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
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
|
<!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: viennacl/linalg/host_based/sse_kernels.hpp Source File</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">1.6.2</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('sse__kernels_8hpp_source.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">sse_kernels.hpp</div> </div>
</div><!--header-->
<div class="contents">
<a href="sse__kernels_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="preprocessor">#ifndef VIENNACL_LINALG_HOST_BASED_SSE_KERNELS_HPP_</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor">#define VIENNACL_LINALG_HOST_BASED_SSE_KERNELS_HPP_</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> </div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">/* =========================================================================</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> Copyright (c) 2010-2014, Institute for Microelectronics,</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> Institute for Analysis and Scientific Computing,</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> TU Wien.</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> Portions of this software are copyright by UChicago Argonne, LLC.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"></span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> -----------------</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> ViennaCL - The Vienna Computing Library</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> -----------------</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"></span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> Project Head: Karl Rupp rupp@iue.tuwien.ac.at</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"></span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> (A list of authors and contributors can be found in the PDF manual)</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"></span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> License: MIT (X11), see file LICENSE in the base directory</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">============================================================================= */</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> </div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#ifdef VIENNACL_WITH_OPENMP</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include <omp.h></span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#include <iostream></span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#include <vector></span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">//for std::min</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor">#include <algorithm></span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="preprocessor">#include "<a class="code" href="sse__blas_8hpp.html">viennacl/linalg/host_based/sse_blas.hpp</a>"</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> </div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="keyword">namespace </span>viennacl</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keyword">namespace </span>linalg</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  {</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keyword">namespace </span>host_based</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  {</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keyword">namespace </span>detail</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> </div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="comment">// returns true if the matrix is hermitian (or real symmetric), false otherwise</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keyword">template</span><<span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00050"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#acd0ccc877ddce3ae3ac5c4cb1393ccea"> 50</a></span>  <span class="keywordtype">bool</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#acd0ccc877ddce3ae3ac5c4cb1393ccea">isHermitian</a>(<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> ** <span class="keyword">const</span> A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> n)</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  {</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0;i<n;i++)</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=i;j<n;j++)</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordflow">if</span> (A[i][j] != <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#ae2a590df1af999034308d5583cca4020">conjIfComplex</a>(A[j][i]))</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  }</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> </div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="comment">// returns the bandwidth of a hermitian (or real symmetric) matrix</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keyword">template</span><<span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00061"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#a537ac5e83bd3ad6927f1ab8389451ebd"> 61</a></span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#a537ac5e83bd3ad6927f1ab8389451ebd">getHermitianBandwidth</a>(<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> ** <span class="keyword">const</span> A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> n)</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  {</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=n-1;i>=0;i--)</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=0;j<n-i;j++)</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordflow">if</span> (A[i+j][j]!=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0))</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordflow">return</span> 2*i+1;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  }</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">// helper for tridiagonalizeBandedMatrix</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">// does a householder similarity transform to eliminate a range of nonzeros in a row of a hermitian matrix</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keyword">template</span><<span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00073"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#af014b25ce5cbd2c46fd1316de20429c2"> 73</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#af014b25ce5cbd2c46fd1316de20429c2">eliminateHermitian</a>(<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> ** A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> from, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> to, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> width, <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> * ss)</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  {</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">if</span> (from>=to)</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> </div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> norm=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#ae89662d7ae3d65b0f2beca565c0c8a78">_nrm2</a>(&A[row][row+from],to-from);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">if</span> (norm != <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0))</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  {</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">//pick the better of two reflectors, to 1 or -1</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="comment">//this is wierd syntax that also works with std::complex</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordflow">if</span> (std::abs(A[row][row+from]-<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1))>std::abs(A[row][row+from]+<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1)))</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  norm=-norm;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=row+from;i<row+to;i++)</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  A[row][i]/=norm;</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][row+from]+=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1);</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="comment">//apply the similarity transformation</span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> </div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="comment">//left