 | <tr> | |
587 | <td><code>c</code></td> | |
588 | <td>Object of type <code>C</code></td> | |
589 | </tr> | |
590 | </tbody> | |
591 | </table> | |
592 | <h4>Definitions</h4> | |
593 | <h4>Valid expressions</h4> | |
594 | <p>In addition to the expressions defined for Assignable, Equality | |
595 | Comparable and Default Constructible, the following expressions | |
596 | must be valid.</p> | |
597 | <table border="1" summary="expressions"> | |
598 | <tbody> | |
599 | <tr> | |
600 | <th>Name</th> | |
601 | <th>Expression</th> | |
602 | <th>Type requirements</th> | |
603 | <th>Return type</th> | |
604 | </tr> | |
605 | <tr> | |
606 | <td>Default constructor</td> | |
607 | <td><code>I1 it</code></td> | |
608 | <td> </td> | |
609 | <td> </td> | |
610 | </tr> | |
611 | <tr> | |
612 | <td>Dereference</td> | |
613 | <td><code>*it</code></td> | |
614 | <td> </td> | |
615 | <td>Convertible to <code>T</code>.</td> | |
616 | </tr> | |
617 | <tr> | |
618 | <td>Dereference assignment</td> | |
619 | <td><code>*it = t</code></td> | |
620 | <td><code>I1</code> is mutable.</td> | |
621 | <td> </td> | |
622 | </tr> | |
623 | <tr> | |
624 | <td>Member access</td> | |
625 | <td><code>it->m</code></td> | |
626 | <td><code>T</code> is a type for which <code>t.m</code> is | |
627 | defined.</td> | |
628 | <td> </td> | |
629 | </tr> | |
630 | <tr> | |
631 | <td>Preincrement</td> | |
632 | <td><code>++ it</code></td> | |
633 | <td> </td> | |
634 | <td><code>I1 &</code></td> | |
635 | </tr> | |
636 | <tr> | |
637 | <td>Postincrement</td> | |
638 | <td><code>it ++</code></td> | |
639 | <td> </td> | |
640 | <td><code>I1</code></td> | |
641 | </tr> | |
642 | <tr> | |
643 | <td>Predecrement</td> | |
644 | <td><code>-- it</code></td> | |
645 | <td> </td> | |
646 | <td><code>I1 &</code></td> | |
647 | </tr> | |
648 | <tr> | |
649 | <td>Postdecrement</td> | |
650 | <td><code>it --</code></td> | |
651 | <td> </td> | |
652 | <td><code>I1</code></td> | |
653 | </tr> | |
654 | <tr> | |
655 | <td>Row Index</td> | |
656 | <td><code>it.index1 ()</code></td> | |
657 | <td> </td> | |
658 | <td><code>C::size_type</code></td> | |
659 | </tr> | |
660 | <tr> | |
661 | <td>Column Index</td> | |
662 | <td><code>it.index2 ()</code></td> | |
663 | <td> </td> | |
664 | <td><code>C::size_type</code></td> | |
665 | </tr> | |
666 | <tr> | |
667 | <td>Row/Column Begin</td> | |
668 | <td><code>it.begin ()</code></td> | |
669 | <td> </td> | |
670 | <td><code>I2</code></td> | |
671 | </tr> | |
672 | <tr> | |
673 | <td>Row/Column End</td> | |
674 | <td><code>it.end ()</code></td> | |
675 | <td> </td> | |
676 | <td><code>I2</code></td> | |
677 | </tr> | |
678 | <tr> | |
679 | <td>Reverse Row/Column Begin</td> | |
680 | <td><code>it.rbegin ()</code></td> | |
681 | <td> </td> | |
682 | <td><code>reverse_iterator<I2></code></td> | |
683 | </tr> | |
684 | <tr> | |
685 | <td>Reverse Row/Column End</td> | |
686 | <td><code>it.rend ()</code></td> | |
687 | <td> </td> | |
688 | <td><code>reverse_iterator<I2></code></td> | |
689 | </tr> | |
690 | </tbody> | |
691 | </table> | |
692 | <h4>Expression Semantics</h4> | |
693 | <p>Semantics of an expression is defined only where it differs | |
