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

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  13 <title>Sparse Matrix</title>
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  16 <h1><img src="../../../../boost.png" align="middle" />Sparse Matricies</h1>
  17 <div class="toc" id="toc"></div>
  18 <h2><a name="mapped_matrix"></a>Mapped Matrix</h2>
  19 <h4>Description</h4>
  20 <p>The templated class <code>mapped_matrix&lt;T, F, A&gt;</code> is
  21 the base container adaptor for sparse matricies using element maps.
  22 For a <em>(m xn</em>)-dimensional sparse matrix and <em>0 &lt;= i &lt; m</em>,
  23 <em>0 &lt;= j &lt; n</em> the non-zero elements
  24 <em>m</em><sub><em>i, j</em></sub> are mapped via <em>(i x n +
  25 j)</em> for row major orientation or via <em>(i + j x m)</em> for
  26 column major orientation to consecutive elements of the associative
  27 container, i.e. for elements <em>k</em> =
  28 <em>m</em><sub><em>i</em></sub><sub><sub><em>1</em></sub></sub><sub>
  29 <em>,j</em></sub><sub><sub><em>1</em></sub></sub>and <em>k + 1 =
  30 m</em><sub><em>i</em></sub><sub><sub><em>2</em></sub></sub><sub><em>
  31 ,j</em></sub><sub><sub><em>2</em></sub></sub>of the container holds
  32 <em>i</em><sub><em>1</em></sub> <em>&lt;
  33 i</em><sub><em>2</em></sub> or <em>(i</em><sub><em>1</em></sub>
  34 <em>= i</em><sub><em>2</em></sub> and
  35 <em>j</em><sub><em>1</em></sub> <em>&lt;
  36 j</em><sub><em>2</em></sub><em>)</em> with row major orientation or
  37 <em>j</em><sub><em>1</em></sub> <em>&lt;
  38 j</em><sub><em>2</em></sub> or <em>(j</em><sub><em>1</em></sub>
  39 <em>= j</em><sub><em>2</em></sub> and
  40 <em>i</em><sub><em>1</em></sub> <em>&lt;
  41 i</em><sub><em>2</em></sub><em>)</em> with column major
  42 orientation.</p>
  43 <h4>Example</h4>
  44 <pre>
  45 #include &lt;boost/numeric/ublas/matrix_sparse.hpp&gt;
  46 #include &lt;boost/numeric/ublas/io.hpp&gt;
  47
  48 int main () {
  49     using namespace boost::numeric::ublas;
  50     mapped_matrix&lt;double&gt; m (3, 3, 3 * 3);
  51     for (unsigned i = 0; i &lt; m.size1 (); ++ i)
  52         for (unsigned j = 0; j &lt; m.size2 (); ++ j)
  53             m (i, j) = 3 * i + j;
  54     std::cout &lt;&lt; m &lt;&lt; std::endl;
  55 }
  56 </pre>
  57 <h4>Definition</h4>
  58 <p>Defined in the header matrix_sparse.hpp.</p>
  59 <h4>Template parameters</h4>
  60 <table border="1" summary="parameters">
  61 <tbody>
  62 <tr>
  63 <th>Parameter</th>
  64 <th>Description</th>
  65 <th>Default</th>
  66 </tr>
  67 <tr>
  68 <td><code>T</code></td>
  69 <td>The type of object stored in the mapped matrix.</td>
  70 <td></td>
  71 </tr>
  72 <tr>
  73 <td><code>F</code></td>
  74 <td>Functor describing the storage organization. <a href=
  75 "#mapped_matrix_1">[1]</a></td>
  76 <td><code>row_major</code></td>
  77 </tr>
  78 <tr>
  79 <td><code>A</code></td>
  80 <td>The type of the adapted array. <a href=
  81 "#mapped_matrix_2">[2]</a></td>
  82 <td><code>map_std&lt;std::size_t, T&gt;</code></td>
  83 </tr>
  84 </tbody>
  85 </table>
  86 <h4>Model of</h4>
  87 <p><a href="container_concept.html#matrix">Matrix</a> .</p>
  88 <h4>Type requirements</h4>
  89 <p>None, except for those imposed by the requirements of <a href=
  90 "container_concept.html#matrix">Matrix</a> .</p>
  91 <h4>Public base classes</h4>
  92 <p><code>matrix_container&lt;mapped_matrix&lt;T, F, A&gt;
  93 &gt;</code></p>
  94 <h4>Members</h4>
  95 <table border="1" summary="members">
  96 <tbody>
  97 <tr>
  98 <th>Member</th>
  99 <th>Description</th>
 100 </tr>
 101 <tr>
 102 <td><code>mapped_matrix ()</code></td>
 103 <td>Allocates a <code>mapped_matrix</code> that holds at most zero
 104 rows of zero elements.</td>
 105 </tr>
 106 <tr>
 107 <td><code>mapped_matrix (size_type size1, size_type2, size_type non_zeros = 0)</code></td>
 108 <td>Allocates a <code>mapped_matrix</code> that holds at most
 109 <code>size1</code> rows of <code>size2</code> elements.</td>
 110 </tr>
 111 <tr>
 112 <td><code>mapped_matrix (const mapped_matrix &amp;m)</code></td>
 113 <td>The copy constructor.</td>
 114 </tr>
 115 <tr>
 116 <td><code>template&lt;class AE&gt;<br />
 117 mapped_matrix (size_type non_zeros, const
 118 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 119 <td>The extended copy constructor.</td>
 120 </tr>
 121 <tr>
 122 <td><code>void resize (size_type size1, size_type size2, bool preserve = true)</code></td>
 123 <td>Reallocates a <code>mapped_matrix</code> to hold at most
 124 <code>size1</code> rows of <code>size2</code> elements. The
 125 existing elements of the <code>mapped_matrix</code> are preseved
 126 when specified.</td>
 127 </tr>
 128 <tr>
 129 <td><code>size_type size1 () const</code></td>
