1<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" 2 "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> 3<html xmlns="http://www.w3.org/1999/xhtml"> 4<head> 5<meta name="generator" content= 6"HTML Tidy for Linux/x86 (vers 1st March 2004), see www.w3.org" /> 7<meta http-equiv="Content-Type" content= 8"text/html; charset=us-ascii" /> 9<link rel="stylesheet" href="../../../../boost.css" type="text/css"/> 10<link rel="stylesheet" href="ublas.css" type="text/css" /> 11<script type="text/javascript" src="js/jquery-1.3.2.min.js" async="async" ></script> 12<script type="text/javascript" src="js/jquery.toc-gw.js" async="async" ></script> 13<title>Vector Expressions</title> 14</head> 15<body> 16<h1><img src="../../../../boost.png" align="middle" />Vector Expressions</h1> 17<div class="toc" id="toc"></div> 18<h2><a name="vector_expression"></a>Vector Expression</h2> 19<h4>Description</h4> 20<p>The templated class <code>vector_expression<E></code> 21is required to be a public base of all classes which model the Vector Expression concept.</p> 22<h4>Definition</h4> 23<p>Defined in the header expression_types.hpp.</p> 24<h4>Template parameters</h4> 25<table border="1" summary="parameters"> 26<tbody> 27<tr> 28<th>Parameter</th> 29<th>Description</th> 30<th>Default</th> 31</tr> 32<tr> 33<td><code>E</code></td> 34<td>The type of the vector expression.</td> 35<td> </td> 36</tr> 37</tbody> 38</table> 39<h4>Model of</h4> 40<p>None. <u>Not a Vector Expression</u>! 41</p> 42<h4>Type requirements</h4> 43<p>None.</p> 44<h4>Public base classes</h4> 45<p>None.</p> 46<h4>Members</h4> 47<table border="1" summary="members"> 48<tbody> 49<tr> 50<th>Member</th> 51<th>Description</th> 52</tr> 53<tr> 54<td><code>const expression_type &operator () () 55const</code></td> 56<td>Returns a <code>const</code> reference of the expression.</td> 57</tr> 58<tr> 59<td><code>expression_type &operator () ()</code></td> 60<td>Returns a reference of the expression.</td> 61</tr> 62</tbody> 63</table> 64<h4>Notes</h4> 65<p>The <code>range</code>, <code>slice</code> and <code>project</code> functions have been removed. Use the free functions defined in <a href="vector_proxy.html">vector proxy</a> instead.</p> 66 67<h2><a name="vector_container"></a>Vector Container</h2> 68<h4>Description</h4> 69<p>The templated class <code>vector_container<C></code> 70is required to be a public base of all classes which model the Vector concept. 71This includes the class <code>vector</code> itself.</p> 72<h4>Definition</h4> 73<p>Defined in the header expression_types.hpp.</p> 74<h4>Template parameters</h4> 75<table border="1" summary="parameters"> 76<tbody> 77<tr> 78<th>Parameter</th> 79<th>Description</th> 80<th>Default</th> 81</tr> 82<tr> 83<td><code>C</code></td> 84<td>The type of the vector container.</td> 85<td> </td> 86</tr> 87</tbody> 88</table> 89<h4>Model of</h4> 90<p>None. <u>Not a Vector Expression OR Vector</u>! 91</p> 92<h4>Type requirements</h4> 93<p>None.</p> 94<h4>Public base classes</h4> 95<p><code>vector_expression<C></code></p> 96<h4>Members</h4> 97<table border="1" summary="members"> 98<tbody> 99<tr> 100<th>Member</th> 101<th>Description</th> 102</tr> 103<tr> 104<td><code>const container_type &operator () () 105const</code></td> 106<td>Returns a <code>const</code> reference of the container.</td> 107</tr> 108<tr> 109<td><code>container_type &operator () ()</code></td> 110<td>Returns a reference of the container.</td> 111</tr> 112</tbody> 113</table> 114 115<h2><a name="vector_references"></a>Vector References</h2> 116<h3>Reference</h3> 117<h4>Description</h4> 118<p>The templated class <code>vector_reference<E></code> 119contains a reference to a vector expression.</p> 120<h4>Definition</h4> 121<p>Defined in the header vector_expression.hpp.</p> 122<h4>Template parameters</h4> 123<table border="1" summary="parameters"> 124<tbody> 125<tr> 126<th>Parameter</th> 127<th>Description</th> 128<th>Default</th> 129</tr> 130<tr> 131<td><code>E</code></td> 132<td>The type of the vector expression.