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

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  16 <h1><img src="../../../../boost.png" align="middle" />Container Concepts</h1>
  17 <div class="toc" id="toc"></div>
  18 <h2><a name="vector"></a>Vector</h2>
  19 <h4>Description</h4>
  20 <p>A Vector describes common aspects of dense, packed and sparse
  21 vectors.</p>
  22 <h4>Refinement of</h4>
  23 <p><a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>,
  24 <a href="expression_concept.html#vector_expression">Vector Expression</a>
  25 <a href="#vector_expression_note">[1]</a>.</p>
  26 <h4>Associated types</h4>
  27 <p>In addition to the types defined by <a href="expression_concept.html#vector_expression">Vector Expression</a></p>
  28 <table border="1" summary="types">
  29 <tbody>
  30 <tr>
  31 <td>Public base</td>
  32 <td>vector_container&lt;V&gt;</td>
  33 <td>V must be derived from this public base type.</td>
  34 </tr>
  35 <tr>
  36 <td>Storage array</td>
  37 <td>V::array_type</td>
  38 <td>
  39 Dense Vector ONLY. The type of underlying storage array used to store the elements. The array_type must model the
  40 <a href="storage_concept.html"><b>Storage</b></a> concept.</td>
  41 </tr>
  42 </tbody>
  43 </table>
  44 <h4>Notation</h4>
  45 <table border="0" summary="notation">
  46 <tbody>
  47 <tr>
  48 <td><code>V</code></td>
  49 <td>A type that is a model of Vector</td>
  50 </tr>
  51 <tr>
  52 <td><code>v</code></td>
  53 <td>Objects of type <code>V</code></td>
  54 </tr>
  55 <tr>
  56 <td><code>n, i</code></td>
  57 <td>Objects of a type convertible to <code>size_type</code></td>
  58 </tr>
  59 <tr>
  60 <td><code>t</code></td>
  61 <td>Object of a type convertible to <code>value_type</code></td>
  62 </tr>
  63 <tr>
  64 <td><code>p</code></td>
  65 <td>Object of a type convertible to <code>bool</code></td>
  66 </tr>
  67 </tbody>
  68 </table>
  69 <h4>Definitions</h4>
  70 <h4>Valid expressions</h4>
  71 <p>In addition to the expressions defined in <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>,
  72 <a href="expression_concept.html#vector_expression">Vector Expression</a> the following expressions must be valid.</p>
  73 <table border="1" summary="expressions">
  74 <tbody>
  75 <tr>
  76 <th>Name</th>
  77 <th>Expression</th>
  78 <th>Type requirements</th>
  79 <th>Return type</th>
  80 </tr>
  81 <tr>
  82 <td>Sizing constructor</td>
  83 <td><code>V v (n)</code></td>
  84 <td>&nbsp;</td>
  85 <td><code>V</code></td>
  86 </tr>
  87 <tr>
  88 <td>Insert</td>
  89 <td><code>v.insert_element (i, t)</code></td>
  90 <td><code>v</code> is mutable.</td>
  91 <td><code>void</code></td>
  92 </tr>
  93 <tr>
  94 <td>Erase</td>
  95 <td><code>v.erase_element (i)</code></td>
  96 <td><code>v</code> is mutable.</td>
  97 <td><code>void</code></td>
  98 </tr>
  99 <tr>
 100 <td>Clear</td>
 101 <td><code>v.clear ()</code></td>
 102 <td><code>v</code> is mutable.</td>
 103 <td><code>void</code></td>
 104 </tr>
 105 <tr>
 106 <td>Resize</td>
 107 <td><code>v.resize (n)</code><br />
 108 <code>v.resize (n, p)</code></td>
 109 <td><code>v</code> is mutable.</td>
 110 <td><code>void</code></td>
 111 </tr>
 112 <tr>
 113 <td>Storage</td>
 114 <td><code>v.data()</code></td>
 115 <td><code>v</code> is mutable and Dense.</td>
 116 <td><code>array_type&amp;</code> if <code>v</code> is mutable, <code>const array_type&amp;</code> otherwise</td>
 117 </tr>
 118 </tbody>
 119 </table>
 120 <h4>Expression semantics</h4>
 121 <p>Semantics of an expression is defined only where it differs
 122 from, or is not defined in <a href=
 123 "expression_concept.html#vector_expression">Vector Expression</a> .</p>
 124 <table border="1" summary="semantics">
 125 <tr>
 126 <th>Name</th>
 127 <th>Expression</th>
 128 <th>Precondition</th>
 129 <th>Semantics</th>
 130 <th>Postcondition</th>
 131 </tr>
 132 <tr>
 133 <td>Sizing constructor</td>
 134 <td><code>V v (n)</code></td>
 135 <td><code>n &gt;= 0</code></td>
 136 <td>Allocates a vector of<code>n</code> elements.</td>
 137 <td><code>v.size () == n</code>.</td>
 138 </tr>
 139 <tr>
 140 <td>Element access <a href="#element_access_note">[2]</a></td>
 141 <td><code>v[n]</code></td>
 142 <td><code>0&lt;n&gt;v.size()</code></td>
 143 <td>returns the n-th element in v</td>
 144 <td>&nbsp;</td>
 145 </tr>
 146 <tr>
 147 <td>Insert</td>
 148 <td><code>v.insert_element (i, t)</code></td>
 149 <td><code>0 &lt;= i &lt; v.size ()</code>.</td>
 150 <td>Inserts an element at <code>v (i)</code> with value <code>t</code>.
