1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.8.6"/>
<title>ViennaCL - The Vienna Computing Library: qr.cpp</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="resize.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<script type="text/javascript">
$(document).ready(initResizable);
$(window).load(resizeHeight);
</script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/javascript">
$(document).ready(function() { searchBox.OnSelectItem(0); });
</script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr style="height: 56px;">
<td style="padding-left: 0.5em;">
<div id="projectname">ViennaCL - The Vienna Computing Library
 <span id="projectnumber">1.7.1</span>
</div>
<div id="projectbrief">Free open-source GPU-accelerated linear algebra and solver library.</div>
</td>
<td> <div id="MSearchBox" class="MSearchBoxInactive">
<span class="left">
<img id="MSearchSelect" src="search/mag_sel.png"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
alt=""/>
<input type="text" id="MSearchField" value="Search" accesskey="S"
onfocus="searchBox.OnSearchFieldFocus(true)"
onblur="searchBox.OnSearchFieldFocus(false)"
onkeyup="searchBox.OnSearchFieldChange(event)"/>
</span><span class="right">
<a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a>
</span>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.8.6 -->
<script type="text/javascript">
var searchBox = new SearchBox("searchBox", "search",false,'Search');
</script>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
<div id="nav-tree">
<div id="nav-tree-contents">
<div id="nav-sync" class="sync"></div>
</div>
</div>
<div id="splitbar" style="-moz-user-select:none;"
class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
$(document).ready(function(){initNavTree('qr_8cpp-example.html','');});
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
onkeydown="return searchBox.OnSearchSelectKey(event)">
<a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(0)"><span class="SelectionMark"> </span>All</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(1)"><span class="SelectionMark"> </span>Classes</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(2)"><span class="SelectionMark"> </span>Namespaces</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(3)"><span class="SelectionMark"> </span>Files</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(4)"><span class="SelectionMark"> </span>Functions</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(5)"><span class="SelectionMark"> </span>Variables</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(6)"><span class="SelectionMark"> </span>Typedefs</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(7)"><span class="SelectionMark"> </span>Enumerations</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(8)"><span class="SelectionMark"> </span>Enumerator</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(9)"><span class="SelectionMark"> </span>Friends</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(10)"><span class="SelectionMark"> </span>Macros</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(11)"><span class="SelectionMark"> </span>Pages</a></div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0"
name="MSearchResults" id="MSearchResults">
</iframe>
</div>
<div class="header">
<div class="headertitle">
<div class="title">qr.cpp</div> </div>
</div><!--header-->
<div class="contents">
<p>This tutorial shows how the QR factorization of matrices from ViennaCL or Boost.uBLAS can be computed.</p>
<div class="fragment"><div class="line"><span class="comment">// Activate ublas support in ViennaCL</span></div>
<div class="line"><span class="preprocessor">#define VIENNACL_WITH_UBLAS</span></div>
<div class="line"></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="comment">// Include necessary system headers</span></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="preprocessor">#include <iostream></span></div>
<div class="line"></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="comment">// ViennaCL includes</span></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="matrix_8hpp.html">viennacl/matrix.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="prod_8hpp.html">viennacl/linalg/prod.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="qr_8hpp.html">viennacl/linalg/qr.hpp</a>"</span></div>
<div class="line"></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="comment">// Boost includes</span></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/vector.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/matrix.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/io.hpp></span></div>
</div><!-- fragment --><p> A helper function comparing two matrices and returning the maximum entry-wise relative error encountered. </p>
