ceph/src/boost/libs/numeric/ublas/doc/banded.html

   1 <!DOCTYPE html PUBLIC "-//W3C/utf-8XHTML 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>Banded Matrix</title>
  14 </head>
  15 <body>
  16 <h1><img src="../../../../boost.png" align="middle" />Banded Matrix</h1>
  17 <div class="toc" id="toc"></div>
  18 <h2><a name="banded_matrix"></a>Banded Matrix</h2>
  19 <h4>Description</h4>
  20 <p>The templated class <code>banded_matrix&lt;T, F, A&gt;</code> is
  21 the base container adaptor for banded matrices. For a <em>(m x
  22 n</em>)-dimensional banded matrix with <em>l</em> lower and
  23 <em>u</em> upper diagonals and <em>0 &lt;= i &lt; m</em>, <em>0
  24 &lt;= j &lt; n</em> holds <em>b</em><sub><em>i, j</em></sub> <em>=
  25 0</em>, if <em>i &gt; j + l</em> or <em>i &lt; j - u</em>. The
  26 storage of banded matrices is packed.</p>
  27 <h4>Example</h4>
  28 <pre>
  29 #include &lt;boost/numeric/ublas/banded.hpp&gt;
  30 #include &lt;boost/numeric/ublas/io.hpp&gt;
  31
  32 int main () {
  33     using namespace boost::numeric::ublas;
  34     banded_matrix&lt;double&gt; m (3, 3, 1, 1);
  35     for (signed i = 0; i &lt; signed (m.size1 ()); ++ i)
  36         for (signed j = std::max (i - 1, 0); j &lt; std::min (i + 2, signed (m.size2 ())); ++ j)
  37             m (i, j) = 3 * i + j;
  38     std::cout &lt;&lt; m &lt;&lt; std::endl;
  39 }
  40 </pre>
  41 <h4>Definition</h4>
  42 <p>Defined in the header banded.hpp.</p>
  43 <h4>Template parameters</h4>
  44 <table border="1" summary="parameters">
  45 <tbody>
  46 <tr>
  47 <th>Parameter</th>
  48 <th>Description</th>
  49 <th>Default</th>
  50 </tr>
  51 <tr>
  52 <td><code>T</code></td>
  53 <td>The type of object stored in the matrix.</td>
  54 <td></td>
  55 </tr>
  56 <tr>
  57 <td><code>F</code></td>
  58 <td>Functor describing the storage organization. <a href=
  59 "#banded_matrix_1">[1]</a></td>
  60 <td><code>row_major</code></td>
  61 </tr>
  62 <tr>
  63 <td><code>A</code></td>
  64 <td>The type of the adapted array. <a href=
  65 "#banded_matrix_2">[2]</a></td>
  66 <td><code>unbounded_array&lt;T&gt;</code></td>
  67 </tr>
  68 </tbody>
  69 </table>
  70 <h4>Model of</h4>
  71 <p><a href="container_concept.html#matrix">Matrix</a> .</p>
  72 <h4>Type requirements</h4>
  73 <p>None, except for those imposed by the requirements of <a href=
  74 "container_concept.html#matrix">Matrix</a> .</p>
  75 <h4>Public base classes</h4>
  76 <p><code>matrix_container&lt;banded_matrix&lt;T, F, A&gt;
  77 &gt;</code></p>
  78 <h4>Members</h4>
  79 <table border="1" summary="members">
  80 <tbody>
  81 <tr>
  82 <th>Member</th>
  83 <th>Description</th>
  84 </tr>
  85 <tr>
  86 <td><code>banded_matrix ()</code></td>
  87 <td>Allocates an uninitialized <code>banded_matrix</code> that
  88 holds zero rows of zero elements.</td>
  89 </tr>
  90 <tr>
  91 <td><code>banded_matrix (size_type size1, size_type size2,
  92 size_type lower = 0, size_type upper = 0)</code></td>
  93 <td>Allocates an uninitialized <code>banded_matrix</code> that
  94 holds <code>(lower + 1 + upper)</code> diagonals around the main
  95 diagonal of a matrix with <code>size1</code> rows of
  96 <code>size2</code> elements.</td>
  97 </tr>
  98 <tr>
  99 <td><code>banded_matrix (const banded_matrix &amp;m)</code></td>
 100 <td>The copy constructor.</td>
 101 </tr>
 102 <tr>
 103 <td><code>template&lt;class AE&gt;<br />
 104 banded_matrix (const matrix_expression&lt;AE&gt;
 105 &amp;ae)</code></td>
 106 <td>The extended copy constructor.</td>