</td> 133<td> </td> 134</tr> 135</tbody> 136</table> 137<h4>Model of</h4> 138<p><a href="expression_concept.html#vector_expression">Vector Expression</a> 139.</p> 140<h4>Type requirements</h4> 141<p>None, except for those imposed by the requirements of <a href= 142"expression_concept.html#vector_expression">Vector Expression</a> .</p> 143<h4>Public base classes</h4> 144<p><code>vector_expression<vector_reference<E> 145></code></p> 146<h4>Members</h4> 147<table border="1" summary="members"> 148<tbody> 149<tr> 150<th>Member</th> 151<th>Description</th> 152</tr> 153<tr> 154<td><code>vector_reference (expression_type &e)</code></td> 155<td>Constructs a reference of the expression.</td> 156</tr> 157<tr> 158<td><code>void resize (size_type size)</code></td> 159<td>Resizes the expression to hold at most <code>size</code> 160elements.</td> 161</tr> 162<tr> 163<td><code>size_type size () const</code></td> 164<td>Returns the size of the expression.</td> 165</tr> 166<tr> 167<td><code>const_reference operator () (size_type i) 168const</code></td> 169<td>Returns the value of the <code>i</code>-th element.</td> 170</tr> 171<tr> 172<td><code>reference operator () (size_type i)</code></td> 173<td>Returns a reference of the <code>i</code>-th element.</td> 174</tr> 175<tr> 176<td><code>const_iterator begin () const</code></td> 177<td>Returns a <code>const_iterator</code> pointing to the beginning 178of the expression.</td> 179</tr> 180<tr> 181<td><code>const_iterator end () const</code></td> 182<td>Returns a <code>const_iterator</code> pointing to the end of 183the expression.</td> 184</tr> 185<tr> 186<td><code>iterator begin ()</code></td> 187<td>Returns a <code>iterator</code> pointing to the beginning of 188the expression.</td> 189</tr> 190<tr> 191<td><code>iterator end ()</code></td> 192<td>Returns a <code>iterator</code> pointing to the end of the 193expression.</td> 194</tr> 195<tr> 196<td><code>const_reverse_iterator rbegin () const</code></td> 197<td>Returns a <code>const_reverse_iterator</code> pointing to the 198beginning of the reversed expression.</td> 199</tr> 200<tr> 201<td><code>const_reverse_iterator rend () const</code></td> 202<td>Returns a <code>const_reverse_iterator</code> pointing to the 203end of the reversed expression.</td> 204</tr> 205<tr> 206<td><code>reverse_iterator rbegin ()</code></td> 207<td>Returns a <code>reverse_iterator</code> pointing to the 208beginning of the reversed expression.</td> 209</tr> 210<tr> 211<td><code>reverse_iterator rend ()</code></td> 212<td>Returns a <code>reverse_iterator</code> pointing to the end of 213the reversed expression.</td> 214</tr> 215</tbody> 216</table> 217<h2><a name="vector_operations"></a>Vector Operations</h2> 218<h3>Unary Operation Description</h3> 219<h4>Description</h4> 220<p>The templated class <code>vector_unary<E, F></code> 221describes a unary vector operation.</p> 222<h4>Definition</h4> 223<p>Defined in the header vector_expression.hpp.</p> 224<h4>Template parameters</h4> 225<table border="1" summary="parameters"> 226<tbody> 227<tr> 228<th>Parameter</th> 229<th>Description</th> 230<th>Default</th> 231</tr> 232<tr> 233<td><code>E</code></td> 234<td>The type of the vector expression.</td> 235<td> </td> 236</tr> 237<tr> 238<td><code>F</code></td> 239<td>The type of the operation.</td> 240<td> </td> 241</tr> 242</tbody> 243</table> 244<h4>Model of</h4> 245<p><a href="expression_concept.html#vector_expression">Vector Expression</a> 246.</p> 247<h4>Type requirements</h4> 248<p>None, except for those imposed by the requirements of <a href= 249"expression_concept.html#vector_expression">Vector Expression</a> .</p> 250<h4>Public base classes</h4> 251<p><code>vector_expression<vector_unary<E, F> 252></code></p> 253<h4>Members</h4> 254<table border="1" summary="members"> 255<tbody> 256<tr> 257<th>Member</th> 258<th>Description</th> 259</tr> 260<tr> 261<td><code>vector_unary (const expression_type &e)</code></td> 262<td>Constructs a description of the expression.