transformation</span></div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=row+1;j<row+width;j++)</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  {</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> s=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#aabc74969faf4707d9278db966e30cc12">_dotc</a>(to-from,&A[row][row+from],&A[j][row+from]);</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  s=-s/A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][row+from];</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(&A[row][row+from],&A[j][row+from],to-from,s);</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  }</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="comment">//conjugate householder reflector for right transformation</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=row+from;i<row+to;i++)</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  A[row][i]=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#ae2a590df1af999034308d5583cca4020">conjIfComplex</a>(A[row][i]);</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="comment">//right transformation (cache aligned)</span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0;i<width;i++)</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  ss[i]=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0);</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=from;i<to;i++)</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(&A[row+i][row],ss,width,<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#ae2a590df1af999034308d5583cca4020">conjIfComplex</a>(A[row][row+i]));</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0;i<width;i++)</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  ss[i]=-ss[i]/A[row][row+from];</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=from;i<to;i++)</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(ss,&A[row+i][row],width,A[row][row+i]);</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="comment">//clean up the householder reflector</span></div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> col=row+from;col<row+to;col++)</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  A[row][col]=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#ae2a590df1af999034308d5583cca4020">conjIfComplex</a>(A[col][row]);</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> </div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  }</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  }</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> </div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="comment">// reduces a hermitian (or symmetric real) banded matrix to a hermitian (or symmetric real) tridiagonal matrix,</span></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="comment">// using householder similarity transforms, so eigenvalues are preserved.</span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="comment">// bandwidth should be an odd integer, such as 3 for an already tridiagonal matrix</span></div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="comment">// based on http://www.netlib.org/lapack/lawnspdf/lawn208.pdf</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keyword">template</span><<span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00127"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#a9d7508e012aea146e6f35e08bc09c339"> 127</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#a9d7508e012aea146e6f35e08bc09c339">tridiagonalizeHermitianBandedMatrix</a>(<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> ** A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> n, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bandwidth)</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  {</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keywordflow">if</span> (bandwidth<=3)</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> belowDiagonal=(bandwidth-1)/2;</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> *ss=<span class="keyword">new</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>[bandwidth+belowDiagonal];</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span> </div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="comment">//eliminate and chase bulges where the elimination makes a bulge</span></div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k=0;</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordflow">for</span> (;k<n-belowDiagonal;k++)</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  {</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> </div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="comment">//eliminate below the diagonal</span></div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#af014b25ce5cbd2c46fd1316de20429c2">eliminateHermitian</a>(A,k,1,1+belowDiagonal,<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(n-k,2*belowDiagonal+1),ss);</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="comment">//chase the bulge</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bulgeStart=k+1;bulgeStart<n-belowDiagonal;bulgeStart+=belowDiagonal)</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0;i<belowDiagonal-1;i++)</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#af014b25ce5cbd2c46fd1316de20429c2">eliminateHermitian</a>(A,bulgeStart+i,belowDiagonal,<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(n-bulgeStart-i,belowDiagonal*2-i),<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(n-bulgeStart-i,bandwidth+belowDiagonal),ss);</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  }</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span> </div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="comment">//eliminate beyond where elimination makes bulges</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordflow">for</span> (;k<n-2;k++)</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#af014b25ce5cbd2c46fd1316de20429c2">eliminateHermitian</a>(A,k,1,n-k,n-k,ss);</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> </div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="keyword">delete</span> [] ss;</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  }</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> </div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="comment">// reduces a hermitian (or symmetric real) matrix to a hermitian (or symmetric real) banded matrix with bandwidth 2*block_size+1</span></div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="comment">// using householder similarity transformations, so eigenvalues are preserved. reduceToBandedMatrix(A,1) reduces the matrix to tridiagonal</span></div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keyword">template</span><<span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00159"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#ada3cb15238c1c502bde216d770949a00"> 159</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#ada3cb15238c1c502bde216d770949a00">reduceHermitianToBandedMatrix</a>(<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> ** A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> n, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> block_size, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> num_threads)</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  {</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>* norms=<span class="keyword">new</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>[block_size];</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>* ss=<span class="keyword">new</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>[n];</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> </div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k=0;k<n-block_size;k+=block_size)</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  {</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi=0;bi<<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(block_size,n-k-block_size);bi++)</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  {</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> </div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="comment">//this is the same as the norm of the column, since it's hermetian</span></div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  norms[bi]=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#ae89662d7ae3d65b0f2beca565c0c8a78">_nrm2</a>(&A[k+bi][k+bi+block_size],n-k-bi-block_size);</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> </div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordflow">if</span> (norms[bi]!