 107 </tr>
 108 <tr>
 109 <td><code>void resize (size_type size1, size_type size2, size_type
 110 lower = 0, size_type upper = 0, bool preserve = true)</code></td>
 111 <td>Reallocates a <code>banded_matrix</code> to hold <code>(lower +
 112 1 + upper)</code> diagonals around the main diagonal of a matrix
 113 with <code>size1</code> rows of <code>size2</code> elements. The
 114 existing elements of the <code>banded_matrix</code> are preseved
 115 when specified.</td>
 116 </tr>
 117 <tr>
 118 <td><code>size_type size1 () const</code></td>
 119 <td>Returns the number of rows.</td>
 120 </tr>
 121 <tr>
 122 <td><code>size_type size2 () const</code></td>
 123 <td>Returns the number of columns.</td>
 124 </tr>
 125 <tr>
 126 <td><code>size_type lower () const</code></td>
 127 <td>Returns the number of diagonals below the main diagonal.</td>
 128 </tr>
 129 <tr>
 130 <td><code>size_type upper () const</code></td>
 131 <td>Returns the number of diagonals above the main diagonal.</td>
 132 </tr>
 133 <tr>
 134 <td><code>const_reference operator () (size_type i, size_type j)
 135 const</code></td>
 136 <td>Returns a <code>const</code> reference of the <code>j</code>
 137 -th element in the <code>i</code>-th row.</td>
 138 </tr>
 139 <tr>
 140 <td><code>reference operator () (size_type i, size_type
 141 j)</code></td>
 142 <td>Returns a reference of the <code>j</code>-th element in the
 143 <code>i</code>-th row.</td>
 144 </tr>
 145 <tr>
 146 <td><code>banded_matrix &amp;operator = (const banded_matrix
 147 &amp;m)</code></td>
 148 <td>The assignment operator.</td>
 149 </tr>
 150 <tr>
 151 <td><code>banded_matrix &amp;assign_temporary (banded_matrix
 152 &amp;m)</code></td>
 153 <td>Assigns a temporary. May change the banded matrix
 154 <code>m</code> .</td>
 155 </tr>
 156 <tr>
 157 <td><code>template&lt;class AE&gt;<br />
 158 banded_matrix &amp;operator = (const matrix_expression&lt;AE&gt;
 159 &amp;ae)</code></td>
 160 <td>The extended assignment operator.</td>
 161 </tr>
 162 <tr>
 163 <td><code>template&lt;class AE&gt;<br />
 164 banded_matrix &amp;assign (const matrix_expression&lt;AE&gt;
 165 &amp;ae)</code></td>
 166 <td>Assigns a matrix expression to the banded matrix. Left and
 167 right hand side of the assignment should be independent.</td>
 168 </tr>
 169 <tr>
 170 <td><code>template&lt;class AE&gt;<br />
 171 banded_matrix &amp;operator += (const matrix_expression&lt;AE&gt;
 172 &amp;ae)</code></td>
 173 <td>A computed assignment operator. Adds the matrix expression to
 174 the banded matrix.</td>
 175 </tr>
 176 <tr>
 177 <td><code>template&lt;class AE&gt;<br />
 178 banded_matrix &amp;plus_assign (const matrix_expression&lt;AE&gt;
 179 &amp;ae)</code></td>
 180 <td>Adds a matrix expression to the banded matrix. Left and right
 181 hand side of the assignment should be independent.</td>
 182 </tr>
 183 <tr>
 184 <td><code>template&lt;class AE&gt;<br />
 185 banded_matrix &amp;operator -= (const matrix_expression&lt;AE&gt;
 186 &amp;ae)</code></td>
 187 <td>A computed assignment operator. Subtracts the matrix expression
 188 from the banded matrix.</td>
 189 </tr>
 190 <tr>
 191 <td><code>template&lt;class AE&gt;<br />
 192 banded_matrix &amp;minus_assign (const matrix_expression&lt;AE&gt;
 193 &amp;ae)</code></td>
 194 <td>Subtracts a matrix expression from the banded matrix. Left and
 195 right hand side of the assignment should be independent.</td>
 196 </tr>
 197 <tr>
 198 <td><code>template&lt;class AT&gt;<br />
 199 banded_matrix &amp;operator *= (const AT &amp;at)</code></td>
