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

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  13 <title>Hermitian Matrix</title>
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  16 <h1><img src="../../../../boost.png" align="middle" />Hermitian Matrix</h1>
  17 <div class="toc" id="toc"></div>
  18 <h2><a name="hermitian_matrix"></a>Hermitian Matrix</h2>
  19 <h4>Description</h4>
  20 <p>The templated class <code>hermitian_matrix&lt;T, F1, F2,
  21 A&gt;</code> is the base container adaptor for hermitian matrices.
  22 For a <em>(n x n</em> )-dimensional hermitian matrix and <em>0
  23 &lt;= i &lt; n</em>, <em>0 &lt;= j &lt; n</em> holds
  24 <em>h</em><sub><em>i, j</em></sub> <em>= h</em><sub><em>j,
  25 i</em></sub><sup><em>-</em></sup>. The storage of hermitian
  26 matrices is packed.</p>
  27 <h4>Example</h4>
  28 <pre>
  29 #include &lt;boost/numeric/ublas/hermitian.hpp&gt;
  30 #include &lt;boost/numeric/ublas/io.hpp&gt;
  31
  32 int main () {
  33     using namespace boost::numeric::ublas;
  34     hermitian_matrix&lt;std::complex&lt;double&gt;, lower&gt; ml (3, 3);
  35     for (unsigned i = 0; i &lt; ml.size1 (); ++ i) {
  36         for (unsigned j = 0; j &lt; i; ++ j)
  37             ml (i, j) = std::complex&lt;double&gt; (3 * i + j, 3 * i + j);
  38         ml (i, i) = std::complex&lt;double&gt; (4 * i, 0);
  39     }
  40     std::cout &lt;&lt; ml &lt;&lt; std::endl;
  41     hermitian_matrix&lt;std::complex&lt;double&gt;, upper&gt; mu (3, 3);
  42     for (unsigned i = 0; i &lt; mu.size1 (); ++ i) {
  43         mu (i, i) = std::complex&lt;double&gt; (4 * i, 0);
  44         for (unsigned j = i + 1; j &lt; mu.size2 (); ++ j)
  45             mu (i, j) = std::complex&lt;double&gt; (3 * i + j, 3 * i + j);
  46     }
  47     std::cout &lt;&lt; mu &lt;&lt; std::endl;
  48 }
  49 </pre>
  50 <h4>Definition</h4>
  51 <p>Defined in the header hermitian.hpp.</p>
  52 <h4>Template parameters</h4>
  53 <table border="1" summary="parameters">
  54 <tbody>
  55 <tr>
  56 <th>Parameter</th>
  57 <th>Description</th>
  58 <th>Default</th>
  59 </tr>
  60 <tr>
  61 <td><code>T</code></td>
  62 <td>The type of object stored in the matrix.</td>
  63 <td></td>
  64 </tr>
  65 <tr>
  66 <td><code>F1</code></td>
  67 <td>Functor describing the type of the hermitian matrix. <a href=
  68 "#hermitian_matrix_1">[1]</a></td>
  69 <td><code>lower</code></td>
  70 </tr>
  71 <tr>
  72 <td><code>F2</code></td>
  73 <td>Functor describing the storage organization. <a href=
  74 "#hermitian_matrix_2">[2]</a></td>
  75 <td><code>row_major</code></td>
  76 </tr>
  77 <tr>
  78 <td><code>A</code></td>
  79 <td>The type of the adapted array. <a href=
  80 "#hermitian_matrix_3">[3]</a></td>
  81 <td><code>unbounded_array&lt;T&gt;</code></td>
  82 </tr>
  83 </tbody>
  84 </table>
  85 <h4>Model of</h4>
  86 <p><a href="container_concept.html#matrix">Matrix</a> .</p>
  87 <h4>Type requirements</h4>
  88 <p>None, except for those imposed by the requirements of <a href=
  89 "container_concept.html#matrix">Matrix</a> .</p>
  90 <h4>Public base classes</h4>
  91 <p><code>matrix_container&lt;hermitian_matrix&lt;T, F1, F2, A&gt;
  92 &gt;</code></p>
  93 <h4>Members</h4>
  94 <table border="1" summary="members">
  95 <tbody>
  96 <tr>
  97 <th>Member</th>
  98 <th>Description</th>
  99 </tr>
 100 <tr>
 101 <td><code>hermitian_matrix ()</code></td>
 102 <td>Allocates an uninitialized <code>hermitian_matrix</code> that
 103 holds zero rows of zero elements.</td>
 104 </tr>
 105 <tr>
 106 <td><code>hermitian_matrix (size_type size)</code></td>
 107 <td>Allocates an uninitialized <code>hermitian_matrix</code> that
 108 holds <code>size</code> rows of <code>size</code> elements.</td>