 151 The storage requirement of the Vector may be increased.</td>
 152 <td><code>v (i)</code> is equal to <code>t</code>.</td>
 153 </tr>
 154 <tr>
 155 <td>Erase</td>
 156 <td><code>v.erase_element (i)</code></td>
 157 <td><code>0 &lt;= i &lt; v.size ()</code></td>
 158 <td>Destroys the element as <code>v (i)</code> and replaces it with the default
 159 <code>value_type ()</code>.
 160 The storage requirement of the Vector may be decreased.</td>
 161 <td><code>v (i)</code> is equal to <code>value_type ()</code>.</td>
 162 </tr>
 163 <tr>
 164 <td>Clear</td>
 165 <td><code>v.clear ()</code></td>
 166 <td>&nbsp;</td>
 167 <td>Equivalent to<br />
 168 <code>for (i = 0; i &lt; v.size (); ++ i)</code><br />
 169 &nbsp; <code>v.erase_element (i);</code></td>
 170 <td>&nbsp;</td>
 171 </tr>
 172 <tr>
 173 <td>Resize</td>
 174 <td><code>v.resize (n)
 175 <br />v.resize (n, p)</code></td>
 176 <td>&nbsp;</td>
 177 <td>Reallocates the vector so that it can hold <code>n</code>
 178 elements.<br />
 179 Erases or appends elements in order to bring the vector to the prescribed size. Appended elements copies of <code>value_type()</code>.
 180 <br />
 181 When <code>p == false</code> then existing elements are not preserved and elements will not appended as normal. Instead the vector is in the same state as that after an equivalent sizing constructor.</td>
 182 <td><code>v.size () == n</code>.</td>
 183 </tr>
 184 <tr>
 185 <td>Storage</td>
 186 <td><code>v.data()</code></td>
 187 <td></td>
 188 <td>Returns a reference to the underlying dense storage.</td>
 189 <td>&nbsp;</td>
 190 </tr>
 191 </table>
 192 <h4>Complexity guarantees</h4>
 193 <p>The run-time complexity of the sizing constructor is linear in
 194 the vector's size.</p>
 195 <p>The run-time complexity of insert_element and erase_element is specific for the
 196 Vector model and it depends on increases/decreases in storage requirements.</p>
 197 <p>The run-time complexity of resize is linear in the vector's
 198 size.</p>
 199 <h4>Invariants</h4>
 200 <h4>Models</h4>
 201 <ul>
 202 <li><code>vector</code>, <code>bounded_vector</code>, <code>c_vector</code></li>
 203 <li><code>unit_vector</code>, <code>zero_vector</code>, <code>scalar_vector</code></li>
 204 <li><code>mapped_vector;</code>, <code>compressed_vector</code>, <code>coordinate_vector</code></li>
 205 </ul>
 206 <h4>Notes</h4>
 207 <p><a name="vector_expression_note">[1]</a>
 208 As a user you need not care about <tt>Vector</tt> being a refinement of the VectorExpression. Being a refinement of the VectorExpression is only important for the template-expression engine but not the user.</p>
 209 <p><a name="element_access_note">[2]</a>
 210 The <code>operator[]</code> is added purely for convenience
 211 and compatibility with the <code>std::vector</code>. In uBLAS however,
 212 generally <code>operator()</code> is used for indexing because this can be
 213 used for both vectors and matrices.</p>
 214 <h2><a name="matrix"></a>Matrix</h2>
 215 <h4>Description</h4>
 216 <p>A Matrix describes common aspects of dense, packed and sparse
 217 matrices.</p>
 218 <h4>Refinement of</h4>
 219 <p><a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>,
 220 <a href="expression_concept.html#matrix_expression">Matrix Expression</a>
 221 <a href="#matrix_expression_note">[1]</a>
 222 .</p>
 223 <h4>Associated types</h4>
 224 <p>In addition to the types defined by <a href="expression_concept.html#matrix_expression">Matrix Expression</a></p>
 225 <table border="1" summary="types">
 226 <tbody>
 227 <tr>
 228 <td>Public base</td>