 200 <td>A computed assignment operator. Multiplies the banded matrix
 201 with a scalar.</td>
 202 </tr>
 203 <tr>
 204 <td><code>template&lt;class AT&gt;<br />
 205 banded_matrix &amp;operator /= (const AT &amp;at)</code></td>
 206 <td>A computed assignment operator. Divides the banded matrix
 207 through a scalar.</td>
 208 </tr>
 209 <tr>
 210 <td><code>void swap (banded_matrix &amp;m)</code></td>
 211 <td>Swaps the contents of the banded matrices.</td>
 212 </tr>
 213 <tr>
 214 <td><code>void insert (size_type i, size_type j, const_reference
 215 t)</code></td>
 216 <td>Inserts the value <code>t</code> at the <code>j</code>-th
 217 element of the <code>i</code>-th row.</td>
 218 </tr>
 219 <tr>
 220 <td><code>void erase (size_type i, size_type j)</code></td>
 221 <td>Erases the value at the <code>j</code>-th elemenst of the
 222 <code>i</code>-th row.</td>
 223 </tr>
 224 <tr>
 225 <td><code>void clear ()</code></td>
 226 <td>Clears the matrix.</td>
 227 </tr>
 228 <tr>
 229 <td><code>const_iterator1 begin1 () const</code></td>
 230 <td>Returns a <code>const_iterator1</code> pointing to the
 231 beginning of the <code>banded_matrix</code>.</td>
 232 </tr>
 233 <tr>
 234 <td><code>const_iterator1 end1 () const</code></td>
 235 <td>Returns a <code>const_iterator1</code> pointing to the end of
 236 the <code>banded_matrix</code>.</td>
 237 </tr>
 238 <tr>
 239 <td><code>iterator1 begin1 ()</code></td>
 240 <td>Returns a <code>iterator1</code> pointing to the beginning of
 241 the <code>banded_matrix</code>.</td>
 242 </tr>
 243 <tr>
 244 <td><code>iterator1 end1 ()</code></td>
 245 <td>Returns a <code>iterator1</code> pointing to the end of the
 246 <code>banded_matrix</code>.</td>
 247 </tr>
 248 <tr>
 249 <td><code>const_iterator2 begin2 () const</code></td>
 250 <td>Returns a <code>const_iterator2</code> pointing to the
 251 beginning of the <code>banded_matrix</code>.</td>
 252 </tr>
 253 <tr>
 254 <td><code>const_iterator2 end2 () const</code></td>
 255 <td>Returns a <code>const_iterator2</code> pointing to the end of
 256 the <code>banded_matrix</code>.</td>
 257 </tr>
 258 <tr>
 259 <td><code>iterator2 begin2 ()</code></td>
 260 <td>Returns a <code>iterator2</code> pointing to the beginning of
 261 the <code>banded_matrix</code>.</td>
 262 </tr>
 263 <tr>
 264 <td><code>iterator2 end2 ()</code></td>
 265 <td>Returns a <code>iterator2</code> pointing to the end of the
 266 <code>banded_matrix</code>.</td>
 267 </tr>
 268 <tr>
 269 <td><code>const_reverse_iterator1 rbegin1 () const</code></td>
 270 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 271 beginning of the reversed <code>banded_matrix</code>.</td>
 272 </tr>
 273 <tr>
 274 <td><code>const_reverse_iterator1 rend1 () const</code></td>
 275 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 276 end of the reversed <code>banded_matrix</code>.</td>
 277 </tr>
 278 <tr>
 279 <td><code>reverse_iterator1 rbegin1 ()</code></td>
 280 <td>Returns a <code>reverse_iterator1</code> pointing to the
 281 beginning of the reversed <code>banded_matrix</code>.</td>
 282 </tr>
 283 <tr>
 284 <td><code>reverse_iterator1 rend1 ()</code></td>
 285 <td>Returns a <code>reverse_iterator1</code> pointing to the end of
 286 the reversed <code>banded_matrix</code>.</td>
 287 </tr>
 288 <tr>
 289 <td><code>const_reverse_iterator2 rbegin2 () const</code></td>
 290 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 291 beginning of the reversed <code>banded_matrix</code>.</td>
 292 </tr>
 293 <tr>