<div class="fragment"><div class="line"><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><span class="keywordtype">double</span> <a name="a0"></a><a class="code" href="libviennacl__blas1_8cpp.html#ade615bbf93f6f668af70fb8e6b427d17">check</a>(MatrixType <span class="keyword">const</span> & qr, MatrixType <span class="keyword">const</span> & ref)</div>
<div class="line">{</div>
<div class="line"> <span class="keywordtype">bool</span> do_break = <span class="keyword">false</span>;</div>
<div class="line"> <span class="keywordtype">double</span> max_error = 0;</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t i=0; i<ref.size1(); ++i)</div>
<div class="line"> {</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t j=0; j<ref.size2(); ++j)</div>
<div class="line"> {</div>
<div class="line"> <span class="keywordflow">if</span> (qr(i,j) != 0.0 && ref(i,j) != 0.0)</div>
<div class="line"> {</div>
<div class="line"> <span class="keywordtype">double</span> rel_err = fabs(qr(i,j) - ref(i,j)) / fabs(ref(i,j) );</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">if</span> (rel_err > max_error)</div>
<div class="line"> max_error = rel_err;</div>
<div class="line"> }</div>
<div class="line"></div>
<div class="line"></div>
<div class="line"> <span class="comment">/* Uncomment the following if you also want to check for NaNs.</span></div>
<div class="line"><span class="comment"> if (qr(i,j) != qr(i,j))</span></div>
<div class="line"><span class="comment"> {</span></div>
<div class="line"><span class="comment"> std::cout << "!!!" << std::endl;</span></div>
<div class="line"><span class="comment"> std::cout << "!!! NaN detected at i=" << i << " and j=" << j << std::endl;</span></div>
<div class="line"><span class="comment"> std::cout << "!!!" << std::endl;</span></div>
<div class="line"><span class="comment"> do_break = true;</span></div>
<div class="line"><span class="comment"> break;</span></div>
<div class="line"><span class="comment"> }*/</span></div>
<div class="line"> }</div>
<div class="line"> <span class="keywordflow">if</span> (do_break)</div>
<div class="line"> <span class="keywordflow">break</span>;</div>
<div class="line"> }</div>
<div class="line"> <span class="keywordflow">return</span> max_error;</div>
<div class="line">}</div>
</div><!-- fragment --><p> We set up a random matrix using Boost.uBLAS and use it to initialize a ViennaCL matrix. Then we compute the QR factorization directly for the uBLAS matrix as well as the ViennaCL matrix. </p>
<div class="fragment"><div class="line"><span class="keywordtype">int</span> <a name="a1"></a><a class="code" href="benchmarks_2qr_8cpp.html#ac0f2228420376f4db7e1274f2b41667c">main</a> (<span class="keywordtype">int</span>, <span class="keyword">const</span> <span class="keywordtype">char</span> **)</div>
<div class="line">{</div>
<div class="line"> <span class="keyword">typedef</span> <span class="keywordtype">double</span> <a name="a2"></a><a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>; <span class="comment">//feel free to change this to 'double' if supported by your hardware</span></div>
<div class="line"> <span class="keyword">typedef</span> boost::numeric::ublas::matrix<ScalarType> MatrixType;</div>
<div class="line"> <span class="keyword">typedef</span> <a name="_a3"></a><a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType, viennacl::column_major></a> VCLMatrixType;</div>
<div class="line"></div>
<div class="line"> std::size_t rows = 113; <span class="comment">// number of rows in the matrix</span></div>
<div class="line"> std::size_t cols = 54; <span class="comment">// number of columns</span></div>
</div><!-- fragment --><p> Create uBLAS matrices with some random input data. </p>
<div class="fragment"><div class="line">MatrixType ublas_A(rows, cols);</div>
<div class="line">MatrixType Q(rows, rows);</div>
<div class="line">MatrixType R(rows, cols);</div>
<div class="line"></div>
<div class="line"><span class="comment">// Some random data with a bit of extra weight on the diagonal</span></div>
<div class="line"><span class="keywordflow">for</span> (std::size_t i=0; i<rows; ++i)</div>
<div class="line">{</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t j=0; j<cols; ++j)</div>
<div class="line"> {</div>
<div class="line"> ublas_A(i,j) = <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(-1.0) + <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>((i+1)*(j+1))</div>
<div class="line"> + <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>( (rand() % 1000) - 500.0) / <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1000.0);</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">if</span> (i == j)</div>
<div class="line"> ublas_A(i,j) += <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(10.0);</div>
<div class="line"></div>
<div class="line"> R(i,j) = 0.0;</div>
<div class="line"> }</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t j=0; j<rows; ++j)</div>
