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
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
|
<!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/gmres.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">1.7.1</span>
</div>
<div id="projectbrief">Free open-source GPU-accelerated linear algebra and solver library.</div>
</td>
<td> <div id="MSearchBox" class="MSearchBoxInactive">
<span class="left">
<img id="MSearchSelect" src="search/mag_sel.png"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
alt=""/>
<input type="text" id="MSearchField" value="Search" accesskey="S"
onfocus="searchBox.OnSearchFieldFocus(true)"
onblur="searchBox.OnSearchFieldFocus(false)"
onkeyup="searchBox.OnSearchFieldChange(event)"/>
</span><span class="right">
<a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a>
</span>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.8.6 -->
<script type="text/javascript">
var searchBox = new SearchBox("searchBox", "search",false,'Search');
</script>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
<div id="nav-tree">
<div id="nav-tree-contents">
<div id="nav-sync" class="sync"></div>
</div>
</div>
<div id="splitbar" style="-moz-user-select:none;"
class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
$(document).ready(function(){initNavTree('gmres_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">gmres.hpp</div> </div>
</div><!--header-->
<div class="contents">
<a href="gmres_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_GMRES_HPP_</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor">#define VIENNACL_GMRES_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) 2010-2016, 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 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="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#include <vector></span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include <cmath></span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include <limits></span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include "<a class="code" href="forwards_8h.html">viennacl/forwards.h</a>"</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include "<a class="code" href="tools_8hpp.html">viennacl/tools/tools.hpp</a>"</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#include "<a class="code" href="norm__2_8hpp.html">viennacl/linalg/norm_2.hpp</a>"</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#include "<a class="code" href="prod_8hpp.html">viennacl/linalg/prod.hpp</a>"</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#include "<a class="code" href="inner__prod_8hpp.html">viennacl/linalg/inner_prod.hpp</a>"</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor">#include "<a class="code" href="clear_8hpp.html">viennacl/traits/clear.hpp</a>"</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="preprocessor">#include "<a class="code" href="size_8hpp.html">viennacl/traits/size.hpp</a>"</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor">#include "<a class="code" href="traits_2context_8hpp.html">viennacl/traits/context.hpp</a>"</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="preprocessor">#include "<a class="code" href="result__of_8hpp.html">viennacl/meta/result_of.hpp</a>"</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="preprocessor">#include "<a class="code" href="iterative__operations_8hpp.html">viennacl/linalg/iterative_operations.hpp</a>"</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="preprocessor">#include "<a class="code" href="vector__proxy_8hpp.html">viennacl/vector_proxy.hpp</a>"</span></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> </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="keyword">namespace </span>viennacl</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> {</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="keyword">namespace </span>linalg</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> {</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> </div>
<div class="line"><a name="l00049"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__tag.html"> 49</a></span> <span class="keyword">class </span><a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> <span class="comment">//generalized minimum residual</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> {</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00058"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__tag.html#ad6e4eb92dd1cc1ad15eada6ed1b2a8f1"> 58</a></span>  <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#ad6e4eb92dd1cc1ad15eada6ed1b2a8f1">gmres_tag</a>(<span class="keywordtype">double</span> tol = 1e-10, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a14c5e80e1d5da7563e333337b13bd922">max_iterations</a> = 300, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a> = 20)</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  : tol_(tol), abs_tol_(0), iterations_(<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a14c5e80e1d5da7563e333337b13bd922">max_iterations</a>), krylov_dim_(<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>), iters_taken_(0) {}</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a name="l00062"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa055ac8c0bc4144295c4ac2c176a6c0a"> 62</a></span>  <span class="keywordtype">double</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa055ac8c0bc4144295c4ac2c176a6c0a">tolerance</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> tol_; }</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a name="l00065"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__tag.html#a8df40f7ba3716b9b5594ff5c3d8b415f"> 65</a></span>  <span class="keywordtype">double</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a8df40f7ba3716b9b5594ff5c3d8b415f">abs_tolerance</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> abs_tol_; }</div>
<div class="line"><a name="l00067"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__tag.html#aeed1d3814b1ec24110228ffb9307569d"> 67</a></span>  <span class="keywordtype">void</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aeed1d3814b1ec24110228ffb9307569d">abs_tolerance</a>(<span class="keywordtype">double</span> new_tol) { <span class="keywordflow">if</span> (new_tol >= 0) abs_tol_ = new_tol; }</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a name="l00070"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__tag.html#a14c5e80e1d5da7563e333337b13bd922"> 70</a></span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a14c5e80e1d5da7563e333337b13bd922">max_iterations</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> iterations_; }</div>