 294 <td><code>const_reverse_iterator2 rend2 () const</code></td>
 295 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 296 end of the reversed <code>banded_matrix</code>.</td>
 297 </tr>
 298 <tr>
 299 <td><code>reverse_iterator2 rbegin2 ()</code></td>
 300 <td>Returns a <code>reverse_iterator2</code> pointing to the
 301 beginning of the reversed <code>banded_matrix</code>.</td>
 302 </tr>
 303 <tr>
 304 <td><code>reverse_iterator2 rend2 ()</code></td>
 305 <td>Returns a <code>reverse_iterator2</code> pointing to the end of
 306 the reversed <code>banded_matrix</code>.</td>
 307 </tr>
 308 </tbody>
 309 </table>
 310 <h4>Notes</h4>
 311 <p><a name="banded_matrix_1" id="banded_matrix_1">[1]</a> Supported
 312 parameters for the storage organization are <code>row_major</code>
 313 and <code>column_major</code>.</p>
 314 <p><a name="banded_matrix_2" id="banded_matrix_2">[2]</a> Supported
 315 parameters for the adapted array are
 316 <code>unbounded_array&lt;T&gt;</code> ,
 317 <code>bounded_array&lt;T&gt;</code> and
 318 <code>std::vector&lt;T&gt;</code> .</p>
 319 <h2><a name="banded_adaptor"></a>Banded Adaptor</h2>
 320 <h4>Description</h4>
 321 <p>The templated class <code>banded_adaptor&lt;M&gt;</code> is a
 322 banded matrix adaptor for other matrices.</p>
 323 <h4>Example</h4>
 324 <pre>
 325 #include &lt;boost/numeric/ublas/banded.hpp&gt;
 326 #include &lt;boost/numeric/ublas/io.hpp&gt;
 327
 328 int main () {
 329     using namespace boost::numeric::ublas;
 330     matrix&lt;double&gt; m (3, 3);
 331     banded_adaptor&lt;matrix&lt;double&gt; &gt; ba (m, 1, 1);
 332     for (signed i = 0; i &lt; signed (ba.size1 ()); ++ i)
 333         for (signed j = std::max (i - 1, 0); j &lt; std::min (i + 2, signed (ba.size2 ())); ++ j)
 334             ba (i, j) = 3 * i + j;
 335     std::cout &lt;&lt; ba &lt;&lt; std::endl;
 336 }
 337 </pre>
 338 <h4>Definition</h4>
 339 <p>Defined in the header banded.hpp.</p>
 340 <h4>Template parameters</h4>
 341 <table border="1" summary="parameters">
 342 <tbody>
 343 <tr>
 344 <th>Parameter</th>
 345 <th>Description</th>
 346 <th>Default</th>
 347 </tr>
 348 <tr>
 349 <td><code>M</code></td>
 350 <td>The type of the adapted matrix.</td>
 351 <td></td>
 352 </tr>
 353 </tbody>
 354 </table>
 355 <h4>Model of</h4>
 356 <p><a href="expression_concept.html#matrix_expression">Matrix Expression</a>
 357 .</p>
 358 <h4>Type requirements</h4>
 359 <p>None, except for those imposed by the requirements of <a href=
 360 "expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
 361 <h4>Public base classes</h4>
 362 <p><code>matrix_expression&lt;banded_adaptor&lt;M&gt;
 363 &gt;</code></p>
 364 <h4>Members</h4>
 365 <table border="1" summary="members">
 366 <tbody>
 367 <tr>
 368 <th>Member</th>
 369 <th>Description</th>
 370 </tr>
 371 <tr>
 372 <td><code>banded_adaptor (matrix_type &amp;data, size_type lower =
 373 0, size_type upper = 0)</code></td>
 374 <td>Constructs a <code>banded_adaptor</code> that holds
 375 <code>(lower + 1 + upper)</code> diagonals around the main diagonal
 376 of a matrix.</td>
 377 </tr>
 378 <tr>
 379 <td><code>banded_adaptor (const banded_adaptor &amp;m)</code></td>
 380 <td>The copy constructor.</td>
 381 </tr>
 382 <tr>
 383 <td><code>template&lt;class AE&gt;<br />
 384 banded_adaptor (const matrix_expression&lt;AE&gt;
 385 &amp;ae)</code></td>
 386 <td>The extended copy constructor.</td>
 387 </tr>
 388 <tr>
 389 <td><code>size_type size1 () const</code></td>
 390 <td>Returns the number of rows.</td>
 391 </tr>
 392 <tr>