<div class="line"> Q(i,j) = <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0.0);</div>
<div class="line">}</div>
<div class="line"></div>
<div class="line"><span class="comment">// keep initial input matrix for comparison</span></div>
<div class="line">MatrixType ublas_A_backup(ublas_A);</div>
</div><!-- fragment --><p> Setup the matrix in ViennaCL and copy the data from the uBLAS matrix: </p>
<div class="fragment"><div class="line">VCLMatrixType vcl_A(ublas_A.size1(), ublas_A.size2());</div>
<div class="line"></div>
<div class="line"><a name="a4"></a><a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ublas_A, vcl_A);</div>
</div><!-- fragment --> <h2>QR Factorization with Boost.uBLAS Matrices</h2>
<p>Compute QR factorization of A. A is overwritten with Householder vectors. Coefficients are returned and a block size of 3 is used. Note that at the moment the number of columns of A must be divisible by the block size </p>
<div class="fragment"><div class="line">std::cout << <span class="stringliteral">"--- Boost.uBLAS ---"</span> << std::endl;</div>
<div class="line">std::vector<ScalarType> ublas_betas = <a name="a5"></a><a class="code" href="namespaceviennacl_1_1linalg.html#a83f573386903bae3a5379ab4cbfc5e2d">viennacl::linalg::inplace_qr</a>(ublas_A); <span class="comment">//computes the QR factorization</span></div>
</div><!-- fragment --><p> Let us check for the correct result: </p>
<div class="fragment"><div class="line"><a name="a6"></a><a class="code" href="namespaceviennacl_1_1linalg.html#a76fc8bf8f5a20c576b7ddbad32d3e56d">viennacl::linalg::recoverQ</a>(ublas_A, ublas_betas, Q, R);</div>
<div class="line">MatrixType ublas_QR = <a name="a7"></a><a class="code" href="sparse__prod_8cpp.html#a2c8637b3d6a972d1d8fd85fb3089c6da">prod</a>(Q, R);</div>
<div class="line"><span class="keywordtype">double</span> ublas_error = <a class="code" href="libviennacl__blas1_8cpp.html#ade615bbf93f6f668af70fb8e6b427d17">check</a>(ublas_QR, ublas_A_backup);</div>
<div class="line">std::cout << <span class="stringliteral">"Maximum relative error (ublas): "</span> << ublas_error << std::endl;</div>
</div><!-- fragment --> <h2>QR Factorization with Boost.uBLAS Matrices</h2>
<p>We now compute the QR factorization from a ViennaCL matrix. Internally it uses Boost.uBLAS for the panel factorization. </p>
<div class="fragment"><div class="line">std::cout << <span class="stringliteral">"--- Hybrid (default) ---"</span> << std::endl;</div>
<div class="line"><a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ublas_A_backup, vcl_A);</div>
<div class="line">std::vector<ScalarType> <a name="a8"></a><a class="code" href="least-squares_8cpp.html#ac887df28e24b43a0bda14bd218659c78">hybrid_betas</a> = <a class="code" href="namespaceviennacl_1_1linalg.html#a83f573386903bae3a5379ab4cbfc5e2d">viennacl::linalg::inplace_qr</a>(vcl_A);</div>
</div><!-- fragment --><p> Let us check for the correct result: </p>
<div class="fragment"><div class="line"><a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(vcl_A, ublas_A);</div>
<div class="line">Q.clear(); R.clear();</div>
<div class="line"><a class="code" href="namespaceviennacl_1_1linalg.html#a76fc8bf8f5a20c576b7ddbad32d3e56d">viennacl::linalg::recoverQ</a>(ublas_A, hybrid_betas, Q, R);</div>
<div class="line"><span class="keywordtype">double</span> hybrid_error = <a class="code" href="libviennacl__blas1_8cpp.html#ade615bbf93f6f668af70fb8e6b427d17">check</a>(ublas_QR, ublas_A_backup);</div>
<div class="line">std::cout << <span class="stringliteral">"Maximum relative error (hybrid): "</span> << hybrid_error << std::endl;</div>
</div><!-- fragment --><p> That's it. Print a success message and exit. </p>
<div class="fragment"><div class="line"> std::cout << <span class="stringliteral">"!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!"</span> << std::endl;</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">return</span> EXIT_SUCCESS;</div>
<div class="line">}</div>
</div><!-- fragment --> <h2>Full Example Code</h2>
<div class="fragment"><div class="line"><span class="comment">/* =========================================================================</span></div>
<div class="line"><span class="comment"> Copyright (c) 2010-2016, Institute for Microelectronics,</span></div>
<div class="line"><span class="comment"> Institute for Analysis and Scientific Computing,</span></div>
<div class="line"><span class="comment"> TU Wien.</span></div>
<div class="line"><span class="comment"> Portions of this software are copyright by UChicago Argonne, LLC.</span></div>
<div class="line"><span class="comment"></span></div>
<div class="line"><span class="comment"> -----------------</span></div>
<div class="line"><span class="comment"> ViennaCL - The Vienna Computing Library</span></div>