 109 </tr>
 110 <tr>
 111 <td><code>hermitian_matrix (const hermitian_matrix
 112 &amp;m)</code></td>
 113 <td>The copy constructor.</td>
 114 </tr>
 115 <tr>
 116 <td><code>template&lt;class AE&gt;<br />
 117 hermitian_matrix (const matrix_expression&lt;AE&gt;
 118 &amp;ae)</code></td>
 119 <td>The extended copy constructor.</td>
 120 </tr>
 121 <tr>
 122 <td><code>void resize (size_type size, bool preserve =
 123 true)</code></td>
 124 <td>Reallocates a <code>hermitian_matrix</code> to hold
 125 <code>size</code> rows of <code>size</code> elements. The existing
 126 elements of the <code>hermitian_matrix</code> are preseved when
 127 specified.</td>
 128 </tr>
 129 <tr>
 130 <td><code>size_type size1 () const</code></td>
 131 <td>Returns the number of rows.</td>
 132 </tr>
 133 <tr>
 134 <td><code>size_type size2 () const</code></td>
 135 <td>Returns the number of columns.</td>
 136 </tr>
 137 <tr>
 138 <td><code>const_reference operator () (size_type i, size_type j)
 139 const</code></td>
 140 <td>Returns a <code>const</code> reference of the <code>j</code>
 141 -th element in the <code>i</code>-th row.</td>
 142 </tr>
 143 <tr>
 144 <td><code>reference operator () (size_type i, size_type
 145 j)</code></td>
 146 <td>Returns a reference of the <code>j</code>-th element in the
 147 <code>i</code>-th row.</td>
 148 </tr>
 149 <tr>
 150 <td><code>hermitian_matrix &amp;operator = (const hermitian_matrix
 151 &amp;m)</code></td>
 152 <td>The assignment operator.</td>
 153 </tr>
 154 <tr>
 155 <td><code>hermitian_matrix &amp;assign_temporary (hermitian_matrix
 156 &amp;m)</code></td>
 157 <td>Assigns a temporary. May change the hermitian matrix
 158 <code>m</code> .</td>
 159 </tr>
 160 <tr>
 161 <td><code>template&lt;class AE&gt;<br />
 162 hermitian_matrix &amp;operator = (const matrix_expression&lt;AE&gt;
 163 &amp;ae)</code></td>
 164 <td>The extended assignment operator.</td>
 165 </tr>
 166 <tr>
 167 <td><code>template&lt;class AE&gt;<br />
 168 hermitian_matrix &amp;assign (const matrix_expression&lt;AE&gt;
 169 &amp;ae)</code></td>
 170 <td>Assigns a matrix expression to the hermitian matrix. Left and
 171 right hand side of the assignment should be independent.</td>
 172 </tr>
 173 <tr>
 174 <td><code>template&lt;class AE&gt;<br />
 175 hermitian_matrix &amp;operator += (const
 176 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 177 <td>A computed assignment operator. Adds the matrix expression to
 178 the hermitian matrix.</td>
 179 </tr>
 180 <tr>
 181 <td><code>template&lt;class AE&gt;<br />
 182 hermitian_matrix &amp;plus_assign (const
 183 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 184 <td>Adds a matrix expression to the hermitian matrix. Left and
 185 right hand side of the assignment should be independent.</td>
 186 </tr>
 187 <tr>
 188 <td><code>template&lt;class AE&gt;<br />
 189 hermitian_matrix &amp;operator -= (const
 190 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 191 <td>A computed assignment operator. Subtracts the matrix expression
 192 from the hermitian matrix.</td>
 193 </tr>
 194 <tr>
 195 <td><code>template&lt;class AE&gt;<br />
 196 hermitian_matrix &amp;minus_assign (const
 197 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 198 <td>Subtracts a matrix expression from the hermitian matrix. Left
 199 and right hand side of the assignment should be independent.</td>
 200 </tr>
 201 <tr>
 202 <td><code>template&lt;class AT&gt;<br />
 203 hermitian_matrix &amp;operator *= (const AT &amp;at)</code></td>
 204 <td>A computed assignment operator. Multiplies the hermitian matrix
 205 with a scalar.</td>
 206 </tr>
 207 <tr>
 208 <td><code>template&lt;class AT&gt;<br />