</td> 263</tr> 264<tr> 265<td><code>size_type size () const</code></td> 266<td>Returns the size of the expression.</td> 267</tr> 268<tr> 269<td><code>const_reference operator () (size_type i) 270const</code></td> 271<td>Returns the value of the <code>i</code>-th element.</td> 272</tr> 273<tr> 274<td><code>const_iterator begin () const</code></td> 275<td>Returns a <code>const_iterator</code> pointing to the beginning 276of the expression.</td> 277</tr> 278<tr> 279<td><code>const_iterator end () const</code></td> 280<td>Returns a <code>const_iterator</code> pointing to the end of 281the expression.</td> 282</tr> 283<tr> 284<td><code>const_reverse_iterator rbegin () const</code></td> 285<td>Returns a <code>const_reverse_iterator</code> pointing to the 286beginning of the reversed expression.</td> 287</tr> 288<tr> 289<td><code>const_reverse_iterator rend () const</code></td> 290<td>Returns a <code>const_reverse_iterator</code> pointing to the 291end of the reversed expression.</td> 292</tr> 293</tbody> 294</table> 295<h3>Unary Operations</h3> 296<h4>Prototypes</h4> 297<pre> 298<code>template<class E, class F> 299 struct vector_unary_traits { 300 typedef vector_unary<typename E::const_closure_type, F> expression_type; 301 typedef expression_type result_type; 302 }; 303 304 // (- v) [i] = - v [i] 305 template<class E> 306 typename vector_unary_traits<E, scalar_negate<typename E::value_type> >::result_type 307 operator - (const vector_expression<E> &e); 308 309 // (conj v) [i] = conj (v [i]) 310 template<class E> 311 typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type 312 conj (const vector_expression<E> &e); 313 314 // (real v) [i] = real (v [i]) 315 template<class E> 316 typename vector_unary_traits<E, scalar_real<typename E::value_type> >::result_type 317 real (const vector_expression<E> &e); 318 319 // (imag v) [i] = imag (v [i]) 320 template<class E> 321 typename vector_unary_traits<E, scalar_imag<typename E::value_type> >::result_type 322 imag (const vector_expression<E> &e); 323 324 // (trans v) [i] = v [i] 325 template<class E> 326 typename vector_unary_traits<E, scalar_identity<typename E::value_type> >::result_type 327 trans (const vector_expression<E> &e); 328 329 // (herm v) [i] = conj (v [i]) 330 template<class E> 331 typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type 332 herm (const vector_expression<E> &e);</code> 333</pre> 334<h4>Description</h4> 335<p><code>operator -</code> computes the additive inverse of a 336vector expression. <code>conj</code> computes the complex conjugate 337of a vector expression. <code>real</code> and <code>imag</code> 338compute the real and imaginary parts of a vector expression. 339<code>trans</code> computes the transpose of a vector expression. 340<code>herm</code> computes the hermitian, i.e. the complex 341conjugate of the transpose of a vector expression.</p> 342<h4>Definition</h4> 343<p>Defined in the header vector_expression.hpp.</p> 344<h4>Type requirements</h4> 345<ul> 346<li><code>E</code> is a model of <a href= 347"expression_concept.html#vector_expression">Vector Expression</a> .</li> 348</ul> 349<h4>Preconditions</h4> 350<p>None.</p> 351<h4>Complexity</h4> 352<p>Linear depending from the size of the vector expression.</p> 353<h4>Examples</h4> 354<pre> 355#include <boost/numeric/ublas/vector.hpp> 356#include <boost/numeric/ublas/io.hpp> 357 358int main () { 359 using namespace boost::numeric::ublas; 360 vector<std::complex<double> > v (3); 361 for (unsigned i = 0; i < v.size (); ++ i) 362 v (i) = std::complex<double> (i, i); 363 364 std::cout << - v << std::endl; 365 std::cout << conj (v) << std::endl; 366 std::cout << real (v) << std::endl; 367 std::cout << imag (v) << std::endl; 368 std::cout << trans (v) << std::endl; 369 std::cout << herm (v) << std::endl; 370} 371</pre> 372<h3>Binary Operation Description</h3> 373<h4>Description</h4> 374<p>The templated class <code>vector_binary<E1, E2, F></code> 375describes a binary vector operation.