 130 <td>Returns the number of rows.</td>
 131 </tr>
 132 <tr>
 133 <td><code>size_type size2 () const</code></td>
 134 <td>Returns the number of columns.</td>
 135 </tr>
 136 <tr>
 137 <td><code>const_reference operator () (size_type i, size_type j)
 138 const</code></td>
 139 <td>Returns the value of the <code>j</code>-th element in the
 140 <code>i</code>-th row.</td>
 141 </tr>
 142 <tr>
 143 <td><code>reference operator () (size_type i, size_type
 144 j)</code></td>
 145 <td>Returns a reference of the <code>j</code>-th element in the
 146 <code>i</code>-th row.</td>
 147 </tr>
 148 <tr>
 149 <td><code>mapped_matrix &amp;operator = (const mapped_matrix
 150 &amp;m)</code></td>
 151 <td>The assignment operator.</td>
 152 </tr>
 153 <tr>
 154 <td><code>mapped_matrix &amp;assign_temporary (mapped_matrix
 155 &amp;m)</code></td>
 156 <td>Assigns a temporary. May change the mapped matrix
 157 <code>m</code> .</td>
 158 </tr>
 159 <tr>
 160 <td><code>template&lt;class AE&gt;<br />
 161 mapped_matrix &amp;operator = (const matrix_expression&lt;AE&gt;
 162 &amp;ae)</code></td>
 163 <td>The extended assignment operator.</td>
 164 </tr>
 165 <tr>
 166 <td><code>template&lt;class AE&gt;<br />
 167 mapped_matrix &amp;assign (const matrix_expression&lt;AE&gt;
 168 &amp;ae)</code></td>
 169 <td>Assigns a matrix expression to the mapped matrix. Left and
 170 right hand side of the assignment should be independent.</td>
 171 </tr>
 172 <tr>
 173 <td><code>template&lt;class AE&gt;<br />
 174 mapped_matrix &amp;operator += (const matrix_expression&lt;AE&gt;
 175 &amp;ae)</code></td>
 176 <td>A computed assignment operator. Adds the matrix expression to
 177 the mapped matrix.</td>
 178 </tr>
 179 <tr>
 180 <td><code>template&lt;class AE&gt;<br />
 181 mapped_matrix &amp;plus_assign (const matrix_expression&lt;AE&gt;
 182 &amp;ae)</code></td>
 183 <td>Adds a matrix expression to the mapped matrix. Left and right
 184 hand side of the assignment should be independent.</td>
 185 </tr>
 186 <tr>
 187 <td><code>template&lt;class AE&gt;<br />
 188 mapped_matrix &amp;operator -= (const matrix_expression&lt;AE&gt;
 189 &amp;ae)</code></td>
 190 <td>A computed assignment operator. Subtracts the matrix expression
 191 from the mapped matrix.</td>
 192 </tr>
 193 <tr>
 194 <td><code>template&lt;class AE&gt;<br />
 195 mapped_matrix &amp;minus_assign (const matrix_expression&lt;AE&gt;
 196 &amp;ae)</code></td>
 197 <td>Subtracts a matrix expression from the mapped matrix. Left and
 198 right hand side of the assignment should be independent.</td>
 199 </tr>
 200 <tr>
 201 <td><code>template&lt;class AT&gt;<br />
 202 mapped_matrix &amp;operator *= (const AT &amp;at)</code></td>
 203 <td>A computed assignment operator. Multiplies the mapped matrix
 204 with a scalar.</td>
 205 </tr>
 206 <tr>
 207 <td><code>template&lt;class AT&gt;<br />
 208 mapped_matrix &amp;operator /= (const AT &amp;at)</code></td>
 209 <td>A computed assignment operator. Divides the mapped matrix
 210 through a scalar.</td>
 211 </tr>
 212 <tr>
 213 <td><code>void swap (mapped_matrix &amp;m)</code></td>
 214 <td>Swaps the contents of the mapped matrices.</td>
 215 </tr>
 216 <tr>
 217 <td><code>true_refrence insert_element (size_type i, size_type j, const_reference
 218 t)</code></td>
 219 <td>Inserts the value <code>t</code> at the <code>j</code>-th
 220 element of the <code>i</code>-th row. Duplicates elements are not allowed.</td>
 221 </tr>
 222 <tr>
 223 <td><code>void erase_element (size_type i, size_type j)</code></td>
 224 <td>Erases the value at the <code>j</code>-th element of the
 225 <code>i</code>-th row.</td>
 226 </tr>
 227 <tr>
 228 <td><code>void clear ()</code></td>
 229 <td>Clears the mapped matrix.</td>
 230 </tr>
 231 <tr>
 232 <td><code>const_iterator1 begin1 () const</code></td>
 233 <td>Returns a <code>const_iterator1</code> pointing to the
 234 beginning of the <code>mapped_matrix</code>.</td>
 235 </tr>
 236 <tr>
 237 <td><code>const_iterator1 end1 () const</code></td>
 238 <td>Returns a <code>const_iterator1</code> pointing to the end of
 239 the <code>mapped_matrix</code>.</td>
 240 </tr>
 241 <tr>
 242 <td><code>iterator1 begin1 ()</code></td>
 243 <td>Returns a <code>iterator1</code> pointing to the beginning of
 244 the <code>mapped_matrix</code>.</td>
 245 </tr>
 246 <tr>
 247 <td><code>iterator1 end1 ()</code></td>
 248 <td>Returns a <code>iterator1</code> pointing to the end of the
 249 <code>mapped_matrix</code>.</td>
 250 </tr>
 251 <tr>
 252 <td><code>const_iterator2 begin2 () const</code></td>
 253 <td>Returns a <code>const_iterator2</code> pointing to the
 254 beginning of the <code>mapped_matrix</code>.</td>
 255 </tr>
 256 <tr>
 257 <td><code>const_iterator2 end2 () const</code></td>