=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0))</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  {</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> </div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="comment">//pick the better of two reflectors, to 1 or -1</span></div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="comment">//this is wierd syntax that also works with std::complex</span></div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordflow">if</span> (std::abs(A[k+bi][k+bi+block_size]-<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1))>std::abs(A[k+bi][k+bi+block_size]+<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1)))</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  norms[bi]=-norms[bi];</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=k+bi+block_size;i<n;i++)</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  A[k+bi][i]/=norms[bi];</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  A[k+bi][k+bi+block_size]+=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1);</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> </div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="comment">// Apply transformation to remaining rows within the block</span></div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=k+bi+1;j<k+block_size;j++)</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  {</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> s=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#aabc74969faf4707d9278db966e30cc12">_dotc</a>(n-k-bi-block_size,&A[k+bi][k+bi+block_size],&A[j][k+bi+block_size]);</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  s=-s/A[k+bi][k+bi+block_size];</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(&A[k+bi][k+bi+block_size],&A[j][k+bi+block_size],n-k-bi-block_size,s);</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  }</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  }</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  }</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> </div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="comment">//apply transformations from block to remaining rows and columns the block in parallel</span></div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> </div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="comment">//left transformations</span></div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="preprocessor"> #ifdef VIENNACL_WITH_OPENMP</span></div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="preprocessor"> #pragma omp parallel for</span></div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j=k+block_size;j<(int)n;j++)</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  #<span class="keywordflow">else</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=k+block_size;j<n;j++)</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  #endif</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  {</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi=0;bi<<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(block_size,n-k-block_size);bi++)</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  {</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keywordflow">if</span> (norms[bi]!=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0))</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  {</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> s=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#aabc74969faf4707d9278db966e30cc12">_dotc</a>(n-k-bi-block_size,&A[k+bi][k+bi+block_size],&A[j][k+bi+block_size]);</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  s=-s/A[k+bi][k+bi+block_size];</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(&A[k+bi][k+bi+block_size],&A[j][k+bi+block_size],n-k-bi-block_size,s);</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  }</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  }</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  }</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> </div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="comment">//conjugate householder reflectors for right transformations</span></div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi=0;bi<block_size;bi++)</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=k+bi+block_size;i<n;i++)</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  A[k+bi][i]=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#ae2a590df1af999034308d5583cca4020">conjIfComplex</a>(A[k+bi][i]);</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> </div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="comment">//right transformations (cache aligned)</span></div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="preprocessor"> #ifdef VIENNACL_WITH_OPENMP</span></div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="preprocessor"> #pragma omp parallel for</span></div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> section=0;section<(int)num_threads;section++)</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  #<span class="keywordflow">else</span></div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> section=0;section<num_threads;section++)</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  #endif</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  {</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">start</a>=((n-k)*(section+0))/num_threads+k;</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> end =((n-k)*(section+1))/num_threads+k;</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> length=end-<a class="code" href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">start</a>;</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi=0;bi<<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(block_size,n-k-block_size);bi++)</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  {</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keywordflow">if</span> (norms[bi]!=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0))</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  {</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=start;i<end;i++)</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  ss[i]=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0);</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=k+bi+block_size;i<n;i++)</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(&A[i][start],ss+start,length,<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#ae2a590df1af999034308d5583cca4020">conjIfComplex</a>(A[k+bi][i]));</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=start;i<end;i++)</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  ss[i]=-ss[i]/A[k+bi][k+bi+block_size];</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=k+bi+block_size;i<n;i++)</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(ss+start,&A[i][start],length,A[k+bi][i]);</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  }</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  }</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  }</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span> </div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="comment">//clean up householder reflectors</span></div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>=k;<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a><k+block_size;<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>++)</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> col=<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>+block_size;col<n;col++)</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][col]=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#ae2a590df1af999034308d5583cca4020">conjIfComplex</a>(A[col][<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>]);</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  }</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keyword">delete</span> [] norms;</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="keyword">delete</span> [] ss;</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  }</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> </div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  } <span class="comment">//namespace detail</span></div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span> </div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keyword">template</span><<span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00266"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1host__based.html#a186586aced1407e7106fd3f7f432f582"> 266</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a186586aced1407e7106fd3f7f432f582">inplace_tred2</a>(<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> ** A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> n, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> block_size = 1, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> num_threads = 1)</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  {</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keywordflow">if</span> (!