</p> 376<h4>Definition</h4> 377<p>Defined in the header vector_expression.hpp.</p> 378<h4>Template parameters</h4> 379<table border="1" summary="parameters"> 380<tbody> 381<tr> 382<th>Parameter</th> 383<th>Description</th> 384<th>Default</th> 385</tr> 386<tr> 387<td><code>E1</code></td> 388<td>The type of the first vector expression.</td> 389<td></td> 390</tr> 391<tr> 392<td><code>E2</code></td> 393<td>The type of the second vector expression.</td> 394<td></td> 395</tr> 396<tr> 397<td><code>F</code></td> 398<td>The type of the operation.</td> 399<td></td> 400</tr> 401</tbody> 402</table> 403<h4>Model of</h4> 404<p><a href="expression_concept.html#vector_expression">Vector Expression</a> 405.</p> 406<h4>Type requirements</h4> 407<p>None, except for those imposed by the requirements of <a href= 408"expression_concept.html#vector_expression">Vector Expression</a> .</p> 409<h4>Public base classes</h4> 410<p><code>vector_expression<vector_binary<E1, E2, F> 411></code></p> 412<h4>Members</h4> 413<table border="1" summary="members"> 414<tbody> 415<tr> 416<th>Member</th> 417<th>Description</th> 418</tr> 419<tr> 420<td><code>vector_binary (const expression1_type &e1, const 421expression2_type &e2)</code></td> 422<td>Constructs a description of the expression.</td> 423</tr> 424<tr> 425<td><code>size_type size () const</code></td> 426<td>Returns the size of the expression.</td> 427</tr> 428<tr> 429<td><code>const_reference operator () (size_type i) 430const</code></td> 431<td>Returns the value of the <code>i</code>-th element.</td> 432</tr> 433<tr> 434<td><code>const_iterator begin () const</code></td> 435<td>Returns a <code>const_iterator</code> pointing to the beginning 436of the expression.</td> 437</tr> 438<tr> 439<td><code>const_iterator end () const</code></td> 440<td>Returns a <code>const_iterator</code> pointing to the end of 441the expression.</td> 442</tr> 443<tr> 444<td><code>const_reverse_iterator rbegin () const</code></td> 445<td>Returns a <code>const_reverse_iterator</code> pointing to the 446beginning of the reversed expression.</td> 447</tr> 448<tr> 449<td><code>const_reverse_iterator rend () const</code></td> 450<td>Returns a <code>const_reverse_iterator</code> pointing to the 451end of the reversed expression.</td> 452</tr> 453</tbody> 454</table> 455<h3>Binary Operations</h3> 456<h4>Prototypes</h4> 457<pre> 458<code>template<class E1, class E2, class F> 459 struct vector_binary_traits { 460 typedef vector_binary<typename E1::const_closure_type, 461 typename E2::const_closure_type, F> expression_type; 462 typedef expression_type result_type; 463 }; 464 465 // (v1 + v2) [i] = v1 [i] + v2 [i] 466 template<class E1, class E2> 467 typename vector_binary_traits<E1, E2, scalar_plus<typename E1::value_type, 468 typename E2::value_type> >::result_type 469 operator + (const vector_expression<E1> &e1, 470 const vector_expression<E2> &e2); 471 472 // (v1 - v2) [i] = v1 [i] - v2 [i] 473 template<class E1, class E2> 474 typename vector_binary_traits<E1, E2, scalar_minus<typename E1::value_type, 475 typename E2::value_type> >::result_type 476 operator - (const vector_expression<E1> &e1, 477 const vector_expression<E2> &e2);</code> 478</pre> 479<h4>Description</h4> 480<p><code>operator +</code> computes the sum of two vector 481expressions. <code>operator -</code> computes the difference of two 482vector expressions.</p> 483<h4>Definition</h4> 484<p>Defined in the header vector_expression.hpp.</p> 485<h4>Type requirements</h4> 486<ul> 487<li><code>E1</code> is a model of <a href= 488"expression_concept.html#vector_expression">Vector Expression</a> .</li> 489<li><code>E2</code> is a model of <a href= 490"expression_concept.html#vector_expression">Vector Expression</a> .</li> 491</ul> 492<h4>Preconditions</h4> 493<ul> 494<li><code>e1 ().size () == e2 ().size ()</code></li> 495</ul> 496<h4>Complexity</h4> 497<p>Linear depending from the size of the vector expressions.