 258 <td>Returns a <code>const_iterator2</code> pointing to the end of
 259 the <code>mapped_matrix</code>.</td>
 260 </tr>
 261 <tr>
 262 <td><code>iterator2 begin2 ()</code></td>
 263 <td>Returns a <code>iterator2</code> pointing to the beginning of
 264 the <code>mapped_matrix</code>.</td>
 265 </tr>
 266 <tr>
 267 <td><code>iterator2 end2 ()</code></td>
 268 <td>Returns a <code>iterator2</code> pointing to the end of the
 269 <code>mapped_matrix</code>.</td>
 270 </tr>
 271 <tr>
 272 <td><code>const_reverse_iterator1 rbegin1 () const</code></td>
 273 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 274 beginning of the reversed <code>mapped_matrix</code>.</td>
 275 </tr>
 276 <tr>
 277 <td><code>const_reverse_iterator1 rend1 () const</code></td>
 278 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 279 end of the reversed <code>mapped_matrix</code>.</td>
 280 </tr>
 281 <tr>
 282 <td><code>reverse_iterator1 rbegin1 ()</code></td>
 283 <td>Returns a <code>reverse_iterator1</code> pointing to the
 284 beginning of the reversed <code>mapped_matrix</code>.</td>
 285 </tr>
 286 <tr>
 287 <td><code>reverse_iterator1 rend1 ()</code></td>
 288 <td>Returns a <code>reverse_iterator1</code> pointing to the end of
 289 the reversed <code>mapped_matrix</code>.</td>
 290 </tr>
 291 <tr>
 292 <td><code>const_reverse_iterator2 rbegin2 () const</code></td>
 293 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 294 beginning of the reversed <code>mapped_matrix</code>.</td>
 295 </tr>
 296 <tr>
 297 <td><code>const_reverse_iterator2 rend2 () const</code></td>
 298 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 299 end of the reversed <code>mapped_matrix</code>.</td>
 300 </tr>
 301 <tr>
 302 <td><code>reverse_iterator2 rbegin2 ()</code></td>
 303 <td>Returns a <code>reverse_iterator2</code> pointing to the
 304 beginning of the reversed <code>mapped_matrix</code>.</td>
 305 </tr>
 306 <tr>
 307 <td><code>reverse_iterator2 rend2 ()</code></td>
 308 <td>Returns a <code>reverse_iterator2</code> pointing to the end of
 309 the reversed <code>mapped_matrix</code>.</td>
 310 </tr>
 311 </tbody>
 312 </table>
 313 <h4>Notes</h4>
 314 <p><a name="mapped_matrix_1">[1]</a> Supported
 315 parameters for the storage organization are <code>row_major</code>
 316 and <code>column_major</code>.</p>
 317 <p><a name="mapped_matrix_2">[2]</a> Supported
 318 parameters for the adapted array are
 319 <code>map_array&lt;std::size_t, T&gt;</code> and
 320 <code>map_std&lt;std::size_t, T&gt;</code>. The latter is
 321 equivalent to <code>std::map&lt;std::size_t, T&gt;</code>.</p>
 322 <h2><a name="compressed_matrix"></a>Compressed Matrix</h2>
 323 <h4>Description</h4>
 324 <p>The templated class <code>compressed_matrix&lt;T, F, IB, IA,
 325 TA&gt;</code> is the base container adaptor for compressed
 326 matrices. For a <em>(m x n</em> )-dimensional compressed matrix and
 327 <em>0 &lt;= i &lt; m</em>, <em>0 &lt;= j &lt; n</em> the non-zero
 328 elements <em>m</em><sub><em>i, j</em></sub> are mapped via <em>(i x
 329 n + j)</em> for row major orientation or via <em>(i + j x m)</em>
 330 for column major orientation to consecutive elements of the index
 331 and value containers, i.e. for elements <em>k</em> =
 332 <em>m</em><sub><em>i</em></sub><sub><sub><em>1</em></sub></sub><sub>
 333 <em>,j</em></sub><sub><sub><em>1</em></sub></sub>and <em>k + 1 =
 334 m</em><sub><em>i</em></sub><sub><sub><em>2</em></sub></sub><sub><em>
 335 ,j</em></sub><sub><sub><em>2</em></sub></sub>of the container holds
 336 <em>i</em><sub><em>1</em></sub> <em>&lt;
 337 i</em><sub><em>2</em></sub> or <em>(i</em><sub><em>1</em></sub>
 338 <em>= i</em><sub><em>2</em></sub> and
 339 <em>j</em><sub><em>1</em></sub> <em>&lt;
 340 j</em><sub><em>2</em></sub><em>)</em> with row major orientation or
 341 <em>j</em><sub><em>1</em></sub> <em>&lt;
 342 j</em><sub><em>2</em></sub> or <em>(j</em><sub><em>1</em></sub>
 343 <em>= j</em><sub><em>2</em></sub> and
 344 <em>i</em><sub><em>1</em></sub> <em>&lt;
 345 i</em><sub><em>2</em></sub><em>)</em> with column major
 346 orientation.</p>
 347 <h4>Example</h4>
 348 <pre>
 349 #include &lt;boost/numeric/ublas/matrix_sparse.hpp&gt;
 350 #include &lt;boost/numeric/ublas/io.hpp&gt;
 351
 352 int main () {
 353     using namespace boost::numeric::ublas;
 354     compressed_matrix&lt;double&gt; m (3, 3, 3 * 3);
 355     for (unsigned i = 0; i &lt; m.size1 (); ++ i)
 356         for (unsigned j = 0; j &lt; m.size2 (); ++ j)
 357             m (i, j) = 3 * i + j;
 358     std::cout &lt;&lt; m &lt;&lt; std::endl;
 359 }
 360 </pre>
 361 <h4>Definition</h4>
 362 <p>Defined in the header matrix_sparse.hpp.</p>
 363 <h4>Template parameters</h4>
 364 <table border="1" summary="parameters">
 365 <tbody>
 366 <tr>
 367 <th>Parameter</th>