 393 <td><code>size_type size2 () const</code></td>
 394 <td>Returns the number of columns.</td>
 395 </tr>
 396 <tr>
 397 <td><code>size_type lower () const</code></td>
 398 <td>Returns the number of diagonals below the main diagonal.</td>
 399 </tr>
 400 <tr>
 401 <td><code>size_type upper () const</code></td>
 402 <td>Returns the number of diagonals above the main diagonal.</td>
 403 </tr>
 404 <tr>
 405 <td><code>const_reference operator () (size_type i, size_type j)
 406 const</code></td>
 407 <td>Returns a <code>const</code> reference of the <code>j</code>
 408 -th element in the <code>i</code>-th row.</td>
 409 </tr>
 410 <tr>
 411 <td><code>reference operator () (size_type i, size_type
 412 j)</code></td>
 413 <td>Returns a reference of the <code>j</code>-th element in the
 414 <code>i</code>-th row.</td>
 415 </tr>
 416 <tr>
 417 <td><code>banded_adaptor &amp;operator = (const banded_adaptor
 418 &amp;m)</code></td>
 419 <td>The assignment operator.</td>
 420 </tr>
 421 <tr>
 422 <td><code>banded_adaptor &amp;assign_temporary (banded_adaptor
 423 &amp;m)</code></td>
 424 <td>Assigns a temporary. May change the banded adaptor
 425 <code>m</code> .</td>
 426 </tr>
 427 <tr>
 428 <td><code>template&lt;class AE&gt;<br />
 429 banded_adaptor &amp;operator = (const matrix_expression&lt;AE&gt;
 430 &amp;ae)</code></td>
 431 <td>The extended assignment operator.</td>
 432 </tr>
 433 <tr>
 434 <td><code>template&lt;class AE&gt;<br />
 435 banded_adaptor &amp;assign (const matrix_expression&lt;AE&gt;
 436 &amp;ae)</code></td>
 437 <td>Assigns a matrix expression to the banded adaptor. Left and
 438 right hand side of the assignment should be independent.</td>
 439 </tr>
 440 <tr>
 441 <td><code>template&lt;class AE&gt;<br />
 442 banded_adaptor &amp;operator += (const matrix_expression&lt;AE&gt;
 443 &amp;ae)</code></td>
 444 <td>A computed assignment operator. Adds the matrix expression to
 445 the banded adaptor.</td>
 446 </tr>
 447 <tr>
 448 <td><code>template&lt;class AE&gt;<br />
 449 banded_adaptor &amp;plus_assign (const matrix_expression&lt;AE&gt;
 450 &amp;ae)</code></td>
 451 <td>Adds a matrix expression to the banded adaptor. Left and right
 452 hand side of the assignment should be independent.</td>
 453 </tr>
 454 <tr>
 455 <td><code>template&lt;class AE&gt;<br />
 456 banded_adaptor &amp;operator -= (const matrix_expression&lt;AE&gt;
 457 &amp;ae)</code></td>
 458 <td>A computed assignment operator. Subtracts the matrix expression
 459 from the banded adaptor.</td>
 460 </tr>
 461 <tr>
 462 <td><code>template&lt;class AE&gt;<br />
 463 banded_adaptor &amp;minus_assign (const matrix_expression&lt;AE&gt;
 464 &amp;ae)</code></td>
 465 <td>Subtracts a matrix expression from the banded adaptor. Left and
 466 right hand side of the assignment should be independent.</td>
 467 </tr>
 468 <tr>
 469 <td><code>template&lt;class AT&gt;<br />
 470 banded_adaptor &amp;operator *= (const AT &amp;at)</code></td>
 471 <td>A computed assignment operator. Multiplies the banded adaptor
 472 with a scalar.</td>
 473 </tr>
 474 <tr>
 475 <td><code>template&lt;class AT&gt;<br />
 476 banded_adaptor &amp;operator /= (const AT &amp;at)</code></td>
 477 <td>A computed assignment operator. Divides the banded adaptor
 478 through a scalar.</td>
 479 </tr>
 480 <tr>
 481 <td><code>void swap (banded_adaptor &amp;m)</code></td>
 482 <td>Swaps the contents of the banded adaptors.</td>
 483 </tr>
 484 <tr>
 485 <td><code>const_iterator1 begin1 () const</code></td>
 486 <td>Returns a <code>const_iterator1</code> pointing to the