694 | from, or is not defined in, Assignable, Equality Comparable and | |
695 | Default Constructible.</p> | |
696 | <table border="1" summary="semantics"> | |
697 | <tbody> | |
698 | <tr> | |
699 | <th>Name</th> | |
700 | <th>Expression</th> | |
701 | <th>Precondition</th> | |
702 | <th>Semantics</th> | |
703 | <th>Postcondition</th> | |
704 | </tr> | |
705 | <tr> | |
706 | <td>Default constructor</td> | |
707 | <td><code>I1 it</code></td> | |
708 | <td> </td> | |
709 | <td> </td> | |
710 | <td><code>it</code> is singular.</td> | |
711 | </tr> | |
712 | <tr> | |
713 | <td>Dereference</td> | |
714 | <td><code>*it</code></td> | |
715 | <td><code>it</code> is dereferenceable.</td> | |
716 | <td> </td> | |
717 | <td> </td> | |
718 | </tr> | |
719 | <tr> | |
720 | <td>Dereference assignment</td> | |
721 | <td><code>*it = t</code></td> | |
722 | <td>Same as for <code>*it</code>.</td> | |
723 | <td> </td> | |
724 | <td><code>*it</code> is a copy of t.</td> | |
725 | </tr> | |
726 | <tr> | |
727 | <td>Member access</td> | |
728 | <td><code>it->m</code></td> | |
729 | <td><code>it</code> is dereferenceable.</td> | |
730 | <td>Equivalent to <code>(*it).m</code></td> | |
731 | <td> </td> | |
732 | </tr> | |
733 | <tr> | |
734 | <td>Preincrement</td> | |
735 | <td><code>++ it</code></td> | |
736 | <td><code>it</code> is dereferenceable.</td> | |
737 | <td><code>it</code> is modified to point to the next element of | |
738 | the column/row, i.e. for column iterators holds<br /> | |
739 | <code>it.index1 () < (++ it).index1 ()</code> and<br /> | |
740 | <code>it.index2 () == (++ it).index2 ()</code>,<br /> | |
741 | for row iterators holds<br /> | |
742 | <code>it.index1 () == (++ it).index1 ()</code> and<br /> | |
743 | <code>it.index2 () < (++ it).index2 ()</code>.<br /></td> | |
744 | <td><code>it</code> is dereferenceable or past-the-end. | |
745 | <code><br /> | |
746 | &it == &++ it</code>.<br /> | |
747 | If <code>it1 == it2</code>,<br /> | |
748 | then <code>++ it1 == ++ it2</code>.</td> | |
749 | </tr> | |
750 | <tr> | |
751 | <td>Postincrement</td> | |
752 | <td><code>it ++</code></td> | |
753 | <td>Same as for <code>++ it</code>.</td> | |
754 | <td>Equivalent to<br /> | |
755 | <code>{<br /> | |
756 | I1 itt = it;<br /> | |
757 | ++ it;<br /> | |
758 | return itt;<br /> | |
759 | }</code></td> | |
760 | <td><code>it</code> is dereferenceable or past-the-end.</td> | |
761 | </tr> | |
762 | <tr> | |
763 | <td>Predecrement</td> | |
764 | <td><code>-- it</code></td> | |
765 | <td><code>it</code> is dereferenceable or past-the-end.<br /> | |
766 | There exists a dereferenceable iterator <code>itt</code> such that | |
767 | <code>it == ++ itt</code>.</td> | |
768 | <td><code>it</code> is modified to point to the previous | |
769 | element of the column/row, i.e. for column iterators holds<br /> | |
770 | <code>it.index1 () > (-- it).index1 ()</code> and<br /> | |
771 | <code>it.index2 () == (-- it).index2 ()</code>,<br /> | |
772 | for row iterators holds<br /> | |
773 | <code>it.index1 () == (-- it).index1 ()</code> and<br /> | |
774 | <code>it.index2 () > (-- it).index2 ()</code>.</td> | |