 368 <th>Description</th>
 369 <th>Default</th>
 370 </tr>
 371 <tr>
 372 <td><code>T</code></td>
 373 <td>The type of object stored in the compressed matrix.</td>
 374 <td></td>
 375 </tr>
 376 <tr>
 377 <td><code>F</code></td>
 378 <td>Functor describing the storage organization. <a href=
 379 "#compressed_matrix_1">[1]</a></td>
 380 <td><code>row_major</code></td>
 381 </tr>
 382 <tr>
 383 <td><code>IB</code></td>
 384 <td>The index base of the compressed vector. <a href=
 385 "#compressed_matrix_2">[2]</a></td>
 386 <td><code>0</code></td>
 387 </tr>
 388 <tr>
 389 <td><code>IA</code></td>
 390 <td>The type of the adapted array for indices. <a href=
 391 "#compressed_matrix_3">[3]</a></td>
 392 <td><code>unbounded_array&lt;std::size_t&gt;</code></td>
 393 </tr>
 394 <tr>
 395 <td><code>TA</code></td>
 396 <td>The type of the adapted array for values. <a href=
 397 "#compressed_matrix_3">[3]</a></td>
 398 <td><code>unbounded_array&lt;T&gt;</code></td>
 399 </tr>
 400 </tbody>
 401 </table>
 402 <h4>Model of</h4>
 403 <p><a href="container_concept.html#matrix">Matrix</a> .</p>
 404 <h4>Type requirements</h4>
 405 <p>None, except for those imposed by the requirements of <a href=
 406 "container_concept.html#matrix">Matrix</a> .</p>
 407 <h4>Public base classes</h4>
 408 <p><code>matrix_container&lt;compressed_matrix&lt;T, F, IB, IA,
 409 TA&gt; &gt;</code></p>
 410 <h4>Members</h4>
 411 <table border="1" summary="members">
 412 <tbody>
 413 <tr>
 414 <th>Member</th>
 415 <th>Description</th>
 416 </tr>
 417 <tr>
 418 <td><code>compressed_matrix ()</code></td>
 419 <td>Allocates a <code>compressed_matrix</code> that holds at most
 420 zero rows of zero elements.</td>
 421 </tr>
 422 <tr>
 423 <td><code>compressed_matrix (size_type size1, size_type2, size_type non_zeros = 0)</code></td>
 424 <td>Allocates a <code>compressed_matrix</code> that holds at most
 425 <code>size1</code> rows of <code>size2</code> elements.</td>
 426 </tr>
 427 <tr>
 428 <td><code>compressed_matrix (const compressed_matrix
 429 &amp;m)</code></td>
 430 <td>The copy constructor.</td>
 431 </tr>
 432 <tr>
 433 <td><code>template&lt;class AE&gt;<br />
 434 compressed_matrix (size_type non_zeros, const
 435 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 436 <td>The extended copy constructor.</td>
 437 </tr>
 438 <tr>
 439 <td><code>void resize (size_type size1, size_type size2, bool preserve = true)</code></td>
 440 <td>Reallocates a <code>compressed_matrix</code> to hold at most
 441 <code>size1</code> rows of <code>size2</code> elements. The
 442 existing elements of the <code>compressed_matrix</code> are
 443 preseved when specified.</td>
 444 </tr>
 445 <tr>
 446 <td><code>size_type size1 () const</code></td>
 447 <td>Returns the number of rows.</td>
 448 </tr>
 449 <tr>
 450 <td><code>size_type size2 () const</code></td>
 451 <td>Returns the number of columns.</td>
 452 </tr>
 453 <tr>
 454 <td><code>const_reference operator () (size_type i, size_type j)
 455 const</code></td>
 456 <td>Returns the value of the <code>j</code>-th element in the
 457 <code>i</code>-th row.</td>
 458 </tr>
 459 <tr>
 460 <td><code>reference operator () (size_type i, size_type
 461 j)</code></td>
 462 <td>Returns a reference of the <code>j</code>-th element in the
 463 <code>i</code>-th row.</td>
 464 </tr>
 465 <tr>
 466 <td><code>compressed_matrix &amp;operator = (const
 467 compressed_matrix &amp;m)</code></td>
 468 <td>The assignment operator.</td>
 469 </tr>
 470 <tr>
 471 <td><code>compressed_matrix &amp;assign_temporary
 472 (compressed_matrix &amp;m)</code></td>
 473 <td>Assigns a temporary. May change the compressed matrix
 474 <code>m</code>.</td>
 475 </tr>
 476 <tr>
 477 <td><code>template&lt;class AE&gt;<br />
 478 compressed_matrix &amp;operator = (const
 479 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 480 <td>The extended assignment operator.</td>
 481 </tr>
 482 <tr>
 483 <td><code>template&lt;class AE&gt;<br />
 484 compressed_matrix &amp;assign (const matrix_expression&lt;AE&gt;
 485 &amp;ae)</code></td>
 486 <td>Assigns a matrix expression to the compressed matrix. Left and
 487 right hand side of the assignment should be independent.</td>
 488 </tr>
 489 <tr>
 490 <td><code>template&lt;class AE&gt;<br />
 491 compressed_matrix &amp;operator += (const
 492 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 493 <td>A computed assignment operator. Adds the matrix expression to
 494 the compressed matrix.</td>
 495 </tr>
 496 <tr>
 497 <td><code>template&lt;class AE&gt;<br />
 498 compressed_matrix &amp;plus_assign (const
 499 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 500 <td>Adds a matrix expression to the compressed matrix. Left and
 501 right hand side of the assignment should be independent.</td>