 229 <td>matrix_container&lt;M&gt;</td>
 230 <td>M must be derived from this public base type.</td>
 231 </tr>
 232 <tr>
 233 <td>Storage array</td>
 234 <td>M::array_type</td>
 235 <td>Dense Matrix ONLY. The type of underlying storage array used to store the elements. The array_type must model
 236 the <a href="storage_concept.html"><b>Storage</b></a> concept.</td>
 237 </tr>
 238 </tbody>
 239 </table>
 240 <h4>Notation</h4>
 241 <table border="0" summary="notation">
 242 <tbody>
 243 <tr>
 244 <td><code>M</code></td>
 245 <td>A type that is a model of Matrix</td>
 246 </tr>
 247 <tr>
 248 <td><code>m</code></td>
 249 <td>Objects of type <code>M</code></td>
 250 </tr>
 251 <tr>
 252 <td><code>n1, n2, i, j</code></td>
 253 <td>Objects of a type convertible to <code>size_type</code></td>
 254 </tr>
 255 <tr>
 256 <td><code>t</code></td>
 257 <td>Object of a type convertible to <code>value_type</code></td>
 258 </tr>
 259 <tr>
 260 <td><code>p</code></td>
 261 <td>Object of a type convertible to <code>bool</code></td>
 262 </tr>
 263 </tbody>
 264 </table>
 265 <h4>Definitions</h4>
 266 <h4>Valid expressions</h4>
 267 <p>In addition to the expressions defined in <a href=
 268 "expression_concept.html#matrix_expression">Matrix Expression</a> the
 269 following expressions must be valid.</p>
 270 <table border="1" summary="expressions">
 271 <tbody>
 272 <tr>
 273 <th>Name</th>
 274 <th>Expression</th>
 275 <th>Type requirements</th>
 276 <th>Return type</th>
 277 </tr>
 278 <tr>
 279 <td>Sizing constructor</td>
 280 <td><code>M m (n1, n2)</code></td>
 281 <td>&nbsp;</td>
 282 <td><code>M</code></td>
 283 </tr>
 284 <tr>
 285 <td>Insert</td>
 286 <td><code>m.insert_element (i, j, t)</code></td>
 287 <td><code>m</code> is mutable.</td>
 288 <td><code>void</code></td>
 289 </tr>
 290 <tr>
 291 <td>Erase</td>
 292 <td><code>m.erase_element (i, j)</code></td>
 293 <td><code>m</code> is mutable.</td>
 294 <td><code>void</code></td>
 295 </tr>
 296 <tr>
 297 <td>Clear</td>
 298 <td><code>m.clear ()</code></td>
 299 <td><code>m</code> is mutable.</td>
 300 <td><code>void</code></td>
 301 </tr>
 302 <tr>
 303 <td>Resize</td>
 304 <td><code>m.resize (n1, n2)</code><br />
 305 <code>m.resize (n1, n2, p)</code></td>
 306 <td><code>m</code> is mutable.</td>
 307 <td><code>void</code></td>
 308 </tr>
 309 <tr>
 310 <td>Storage</td>
 311 <td><code>m.data()</code></td>
 312 <td><code>m</code> is mutable and Dense.</td>
 313 <td><code>array_type&amp;</code> if <code>m</code> is mutable, <code>const array_type&amp;</code> otherwise</td>
 314 </tr>
 315 </tbody>
 316 </table>
 317 <h4>Expression semantics</h4>
 318 <p>Semantics of an expression is defined only where it differs
 319 from, or is not defined in <a href=
 320 "expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
 321 <table border="1" summary="semantics">
 322 <tbody>
 323 <tr>
 324 <th>Name</th>
 325 <th>Expression</th>
 326 <th>Precondition</th>
 327 <th>Semantics</th>
 328 <th>Postcondition</th>
 329 </tr>
 330 <tr>
 331 <td>Sizing constructor</td>
 332 <td><code>M m (n1, n2)</code></td>
 333 <td><code>n1 &gt;= 0</code> and <code>n2 &gt;= 0</code></td>
 334 <td>Allocates a matrix of <code>n1</code> rows and <code>n2</code>
 335 columns.</td>
 336 <td><code>m.size1 () == n1</code> and <code>m.size2 () ==
 337 n2</code>.</td>
 338 </tr>
 339 <tr>
 340 <td>Insert</td>
 341 <td><code>m.insert_element (i, j, t)</code></td>
 342 <td><code>0 &lt;= i &lt; m.size1 ()</code>,<br />
 343 <code>0 &lt;= j &lt; m.size2 ()</code>.</td>
 344 <td>Inserts an element at <code>m (i, j)</code> with value <code>t</code>.