775 | <td><code>it</code> is dereferenceable.<br /> | |
776 | <code>&it = &-- it</code>.<br /> | |
777 | If <code>it1 == it2</code>,<br /> | |
778 | then <code>-- it1 == -- it2</code>.</td> | |
779 | </tr> | |
780 | <tr> | |
781 | <td>Postdecrement</td> | |
782 | <td><code>it --</code></td> | |
783 | <td>Same as for -- <code>it</code>.</td> | |
784 | <td>Equivalent to<br /> | |
785 | <code>{<br /> | |
786 | I1 itt = it;<br /> | |
787 | -- it;<br /> | |
788 | return itt;<br /> | |
789 | }</code></td> | |
790 | <td><code>it</code> is dereferenceable. </td> | |
791 | </tr> | |
792 | <tr> | |
793 | <td>Row Index</td> | |
794 | <td><code>it.index1 ()</code></td> | |
795 | <td>If <code>it</code> is a Row iterator then <code>it</code> must be dereferenceable.</td> | |
796 | <td><code>it.index1 () >= 0</code> and<br /> | |
797 | <code>it.index1 () < it () .size1 ()</code></td> | |
798 | <td>If <code>it1 == it2</code>,<br /> | |
799 | then <code>it1.index1 () == 12.index1 ()</code>.<br /> | |
800 | If <code>it1</code>, <code>it2</code> are Row Iterators with <code>it1 == it2</code>,<br /> | |
801 | then <code>it1.index1 () < (++ it2</code>).<code>index1 ()</code>.<br /> | |
802 | and <code>it1.index1 () > (-- it2</code>).<code>index1 ()</code>.</td> | |
803 | </tr> | |
804 | <tr> | |
805 | <td>Column Index</td> | |
806 | <td><code>it.index2 ()</code></td> | |
807 | <td>If <code>it</code> is a Column iterator then <code>it</code> must be dereferenceable.</td> | |
808 | <td><code>it.index2 () >= 0</code> and<br /> | |
809 | <code>it.index2 () < it () .size2 ()</code></td> | |
810 | <td>If <code>it1 == it2</code>,<br /> | |
811 | then <code>it1.index2 () == it2</code>.<code>index2 ()</code> | |
812 | .<br /> | |
813 | If <code>it1</code>, <code>it2</code> are Column Iterators with <code>it1 == i12</code>,<br /> | |
814 | then <code>it1.index2 () < (++ it2</code>).<code>index2 ()</code>.<br /> | |
815 | end <code>it1.index2 () > (-- it2</code>).<code>index2 ()</code>.</td> | |
816 | </tr> | |
817 | <tr> | |
818 | <td>Row/Column Begin</td> | |
819 | <td><code>it.begin ()</code></td> | |
820 | <td><code>it</code> is dereferenceable.</td> | |
821 | <td>If <code>it</code> is a Column Iterator,<br /> | |
822 | then <code>it2 = it.begin ()</code> is a Row Iterator<br /> | |
823 | with <code>it2.index1 () == it.index1 ()</code>. | |
824 | <p>If <code>it</code> is a Row Iterator,<br /> | |
825 | then <code>it2 = it.begin ()</code> is a Column Iterator<br /> | |
826 | with <code>it2.index2 () == it.index2 ()</code>.</p> | |
827 | </td> | |
828 | <td> </td> | |
829 | </tr> | |
830 | <tr> | |
831 | <td>Row/Column End</td> | |
832 | <td><code>it.end ()</code></td> | |
833 | <td><code>it</code> is dereferenceable.</td> | |
834 | <td>If <code>it</code> is a Column Iterator,<br /> | |
835 | then <code>it2 = it.end ()</code> is a Row Iterator<br /> | |
836 | with <code>it2.index1 () == it.index1 ()</code>. | |
837 | <p>If <code>it</code> is a Row Iterator,<br /> | |
838 | then <code>it2 = it.end ()</code> is a Column Iterator<br /> | |
839 | with <code>it2.index2 () == it.index2 ()</code>.</p> | |
840 | </td> | |
841 | <td> </td> | |
842 | </tr> | |