 502 </tr>
 503 <tr>
 504 <td><code>template&lt;class AE&gt;<br />
 505 compressed_matrix &amp;operator -= (const
 506 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 507 <td>A computed assignment operator. Subtracts the matrix expression
 508 from the compressed matrix.</td>
 509 </tr>
 510 <tr>
 511 <td><code>template&lt;class AE&gt;<br />
 512 compressed_matrix &amp;minus_assign (const
 513 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 514 <td>Subtracts a matrix expression from the compressed matrix. Left
 515 and right hand side of the assignment should be independent.</td>
 516 </tr>
 517 <tr>
 518 <td><code>template&lt;class AT&gt;<br />
 519 compressed_matrix &amp;operator *= (const AT &amp;at)</code></td>
 520 <td>A computed assignment operator. Multiplies the compressed
 521 matrix with a scalar.</td>
 522 </tr>
 523 <tr>
 524 <td><code>template&lt;class AT&gt;<br />
 525 compressed_matrix &amp;operator /= (const AT &amp;at)</code></td>
 526 <td>A computed assignment operator. Divides the compressed matrix
 527 through a scalar.</td>
 528 </tr>
 529 <tr>
 530 <td><code>void swap (compressed_matrix &amp;m)</code></td>
 531 <td>Swaps the contents of the compressed matrices.</td>
 532 </tr>
 533 <tr>
 534 <td><code>true_reference insert_element (size_type i, size_type j, const_reference
 535 t)</code></td>
 536 <td>Inserts the value <code>t</code> at the <code>j</code>-th
 537 element of the <code>i</code>-th row. Duplicates elements are not allowed.</td>
 538 </tr>
 539 <tr>
 540 <td><code>void erase_element (size_type i, size_type j)</code></td>
 541 <td>Erases the value at the <code>j</code>-th element of the
 542 <code>i</code>-th row.</td>
 543 </tr>
 544 <tr>
 545 <td><code>void clear ()</code></td>
 546 <td>Clears the compressed matrix.</td>
 547 </tr>
 548 <tr>
 549 <td><code>const_iterator1 begin1 () const</code></td>
 550 <td>Returns a <code>const_iterator1</code> pointing to the
 551 beginning of the <code>compressed_matrix</code>.</td>
 552 </tr>
 553 <tr>
 554 <td><code>const_iterator1 end1 () const</code></td>
 555 <td>Returns a <code>const_iterator1</code> pointing to the end of
 556 the <code>compressed_matrix</code>.</td>
 557 </tr>
 558 <tr>
 559 <td><code>iterator1 begin1 ()</code></td>
 560 <td>Returns a <code>iterator1</code> pointing to the beginning of
 561 the <code>compressed_matrix</code>.</td>
 562 </tr>
 563 <tr>
 564 <td><code>iterator1 end1 ()</code></td>
 565 <td>Returns a <code>iterator1</code> pointing to the end of the
 566 <code>compressed_matrix</code>.</td>
 567 </tr>
 568 <tr>
 569 <td><code>const_iterator2 begin2 () const</code></td>
 570 <td>Returns a <code>const_iterator2</code> pointing to the
 571 beginning of the <code>compressed_matrix</code>.</td>
 572 </tr>
 573 <tr>
 574 <td><code>const_iterator2 end2 () const</code></td>
 575 <td>Returns a <code>const_iterator2</code> pointing to the end of
 576 the <code>compressed_matrix</code>.</td>
 577 </tr>
 578 <tr>
 579 <td><code>iterator2 begin2 ()</code></td>
 580 <td>Returns a <code>iterator2</code> pointing to the beginning of
 581 the <code>compressed_matrix</code>.</td>
 582 </tr>
 583 <tr>
 584 <td><code>iterator2 end2 ()</code></td>
 585 <td>Returns a <code>iterator2</code> pointing to the end of the
 586 <code>compressed_matrix</code>.</td>
 587 </tr>
 588 <tr>
 589 <td><code>const_reverse_iterator1 rbegin1 () const</code></td>
 590 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 591 beginning of the reversed <code>compressed_matrix</code>.</td>
 592 </tr>
 593 <tr>
 594 <td><code>const_reverse_iterator1 rend1 () const</code></td>
 595 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 596 end of the reversed <code>compressed_matrix</code>.</td>
 597 </tr>
 598 <tr>
 599 <td><code>reverse_iterator1 rbegin1 ()</code></td>
 600 <td>Returns a <code>reverse_iterator1</code> pointing to the
 601 beginning of the reversed <code>compressed_matrix</code>.</td>
 602 </tr>
 603 <tr>
 604 <td><code>reverse_iterator1 rend1 ()</code></td>
 605 <td>Returns a <code>reverse_iterator1</code> pointing to the end of
 606 the reversed <code>compressed_matrix</code>.</td>
 607 </tr>
 608 <tr>
 609 <td><code>const_reverse_iterator2 rbegin2 () const</code></td>
 610 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 611 beginning of the reversed <code>compressed_matrix</code>.</td>
 612 </tr>
 613 <tr>
 614 <td><code>const_reverse_iterator2 rend2 () const</code></td>
 615 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 616 end of the reversed <code>compressed_matrix</code>.</td>
 617 </tr>
 618 <tr>
 619 <td><code>reverse_iterator2 rbegin2 ()</code></td>
 620 <td>Returns a <code>reverse_iterator2</code> pointing to the
 621 beginning of the reversed <code>compressed_matrix</code>.</td>