<div class="line"><a name="l00072"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899"> 72</a></span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> krylov_dim_; }</div>
<div class="line"><a name="l00074"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__tag.html#aceaecb48094fac8123d3be0a636ce6df"> 74</a></span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aceaecb48094fac8123d3be0a636ce6df">max_restarts</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> ret = iterations_ / krylov_dim_;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordflow">if</span> (ret > 0 && (ret * krylov_dim_ == iterations_) )</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keywordflow">return</span> ret - 1;</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordflow">return</span> ret;</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  }</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> </div>
<div class="line"><a name="l00083"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__tag.html#a4eb47bfc797a70a4db76d629f18f456a"> 83</a></span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a4eb47bfc797a70a4db76d629f18f456a">iters</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> iters_taken_; }</div>
<div class="line"><a name="l00085"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__tag.html#ab1c7ce4738a05af039a23889d98a09c4"> 85</a></span>  <span class="keywordtype">void</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#ab1c7ce4738a05af039a23889d98a09c4">iters</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i)<span class="keyword"> const </span>{ iters_taken_ = i; }</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a name="l00088"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa9bd21a63747c3f3a2ffe3b726a2a9bb"> 88</a></span>  <span class="keywordtype">double</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa9bd21a63747c3f3a2ffe3b726a2a9bb">error</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> last_error_; }</div>
<div class="line"><a name="l00090"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__tag.html#a2ad9dac58a4cef0fea4e6b6ce3799b5d"> 90</a></span>  <span class="keywordtype">void</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a2ad9dac58a4cef0fea4e6b6ce3799b5d">error</a>(<span class="keywordtype">double</span> e)<span class="keyword"> const </span>{ last_error_ = e; }</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> </div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="keyword">private</span>:</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordtype">double</span> tol_;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordtype">double</span> abs_tol_;</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> iterations_;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> krylov_dim_;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="comment">//return values from solver</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keyword">mutable</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> iters_taken_;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keyword">mutable</span> <span class="keywordtype">double</span> last_error_;</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> };</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> </div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="keyword">namespace </span>detail</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> </div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keyword">template</span><<span class="keyword">typename</span> SrcVectorT, <span class="keyword">typename</span> DestVectorT></div>
<div class="line"><a name="l00107"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a9dace8e3f8cafdc7c5b56282860e5a97"> 107</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a9dace8e3f8cafdc7c5b56282860e5a97">gmres_copy_helper</a>(SrcVectorT <span class="keyword">const</span> & src, DestVectorT & dest, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> len, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">start</a> = 0)</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  {</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<len; ++i)</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  dest[<a class="code" href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">start</a>+i] = src[<a class="code" href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">start</a>+i];</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  }</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span> </div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keyword">template</span><<span class="keyword">typename</span> NumericT, <span class="keyword">typename</span> DestVectorT></div>
<div class="line"><a name="l00114"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#afb24b0bd7c338eff5ecf6b8b35f2757a"> 114</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a9dace8e3f8cafdc7c5b56282860e5a97">gmres_copy_helper</a>(<a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <span class="keyword">const</span> & src, DestVectorT & dest, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> len, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">start</a> = 0)</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  {</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classviennacl_1_1vector.html#a7e683e134c8aad7b3cd057776a58c4c4">viennacl::vector<NumericT>::difference_type</a> difference_type;</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>( src.<a class="code" href="classviennacl_1_1vector__base.html#a762d98e2f912fc534951f25555b6077f">begin</a>() + <span class="keyword">static_cast<</span>difference_type<span class="keyword">></span>(<a class="code" href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">start</a>),</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  src.<a class="code" href="classviennacl_1_1vector__base.html#a762d98e2f912fc534951f25555b6077f">begin</a>() + <span class="keyword">static_cast<</span>difference_type<span class="keyword">></span>(<a class="code" href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">start</a> + len),</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  dest.begin() + <span class="keyword">static_cast<</span>difference_type<span class="keyword">></span>(<a class="code" href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">start</a>));</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="l00130"></a><span class="lineno"> 130</span>  <span class="keyword">template</span><<span class="keyword">typename</span> VectorT, <span class="keyword">typename</span> NumericT></div>