<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#acd0ccc877ddce3ae3ac5c4cb1393ccea">detail::isHermitian</a>(A,n))</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  std::cerr << <span class="stringliteral">"ViennaCL: Warning in inplace_tred2(): Matrix is not hermitian (or real symmetric)"</span> << std::endl;</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span> </div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <span class="comment">// Don't touch the whole matrix if the bandwidth is already small.</span></div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="comment">// There's nothing numerically significant about n*4,</span></div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <span class="comment">// it's just a point I chose to switch to assuming the matrix is full.</span></div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bandwidth=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#a537ac5e83bd3ad6927f1ab8389451ebd">detail::getHermitianBandwidth</a>(A,n);</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="keywordflow">if</span> (bandwidth*bandwidth*num_threads<n*4 || 2*block_size+1>bandwidth)</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#a9d7508e012aea146e6f35e08bc09c339">detail::tridiagonalizeHermitianBandedMatrix</a>(A,n,bandwidth);</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  {</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#ada3cb15238c1c502bde216d770949a00">detail::reduceHermitianToBandedMatrix</a>(A,n,block_size,num_threads);</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#a9d7508e012aea146e6f35e08bc09c339">detail::tridiagonalizeHermitianBandedMatrix</a>(A,n,2*block_size+1);</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  }</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  }</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> </div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="keyword">template</span><<span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00295"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1host__based.html#a29a882acaad6a548f7fadf54598bdc42"> 295</a></span>  <span class="keywordtype">bool</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a29a882acaad6a548f7fadf54598bdc42">lu_factorize_row_major</a>(<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> ** A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> m, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> n, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> * piv = NULL, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> block_size = 8)</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  {</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="comment">// Use a parallel "left-looking", row-operation-based, block Crout/Doolittle algorithm.</span></div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="keywordflow">if</span> (piv)</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<m; i++)</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  piv[i]=i;</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keywordtype">bool</span> pivsign=<span class="keyword">true</span>;</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span> </div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="comment">// Outer loop.</span></div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=0; j<<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(m,n); j+=block_size)</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  {</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  block_size=<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(std::min(m-j,n-j),block_size);</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span> </div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="comment">//do Gaussian elimination with partial pivoting in the block</span></div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="comment">//(in the first few columns of the matrix)</span></div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi=0;bi<block_size;bi++)</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  {</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="comment">// Find pivot and exchange if necessary.</span></div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> p=j+bi;</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="keywordflow">if</span> (piv)</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  {</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=j+bi+1; i<m; i++)</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keywordflow">if</span> (std::abs(A[i][j+bi])>std::abs(A[p][j+bi]))</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  p=i;</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span> </div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="keywordflow">if</span> (p!=j+bi)</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  {</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k=0; k<n; k++)</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  {</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> t=A[p][k];</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  A[p][k]=A[j+bi][k];</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  A[j+bi][k]=t;</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  }</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span> </div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="comment">//swap pivot vector</span></div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = piv[p];</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  piv[p] = piv[j+bi];</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  piv[j+bi] = k;</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  pivsign = !pivsign;</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  }</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  }</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span> </div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="comment">//eliminate below the diagonal in the block</span></div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> elimVal=A[j+bi][j+bi];</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="keywordflow">if</span> (elimVal==<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0))</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  {</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="comment">//apply previous transformations from the block to the top of the submatrix</span></div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>=j+1;<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a><j+bi;<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>++)</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi_=0;bi_<<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>-j;bi_++)</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <span class="keywordflow">if</span> (A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][j+bi_]!