843 | <tr> | |
844 | <td>Reverse Row/Column Begin</td> | |
845 | <td><code>it.rbegin ()</code></td> | |
846 | <td><code>it</code> is dereferenceable.</td> | |
847 | <td>Equivalent to <code>reverse_iterator<I2> (it.end | |
848 | ())</code>.</td> | |
849 | <td> </td> | |
850 | </tr> | |
851 | <tr> | |
852 | <td>Reverse Row/Column End</td> | |
853 | <td><code>it.rend ()</code></td> | |
854 | <td><code>it</code> is dereferenceable.</td> | |
855 | <td>Equivalent to <code>reverse_iterator<I2> (it.begin | |
856 | ())</code>.</td> | |
857 | <td> </td> | |
858 | </tr> | |
859 | </tbody> | |
860 | </table> | |
861 | <h4>Complexity guarantees</h4> | |
862 | <p>The complexity of operations on indexed bidirectional column/row | |
863 | iterators is guaranteed to be logarithmic depending on the size of | |
864 | the container. The complexity of one iterator (depending on the | |
865 | storage layout) can be lifted to be amortized constant time. The | |
866 | complexity of the other iterator (depending on the storage layout | |
867 | and the container) can be lifted to be amortized constant time for | |
868 | the first row/first column respectively.</p> | |
869 | <h4>Invariants</h4> | |
870 | <table border="1" summary="invariants"> | |
871 | <tbody> | |
872 | <tr> | |
873 | <td>Identity</td> | |
874 | <td><code>it1 == it2</code> if and only if <code>&*it1 == | |
875 | &*it2</code>.</td> | |
876 | </tr> | |
877 | <tr> | |
878 | <td>Symmetry of increment and decrement</td> | |
879 | <td>If <code>it</code> is dereferenceable, then <code>++ it; | |
880 | --it;</code> is a null operation. Similarly, <code>-- it; ++ | |
881 | it;</code> is a null operation.</td> | |
882 | </tr> | |
883 | <tr> | |
884 | <td>Relation between iterator index and container element | |
885 | operator</td> | |
886 | <td>If <code>it</code> is dereferenceable, <code>*it == it () | |
887 | (it.index1 (), it.index2 ())</code></td> | |
888 | </tr> | |
889 | <tr> | |
890 | <td>Relation between iterator column/row begin and iterator | |
891 | index</td> | |
892 | <td>If <code>it</code> is a Column Iterator | |
893 | and <code>it2 = it.begin ()</code> then <code>it2.index2 () < | |
894 | it2t.index2 ()</code> for all <code>it2t</code> with <code>it2t () | |
895 | == it2 ()</code> and <code>it2t ().index1 () == it2 ().index1 | |
896 | ()</code>. | |
897 | <p>If <code>it</code> is a Row Iterator and | |
898 | <code>it2 = it.begin ()</code> then <code>it2.index1 () < | |
899 | it2t.index1 ()</code> for all <code>it2t</code> with <code>it2t () | |
900 | == it2 ()</code> and <code>it2t ().index2 () == it2 ().index2 | |
901 | ()</code>.</p> | |
902 | </td> | |
903 | </tr> | |
904 | <tr> | |
905 | <td>Relation between iterator column/row end and iterator | |
906 | index</td> | |
907 | <td>If <code>it</code> is a Column Iterator | |
908 | and <code>it2 = it.end ()</code> then <code>it2.index2 () > | |
909 | it2t.index2 ()</code> for all <code>it2t</code> with <code>it2t () | |
910 | == it2 ()</code> and <code>it2t ().index1 () == it2 ().index1 | |
911 | ()</code>. | |
912 | <p>If <code>it</code> is a Row Iterator and | |
913 | <code>it2 = it.end ()</code> then <code>it2.index1 () > | |