<div class="line"><span class="comment"> -----------------</span></div>
<div class="line"><span class="comment"></span></div>
<div class="line"><span class="comment"> Project Head: Karl Rupp rupp@iue.tuwien.ac.at</span></div>
<div class="line"><span class="comment"></span></div>
<div class="line"><span class="comment"> (A list of authors and contributors can be found in the PDF manual)</span></div>
<div class="line"><span class="comment"></span></div>
<div class="line"><span class="comment"> License: MIT (X11), see file LICENSE in the base directory</span></div>
<div class="line"><span class="comment">============================================================================= */</span></div>
<div class="line"></div>
<div class="line"></div>
<div class="line"><span class="comment">// Activate ublas support in ViennaCL</span></div>
<div class="line"><span class="preprocessor">#define VIENNACL_WITH_UBLAS</span></div>
<div class="line"></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="comment">// Include necessary system headers</span></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="preprocessor">#include <iostream></span></div>
<div class="line"></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="comment">// ViennaCL includes</span></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="matrix_8hpp.html">viennacl/matrix.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="prod_8hpp.html">viennacl/linalg/prod.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="qr_8hpp.html">viennacl/linalg/qr.hpp</a>"</span></div>
<div class="line"></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="comment">// Boost includes</span></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/vector.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/matrix.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/io.hpp></span></div>
<div class="line"></div>
<div class="line"></div>
<div class="line"><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><span class="keywordtype">double</span> <a class="code" href="libviennacl__blas1_8cpp.html#ade615bbf93f6f668af70fb8e6b427d17">check</a>(MatrixType <span class="keyword">const</span> & qr, MatrixType <span class="keyword">const</span> & ref)</div>
<div class="line">{</div>
<div class="line"> <span class="keywordtype">bool</span> do_break = <span class="keyword">false</span>;</div>
<div class="line"> <span class="keywordtype">double</span> max_error = 0;</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t i=0; i<ref.size1(); ++i)</div>
<div class="line"> {</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t j=0; j<ref.size2(); ++j)</div>
<div class="line"> {</div>
<div class="line"> <span class="keywordflow">if</span> (qr(i,j) != 0.0 && ref(i,j) != 0.0)</div>
<div class="line"> {</div>
<div class="line"> <span class="keywordtype">double</span> rel_err = fabs(qr(i,j) - ref(i,j)) / fabs(ref(i,j) );</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">if</span> (rel_err > max_error)</div>
<div class="line"> max_error = rel_err;</div>
<div class="line"> }</div>
<div class="line"></div>
<div class="line"></div>
<div class="line"> <span class="comment">/* Uncomment the following if you also want to check for NaNs.</span></div>
<div class="line"><span class="comment"> if (qr(i,j) != qr(i,j))</span></div>
<div class="line"><span class="comment"> {</span></div>
<div class="line"><span class="comment"> std::cout << "!!!" << std::endl;</span></div>
<div class="line"><span class="comment"> std::cout << "!!! NaN detected at i=" << i << " and j=" << j << std::endl;</span></div>
<div class="line"><span class="comment"> std::cout << "!!!" << std::endl;</span></div>
<div class="line"><span class="comment"> do_break = true;</span></div>
<div class="line"><span class="comment"> break;</span></div>
<div class="line"><span class="comment"> }*/</span></div>
<div class="line"> }</div>
<div class="line"> <span class="keywordflow">if</span> (do_break)</div>
<div class="line"> <span class="keywordflow">break</span>;</div>
<div class="line"> }</div>
<div class="line"> <span class="keywordflow">return</span> max_error;</div>
<div class="line">}</div>
<div class="line"></div>
<div class="line"><span class="keywordtype">int</span> <a class="code" href="benchmarks_2qr_8cpp.html#ac0f2228420376f4db7e1274f2b41667c">main</a> (<span class="keywordtype">int</span>, <span class="keyword">const</span> <span class="keywordtype">char</span> **)</div>
<div class="line">{</div>
<div class="line"> <span class="keyword">typedef</span> <span class="keywordtype">double</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>; <span class="comment">//feel free to change this to 'double' if supported by your hardware</span></div>
<div class="line"> <span class="keyword">typedef</span> boost::numeric::ublas::matrix<ScalarType> MatrixType;</div>