=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0))</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(&(A[j+bi_][j+block_size]),&(A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][j+block_size]),n-j-block_size,-A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][j+bi_]);</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  <span class="keywordflow">return</span> pivsign;</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  }</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>=j+bi+1;<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a><m;<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>++)</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  {</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> multiplier=A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][j+bi]/elimVal;</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> col=j+bi;col<j+block_size;col++)</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][col]-=multiplier*A[j+bi][col];</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][j+bi]=multiplier;</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  }</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  }</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span> </div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <span class="comment">//at this point, the matrix looks something like this (if block size were 4)</span></div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="comment">//U U U U * * * *</span></div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="comment">//L U U U * * * *</span></div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="comment">//L L U U * * * *</span></div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="comment">//L L L U * * * *</span></div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  <span class="comment">//L L L L * * * *</span></div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  <span class="comment">//L L L L * * * *</span></div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <span class="comment">//L L L L * * * *</span></div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="comment">//L L L L * * * *</span></div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span> </div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="comment">//apply previous transformations from the block to the top of the submatrix</span></div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>=j+1;<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a><j+block_size;<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>++)</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi=0;bi<<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>-j;bi++)</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="keywordflow">if</span> (A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][j+bi]!=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0))</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(&(A[j+bi][j+block_size]),&(A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][j+block_size]),n-j-block_size,-A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][j+bi]);</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span> </div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  <span class="comment">//at this point, the matrix looks something like this (if block size were 4)</span></div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  <span class="comment">//U U U U U U U U</span></div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <span class="comment">//L U U U U U U U</span></div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <span class="comment">//L L U U U U U U</span></div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  <span class="comment">//L L L U U U U U</span></div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  <span class="comment">//L L L L * * * *</span></div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <span class="comment">//L L L L * * * *</span></div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="comment">//L L L L * * * *</span></div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="comment">//L L L L * * * *</span></div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span> </div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <span class="comment">//apply previous transformations from the block in parallel to the rest of the submatrix</span></div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span> <span class="preprocessor"> #ifdef VIENNACL_OPENMP</span></div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span> <span class="preprocessor"> #pragma omp parallel for</span></div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>=j+block_size;<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a><(int)m;<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>++)</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  #<span class="keywordflow">else</span></div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>=j+block_size;<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a><m;<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>++)</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  #endif</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi=0;bi<block_size;bi++)</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  <span class="keywordflow">if</span> (A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][j+bi]!=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0))</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(&(A[j+bi][j+block_size]),&(A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][j+block_size]),n-j-block_size,-A[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>][j+bi]);</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  }</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  <span class="keywordflow">return</span> pivsign;</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  }</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span> </div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  <span class="keyword">template</span><<span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00407"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1host__based.html#aaa3af08473cb3a7f5116d54302c02d86"> 407</a></span>  std::vector<ScalarType> <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#aaa3af08473cb3a7f5116d54302c02d86">inplace_qr_col_major</a>(<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> ** A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> m, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> n, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> block_size = 8)</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  {</div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  std::vector<ScalarType> betas(<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(m,n));</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>* norms=<span class="keyword">new</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>[block_size];</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span> </div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k=0; k<<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(m,n); k+=block_size)</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  {</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  block_size=<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(std::min(m-k,n-k),block_size);</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span> </div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi=0;bi<block_size;bi++)</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  {</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span> </div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  <span class="comment">// Compute 2-norm of k+bi-th column below the diagonal</span></div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  norms[bi]=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#ae89662d7ae3d65b0f2beca565c0c8a78">_nrm2</a>(&A[k+bi][k+bi],m-k-bi);</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span> </div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  <span class="keywordflow">if</span> (norms[bi]!