914 | it2t.index1 ()</code> for all <code>it2t</code> with <code>it2t () | |
915 | == it2 ()</code> and <code>it2t ().index2 () == it2 ().index2 | |
916 | ()</code>.</p> | |
917 | </td> | |
918 | </tr> | |
919 | </tbody> | |
920 | </table> | |
921 | <h4>Models</h4> | |
922 | <ul> | |
923 | <li><code>sparse_matrix::iterator1</code></li> | |
924 | <li><code>sparse_matrix::iterator2</code></li> | |
925 | </ul> | |
926 | <h2><a name="indexed_random_access_cr_iterator" | |
927 | ></a>Indexed Random Access Column/Row Iterator</h2> | |
928 | <h4>Description</h4> | |
929 | <p>An Indexed Random Access Column/Row Iterator is an iterator of a | |
930 | container that can be dereferenced, incremented, decremented and | |
931 | carries index information.</p> | |
932 | <h4>Refinement of</h4> | |
933 | <p><a href="#indexed_bidirectional_cr_iterator">Indexed | |
934 | Bidirectional Column/Row Iterator</a> .</p> | |
935 | <h4>Associated types</h4> | |
936 | <table border="1" summary="associated types"> | |
937 | <tbody> | |
938 | <tr> | |
939 | <td>Value type</td> | |
940 | <td>The type of the value obtained by dereferencing a Indexed | |
941 | Random Access Column/Row Iterator</td> | |
942 | </tr> | |
943 | <tr> | |
944 | <td>Container type</td> | |
945 | <td>The type of the container a Indexed Random Access Column/Row | |
946 | Iterator points into.</td> | |
947 | </tr> | |
948 | </tbody> | |
949 | </table> | |
950 | <h4>Notation</h4> | |
951 | <table border="0" summary="notation"> | |
952 | <tbody> | |
953 | <tr> | |
954 | <td><code>I</code></td> | |
955 | <td>A type that is a model of Indexed Random Access Column/Row | |
956 | Iterator</td> | |
957 | </tr> | |
958 | <tr> | |
959 | <td><code>T</code></td> | |
960 | <td>The value type of <code>I</code></td> | |
961 | </tr> | |
962 | <tr> | |
963 | <td><code>C</code></td> | |
964 | <td>The container type of <code>I</code></td> | |
965 | </tr> | |
966 | <tr> | |
967 | <td><code>it</code>, <code>itt, it1</code>, <code>it2</code></td> | |
968 | <td>Objects of type <code>I</code></td> | |
969 | </tr> | |
970 | <tr> | |
971 | <td><code>t</code></td> | |
972 | <td>Object of type <code>T</code></td> | |
973 | </tr> | |
974 | <tr> | |
975 | <td><code>c</code></td> | |
976 | <td>Object of type <code>C</code></td> | |
977 | </tr> | |
978 | </tbody> | |
979 | </table> | |
980 | <h4>Definitions</h4> | |
981 | <h4>Valid expressions</h4> | |
982 | <p>In addition to the expressions defined for <a href= | |
983 | "#indexed_bidirectional_cr_iterator">Indexed Bidirectional | |
984 | Column/Row Iterator</a> , the following expressions must be | |
985 | valid.</p> | |
986 | <table border="1" summary="expressions"> | |
987 | <tbody> | |
988 | <tr> | |
989 | <th>Name</th> | |
990 | <th>Expression</th> | |
991 | <th>Type requirements</th> | |
992 | <th>Return type</th> | |
993 | </tr> | |
994 | <tr> | |
995 | <td>Forward motion</td> | |
996 | <td><code>it += n</code></td> | |
997 | <td> </td> | |
998 | <td><code>I &</code></td> | |
999 | </tr> | |
1000 | <tr> | |
1001 | <td>Iterator addition</td> | |
1002 | <td><code>it + n</code></td> | |
1003 | <td> </td> | |
1004 | <td><code>I</code></td> | |