 209 hermitian_matrix &amp;operator /= (const AT &amp;at)</code></td>
 210 <td>A computed assignment operator. Divides the hermitian matrix
 211 through a scalar.</td>
 212 </tr>
 213 <tr>
 214 <td><code>void swap (hermitian_matrix &amp;m)</code></td>
 215 <td>Swaps the contents of the hermitian matrices.</td>
 216 </tr>
 217 <tr>
 218 <td><code>void insert (size_type i, size_type j, const_reference
 219 t)</code></td>
 220 <td>Inserts the value <code>t</code> at the <code>j</code>-th
 221 element of the <code>i</code>-th row.</td>
 222 </tr>
 223 <tr>
 224 <td><code>void erase (size_type i, size_type j)</code></td>
 225 <td>Erases the value at the <code>j</code>-th elemenst of the
 226 <code>i</code>-th row.</td>
 227 </tr>
 228 <tr>
 229 <td><code>void clear ()</code></td>
 230 <td>Clears the matrix.</td>
 231 </tr>
 232 <tr>
 233 <td><code>const_iterator1 begin1 () const</code></td>
 234 <td>Returns a <code>const_iterator1</code> pointing to the
 235 beginning of the <code>hermitian_matrix</code>.</td>
 236 </tr>
 237 <tr>
 238 <td><code>const_iterator1 end1 () const</code></td>
 239 <td>Returns a <code>const_iterator1</code> pointing to the end of
 240 the <code>hermitian_matrix</code>.</td>
 241 </tr>
 242 <tr>
 243 <td><code>iterator1 begin1 ()</code></td>
 244 <td>Returns a <code>iterator1</code> pointing to the beginning of
 245 the <code>hermitian_matrix</code>.</td>
 246 </tr>
 247 <tr>
 248 <td><code>iterator1 end1 ()</code></td>
 249 <td>Returns a <code>iterator1</code> pointing to the end of the
 250 <code>hermitian_matrix</code>.</td>
 251 </tr>
 252 <tr>
 253 <td><code>const_iterator2 begin2 () const</code></td>
 254 <td>Returns a <code>const_iterator2</code> pointing to the
 255 beginning of the <code>hermitian_matrix</code>.</td>
 256 </tr>
 257 <tr>
 258 <td><code>const_iterator2 end2 () const</code></td>
 259 <td>Returns a <code>const_iterator2</code> pointing to the end of
 260 the <code>hermitian_matrix</code>.</td>
 261 </tr>
 262 <tr>
 263 <td><code>iterator2 begin2 ()</code></td>
 264 <td>Returns a <code>iterator2</code> pointing to the beginning of
 265 the <code>hermitian_matrix</code>.</td>
 266 </tr>
 267 <tr>
 268 <td><code>iterator2 end2 ()</code></td>
 269 <td>Returns a <code>iterator2</code> pointing to the end of the
 270 <code>hermitian_matrix</code>.</td>
 271 </tr>
 272 <tr>
 273 <td><code>const_reverse_iterator1 rbegin1 () const</code></td>
 274 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 275 beginning of the reversed <code>hermitian_matrix</code>.</td>
 276 </tr>
 277 <tr>
 278 <td><code>const_reverse_iterator1 rend1 () const</code></td>
 279 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 280 end of the reversed <code>hermitian_matrix</code>.</td>
 281 </tr>
 282 <tr>
 283 <td><code>reverse_iterator1 rbegin1 ()</code></td>
 284 <td>Returns a <code>reverse_iterator1</code> pointing to the
 285 beginning of the reversed <code>hermitian_matrix</code>.</td>
 286 </tr>
 287 <tr>
 288 <td><code>reverse_iterator1 rend1 ()</code></td>
 289 <td>Returns a <code>reverse_iterator1</code> pointing to the end of
 290 the reversed <code>hermitian_matrix</code>.</td>
 291 </tr>
 292 <tr>
 293 <td><code>const_reverse_iterator2 rbegin2 () const</code></td>
 294 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 295 beginning of the reversed <code>hermitian_matrix</code>.</td>
 296 </tr>
 297 <tr>
 298 <td><code>const_reverse_iterator2 rend2 () const</code></td>
 299 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 300 end of the reversed <code>hermitian_matrix</code>.</td>
 301 </tr>
 302 <tr>
 303 <td><code>reverse_iterator2 rbegin2 ()</code></td>
 304 <td>Returns a <code>reverse_iterator2</code> pointing to the