=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0))</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  {</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <span class="comment">//pick the better of two reflectors, to 1 or -1,</span></div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  <span class="comment">//this is wierd syntax that also works with std::complex</span></div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  <span class="keywordflow">if</span> (std::abs(A[k+bi][k+bi]-<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1))>std::abs(A[k+bi][k+bi]+<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1)))</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  norms[bi]*=-1;</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=k+bi;i<m;i++)</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  A[k+bi][i]/=norms[bi];</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  A[k+bi][k+bi]+=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1);</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span> </div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  <span class="comment">// Apply transformation to columns within the block</span></div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=k+bi+1; j<k+block_size; j++)</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  {</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> s=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#aabc74969faf4707d9278db966e30cc12">_dotc</a>(m-k-bi,&A[k+bi][k+bi],&A[j][k+bi]);</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  s = -s/A[k+bi][k+bi];</div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(&A[k+bi][k+bi],&A[j][k+bi],m-k-bi,s);</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  }</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  }</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  <span class="comment">//temporarily store the diagonal value of R in betas</span></div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  betas[k+bi]=-norms[bi];</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  }</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span> </div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  <span class="comment">//apply transformations from block to remaining columns to the right of the block in parallel</span></div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span> <span class="preprocessor"> #ifdef VIENNACL_OPENMP</span></div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span> <span class="preprocessor"> #pragma omp parallel for</span></div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j=k+block_size; j<(int)n; j++)</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  #<span class="keywordflow">else</span></div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=k+block_size; j<n; j++)</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  #endif</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  {</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi=0;bi<block_size;bi++)</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  {</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="keywordflow">if</span> (norms[bi]!=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0))</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  {</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> s=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#aabc74969faf4707d9278db966e30cc12">_dotc</a>(m-k-bi,&A[k+bi][k+bi],&A[j][k+bi]);</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  s = -s/A[k+bi][k+bi];</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(&A[k+bi][k+bi],A[j]+k+bi,m-k-bi,s);</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  }</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  }</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  }</div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  }</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span> </div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  <span class="comment">//normalize the householder reflectors and store the betas</span></div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=0;j<<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(m,n);j++)</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  {</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> beta=A[j][j];</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=j+1;i<m;i++)</div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  A[j][i]/=beta;</div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  A[j][j]=betas[j];<span class="comment">//R diagonal values were stored temporarily in betas</span></div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  betas[j]=beta;</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  }</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span> </div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  <span class="keyword">delete</span> [] norms;</div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  <span class="keywordflow">return</span> betas;</div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  }</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span> </div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  <span class="keyword">template</span><<span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00487"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1host__based.html#ab1ca91eea2771be83df0a807951388d3"> 487</a></span>  std::vector<ScalarType> <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#ab1ca91eea2771be83df0a807951388d3">inplace_qr_row_major</a>(<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> ** A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> m, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> n, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> block_size = 8, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> num_threads = 1)</div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  {</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  std::vector<ScalarType> betas(<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(m,n));</div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>* norms=<span class="keyword">new</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>[block_size];</div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>* ss=<span class="keyword">new</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>[n];</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span> </div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  <span class="comment">//allocate O(m) memory for temporary column-major storage of the block for blas functions</span></div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>** block_cols=<span class="keyword">new</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>*[block_size];</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0;i<block_size;i++)</div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  block_cols[i]=<span class="keyword">new</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>[m];</div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span> </div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k=0; k<<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(m,n); k+=block_size)</div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  {</div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  block_size=<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(std::min(m-k,n-k),block_size);</div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span> </div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="comment">//copy the block to column-major storage for cache alignment (necessary for _nrm2)</span></div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0;i<m-k;i++)</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi=0;bi<block_size;bi++)</div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  block_cols[bi][i]=A[k+i][k+bi];</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span> </div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi=0;bi<block_size;bi++)</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  {</div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span> </div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <span class="comment">// Compute 2-norm of k+bi-th column below the diagonal</span></div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  norms[bi]=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#ae89662d7ae3d65b0f2beca565c0c8a78">_nrm2</a>(&block_cols[bi][bi],m-k-bi);</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span> </div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  <span class="keywordflow">if</span> (norms[bi]!