<div class="line"><a name="l00131"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a29d6b53b3a99961196a859fa7ef46537"> 131</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a29d6b53b3a99961196a859fa7ef46537">gmres_setup_householder_vector</a>(VectorT <span class="keyword">const</span> & input_vec, VectorT & hh_vec, <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> & beta, <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> & mu, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j)</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  {</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> input_j = input_vec(j);</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">// copy entries from input vector to householder vector:</span></div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a9dace8e3f8cafdc7c5b56282860e5a97">detail::gmres_copy_helper</a>(input_vec, hh_vec, <a class="code" href="namespaceviennacl_1_1traits.html#aa2344ea20469f55fbc15a8e9526494d0">viennacl::traits::size</a>(hh_vec) - (j+1), j+1);</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> </div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> sigma = <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(hh_vec);</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  sigma *= sigma;</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> </div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordflow">if</span> (sigma <= 0)</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>  beta = 0;</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  mu = input_j;</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  }</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordflow">else</span></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>  mu = std::sqrt(sigma + input_j*input_j);</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span> </div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> hh_vec_0 = (input_j <= 0) ? (input_j - mu) : (-sigma / (input_j + mu));</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> </div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  beta = <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(2) * hh_vec_0 * hh_vec_0 / (sigma + hh_vec_0 * hh_vec_0);</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> </div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="comment">//divide hh_vec by its diagonal element hh_vec_0</span></div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  hh_vec /= hh_vec_0;</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  hh_vec[j] = <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(1);</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  }</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  }</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> </div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="comment">// Apply (I - beta h h^T) to x (Householder reflection with Householder vector h)</span></div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keyword">template</span><<span class="keyword">typename</span> VectorT, <span class="keyword">typename</span> NumericT></div>
<div class="line"><a name="l00162"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#ad2b2c8a343124143d1ddc2fee8b2ce73"> 162</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ad2b2c8a343124143d1ddc2fee8b2ce73">gmres_householder_reflect</a>(VectorT & x, VectorT <span class="keyword">const</span> & h, <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> beta)</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>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> hT_in_x = <a class="code" href="namespaceviennacl_1_1linalg.html#ab35950c4374eb3be08a03d852508c01a">viennacl::linalg::inner_prod</a>(h, x);</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  x -= (beta * hT_in_x) * h;</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  }</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="l00181"></a><span class="lineno"> 181</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00182"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#ad01cfe2657d7f178746948b170b8f793"> 182</a></span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a173ef3bf1e3cf75985fbd3989e37290f">pipelined_solve</a>(MatrixType <span class="keyword">const</span> & A,</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> <span class="keyword">const</span> & rhs,</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> <span class="keyword">const</span> & tag,</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <a class="code" href="classviennacl_1_1linalg_1_1no__precond.html">viennacl::linalg::no_precond</a>,</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keywordtype">bool</span> (*monitor)(<a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> <span class="keyword">const</span> &, <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>, <span class="keywordtype">void</span>*) = NULL,</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keywordtype">void</span> *monitor_data = NULL)</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  {</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> residual(rhs);</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> result = <a class="code" href="structviennacl_1_1zero__vector.html">viennacl::zero_vector<ScalarType></a>(rhs.<a class="code" href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">size</a>(), <a class="code" href="namespaceviennacl_1_1traits.html#a6707f5dab8f482170d2046a605f46ef8">viennacl::traits::context</a>(rhs));</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>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> device_krylov_basis(rhs.