 305 beginning of the reversed <code>hermitian_matrix</code>.</td>
 306 </tr>
 307 <tr>
 308 <td><code>reverse_iterator2 rend2 ()</code></td>
 309 <td>Returns a <code>reverse_iterator2</code> pointing to the end of
 310 the reversed <code>hermitian_matrix</code>.</td>
 311 </tr>
 312 </tbody>
 313 </table>
 314 <h4>Notes</h4>
 315 <p><a name="hermitian_matrix_1" id="hermitian_matrix_1">[1]</a>
 316 Supported parameters for the type of the hermitian matrix are
 317 <code>lower</code> and <code>upper</code>.</p>
 318 <p><a name="hermitian_matrix_2" id="hermitian_matrix_2">[2]</a>
 319 Supported parameters for the storage organization are
 320 <code>row_major</code> and <code>column_major</code>.</p>
 321 <p><a name="hermitian_matrix_3" id="hermitian_matrix_3">[3]</a>
 322 Supported parameters for the adapted array are
 323 <code>unbounded_array&lt;T&gt;</code> ,
 324 <code>bounded_array&lt;T&gt;</code> and
 325 <code>std::vector&lt;T&gt;</code> .</p>
 326 <h2><a name="hermitian_adaptor"></a>Hermitian Adaptor</h2>
 327 <h4>Description</h4>
 328 <p>The templated class <code>hermitian_adaptor&lt;M, F&gt;</code>
 329 is a hermitian matrix adaptor for other matrices.</p>
 330 <h4>Example</h4>
 331 <pre>
 332 #include &lt;boost/numeric/ublas/hermitian.hpp&gt;
 333 #include &lt;boost/numeric/ublas/io.hpp&gt;
 334
 335 int main () {
 336     using namespace boost::numeric::ublas;
 337     matrix&lt;std::complex&lt;double&gt; &gt; m (3, 3);
 338     hermitian_adaptor&lt;matrix&lt;std::complex&lt;double&gt; &gt;, lower&gt; hal (m);
 339     for (unsigned i = 0; i &lt; hal.size1 (); ++ i) {
 340         for (unsigned j = 0; j &lt; i; ++ j)
 341             hal (i, j) = std::complex&lt;double&gt; (3 * i + j, 3 * i + j);
 342         hal (i, i) = std::complex&lt;double&gt; (4 * i, 0);
 343     }
 344     std::cout &lt;&lt; hal &lt;&lt; std::endl;
 345     hermitian_adaptor&lt;matrix&lt;std::complex&lt;double&gt; &gt;, upper&gt; hau (m);
 346     for (unsigned i = 0; i &lt; hau.size1 (); ++ i) {
 347         hau (i, i) = std::complex&lt;double&gt; (4 * i, 0);
 348         for (unsigned j = i + 1; j &lt; hau.size2 (); ++ j)
 349             hau (i, j) = std::complex&lt;double&gt; (3 * i + j, 3 * i + j);
 350     }
 351     std::cout &lt;&lt; hau &lt;&lt; std::endl;
 352 }
 353 </pre>
 354 <h4>Definition</h4>
 355 <p>Defined in the header hermitian.hpp.</p>
 356 <h4>Template parameters</h4>
 357 <table border="1" summary="parameters">
 358 <tbody>
 359 <tr>
 360 <th>Parameter</th>
 361 <th>Description</th>
 362 <th>Default</th>
 363 </tr>
 364 <tr>
 365 <td><code>M</code></td>
 366 <td>The type of the adapted matrix.</td>
 367 <td></td>
 368 </tr>
 369 <tr>
 370 <td><code>F</code></td>
 371 <td>Functor describing the type of the hermitian adaptor. <a href=
 372 "#hermitian_adaptor_1">[1]</a></td>
 373 <td><code>lower</code></td>
 374 </tr>
 375 </tbody>
 376 </table>
 377 <h4>Model of</h4>
 378 <p><a href="expression_concept.html#matrix_expression">Matrix Expression</a>
 379 .</p>
 380 <h4>Type requirements</h4>
 381 <p>None, except for those imposed by the requirements of <a href=
 382 "expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
 383 <h4>Public base classes</h4>
 384 <p><code>matrix_expression&lt;hermitian_adaptor&lt;M, F&gt;
 385 &gt;</code></p>
 386 <h4>Members</h4>
 387 <table border="1" summary="members">
 388 <tbody>
 389 <tr>
 390 <th>Member</th>
 391 <th>Description</th>
 392 </tr>
 393 <tr>
 394 <td><code>hermitian_adaptor (matrix_type &amp;data)</code></td>
 395 <td>Constructs a <code>hermitian_adaptor</code> of a matrix.</td>
 396 </tr>
 397 <tr>
 398 <td><code>hermitian_adaptor (const hermitian_adaptor
 399 &amp;m)</code></td>