=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0))</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  {</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <span class="comment">//pick the better of two reflectors, to 1 or -1,</span></div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  <span class="comment">//this is wierd syntax that also works with std::complex</span></div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  <span class="keywordflow">if</span> (std::abs(block_cols[bi][bi]-<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1))>std::abs(block_cols[bi][bi]+<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1)))</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  norms[bi]*=-1;</div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=bi;i<m-k;i++)</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  block_cols[bi][i]/=norms[bi];</div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  block_cols[bi][bi]+=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1);</div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span> </div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  <span class="comment">// Apply transformation to columns within the block</span></div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=bi+1; j<block_size; j++)</div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  {</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> s=<a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#aabc74969faf4707d9278db966e30cc12">_dotc</a>(m-k-bi,&block_cols[bi][bi],&block_cols[j][bi]);</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  s = -s/block_cols[bi][bi];</div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(&block_cols[bi][bi],&block_cols[j][bi],m-k-bi,s);</div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  }</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  }</div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  <span class="comment">//temporarily store the diagonal value of R in betas</span></div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  betas[k+bi]=-norms[bi];</div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  }</div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span> </div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <span class="comment">//copy the block back to row-major storage</span></div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0;i<m-k;i++)</div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi=0;bi<block_size;bi++)</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  A[k+i][k+bi]=block_cols[bi][i];</div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span> </div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  <span class="comment">//apply transformations from block to remaining rows to the right of the block in parallel</span></div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span> <span class="preprocessor"> #ifdef VIENNACL_OPENMP</span></div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span> <span class="preprocessor"> #pragma omp parallel for</span></div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> section=0;section<(int)num_threads;section++)</div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  #<span class="keywordflow">else</span></div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> section=0;section<num_threads;section++)</div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  #endif</div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  {</div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">start</a>=((n-k-block_size)*(section+0))/num_threads+k+block_size;</div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> end =((n-k-block_size)*(section+1))/num_threads+k+block_size;</div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> length=end-<a class="code" href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">start</a>;</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> bi=0;bi<block_size;bi++)</div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  {</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  <span class="keywordflow">if</span> (norms[bi]!=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0))</div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  {</div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=start;i<end;i++)</div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  ss[i]=<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0);</div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=k+bi;i<m;i++)</div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(&A[i][start],ss+start,length,A[i][k+bi]);</div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=start;i<end;i++)</div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  ss[i]=-ss[i]/A[k+bi][k+bi];</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=k+bi;i<m;i++)</div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">_axpy</a>(ss+start,&A[i][start],length,A[i][k+bi]);</div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  }</div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  }</div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  }</div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  }</div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span> </div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  <span class="comment">//normalize the householder reflectors and store the betas</span></div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=0;j<<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(m,n);j++)</div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  {</div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> beta=A[j][j];</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=j+1;i<m;i++)</div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  A[i][j]/=beta;</div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  A[j][j]=betas[j];<span class="comment">//R diagonal values were stored temporarily in betas</span></div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  betas[j]=beta;</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  }</div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span> </div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  <span class="keyword">delete</span> [] norms;</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0;i<block_size;i++)</div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  <span class="keyword">delete</span> [] block_cols[i];</div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  <span class="keyword">delete</span> [] block_cols;</div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  <span class="keyword">delete</span> [] ss;</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span> </div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  <span class="keywordflow">return</span> betas;</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  }</div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span> </div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  } <span class="comment">//namespace host_based</span></div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  } <span class="comment">//namespace linalg</span></div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span> } <span class="comment">//namespace viennacl</span></div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span> <span class="preprocessor">#endif</span></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1host__based_1_1detail_html_ae2a590df1af999034308d5583cca4020"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#ae2a590df1af999034308d5583cca4020">viennacl::linalg::host_based::detail::conjIfComplex</a></div><div class="ttdeci">T conjIfComplex(T x)</div><div class="ttdef"><b>Definition:</b> <a href="sse__blas_8hpp_source.html#l00069">sse_blas.hpp:69</a></div></div>