</p> 498<h4>Examples</h4> 499<pre> 500#include <boost/numeric/ublas/vector.hpp> 501#include <boost/numeric/ublas/io.hpp> 502 503int main () { 504 using namespace boost::numeric::ublas; 505 vector<double> v1 (3), v2 (3); 506 for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i) 507 v1 (i) = v2 (i) = i; 508 509 std::cout << v1 + v2 << std::endl; 510 std::cout << v1 - v2 << std::endl; 511} 512</pre> 513<h3>Binary Outer Operation Description</h3> 514<h4>Description</h4> 515<p>The templated class <code>vector_matrix_binary<E1, E2, 516F></code> describes a binary outer vector operation.</p> 517<h4>Definition</h4> 518<p>Defined in the header matrix_expression.hpp.</p> 519<h4>Template parameters</h4> 520<table border="1" summary="parameters"> 521<tbody> 522<tr> 523<th>Parameter</th> 524<th>Description</th> 525<th>Default</th> 526</tr> 527<tr> 528<td><code>E1</code></td> 529<td>The type of the first vector expression.</td> 530<td></td> 531</tr> 532<tr> 533<td><code>E2</code></td> 534<td>The type of the second vector expression.</td> 535<td></td> 536</tr> 537<tr> 538<td><code>F</code></td> 539<td>The type of the operation.</td> 540<td></td> 541</tr> 542</tbody> 543</table> 544<h4>Model of</h4> 545<p><a href="expression_concept.html#matrix_expression">Matrix Expression</a> 546.</p> 547<h4>Type requirements</h4> 548<p>None, except for those imposed by the requirements of <a href= 549"expression_concept.html#matrix_expression">Matrix Expression</a> .</p> 550<h4>Public base classes</h4> 551<p><code>matrix_expression<vector_matrix_binary<E1, E2, F> 552></code></p> 553<h4>Members</h4> 554<table border="1" summary="members"> 555<tbody> 556<tr> 557<th>Member</th> 558<th>Description</th> 559</tr> 560<tr> 561<td><code>vector_matrix_binary (const expression1_type &e1, 562const expression2_type &e2)</code></td> 563<td>Constructs a description of the expression.</td> 564</tr> 565<tr> 566<td><code>size_type size1 () const</code></td> 567<td>Returns the number of rows.</td> 568</tr> 569<tr> 570<td><code>size_type size2 () const</code></td> 571<td>Returns the number of columns.</td> 572</tr> 573<tr> 574<td><code>const_reference operator () (size_type i, size_type j) 575const</code></td> 576<td>Returns the value of the <code>j</code>-th element in the 577<code>i</code>-th row.</td> 578</tr> 579<tr> 580<td><code>const_iterator1 begin1 () const</code></td> 581<td>Returns a <code>const_iterator1</code> pointing to the 582beginning of the expression.</td> 583</tr> 584<tr> 585<td><code>const_iterator1 end1 () const</code></td> 586<td>Returns a <code>const_iterator1</code> pointing to the end of 587the expression.</td> 588</tr> 589<tr> 590<td><code>const_iterator2 begin2 () const</code></td> 591<td>Returns a <code>const_iterator2</code> pointing to the 592beginning of the expression.</td> 593</tr> 594<tr> 595<td><code>const_iterator2 end2 () const</code></td> 596<td>Returns a <code>const_iterator2</code> pointing to the end of 597the expression.</td> 598</tr> 599<tr> 600<td><code>const_reverse_iterator1 rbegin1 () const</code></td> 601<td>Returns a <code>const_reverse_iterator1</code> pointing to the 602beginning of the reversed expression.</td> 603</tr> 604<tr> 605<td><code>const_reverse_iterator1 rend1 () const</code></td> 606<td>Returns a <code>const_reverse_iterator1</code> pointing to the 607end of the reversed expression.</td> 608</tr> 609<tr> 610<td><code>const_reverse_iterator2 rbegin2 () const</code></td> 611<td>Returns a <code>const_reverse_iterator2</code> pointing to the 612beginning of the reversed expression.</td> 613</tr> 614<tr> 615<td><code>const_reverse_iterator2 rend2 () const</code></td> 616<td>Returns a <code>const_reverse_iterator2</code> pointing to the 617end of the reversed expression.