 400 <td>The copy constructor.</td>
 401 </tr>
 402 <tr>
 403 <td><code>template&lt;class AE&gt;<br />
 404 hermitian_adaptor (const matrix_expression&lt;AE&gt;
 405 &amp;ae)</code></td>
 406 <td>The extended copy constructor.</td>
 407 </tr>
 408 <tr>
 409 <td><code>size_type size1 () const</code></td>
 410 <td>Returns the number of rows.</td>
 411 </tr>
 412 <tr>
 413 <td><code>size_type size2 () const</code></td>
 414 <td>Returns the number of columns.</td>
 415 </tr>
 416 <tr>
 417 <td><code>const_reference operator () (size_type i, size_type j)
 418 const</code></td>
 419 <td>Returns a <code>const</code> reference of the <code>j</code>
 420 -th element in the <code>i</code>-th row.</td>
 421 </tr>
 422 <tr>
 423 <td><code>reference operator () (size_type i, size_type
 424 j)</code></td>
 425 <td>Returns a reference of the <code>j</code>-th element in the
 426 <code>i</code>-th row.</td>
 427 </tr>
 428 <tr>
 429 <td><code>hermitian_adaptor &amp;operator = (const
 430 hermitian_adaptor &amp;m)</code></td>
 431 <td>The assignment operator.</td>
 432 </tr>
 433 <tr>
 434 <td><code>hermitian_adaptor &amp;assign_temporary
 435 (hermitian_adaptor &amp;m)</code></td>
 436 <td>Assigns a temporary. May change the hermitian adaptor
 437 <code>m</code>.</td>
 438 </tr>
 439 <tr>
 440 <td><code>template&lt;class AE&gt;<br />
 441 hermitian_adaptor &amp;operator = (const
 442 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 443 <td>The extended assignment operator.</td>
 444 </tr>
 445 <tr>
 446 <td><code>template&lt;class AE&gt;<br />
 447 hermitian_adaptor &amp;assign (const matrix_expression&lt;AE&gt;
 448 &amp;ae)</code></td>
 449 <td>Assigns a matrix expression to the hermitian adaptor. Left and
 450 right hand side of the assignment should be independent.</td>
 451 </tr>
 452 <tr>
 453 <td><code>template&lt;class AE&gt;<br />
 454 hermitian_adaptor &amp;operator += (const
 455 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 456 <td>A computed assignment operator. Adds the matrix expression to
 457 the hermitian adaptor.</td>
 458 </tr>
 459 <tr>
 460 <td><code>template&lt;class AE&gt;<br />
 461 hermitian_adaptor &amp;plus_assign (const
 462 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 463 <td>Adds a matrix expression to the hermitian adaptor. Left and
 464 right hand side of the assignment should be independent.</td>
 465 </tr>
 466 <tr>
 467 <td><code>template&lt;class AE&gt;<br />
 468 hermitian_adaptor &amp;operator -= (const
 469 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 470 <td>A computed assignment operator. Subtracts the matrix expression
 471 from the hermitian adaptor.</td>
 472 </tr>
 473 <tr>
 474 <td><code>template&lt;class AE&gt;<br />
 475 hermitian_adaptor &amp;minus_assign (const
 476 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 477 <td>Subtracts a matrix expression from the hermitian adaptor. Left
 478 and right hand side of the assignment should be independent.</td>
 479 </tr>
 480 <tr>
 481 <td><code>template&lt;class AT&gt;<br />
 482 hermitian_adaptor &amp;operator *= (const AT &amp;at)</code></td>
 483 <td>A computed assignment operator. Multiplies the hermitian
 484 adaptor with a scalar.</td>
 485 </tr>
 486 <tr>
 487 <td><code>template&lt;class AT&gt;<br />
 488 hermitian_adaptor &amp;operator /= (const AT &amp;at)</code></td>
 489 <td>A computed assignment operator. Divides the hermitian adaptor
 490 through a scalar.</td>
 491 </tr>
 492 <tr>
 493 <td><code>void swap (hermitian_adaptor &amp;m)</code></td>
 494 <td>Swaps the contents of the hermitian adaptors.</td>
 495 </tr>
 496 <tr>
 497 <td><code>const_iterator1 begin1 () const</code></td>
 498 <td>Returns a <code>const_iterator1</code> pointing to the