 622 </tr>
 623 <tr>
 624 <td><code>reverse_iterator2 rend2 ()</code></td>
 625 <td>Returns a <code>reverse_iterator2</code> pointing to the end of
 626 the reversed <code>compressed_matrix</code>.</td>
 627 </tr>
 628 </tbody>
 629 </table>
 630 <h4>Notes</h4>
 631 <p><a name="compressed_matrix_1">[1]</a>
 632 Supported parameters for the storage organization are
 633 <code>row_major</code> and <code>column_major</code>.</p>
 634 <p><a name="compressed_matrix_2">[2]</a>
 635 Supported parameters for the index base are <code>0</code> and
 636 <code>1</code> at least.</p>
 637 <p><a name="compressed_matrix_3">[3]</a>
 638 Supported parameters for the adapted array are
 639 <code>unbounded_array&lt;&gt;</code> ,
 640 <code>bounded_array&lt;&gt;</code> and
 641 <code>std::vector&lt;&gt;</code> .</p>
 642 <h2><a name="coordinate_matrix"></a>Coordinate Matrix</h2>
 643 <h4>Description</h4>
 644 <p>The templated class <code>coordinate_matrix&lt;T, F, IB, IA,
 645 TA&gt;</code> is the base container adaptor for compressed
 646 matrices. For a <em>(m x n</em> )-dimensional sorted coordinate
 647 matrix and <em>0 &lt;= i &lt; m</em>, <em>0 &lt;= j &lt; n</em> the
 648 non-zero elements <em>m</em><sub><em>i, j</em></sub> are mapped via
 649 <em>(i x n + j)</em> for row major orientation or via <em>(i + j x
 650 m)</em> for column major orientation to consecutive elements of the
 651 index and value containers, i.e. for elements <em>k</em> =
 652 <em>m</em><sub><em>i</em></sub><sub><sub><em>1</em></sub></sub><sub>
 653 <em>,j</em></sub><sub><sub><em>1</em></sub></sub>and <em>k + 1 =
 654 m</em><sub><em>i</em></sub><sub><sub><em>2</em></sub></sub><sub><em>
 655 ,j</em></sub><sub><sub><em>2</em></sub></sub>of the container holds
 656 <em>i</em><sub><em>1</em></sub> <em>&lt;
 657 i</em><sub><em>2</em></sub> or <em>(i</em><sub><em>1</em></sub>
 658 <em>= i</em><sub><em>2</em></sub> and
 659 <em>j</em><sub><em>1</em></sub> <em>&lt;
 660 j</em><sub><em>2</em></sub><em>)</em> with row major orientation or
 661 <em>j</em><sub><em>1</em></sub> <em>&lt;
 662 j</em><sub><em>2</em></sub> or <em>(j</em><sub><em>1</em></sub>
 663 <em>= j</em><sub><em>2</em></sub> and
 664 <em>i</em><sub><em>1</em></sub> <em>&lt;
 665 i</em><sub><em>2</em></sub><em>)</em> with column major
 666 orientation.</p>
 667 <h4>Example</h4>
 668 <pre>
 669 #include &lt;boost/numeric/ublas/matrix_sparse.hpp&gt;
 670 #include &lt;boost/numeric/ublas/io.hpp&gt;
 671
 672 int main () {
 673     using namespace boost::numeric::ublas;
 674     coordinate_matrix&lt;double&gt; m (3, 3, 3 * 3);
 675     for (unsigned i = 0; i &lt; m.size1 (); ++ i)
 676         for (unsigned j = 0; j &lt; m.size2 (); ++ j)
 677             m (i, j) = 3 * i + j;
 678     std::cout &lt;&lt; m &lt;&lt; std::endl;
 679 }
 680 </pre>
 681 <h4>Definition</h4>
 682 <p>Defined in the header matrix_sparse.hpp.</p>
 683 <h4>Template parameters</h4>
 684 <table border="1" summary="parameters">
 685 <tbody>
 686 <tr>
 687 <th>Parameter</th>
 688 <th>Description</th>
 689 <th>Default</th>
 690 </tr>
 691 <tr>
 692 <td><code>T</code></td>
 693 <td>The type of object stored in the coordinate matrix.</td>
 694 <td></td>
 695 </tr>
 696 <tr>
 697 <td><code>F</code></td>
 698 <td>Functor describing the storage organization. <a href=
 699 "#coordinate_matrix_1">[1]</a></td>
 700 <td><code>row_major</code></td>
 701 </tr>
 702 <tr>
 703 <td><code>IB</code></td>
 704 <td>The index base of the coordinate vector. <a href=
 705 "#coordinate_matrix_2">[2]</a></td>
 706 <td><code>0</code></td>
 707 </tr>
 708 <tr>
 709 <td><code>IA</code></td>
 710 <td>The type of the adapted array for indices. <a href=
 711 "#coordinate_matrix_3">[3]</a></td>
 712 <td><code>unbounded_array&lt;std::size_t&gt;</code></td>
 713 </tr>
 714 <tr>
 715 <td><code>TA</code></td>
 716 <td>The type of the adapted array for values. <a href=
 717 "#coordinate_matrix_3">[3]</a></td>
 718 <td><code>unbounded_array&lt;T&gt;</code></td>
 719 </tr>
 720 </tbody>
 721 </table>
 722 <h4>Model of</h4>
 723 <p><a href="container_concept.html#matrix">Matrix</a> .</p>
 724 <h4>Type requirements</h4>
 725 <p>None, except for those imposed by the requirements of <a href=
 726 "container_concept.html#matrix">Matrix</a> .</p>
 727 <h4>Public base classes</h4>
 728 <p><code>matrix_container&lt;coordinate_matrix&lt;T, F, IB, IA,
 729 TA&gt; &gt;</code></p>
 730 <h4>Members</h4>
 731 <table border="1" summary="members">
 732 <tbody>
 733 <tr>
 734 <th>Member</th>
 735 <th>Description</th>
 736 </tr>
 737 <tr>
 738 <td><code>coordinate_matrix ()</code></td>
 739 <td>Allocates a <code>coordinate_matrix</code> that holds at most
 740 zero rows of zero elements.</td>
 741 </tr>
 742 <tr>