<a class="code" href="classviennacl_1_1vector__base.html#a47350ccdc4b0a24eaea0e8d5f9fe7fec">internal_size</a>() * tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>(), <a class="code" href="namespaceviennacl_1_1traits.html#a6707f5dab8f482170d2046a605f46ef8">viennacl::traits::context</a>(rhs)); <span class="comment">// not using viennacl::matrix here because of spurious padding in column number</span></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> device_buffer_R(tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>()*tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>(), <a class="code" href="namespaceviennacl_1_1traits.html#a6707f5dab8f482170d2046a605f46ef8">viennacl::traits::context</a>(rhs));</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  std::vector<ScalarType> host_buffer_R(device_buffer_R.size());</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> </div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> buffer_size_per_vector = 128;</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> num_buffer_chunks = 3;</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> device_inner_prod_buffer = <a class="code" href="structviennacl_1_1zero__vector.html">viennacl::zero_vector<ScalarType></a>(num_buffer_chunks*buffer_size_per_vector, <a class="code" href="namespaceviennacl_1_1traits.html#a6707f5dab8f482170d2046a605f46ef8">viennacl::traits::context</a>(rhs)); <span class="comment">// temporary buffer</span></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> device_r_dot_vk_buffer = <a class="code" href="structviennacl_1_1zero__vector.html">viennacl::zero_vector<ScalarType></a>(buffer_size_per_vector * tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>(), <a class="code" href="namespaceviennacl_1_1traits.html#a6707f5dab8f482170d2046a605f46ef8">viennacl::traits::context</a>(rhs)); <span class="comment">// holds result of first reduction stage for <r, v_k> on device</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> device_vi_in_vk_buffer = <a class="code" href="structviennacl_1_1zero__vector.html">viennacl::zero_vector<ScalarType></a>(buffer_size_per_vector * tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>(), <a class="code" href="namespaceviennacl_1_1traits.html#a6707f5dab8f482170d2046a605f46ef8">viennacl::traits::context</a>(rhs)); <span class="comment">// holds <v_i, v_k> for i=0..k-1 on device</span></div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> device_values_xi_k = <a class="code" href="structviennacl_1_1zero__vector.html">viennacl::zero_vector<ScalarType></a>(tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>(), <a class="code" href="namespaceviennacl_1_1traits.html#a6707f5dab8f482170d2046a605f46ef8">viennacl::traits::context</a>(rhs)); <span class="comment">// holds values \xi_k = <r, v_k> on device</span></div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  std::vector<ScalarType> host_r_dot_vk_buffer(device_r_dot_vk_buffer.<a class="code" href="classviennacl_1_1implicit__vector__base.html#a56e5fd972e19933335872a11e6c48bbf">size</a>());</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  std::vector<ScalarType> host_values_xi_k(tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>());</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  std::vector<ScalarType> host_values_eta_k_buffer(tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>());</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  std::vector<ScalarType> host_update_coefficients(tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>());</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> norm_rhs = <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(residual);</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> rho_0 = norm_rhs;</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> rho = <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1);</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>  tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a4eb47bfc797a70a4db76d629f18f456a">iters</a>(0);</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>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> restart_count = 0; restart_count <= tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aceaecb48094fac8123d3be0a636ce6df">max_restarts</a>(); ++restart_count)</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  {</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="comment">// prepare restart:</span></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">if</span> (restart_count > 0)</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  {</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="comment">// compute new residual without introducing a temporary for A*x:</span></div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  residual = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(A, result);</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  residual = rhs - residual;</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span> </div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  rho_0 = <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(residual);</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  }</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>  <span class="keywordflow">if</span> (rho_0 <= <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a8df40f7ba3716b9b5594ff5c3d8b415f">abs_tolerance</a>())) <span class="comment">// trivial right hand side?</span></div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span> </div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  residual /= rho_0;</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  rho = <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1);</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span> </div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="comment">// check for convergence:</span></div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keywordflow">if</span> (rho_0 / norm_rhs < tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa055ac8c0bc4144295c4ac2c176a6c0a">tolerance</a>() || rho_0 < tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a8df40f7ba3716b9b5594ff5c3d8b415f">abs_tolerance</a>())</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span> </div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="comment">// minimize in Krylov basis:</span></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = 0;</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordflow">for</span> (k = 0; k < static_cast<vcl_size_t>(tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>()); ++k)</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>  <span class="keywordflow">if</span> (k == 0)</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>  <span class="comment">// compute v0 = A*r and perform first reduction stage for ||v0||</span></div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <a class="code" href="classviennacl_1_1vector__range.html">viennacl::vector_range<viennacl::vector<ScalarType></a> > v0(device_krylov_basis, <a class="code" href="classviennacl_1_1basic__range.html">viennacl::range</a>(0, rhs.