 499 beginning of the <code>hermitian_adaptor</code>.</td>
 500 </tr>
 501 <tr>
 502 <td><code>const_iterator1 end1 () const</code></td>
 503 <td>Returns a <code>const_iterator1</code> pointing to the end of
 504 the <code>hermitian_adaptor</code>.</td>
 505 </tr>
 506 <tr>
 507 <td><code>iterator1 begin1 ()</code></td>
 508 <td>Returns a <code>iterator1</code> pointing to the beginning of
 509 the <code>hermitian_adaptor</code>.</td>
 510 </tr>
 511 <tr>
 512 <td><code>iterator1 end1 ()</code></td>
 513 <td>Returns a <code>iterator1</code> pointing to the end of the
 514 <code>hermitian_adaptor</code>.</td>
 515 </tr>
 516 <tr>
 517 <td><code>const_iterator2 begin2 () const</code></td>
 518 <td>Returns a <code>const_iterator2</code> pointing to the
 519 beginning of the <code>hermitian_adaptor</code>.</td>
 520 </tr>
 521 <tr>
 522 <td><code>const_iterator2 end2 () const</code></td>
 523 <td>Returns a <code>const_iterator2</code> pointing to the end of
 524 the <code>hermitian_adaptor</code>.</td>
 525 </tr>
 526 <tr>
 527 <td><code>iterator2 begin2 ()</code></td>
 528 <td>Returns a <code>iterator2</code> pointing to the beginning of
 529 the <code>hermitian_adaptor</code>.</td>
 530 </tr>
 531 <tr>
 532 <td><code>iterator2 end2 ()</code></td>
 533 <td>Returns a <code>iterator2</code> pointing to the end of the
 534 <code>hermitian_adaptor</code>.</td>
 535 </tr>
 536 <tr>
 537 <td><code>const_reverse_iterator1 rbegin1 () const</code></td>
 538 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 539 beginning of the reversed <code>hermitian_adaptor</code>.</td>
 540 </tr>
 541 <tr>
 542 <td><code>const_reverse_iterator1 rend1 () const</code></td>
 543 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 544 end of the reversed <code>hermitian_adaptor</code>.</td>
 545 </tr>
 546 <tr>
 547 <td><code>reverse_iterator1 rbegin1 ()</code></td>
 548 <td>Returns a <code>reverse_iterator1</code> pointing to the
 549 beginning of the reversed <code>hermitian_adaptor</code>.</td>
 550 </tr>
 551 <tr>
 552 <td><code>reverse_iterator1 rend1 ()</code></td>
 553 <td>Returns a <code>reverse_iterator1</code> pointing to the end of
 554 the reversed <code>hermitian_adaptor</code>.</td>
 555 </tr>
 556 <tr>
 557 <td><code>const_reverse_iterator2 rbegin2 () const</code></td>
 558 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 559 beginning of the reversed <code>hermitian_adaptor</code>.</td>
 560 </tr>
 561 <tr>
 562 <td><code>const_reverse_iterator2 rend2 () const</code></td>
 563 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 564 end of the reversed <code>hermitian_adaptor</code>.</td>
 565 </tr>
 566 <tr>
 567 <td><code>reverse_iterator2 rbegin2 ()</code></td>
 568 <td>Returns a <code>reverse_iterator2</code> pointing to the
 569 beginning of the reversed <code>hermitian_adaptor</code>.</td>
 570 </tr>
 571 <tr>
 572 <td><code>reverse_iterator2 rend2 ()</code></td>
 573 <td>Returns a <code>reverse_iterator2</code> pointing to the end of
 574 the reversed <code>hermitian_adaptor</code>.</td>
 575 </tr>
 576 </tbody>
 577 </table>
 578 <h4>Notes</h4>
 579 <p><a name="hermitian_adaptor_1" id="hermitian_adaptor_1">[1]</a>
 580 Supported parameters for the type of the hermitian adaptor are
 581 <code>lower</code> and <code>upper</code>.</p>
 582 <hr />
 583 <p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
 584    Use, modification and distribution are subject to the
 585    Boost Software License, Version 1.0.
 586    (See accompanying file LICENSE_1_0.txt
 587    or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
 588       http://www.boost.org/LICENSE_1_0.txt
 589    </a>).
 590 </p>
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