 743 <td><code>coordinate_matrix (size_type size1, size_type2, size_type non_zeros = 0)</code></td>
 744 <td>Allocates a <code>coordinate_matrix</code> that holds at most
 745 <code>size1</code> rows of <code>size2</code> elements.</td>
 746 </tr>
 747 <tr>
 748 <td><code>coordinate_matrix (const coordinate_matrix
 749 &amp;m)</code></td>
 750 <td>The copy constructor.</td>
 751 </tr>
 752 <tr>
 753 <td><code>template&lt;class AE&gt;<br />
 754 coordinate_matrix (size_type non_zeros, const
 755 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 756 <td>The extended copy constructor.</td>
 757 </tr>
 758 <tr>
 759 <td><code>void resize (size_type size1, size_type size2, bool preserve = true)</code></td>
 760 <td>Reallocates a <code>coordinate_matrix</code> to hold at most
 761 <code>size1</code> rows of <code>size2</code> elements. The
 762 existing elements of the <code>coordinate_matrix</code> are
 763 preseved when specified.</td>
 764 </tr>
 765 <tr>
 766 <td><code>size_type size1 () const</code></td>
 767 <td>Returns the number of rows.</td>
 768 </tr>
 769 <tr>
 770 <td><code>size_type size2 () const</code></td>
 771 <td>Returns the number of columns.</td>
 772 </tr>
 773 <tr>
 774 <td><code>const_reference operator () (size_type i, size_type j)
 775 const</code></td>
 776 <td>Returns the value of the <code>j</code>-th element in the
 777 <code>i</code>-th row.</td>
 778 </tr>
 779 <tr>
 780 <td><code>reference operator () (size_type i, size_type
 781 j)</code></td>
 782 <td>Returns a reference of the <code>j</code>-th element in the
 783 <code>i</code>-th row.</td>
 784 </tr>
 785 <tr>
 786 <td><code>coordinate_matrix &amp;operator = (const
 787 coordinate_matrix &amp;m)</code></td>
 788 <td>The assignment operator.</td>
 789 </tr>
 790 <tr>
 791 <td><code>coordinate_matrix &amp;assign_temporary
 792 (coordinate_matrix &amp;m)</code></td>
 793 <td>Assigns a temporary. May change the coordinate matrix
 794 <code>m</code>.</td>
 795 </tr>
 796 <tr>
 797 <td><code>template&lt;class AE&gt;<br />
 798 coordinate_matrix &amp;operator = (const
 799 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 800 <td>The extended assignment operator.</td>
 801 </tr>
 802 <tr>
 803 <td><code>template&lt;class AE&gt;<br />
 804 coordinate_matrix &amp;assign (const matrix_expression&lt;AE&gt;
 805 &amp;ae)</code></td>
 806 <td>Assigns a matrix expression to the coordinate matrix. Left and
 807 right hand side of the assignment should be independent.</td>
 808 </tr>
 809 <tr>
 810 <td><code>template&lt;class AE&gt;<br />
 811 coordinate_matrix &amp;operator += (const
 812 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 813 <td>A computed assignment operator. Adds the matrix expression to
 814 the coordinate matrix.</td>
 815 </tr>
 816 <tr>
 817 <td><code>template&lt;class AE&gt;<br />
 818 coordinate_matrix &amp;plus_assign (const
 819 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 820 <td>Adds a matrix expression to the coordinate matrix. Left and
 821 right hand side of the assignment should be independent.</td>
 822 </tr>
 823 <tr>
 824 <td><code>template&lt;class AE&gt;<br />
 825 coordinate_matrix &amp;operator -= (const
 826 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 827 <td>A computed assignment operator. Subtracts the matrix expression
 828 from the coordinate matrix.</td>
 829 </tr>
 830 <tr>
 831 <td><code>template&lt;class AE&gt;<br />
 832 coordinate_matrix &amp;minus_assign (const
 833 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 834 <td>Subtracts a matrix expression from the coordinate matrix. Left
 835 and right hand side of the assignment should be independent.</td>
 836 </tr>
 837 <tr>
 838 <td><code>template&lt;class AT&gt;<br />
 839 coordinate_matrix &amp;operator *= (const AT &amp;at)</code></td>
 840 <td>A computed assignment operator. Multiplies the coordinate
 841 matrix with a scalar.</td>
 842 </tr>
 843 <tr>
 844 <td><code>template&lt;class AT&gt;<br />
 845 coordinate_matrix &amp;operator /= (const AT &amp;at)</code></td>
 846 <td>A computed assignment operator. Divides the coordinate matrix
 847 through a scalar.</td>
 848 </tr>
 849 <tr>
 850 <td><code>void swap (coordinate_matrix &amp;m)</code></td>
 851 <td>Swaps the contents of the coordinate matrices.</td>
 852 </tr>
 853 <tr>
 854 <td><code>true_reference insert_element (size_type i, size_type j, const_reference
 855 t)</code></td>
 856 <td>Inserts the value <code>t</code> at the <code>j</code>-th
 857 element of the <code>i</code>-th row. Duplicates elements are not allowed.</td>
 858 </tr>
 859 <tr>
 860 <td><code>void append_element (size_type i, size_type j, const_reference t)</code></td>
 861 <td>Appends the value <code>t</code> at the <code>j</code>-th element of the <code>i</code>-th row.