 345 The storage requirement of the Matrix may be increased.</td>
 346 <td><code>m (i, j)</code> is equal to <code>t</code>.</td>
 347 </tr>
 348 <tr>
 349 <td>Erase</td>
 350 <td><code>m.erase_element (i, j)</code></td>
 351 <td><code>0 &lt;= i &lt; m.size1 ()</code>and <code><br />
 352 0 &lt;= j &lt; m.size2</code></td>
 353 <td>Destroys the element as <code>m (i, j)</code> and replaces it with the default
 354 <code>value_type ()</code>.
 355 The storage requirement of the Matrix may be decreased.</td>
 356 <td><code>m (i, j)</code> is equal to <code>value_type ()</code>.</td>
 357 </tr>
 358 <tr>
 359 <td>Clear</td>
 360 <td><code>m.clear ()</code></td>
 361 <td>&nbsp;</td>
 362 <td>Equivalent to<br />
 363 <code>for (i = 0; i &lt; m.size1 (); ++ i)</code><br />
 364 &nbsp; <code>for (j = 0; j &lt; m.size2 (); ++ j)</code><br />
 365 &nbsp; &nbsp; <code>m.erase_element (i, j);</code></td>
 366 <td>&nbsp;</td>
 367 </tr>
 368 <tr>
 369 <td>Resize</td>
 370 <td><code>m.resize (n1, n2)
 371 <br />
 372 m.resize (n1, n2, p)
 373 </code></td>
 374 <td>&nbsp;</td>
 375 <td>Reallocate the matrix so that it can hold <code>n1</code> rows
 376 and <code>n2</code> columns.<br />
 377 Erases or appends elements in order to bring the matrix to the
 378 prescribed size. Appended elements are <code>value_type()</code>
 379 copies.<br />
 380 When <code>p == false</code> then existing elements are not preserved and elements will not appended as normal. Instead the matrix is in the same state as that after an equivalent sizing constructor.</td>
 381 <td><code>m.size1 () == n1</code> and <code>m.size2 () == n2</code>.</td>
 382 </tr>
 383 <tr>
 384 <td>Storage</td>
 385 <td><code>m.data()</code></td>
 386 <td></td>
 387 <td>Returns a reference to the underlying dense storage.</td>
 388 <td>&nbsp;</td>
 389 </tbody>
 390 </table>
 391 <h4>Complexity guarantees</h4>
 392 <p>The run-time complexity of the sizing constructor is quadratic
 393 in the matrix's size.</p>
 394 <p>The run-time complexity of insert_element and erase_element is specific for the
 395 Matrix model and it depends on increases/decreases in storage requirements.</p>
 396 <p>The run-time complexity of resize is quadratic in the matrix's
 397 size.</p>
 398 <h4>Invariants</h4>
 399 <h4>Models</h4>
 400 <ul>
 401 <li><code>matrix</code>, <code>bounded_matrix</code>, <code>c_matrix</code></li>
 402 <li><code>identity_matrix</code> , <code>zero_matrix</code> , <code>scalar_matrix</code></li>
 403 <li><code>triangular_matrix</code> , <code>symmetric_matrix</code> , <code>banded_matrix</code></li>
 404 <li><code>mapped_matrix</code> , <code>compressed_matrix</code> , <code>coordinate_matrix</code></li>
 405 </ul>
 406 <h4>Notes</h4>
 407 <p><a name="matrix_expression_note">[1]</a>
 408 As a user you need not care about <tt>Matrix</tt> being a refinement of the MatrixExpression. Being a refinement of the MatrixExpression is only important for the template-expression engine but not the user.</p>
 409 <hr />
 410 <p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
 411    Use, modification and distribution are subject to the
 412    Boost Software License, Version 1.0.
 413    (See accompanying file LICENSE_1_0.txt
 414    or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
 415       http://www.boost.org/LICENSE_1_0.txt
 416    </a>).
 417 </p>
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