 487 beginning of the <code>banded_adaptor</code>.</td>
 488 </tr>
 489 <tr>
 490 <td><code>const_iterator1 end1 () const</code></td>
 491 <td>Returns a <code>const_iterator1</code> pointing to the end of
 492 the <code>banded_adaptor</code>.</td>
 493 </tr>
 494 <tr>
 495 <td><code>iterator1 begin1 ()</code></td>
 496 <td>Returns a <code>iterator1</code> pointing to the beginning of
 497 the <code>banded_adaptor</code>.</td>
 498 </tr>
 499 <tr>
 500 <td><code>iterator1 end1 ()</code></td>
 501 <td>Returns a <code>iterator1</code> pointing to the end of the
 502 <code>banded_adaptor</code>.</td>
 503 </tr>
 504 <tr>
 505 <td><code>const_iterator2 begin2 () const</code></td>
 506 <td>Returns a <code>const_iterator2</code> pointing to the
 507 beginning of the <code>banded_adaptor</code>.</td>
 508 </tr>
 509 <tr>
 510 <td><code>const_iterator2 end2 () const</code></td>
 511 <td>Returns a <code>const_iterator2</code> pointing to the end of
 512 the <code>banded_adaptor</code>.</td>
 513 </tr>
 514 <tr>
 515 <td><code>iterator2 begin2 ()</code></td>
 516 <td>Returns a <code>iterator2</code> pointing to the beginning of
 517 the <code>banded_adaptor</code>.</td>
 518 </tr>
 519 <tr>
 520 <td><code>iterator2 end2 ()</code></td>
 521 <td>Returns a <code>iterator2</code> pointing to the end of the
 522 <code>banded_adaptor</code>.</td>
 523 </tr>
 524 <tr>
 525 <td><code>const_reverse_iterator1 rbegin1 () const</code></td>
 526 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 527 beginning of the reversed <code>banded_adaptor</code>.</td>
 528 </tr>
 529 <tr>
 530 <td><code>const_reverse_iterator1 rend1 () const</code></td>
 531 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 532 end of the reversed <code>banded_adaptor</code>.</td>
 533 </tr>
 534 <tr>
 535 <td><code>reverse_iterator1 rbegin1 ()</code></td>
 536 <td>Returns a <code>reverse_iterator1</code> pointing to the
 537 beginning of the reversed <code>banded_adaptor</code>.</td>
 538 </tr>
 539 <tr>
 540 <td><code>reverse_iterator1 rend1 ()</code></td>
 541 <td>Returns a <code>reverse_iterator1</code> pointing to the end of
 542 the reversed <code>banded_adaptor</code>.</td>
 543 </tr>
 544 <tr>
 545 <td><code>const_reverse_iterator2 rbegin2 () const</code></td>
 546 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 547 beginning of the reversed <code>banded_adaptor</code>.</td>
 548 </tr>
 549 <tr>
 550 <td><code>const_reverse_iterator2 rend2 () const</code></td>
 551 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 552 end of the reversed <code>banded_adaptor</code>.</td>
 553 </tr>
 554 <tr>
 555 <td><code>reverse_iterator2 rbegin2 ()</code></td>
 556 <td>Returns a <code>reverse_iterator2</code> pointing to the
 557 beginning of the reversed <code>banded_adaptor</code>.</td>
 558 </tr>
 559 <tr>
 560 <td><code>reverse_iterator2 rend2 ()</code></td>
 561 <td>Returns a <code>reverse_iterator2</code> pointing to the end of
 562 the reversed <code>banded_adaptor</code>.</td>
 563 </tr>
 564 </tbody>
 565 </table>
 566 <hr />
 567 <p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
 568    Use, modification and distribution are subject to the
 569    Boost Software License, Version 1.0.
 570    (See accompanying file LICENSE_1_0.txt
 571    or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
 572       http://www.boost.org/LICENSE_1_0.txt</a>).
 573 </p>
 574 <script type="text/javascript">
 575 (function($) {
 576     $('#toc').toc();
 577 })(jQuery);
 578 </script>
 579 </body>
 580 </html>