 862 Duplicate elements can be appended to a <code>coordinate_matrix</code>. They are merged into a single
 863 arithmetically summed element by the <code>sort</code> function.</td>
 864 </tr>
 865 <tr>
 866 <td><code>void erase_element (size_type i, size_type j)</code></td>
 867 <td>Erases the value at the <code>j</code>-th element of the
 868 <code>i</code>-th row.</td>
 869 </tr>
 870 <tr>
 871 <td><code>void clear ()</code></td>
 872 <td>Clears the coordinate matrix.</td>
 873 </tr>
 874 <tr>
 875 <td><code>const_iterator1 begin1 () const</code></td>
 876 <td>Returns a <code>const_iterator1</code> pointing to the
 877 beginning of the <code>coordinate_matrix</code>.</td>
 878 </tr>
 879 <tr>
 880 <td><code>const_iterator1 end1 () const</code></td>
 881 <td>Returns a <code>const_iterator1</code> pointing to the end of
 882 the <code>coordinate_matrix</code>.</td>
 883 </tr>
 884 <tr>
 885 <td><code>iterator1 begin1 ()</code></td>
 886 <td>Returns a <code>iterator1</code> pointing to the beginning of
 887 the <code>coordinate_matrix</code>.</td>
 888 </tr>
 889 <tr>
 890 <td><code>iterator1 end1 ()</code></td>
 891 <td>Returns a <code>iterator1</code> pointing to the end of the
 892 <code>coordinate_matrix</code>.</td>
 893 </tr>
 894 <tr>
 895 <td><code>const_iterator2 begin2 () const</code></td>
 896 <td>Returns a <code>const_iterator2</code> pointing to the
 897 beginning of the <code>coordinate_matrix</code>.</td>
 898 </tr>
 899 <tr>
 900 <td><code>const_iterator2 end2 () const</code></td>
 901 <td>Returns a <code>const_iterator2</code> pointing to the end of
 902 the <code>coordinate_matrix</code>.</td>
 903 </tr>
 904 <tr>
 905 <td><code>iterator2 begin2 ()</code></td>
 906 <td>Returns a <code>iterator2</code> pointing to the beginning of
 907 the <code>coordinate_matrix</code>.</td>
 908 </tr>
 909 <tr>
 910 <td><code>iterator2 end2 ()</code></td>
 911 <td>Returns a <code>iterator2</code> pointing to the end of the
 912 <code>coordinate_matrix</code>.</td>
 913 </tr>
 914 <tr>
 915 <td><code>const_reverse_iterator1 rbegin1 () const</code></td>
 916 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 917 beginning of the reversed <code>coordinate_matrix</code>.</td>
 918 </tr>
 919 <tr>
 920 <td><code>const_reverse_iterator1 rend1 () const</code></td>
 921 <td>Returns a <code>const_reverse_iterator1</code> pointing to the
 922 end of the reversed <code>coordinate_matrix</code>.</td>
 923 </tr>
 924 <tr>
 925 <td><code>reverse_iterator1 rbegin1 ()</code></td>
 926 <td>Returns a <code>reverse_iterator1</code> pointing to the
 927 beginning of the reversed <code>coordinate_matrix</code>.</td>
 928 </tr>
 929 <tr>
 930 <td><code>reverse_iterator1 rend1 ()</code></td>
 931 <td>Returns a <code>reverse_iterator1</code> pointing to the end of
 932 the reversed <code>coordinate_matrix</code>.</td>
 933 </tr>
 934 <tr>
 935 <td><code>const_reverse_iterator2 rbegin2 () const</code></td>
 936 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 937 beginning of the reversed <code>coordinate_matrix</code>.</td>
 938 </tr>
 939 <tr>
 940 <td><code>const_reverse_iterator2 rend2 () const</code></td>
 941 <td>Returns a <code>const_reverse_iterator2</code> pointing to the
 942 end of the reversed <code>coordinate_matrix</code>.</td>
 943 </tr>
 944 <tr>
 945 <td><code>reverse_iterator2 rbegin2 ()</code></td>
 946 <td>Returns a <code>reverse_iterator2</code> pointing to the
 947 beginning of the reversed <code>coordinate_matrix</code>.</td>
 948 </tr>
 949 <tr>
 950 <td><code>reverse_iterator2 rend2 ()</code></td>
 951 <td>Returns a <code>reverse_iterator2</code> pointing to the end of
 952 the reversed <code>coordinate_matrix</code>.</td>
 953 </tr>
 954 </tbody>
 955 </table>
 956 <h4>Notes</h4>
 957 <p><a name="coordinate_matrix_1">[1]</a>
 958 Supported parameters for the storage organization are
 959 <code>row_major</code> and <code>column_major</code>.</p>
 960 <p><a name="coordinate_matrix_2">[2]</a>
 961 Supported parameters for the index base are <code>0</code> and
 962 <code>1</code> at least.</p>
 963 <p><a name="coordinate_matrix_3">[3]</a>
 964 Supported parameters for the adapted array are
 965 <code>unbounded_array&lt;&gt;</code> ,
 966 <code>bounded_array&lt;&gt;</code> and
 967 <code>std::vector&lt;&gt;</code> .</p>
 968 <hr />
 969 <p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
 970    Use, modification and distribution are subject to the
 971    Boost Software License, Version 1.0.
 972    (See accompanying file LICENSE_1_0.txt
 973    or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
 974       http://www.boost.org/LICENSE_1_0.txt
 975    </a>).
 976 </p>
 977 <script type="text/javascript">
 978 (function($) {
 979     $('#toc').toc();
 980 })(jQuery);
 981 </script>
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