<div class="line"> <span class="keyword">typedef</span> <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType, viennacl::column_major></a> VCLMatrixType;</div>
<div class="line"></div>
<div class="line"> std::size_t rows = 113; <span class="comment">// number of rows in the matrix</span></div>
<div class="line"> std::size_t cols = 54; <span class="comment">// number of columns</span></div>
<div class="line"></div>
<div class="line"> MatrixType ublas_A(rows, cols);</div>
<div class="line"> MatrixType Q(rows, rows);</div>
<div class="line"> MatrixType R(rows, cols);</div>
<div class="line"></div>
<div class="line"> <span class="comment">// Some random data with a bit of extra weight on the diagonal</span></div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t i=0; i<rows; ++i)</div>
<div class="line"> {</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t j=0; j<cols; ++j)</div>
<div class="line"> {</div>
<div class="line"> ublas_A(i,j) = <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(-1.0) + <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>((i+1)*(j+1))</div>
<div class="line"> + <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>( (rand() % 1000) - 500.0) / <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1000.0);</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">if</span> (i == j)</div>
<div class="line"> ublas_A(i,j) += <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(10.0);</div>
<div class="line"></div>
<div class="line"> R(i,j) = 0.0;</div>
<div class="line"> }</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t j=0; j<rows; ++j)</div>
<div class="line"> Q(i,j) = <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0.0);</div>
<div class="line"> }</div>
<div class="line"></div>
<div class="line"> <span class="comment">// keep initial input matrix for comparison</span></div>
<div class="line"> MatrixType ublas_A_backup(ublas_A);</div>
<div class="line"></div>
<div class="line"></div>
<div class="line"> VCLMatrixType vcl_A(ublas_A.size1(), ublas_A.size2());</div>
<div class="line"></div>
<div class="line"> <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ublas_A, vcl_A);</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"--- Boost.uBLAS ---"</span> << std::endl;</div>
<div class="line"> std::vector<ScalarType> ublas_betas = <a class="code" href="namespaceviennacl_1_1linalg.html#a83f573386903bae3a5379ab4cbfc5e2d">viennacl::linalg::inplace_qr</a>(ublas_A); <span class="comment">//computes the QR factorization</span></div>
<div class="line"></div>
<div class="line"> <a class="code" href="namespaceviennacl_1_1linalg.html#a76fc8bf8f5a20c576b7ddbad32d3e56d">viennacl::linalg::recoverQ</a>(ublas_A, ublas_betas, Q, R);</div>
<div class="line"> MatrixType ublas_QR = <a class="code" href="sparse__prod_8cpp.html#a2c8637b3d6a972d1d8fd85fb3089c6da">prod</a>(Q, R);</div>
<div class="line"> <span class="keywordtype">double</span> ublas_error = <a class="code" href="libviennacl__blas1_8cpp.html#ade615bbf93f6f668af70fb8e6b427d17">check</a>(ublas_QR, ublas_A_backup);</div>
<div class="line"> std::cout << <span class="stringliteral">"Maximum relative error (ublas): "</span> << ublas_error << std::endl;</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"--- Hybrid (default) ---"</span> << std::endl;</div>
<div class="line"> <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ublas_A_backup, vcl_A);</div>
<div class="line"> std::vector<ScalarType> hybrid_betas = <a class="code" href="namespaceviennacl_1_1linalg.html#a83f573386903bae3a5379ab4cbfc5e2d">viennacl::linalg::inplace_qr</a>(vcl_A);</div>
<div class="line"></div>
<div class="line"> <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(vcl_A, ublas_A);</div>
<div class="line"> Q.clear(); R.clear();</div>
<div class="line"> <a class="code" href="namespaceviennacl_1_1linalg.html#a76fc8bf8f5a20c576b7ddbad32d3e56d">viennacl::linalg::recoverQ</a>(ublas_A, hybrid_betas, Q, R);</div>
<div class="line"> <span class="keywordtype">double</span> hybrid_error = <a class="code" href="libviennacl__blas1_8cpp.html#ade615bbf93f6f668af70fb8e6b427d17">check</a>(ublas_QR, ublas_A_backup);</div>
<div class="line"> std::cout << <span class="stringliteral">"Maximum relative error (hybrid): "</span> << hybrid_error << std::endl;</div>
<div class="line"></div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!"</span> << std::endl;</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">return</span> EXIT_SUCCESS;</div>
<div class="line">}</div>
<div class="line"></div>
</div><!-- fragment --> </div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="footer">Generated on Wed Jan 20 2016 22:32:38 for ViennaCL - The Vienna Computing Library by
<a href="http://www.doxygen.org/index.html">
<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.6 </li>
</ul>
</div>
</body>
</html>
|