1005 | </tr> | |
1006 | <tr> | |
1007 | <td>Backward motion</td> | |
1008 | <td><code>i -= n</code></td> | |
1009 | <td> </td> | |
1010 | <td><code>I &</code></td> | |
1011 | </tr> | |
1012 | <tr> | |
1013 | <td>Iterator subtraction</td> | |
1014 | <td><code>it - n</code></td> | |
1015 | <td> </td> | |
1016 | <td><code>I</code> </td> | |
1017 | </tr> | |
1018 | <tr> | |
1019 | <td>Difference</td> | |
1020 | <td><code>it1 - it2</code></td> | |
1021 | <td> </td> | |
1022 | <td><code>C::difference_type</code></td> | |
1023 | </tr> | |
1024 | <tr> | |
1025 | <td>Element operator</td> | |
1026 | <td><code>it [n]</code></td> | |
1027 | <td> </td> | |
1028 | <td>Convertible to <code>T</code>.</td> | |
1029 | </tr> | |
1030 | <tr> | |
1031 | <td>Element assignment</td> | |
1032 | <td><code>it [n] = t</code></td> | |
1033 | <td><code>I</code> is mutable</td> | |
1034 | <td>Convertible to <code>T</code>.</td> | |
1035 | </tr> | |
1036 | </tbody> | |
1037 | </table> | |
1038 | <h4>Expression Semantics</h4> | |
1039 | <p>Semantics of an expression is defined only where it differs | |
1040 | from, or is not defined in, <a href= | |
1041 | "#indexed_bidirectional_cr_iterator">Indexed Bidirectional | |
1042 | Column/Row Iterator</a> .</p> | |
1043 | <table border="1" summary="semantics"> | |
1044 | <tbody> | |
1045 | <tr> | |
1046 | <th>Name</th> | |
1047 | <th>Expression</th> | |
1048 | <th>Precondition</th> | |
1049 | <th>Semantics</th> | |
1050 | <th>Postcondition</th> | |
1051 | </tr> | |
1052 | <tr> | |
1053 | <td>Forward motion</td> | |
1054 | <td><code>it += n</code></td> | |
1055 | <td>Including <code>it</code> itself, there must be <code>n</code> | |
1056 | dereferenceable or past-the-end iterators following or preceding | |
1057 | <code>it</code>, depending on whether <code>n</code> is positive or | |
1058 | negative.</td> | |
1059 | <td>If <code>n > 0</code>, equivalent to executing <code>++ | |
1060 | it</code> <code>n</code> times. If <code>n < 0</code>, | |
1061 | equivalent to executing <code>-- it</code> <code>n</code> times. If | |
1062 | <code>n == 0</code>, this is a null operation.</td> | |
1063 | <td><code>it</code> is dereferenceable or past-the-end.</td> | |
1064 | </tr> | |
1065 | <tr> | |
1066 | <td>Iterator addition</td> | |
1067 | <td><code>it + n</code></td> | |
1068 | <td>Same as for <code>i += n</code>.</td> | |
1069 | <td>Equivalent to<br /> | |
1070 | <code>{<br /> | |
1071 | I itt = it;<br /> | |
1072 | return itt += n;<br /> | |
1073 | }</code></td> | |
1074 | <td>Result is dereferenceable or past-the-end.</td> | |
1075 | </tr> | |
1076 | <tr> | |
1077 | <td>Backward motion</td> | |
1078 | <td><code>it -= n</code></td> | |
1079 | <td>Including <code>it</code> itself, there must be <code>n</code> | |
1080 | dereferenceable or past-the-end iterators preceding or following | |
1081 | <code>it</code>, depending on whether <code>n</code> is positive or | |
1082 | negative.</td> | |
1083 | <td>Equivalent to <code>it += (-n)</code>.</td> | |
1084 | <td><code>it</code> is dereferenceable or past-the-end.</td> | |
1085 | </tr> | |
1086 | <tr> | |
1087 | <td>Iterator subtraction</td> | |