</td> 618</tr> 619</tbody> 620</table> 621<h3>Binary Outer Operations</h3> 622<h4>Prototypes</h4> 623<pre> 624<code>template<class E1, class E2, class F> 625 struct vector_matrix_binary_traits { 626 typedef vector_matrix_binary<typename E1::const_closure_type, 627 typename E2::const_closure_type, F> expression_type; 628 typedef expression_type result_type; 629 }; 630 631 // (outer_prod (v1, v2)) [i] [j] = v1 [i] * v2 [j] 632 template<class E1, class E2> 633 typename vector_matrix_binary_traits<E1, E2, scalar_multiplies<typename E1::value_type, typename E2::value_type> >::result_type 634 outer_prod (const vector_expression<E1> &e1, 635 const vector_expression<E2> &e2);</code> 636</pre> 637<h4>Description</h4> 638<p><code>outer_prod</code> computes the outer product of two vector 639expressions.</p> 640<h4>Definition</h4> 641<p>Defined in the header matrix_expression.hpp.</p> 642<h4>Type requirements</h4> 643<ul> 644<li><code>E1</code> is a model of <a href= 645"expression_concept.html#vector_expression">Vector Expression</a> .</li> 646<li><code>E2</code> is a model of <a href= 647"expression_concept.html#vector_expression">Vector Expression</a> .</li> 648</ul> 649<h4>Preconditions</h4> 650<p>None.</p> 651<h4>Complexity</h4> 652<p>Quadratic depending from the size of the vector expressions.</p> 653<h4>Examples</h4> 654<pre> 655#include <boost/numeric/ublas/matrix.hpp> 656#include <boost/numeric/ublas/io.hpp> 657 658int main () { 659 using namespace boost::numeric::ublas; 660 vector<double> v1 (3), v2 (3); 661 for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i) 662 v1 (i) = v2 (i) = i; 663 664 std::cout << outer_prod (v1, v2) << std::endl; 665} 666</pre> 667<h3>Scalar Vector Operation Description</h3> 668<h4>Description</h4> 669<p>The templated classes <code>vector_binary_scalar1<E1, E2, 670F></code> and <code>vector_binary_scalar2<E1, E2, 671F></code> describe binary operations between a scalar and a 672vector.</p> 673<h4>Definition</h4> 674<p>Defined in the header vector_expression.hpp.</p> 675<h4>Template parameters</h4> 676<table border="1" summary="parameters"> 677<tbody> 678<tr> 679<th>Parameter</th> 680<th>Description</th> 681<th>Default</th> 682</tr> 683<tr> 684<td><code>E1/E2</code></td> 685<td>The type of the scalar expression.</td> 686<td></td> 687</tr> 688<tr> 689<td><code>E2/E1</code></td> 690<td>The type of the vector expression.</td> 691<td></td> 692</tr> 693<tr> 694<td><code>F</code></td> 695<td>The type of the operation.</td> 696<td></td> 697</tr> 698</tbody> 699</table> 700<h4>Model of</h4> 701<p><a href="expression_concept.html#vector_expression">Vector Expression</a> 702.</p> 703<h4>Type requirements</h4> 704<p>None, except for those imposed by the requirements of <a href= 705"expression_concept.html#vector_expression">Vector Expression</a> .</p> 706<h4>Public base classes</h4> 707<p><code>vector_expression<vector_binary_scalar1<E1, E2, 708F> ></code> and 709<code>vector_expression<vector_binary_scalar2<E1, E2, F> 710></code> resp.</p> 711<h4>Members</h4> 712<table border="1" summary="members"> 713<tbody> 714<tr> 715<th>Member</th> 716<th>Description</th> 717</tr> 718<tr> 719<td><code>vector_binary_scalar1 (const expression1_type &e1, 720const expression2_type &e2)</code></td> 721<td>Constructs a description of the expression.</td> 722</tr> 723<tr> 724<td><code>vector_binary_scalar2 (const expression1_type &e1, 725const expression2_type &e2)</code></td> 726<td>Constructs a description of the expression.</td> 727</tr> 728<tr> 729<td><code>size_type size () const</code></td> 730<td>Returns the size of the expression.</td> 731</tr> 732<tr> 733<td><code>const_reference operator () (size_type i) 734const</code></td> 735<td>Returns the value of the <code>i</code>-th element.</td> 736</tr> 737<tr> 738<td><code>const_iterator begin () const</code></td> 739<td>Returns a <code>const_iterator</code> pointing to the beginning 740of the expression.</td> 741</tr> 742<tr> 743<td><code>const_iterator end () const</code></td> 744<td>Returns a <code>const_iterator</code> pointing to the end of 745the expression.</td> 746</tr> 747<tr> 748<td><code>const_reverse_iterator rbegin () const</code></td> 749<td>Returns a <code>const_reverse_iterator</code> pointing to the 750beginning of the reversed expression.