<a class="code" href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">size</a>()));</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a6faa475e03dfe776021e91f5a66f9319">viennacl::linalg::pipelined_gmres_prod</a>(A, residual, v0, device_inner_prod_buffer);</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span> </div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="comment">// Normalize v_1 and compute first reduction stage for <r, v_0> in device_r_dot_vk_buffer:</span></div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#aaca868298580acb7df97aff002bf6867">viennacl::linalg::pipelined_gmres_normalize_vk</a>(v0, residual,</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  device_buffer_R, k*tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>() + k,</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  device_inner_prod_buffer, device_r_dot_vk_buffer,</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  buffer_size_per_vector, k*buffer_size_per_vector);</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="keywordflow">else</span></div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  {</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="comment">// compute v0 = A*r and perform first reduction stage for ||v0||</span></div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <a class="code" href="classviennacl_1_1vector__range.html">viennacl::vector_range<viennacl::vector<ScalarType></a> > vk (device_krylov_basis, <a class="code" href="classviennacl_1_1basic__range.html">viennacl::range</a>( k *rhs.<a class="code" href="classviennacl_1_1vector__base.html#a47350ccdc4b0a24eaea0e8d5f9fe7fec">internal_size</a>(), k *rhs.<a class="code" href="classviennacl_1_1vector__base.html#a47350ccdc4b0a24eaea0e8d5f9fe7fec">internal_size</a>() + rhs.<a class="code" href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">size</a>()));</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <a class="code" href="classviennacl_1_1vector__range.html">viennacl::vector_range<viennacl::vector<ScalarType></a> > vk_minus_1(device_krylov_basis, <a class="code" href="classviennacl_1_1basic__range.html">viennacl::range</a>((k-1)*rhs.<a class="code" href="classviennacl_1_1vector__base.html#a47350ccdc4b0a24eaea0e8d5f9fe7fec">internal_size</a>(), (k-1)*rhs.<a class="code" href="classviennacl_1_1vector__base.html#a47350ccdc4b0a24eaea0e8d5f9fe7fec">internal_size</a>() + rhs.<a class="code" href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">size</a>()));</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a6faa475e03dfe776021e91f5a66f9319">viennacl::linalg::pipelined_gmres_prod</a>(A, vk_minus_1, vk, device_inner_prod_buffer);</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span> </div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="comment">// Gram-Schmidt, stage 1: compute first reduction stage of <v_i, v_k></span></div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a26e6e73c2c27a83fa958ca25e468b8ad">viennacl::linalg::pipelined_gmres_gram_schmidt_stage1</a>(device_krylov_basis, rhs.<a class="code" href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">size</a>(), rhs.<a class="code" href="classviennacl_1_1vector__base.html#a47350ccdc4b0a24eaea0e8d5f9fe7fec">internal_size</a>(), k, device_vi_in_vk_buffer, buffer_size_per_vector);</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span> </div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="comment">// Gram-Schmidt, stage 2: compute second reduction stage of <v_i, v_k> and use that to compute v_k -= sum_i <v_i, v_k> v_i.</span></div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="comment">// Store <v_i, v_k> in R-matrix and compute first reduction stage for ||v_k||</span></div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a39b768f9d8385b980d2e5e9073d09530">viennacl::linalg::pipelined_gmres_gram_schmidt_stage2</a>(device_krylov_basis, rhs.<a class="code" href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">size</a>(), rhs.<a class="code" href="classviennacl_1_1vector__base.html#a47350ccdc4b0a24eaea0e8d5f9fe7fec">internal_size</a>(), k,</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  device_vi_in_vk_buffer,</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  device_buffer_R, tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>(),</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  device_inner_prod_buffer, buffer_size_per_vector);</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> </div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="comment">// Normalize v_k and compute first reduction stage for <r, v_k> in device_r_dot_vk_buffer:</span></div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#aaca868298580acb7df97aff002bf6867">viennacl::linalg::pipelined_gmres_normalize_vk</a>(vk, residual,</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  device_buffer_R, k*tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>() + k,</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  device_inner_prod_buffer, device_r_dot_vk_buffer,</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  buffer_size_per_vector, k*buffer_size_per_vector);</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  }</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  }</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span> </div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="comment">// Run reduction to obtain the values \xi_k = <r, v_k>.</span></div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="comment">// Note that unlike Algorithm 2.1 in Walker: "A Simpler GMRES", we do not update the residual</span></div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <a class="code" href="namespaceviennacl.html#aaa5c8726b45bc89a523ca2fa8c42107a">viennacl::fast_copy</a>(device_r_dot_vk_buffer.begin(), device_r_dot_vk_buffer.end(), host_r_dot_vk_buffer.begin());</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="keywordflow">for</span> (std::size_t i=0; i<k; ++i)</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  {</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  host_values_xi_k[i] = <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0);</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="keywordflow">for</span> (std::size_t j=0; j<buffer_size_per_vector; ++j)</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  host_values_xi_k[i] += host_r_dot_vk_buffer[i*buffer_size_per_vector + j];</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> </div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="comment">// Bring values in R back to host:</span></div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <a class="code" href="namespaceviennacl.html#aaa5c8726b45bc89a523ca2fa8c42107a">viennacl::fast_copy</a>(device_buffer_R.begin(), device_buffer_R.end(), host_buffer_R.begin());</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">//</span></div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="comment">// Check for premature convergence: If the diagonal element drops too far below the first norm, we're done and restrict the Krylov size accordingly.