1088 | <td><code>it - n</code></td> | |
1089 | <td>Same as for <code>i -= n</code>.</td> | |
1090 | <td>Equivalent to<br /> | |
1091 | <code>{<br /> | |
1092 | I itt = it;<br /> | |
1093 | return itt -= n;<br /> | |
1094 | }</code></td> | |
1095 | <td>Result is dereferenceable or past-the-end.</td> | |
1096 | </tr> | |
1097 | <tr> | |
1098 | <td>Difference</td> | |
1099 | <td><code>it1 - it2</code></td> | |
1100 | <td>Either <code>it1</code> is reachable from <code>it2</code> or | |
1101 | <code>it2</code> is reachable from <code>it1</code>, or both.</td> | |
1102 | <td>Returns a number <code>n</code> such that <code>it1 == it2 + | |
1103 | n</code></td> | |
1104 | <td> </td> | |
1105 | </tr> | |
1106 | <tr> | |
1107 | <td>Element operator</td> | |
1108 | <td><code>it [n]</code></td> | |
1109 | <td><code>it + n</code> exists and is dereferenceable.</td> | |
1110 | <td>Equivalent to <code>*(it + n)</code></td> | |
1111 | <td> </td> | |
1112 | </tr> | |
1113 | <tr> | |
1114 | <td>Element assignment</td> | |
1115 | <td><code>i[n] = t</code></td> | |
1116 | <td>Same as for <code>it [n]</code>.</td> | |
1117 | <td>Equivalent to <code>*(it + n) = t</code></td> | |
1118 | <td> </td> | |
1119 | </tr> | |
1120 | </tbody> | |
1121 | </table> | |
1122 | <h4>Complexity guarantees</h4> | |
1123 | <p>The complexity of operations on indexed random access Column/Row | |
1124 | iterators is guaranteed to be amortized constant time.</p> | |
1125 | <h4>Invariants</h4> | |
1126 | <table border="1" summary="invariants"> | |
1127 | <tbody> | |
1128 | <tr> | |
1129 | <td>Symmetry of addition and subtraction</td> | |
1130 | <td>If <code>it + n</code> is well-defined, then <code>it += n; it | |
1131 | -= n;</code> and <code>(it + n) - n</code> are null operations. | |
1132 | Similarly, if <code>it - n</code> is well-defined, then <code>it -= | |
1133 | n; it += n;</code> and <code>(it - n) + n</code> are null | |
1134 | operations.</td> | |
1135 | </tr> | |
1136 | <tr> | |
1137 | <td>Relation between distance and addition</td> | |
1138 | <td>If <code>it1 - it2</code> is well-defined, then <code>it1 == | |
1139 | it2 + (it1 - it2)</code>.</td> | |
1140 | </tr> | |
1141 | <tr> | |
1142 | <td>Reachability and distance</td> | |
1143 | <td>If <code>it1</code> is reachable from <code>it2</code>, then | |
1144 | <code>it1 - it2 >= 0</code>.</td> | |
1145 | </tr> | |
1146 | </tbody> | |
1147 | </table> | |
1148 | <h4>Models</h4> | |
1149 | <ul> | |
1150 | <li><code>matrix::iterator1</code></li> | |
1151 | <li><code>matrix::iterator2</code></li> | |
1152 | </ul> | |
1153 | <hr /> | |
1154 | <p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch<br /> | |
1155 | Use, modification and distribution are subject to the | |
1156 | Boost Software License, Version 1.0. | |
1157 | (See accompanying file LICENSE_1_0.txt | |
1158 | or copy at <a href="http://www.boost.org/LICENSE_1_0.txt"> | |
1159 | http://www.boost.org/LICENSE_1_0.txt | |
1160 | </a>). | |
1161 | </p> | |
1162 | <script type="text/javascript"> | |
1163 | (function($) { | |
1164 | $('#toc').toc(); | |
1165 | })(jQuery); | |
1166 | </script> | |
1167 | </body> | |
1168 | </html> |