</td> 751</tr> 752<tr> 753<td><code>const_reverse_iterator rend () const</code></td> 754<td>Returns a <code>const_reverse_iterator</code> pointing to the 755end of the reversed expression.</td> 756</tr> 757</tbody> 758</table> 759<h3>Scalar Vector Operations</h3> 760<h4>Prototypes</h4> 761<pre> 762<code>template<class T1, class E2, class F> 763 struct vector_binary_scalar1_traits { 764 typedef vector_binary_scalar1<scalar_const_reference<T1>, 765 typename E2::const_closure_type, F> expression_type; 766 typedef expression_type result_type; 767 }; 768 769 // (t * v) [i] = t * v [i] 770 template<class T1, class E2> 771 typename vector_binary_scalar1_traits<T1, E2, scalar_multiplies<T1, typename E2::value_type> >::result_type 772 operator * (const T1 &e1, 773 const vector_expression<E2> &e2); 774 775 template<class E1, class T2, class F> 776 struct vector_binary_scalar2_traits { 777 typedef vector_binary_scalar2<typename E1::const_closure_type, 778 scalar_const_reference<T2>, F> expression_type; 779 typedef expression_type result_type; 780 }; 781 782 // (v * t) [i] = v [i] * t 783 template<class E1, class T2> 784 typename vector_binary_scalar2_traits<E1, T2, scalar_multiplies<typename E1::value_type, T2> >::result_type 785 operator * (const vector_expression<E1> &e1, 786 const T2 &e2); 787 788 // (v / t) [i] = v [i] / t 789 template<class E1, class T2> 790 typename vector_binary_scalar2_traits<E1, T2, scalar_divides<typename E1::value_type, T2> >::result_type 791 operator / (const vector_expression<E1> &e1, 792 const T2 &e2);</code> 793</pre> 794<h4>Description</h4> 795<p><code>operator *</code> computes the product of a scalar and a 796vector expression. <code>operator /</code> multiplies the vector 797with the reciprocal of the scalar.</p> 798<h4>Definition</h4> 799<p>Defined in the header vector_expression.hpp.</p> 800<h4>Type requirements</h4> 801<ul> 802<li><code>T1/T2</code> is a model of <a href= 803"expression_concept.html#scalar_expression">Scalar Expression</a> .</li> 804<li><code>E2/E1</code> is a model of <a href= 805"expression_concept.html#vector_expression">Vector Expression</a> .</li> 806</ul> 807<h4>Preconditions</h4> 808<p>None.</p> 809<h4>Complexity</h4> 810<p>Linear depending from the size of the vector expression.</p> 811<h4>Examples</h4> 812<pre> 813#include <boost/numeric/ublas/vector.hpp> 814#include <boost/numeric/ublas/io.hpp> 815 816int main () { 817 using namespace boost::numeric::ublas; 818 vector<double> v (3); 819 for (unsigned i = 0; i < v.size (); ++ i) 820 v (i) = i; 821 822 std::cout << 2.0 * v << std::endl; 823 std::cout << v * 2.0 << std::endl; 824} 825</pre> 826<h2><a name="vector_reductions"></a>Vector Reductions</h2> 827<h3>Unary Reductions</h3> 828<h4>Prototypes</h4> 829<pre> 830<code>template<class E, class F> 831 struct vector_scalar_unary_traits { 832 typedef typename F::result_type result_type; 833 }; 834 835 // sum v = sum (v [i]) 836 template<class E> 837 typename vector_scalar_unary_traits<E, vector_sum<typename E::value_type> >::result_type 838 sum (const vector_expression<E> &e); 839 840 // norm_1 v = sum (abs (v [i])) 841 template<class E> 842 typename vector_scalar_unary_traits<E, vector_norm_1<typename E::value_type> >::result_type 843 norm_1 (const vector_expression<E> &e); 844 845 // norm_2 v = sqrt (sum (v [i] * v [i])) 846 template<class E> 847 typename vector_scalar_unary_traits<E, vector_norm_2<typename E::value_type> >::result_type 848 norm_2 (const vector_expression<E> &e); 849 850 // norm_2_square v = sum (v [i] * v [i]) 851 template<class E> 852 typename vector_scalar_unary_traits<E, vector_norm_2_square<typename E::value_type> >::result_type 853 norm_2_square (const vector_expression<E> &e); 854 855 // norm_inf v = max (abs (v [i])) 856 template<class E> 857 typename vector_scalar_unary_traits<E, vector_norm_inf<typename E::value_type> >::result_type 858 norm_inf (const vector_expression<E> &e); 859 860 // index_norm_inf v = min (i: abs (v [i]) == max (abs (v [i]))) 861 template<class E> 862 typename vector_scalar_unary_traits<E, vector_index_norm_inf<typename E::value_type> >::result_type 863 index_norm_inf (const vector_expression<E> &e);</code> 864</pre> 865<h4>Description</h4> 866<p><code>sum</code> computes the sum of the vector expression's 867elements. <code>norm_1</code>, <code>norm_2</code> and 868<code>norm_inf</code> compute the corresponding 869<em>||.