Brian Silverman | dc6866b | 2018-08-05 00:18:23 -0700 | [diff] [blame^] | 1 | <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" |
| 2 | "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> |
| 3 | <html xmlns="http://www.w3.org/1999/xhtml"> |
| 4 | <head> |
| 5 | <meta name="generator" content= |
| 6 | "HTML Tidy for Linux/x86 (vers 1st March 2004), see www.w3.org" /> |
| 7 | <meta http-equiv="Content-Type" content= |
| 8 | "text/html; charset=us-ascii" /> |
| 9 | <link rel="stylesheet" href="../../../../boost.css" type="text/css"/> |
| 10 | <link rel="stylesheet" href="ublas.css" type="text/css" /> |
| 11 | <script type="text/javascript" src="js/jquery-1.3.2.min.js" async="async" ></script> |
| 12 | <script type="text/javascript" src="js/jquery.toc-gw.js" async="async" ></script> |
| 13 | <title>Iterator Concepts</title> |
| 14 | </head> |
| 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> |