<div class="ttc" id="sse__blas_8hpp_html"><div class="ttname"><a href="sse__blas_8hpp.html">sse_blas.hpp</a></div><div class="ttdoc">optimized BLAS functions using SSE2 and SSE3 intrinsic functions </div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1host__based_html_ab1ca91eea2771be83df0a807951388d3"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1host__based.html#ab1ca91eea2771be83df0a807951388d3">viennacl::linalg::host_based::inplace_qr_row_major</a></div><div class="ttdeci">std::vector< ScalarType > inplace_qr_row_major(ScalarType **A, vcl_size_t m, vcl_size_t n, vcl_size_t block_size=8, vcl_size_t num_threads=1)</div><div class="ttdoc">Inplace qr factorization of an m x n dense row-major matrix, returning the householder normalization ...</div><div class="ttdef"><b>Definition:</b> <a href="sse__kernels_8hpp_source.html#l00487">sse_kernels.hpp:487</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1host__based_html_a9b6f43691b2c9cb686f6941029255286"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1host__based.html#a9b6f43691b2c9cb686f6941029255286">viennacl::linalg::host_based::_axpy</a></div><div class="ttdeci">void _axpy(const T *, T *, vcl_size_t, T)</div><div class="ttdef"><b>Definition:</b> <a href="sse__blas_8hpp_source.html#l00073">sse_blas.hpp:73</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1host__based_html_aaa3af08473cb3a7f5116d54302c02d86"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1host__based.html#aaa3af08473cb3a7f5116d54302c02d86">viennacl::linalg::host_based::inplace_qr_col_major</a></div><div class="ttdeci">std::vector< ScalarType > inplace_qr_col_major(ScalarType **A, vcl_size_t m, vcl_size_t n, vcl_size_t block_size=8)</div><div class="ttdoc">Inplace qr factorization of an m x n dense column-major matrix, returning the householder normalizati...</div><div class="ttdef"><b>Definition:</b> <a href="sse__kernels_8hpp_source.html#l00407">sse_kernels.hpp:407</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1host__based_1_1detail_html_af014b25ce5cbd2c46fd1316de20429c2"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#af014b25ce5cbd2c46fd1316de20429c2">viennacl::linalg::host_based::detail::eliminateHermitian</a></div><div class="ttdeci">void eliminateHermitian(ScalarType **A, vcl_size_t row, vcl_size_t from, vcl_size_t to, vcl_size_t width, ScalarType *ss)</div><div class="ttdef"><b>Definition:</b> <a href="sse__kernels_8hpp_source.html#l00073">sse_kernels.hpp:73</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1host__based_1_1detail_html_ada3cb15238c1c502bde216d770949a00"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#ada3cb15238c1c502bde216d770949a00">viennacl::linalg::host_based::detail::reduceHermitianToBandedMatrix</a></div><div class="ttdeci">void reduceHermitianToBandedMatrix(ScalarType **A, vcl_size_t n, vcl_size_t block_size, vcl_size_t num_threads)</div><div class="ttdef"><b>Definition:</b> <a href="sse__kernels_8hpp_source.html#l00159">sse_kernels.hpp:159</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1traits_html_a68603a1e1ca1bfb6d107831ba5096786"><div class="ttname"><a href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">viennacl::traits::start</a></div><div class="ttdeci">result_of::size_type< T >::type start(T const &obj)</div><div class="ttdef"><b>Definition:</b> <a href="start_8hpp_source.html#l00044">start.hpp:44</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1host__based_html_a29a882acaad6a548f7fadf54598bdc42"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1host__based.html#a29a882acaad6a548f7fadf54598bdc42">viennacl::linalg::host_based::lu_factorize_row_major</a></div><div class="ttdeci">bool lu_factorize_row_major(ScalarType **A, vcl_size_t m, vcl_size_t n, vcl_size_t *piv=NULL, vcl_size_t block_size=8)</div><div class="ttdoc">Inplace lu factorization of an m x n dense row-major matrix with optional partial pivoting...</div><div class="ttdef"><b>Definition:</b> <a href="sse__kernels_8hpp_source.html#l00295">sse_kernels.hpp:295</a></div></div>
<div class="ttc" id="namespaceviennacl_html_a98a0afcc513111ffa0bd138f891930df"><div class="ttname"><a href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">viennacl::vcl_size_t</a></div><div class="ttdeci">std::size_t vcl_size_t</div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00074">forwards.h:74</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1host__based_html_ae89662d7ae3d65b0f2beca565c0c8a78"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1host__based.html#ae89662d7ae3d65b0f2beca565c0c8a78">viennacl::linalg::host_based::_nrm2</a></div><div class="ttdeci">T _nrm2(const T *, vcl_size_t)</div><div class="ttdef"><b>Definition:</b> <a href="sse__blas_8hpp_source.html#l00117">sse_blas.hpp:117</a></div></div>
<div class="ttc" id="namespaceviennacl_html_a0a574e6cd04ca0e42298b4ab845700e4"><div class="ttname"><a href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">viennacl::row</a></div><div class="ttdeci">vector_expression< const matrix_base< NumericT, F >, const unsigned int, op_row > row(const matrix_base< NumericT, F > &A, unsigned int i)</div><div class="ttdef"><b>Definition:</b> <a href="matrix_8hpp_source.html#l00853">matrix.hpp:853</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1host__based_html_aabc74969faf4707d9278db966e30cc12"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1host__based.html#aabc74969faf4707d9278db966e30cc12">viennacl::linalg::host_based::_dotc</a></div><div class="ttdeci">T _dotc(vcl_size_t, const T *, const T *)</div><div class="ttdef"><b>Definition:</b> <a href="sse__blas_8hpp_source.html#l00089">sse_blas.hpp:89</a></div></div>
<div class="ttc" id="fft__1d_8cpp_html_ad5c19ca4f47d3f8ec21232a5af2624e5"><div class="ttname"><a href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a></div><div class="ttdeci">float ScalarType</div><div class="ttdef"><b>Definition:</b> <a href="fft__1d_8cpp_source.html#l00042">fft_1d.cpp:42</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1host__based_1_1detail_html_acd0ccc877ddce3ae3ac5c4cb1393ccea"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#acd0ccc877ddce3ae3ac5c4cb1393ccea">viennacl::linalg::host_based::detail::isHermitian</a></div><div class="ttdeci">bool isHermitian(ScalarType **const A, vcl_size_t n)</div><div class="ttdef"><b>Definition:</b> <a href="sse__kernels_8hpp_source.html#l00050">sse_kernels.hpp:50</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1host__based_1_1detail_html_a537ac5e83bd3ad6927f1ab8389451ebd"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#a537ac5e83bd3ad6927f1ab8389451ebd">viennacl::linalg::host_based::detail::getHermitianBandwidth</a></div><div class="ttdeci">vcl_size_t getHermitianBandwidth(ScalarType **const A, vcl_size_t n)</div><div class="ttdef"><b>Definition:</b> <a href="sse__kernels_8hpp_source.html#l00061">sse_kernels.hpp:61</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_aef015779a92be597e546c3491cebf6c1"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">viennacl::linalg::detail::min</a></div><div class="ttdeci">T min(const T &lhs, const T &rhs)</div><div class="ttdoc">Minimum. </div><div class="ttdef"><b>Definition:</b> <a href="linalg_2detail_2bisect_2util_8hpp_source.html#l00045">util.hpp:45</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1host__based_1_1detail_html_a9d7508e012aea146e6f35e08bc09c339"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1host__based_1_1detail.html#a9d7508e012aea146e6f35e08bc09c339">viennacl::linalg::host_based::detail::tridiagonalizeHermitianBandedMatrix</a></div><div class="ttdeci">void tridiagonalizeHermitianBandedMatrix(ScalarType **A, vcl_size_t n, vcl_size_t bandwidth)</div><div class="ttdef"><b>Definition:</b> <a href="sse__kernels_8hpp_source.html#l00127">sse_kernels.hpp:127</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1host__based_html_a186586aced1407e7106fd3f7f432f582"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1host__based.html#a186586aced1407e7106fd3f7f432f582">viennacl::linalg::host_based::inplace_tred2</a></div><div class="ttdeci">void inplace_tred2(ScalarType **A, vcl_size_t n, vcl_size_t block_size=1, vcl_size_t num_threads=1)</div><div class="ttdoc">Inplace reduction of a dense n x n row-major or column-major hermitian (or real symmetric) matrix to ...</div><div class="ttdef"><b>Definition:</b> <a href="sse__kernels_8hpp_source.html#l00266">sse_kernels.hpp:266</a></div></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="navelem"><a class="el" href="dir_c82e3d11dd171600f4a6e0cab1ec1e0d.html">viennacl</a></li><li class="navelem"><a class="el" href="dir_63cde087767c4ed65c7901ffc6e293fe.html">linalg</a></li><li class="navelem"><a class="el" href="dir_8d734bf48796b8afc2ea3e50ddaea273.html">host_based</a></li><li class="navelem"><a class="el" href="sse__kernels_8hpp.html">sse_kernels.hpp</a></li>
<li class="footer">Generated on Thu Dec 11 2014 23:28:03 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>
|