||</em><sub><em>1</em></sub>, 870<em>||.||</em><sub><em>2</em></sub> and 871<em>||.||</em><sub><em>inf</em></sub> vector norms. 872<code>index_norm_1</code> computes the index of the vector 873expression's first element having maximal absolute value.</p> 874<h4>Definition</h4> 875<p>Defined in the header vector_expression.hpp.</p> 876<h4>Type requirements</h4> 877<ul> 878<li><code>E</code> is a model of <a href= 879"#vector_expression">Vector Expression</a> .</li> 880</ul> 881<h4>Preconditions</h4> 882<p>None.</p> 883<h4>Complexity</h4> 884<p>Linear depending from the size of the vector expression.</p> 885<h4>Examples</h4> 886<pre> 887#include <boost/numeric/ublas/vector.hpp> 888 889int main () { 890 using namespace boost::numeric::ublas; 891 vector<double> v (3); 892 for (unsigned i = 0; i < v.size (); ++ i) 893 v (i) = i; 894 895 std::cout << sum (v) << std::endl; 896 std::cout << norm_1 (v) << std::endl; 897 std::cout << norm_2 (v) << std::endl; 898 std::cout << norm_inf (v) << std::endl; 899 std::cout << index_norm_inf (v) << std::endl; 900} 901</pre> 902<h3>Binary Reductions</h3> 903<h4>Prototypes</h4> 904<pre> 905<code>template<class E1, class E2, class F> 906 struct vector_scalar_binary_traits { 907 typedef typename F::result_type result_type; 908 }; 909 910 // inner_prod (v1, v2) = sum (v1 [i] * v2 [i]) 911 template<class E1, class E2> 912 typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<typename E1::value_type, 913 typename E2::value_type, 914 typename promote_traits<typename E1::value_type, 915 typename E2::value_type>::promote_type> >::result_type 916 inner_prod (const vector_expression<E1> &e1, 917 const vector_expression<E2> &e2); 918 919 template<class E1, class E2> 920 typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<typename E1::value_type, 921 typename E2::value_type, 922 typename type_traits<typename promote_traits<typename E1::value_type, 923 typename E2::value_type>::promote_type>::precision_type> >::result_type 924 prec_inner_prod (const vector_expression<E1> &e1, 925 const vector_expression<E2> &e2);</code> 926</pre> 927<h4>Description</h4> 928<p><code>inner_prod</code> computes the inner product of the vector 929expressions. <code>prec_inner_prod</code> computes the double 930precision inner product of the vector expressions<code>.</code></p> 931<h4>Definition</h4> 932<p>Defined in the header vector_expression.hpp.</p> 933<h4>Type requirements</h4> 934<ul> 935<li><code>E1</code> is a model of <a href= 936"#vector_expression">Vector Expression</a> .</li> 937<li><code>E2</code> is a model of <a href= 938"#vector_expression">Vector Expression</a> .</li> 939</ul> 940<h4>Preconditions</h4> 941<ul> 942<li><code>e1 ().size () == e2 ().size ()</code></li> 943</ul> 944<h4>Complexity</h4> 945<p>Linear depending from the size of the vector expressions.</p> 946<h4>Examples</h4> 947<pre> 948#include <boost/numeric/ublas/vector.hpp> 949 950int main () { 951 using namespace boost::numeric::ublas; 952 vector<double> v1 (3), v2 (3); 953 for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i) 954 v1 (i) = v2 (i) = i; 955 956 std::cout << inner_prod (v1, v2) << std::endl; 957} 958</pre> 959<hr /> 960<p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch<br /> 961 Use, modification and distribution are subject to the 962 Boost Software License, Version 1.0. 963 (See accompanying file LICENSE_1_0.txt 964 or copy at <a href="http://www.boost.org/LICENSE_1_0.txt"> 965 http://www.boost.org/LICENSE_1_0.txt 966 </a>). 967</p> 968<script type="text/javascript"> 969(function($) { 970 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