</span></div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> full_krylov_dim = k; <span class="comment">//needed for proper access to R</span></div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="keywordflow">for</span> (std::size_t i=0; i<k; ++i)</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  {</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="keywordflow">if</span> (std::fabs(host_buffer_R[i + i*k]) < tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa055ac8c0bc4144295c4ac2c176a6c0a">tolerance</a>() * host_buffer_R[0])</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  {</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  k = i;</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  }</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  }</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> </div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="comment">// Compute error estimator:</span></div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="keywordflow">for</span> (std::size_t i=0; i<k; ++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>  tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a4eb47bfc797a70a4db76d629f18f456a">iters</a>( tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a4eb47bfc797a70a4db76d629f18f456a">iters</a>() + 1 ); <span class="comment">//increase iteration counter</span></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="comment">// check for accumulation of round-off errors for poorly conditioned systems</span></div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="keywordflow">if</span> (host_values_xi_k[i] >= rho || host_values_xi_k[i] <= -rho)</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  {</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  k = i;</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <span class="keywordflow">break</span>; <span class="comment">// restrict Krylov space at this point. No gain from using additional basis vectors, since orthogonality is lost.</span></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">// update error estimator</span></div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  rho *= std::sin( std::acos(host_values_xi_k[i] / rho) );</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  }</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span> </div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="comment">// Solve minimization problem:</span></div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  host_values_eta_k_buffer = host_values_xi_k;</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span> </div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i2=static_cast<int>(k)-1; i2>-1; --i2)</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  {</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i = <span class="keyword">static_cast<</span><a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a><span class="keyword">></span>(i2);</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=static_cast<vcl_size_t>(i)+1; j<k; ++j)</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  host_values_eta_k_buffer[i] -= host_buffer_R[i + j*full_krylov_dim] * host_values_eta_k_buffer[j];</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span> </div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  host_values_eta_k_buffer[i] /= host_buffer_R[i + i*full_krylov_dim];</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  }</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span> </div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="comment">// Update x += rho * z with z = \eta_0 * residual + sum_{i=0}^{k-1} \eta_{i+1} v_i</span></div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="comment">// Note that we have not updated the residual yet, hence this slightly modified as compared to the form given in Algorithm 2.1 in Walker: "A Simpler GMRES"</span></div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <span class="comment">//</span></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> i=0; i<k; ++i)</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  host_update_coefficients[i] = rho_0 * host_values_eta_k_buffer[i];</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span> </div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <a class="code" href="namespaceviennacl.html#aaa5c8726b45bc89a523ca2fa8c42107a">viennacl::fast_copy</a>(host_update_coefficients.begin(), host_update_coefficients.end(), device_values_xi_k.begin()); <span class="comment">//reuse device_values_xi_k_buffer here for simplicity</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>  <a class="code" href="namespaceviennacl_1_1linalg.html#a8783d68cc82f47d4862d7bb77bed2bab">viennacl::linalg::pipelined_gmres_update_result</a>(result, residual,</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  device_krylov_basis, rhs.<a class="code" href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">size</a>(), rhs.<a class="code" href="classviennacl_1_1vector__base.html#a47350ccdc4b0a24eaea0e8d5f9fe7fec">internal_size</a>(),</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  device_values_xi_k, k);</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span> </div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa9bd21a63747c3f3a2ffe3b726a2a9bb">error</a>( std::fabs(rho*rho_0 / norm_rhs) );</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span> </div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="keywordflow">if</span> (monitor && monitor(result, std::fabs(rho*rho_0 / norm_rhs), monitor_data))</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  }</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span> </div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="keywordflow">return</span> result;</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> </div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  <span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><a name="l00371"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a89ed827282d58af58d30de400004a51a"> 371</a></span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ae33ca2ea245229d9d1cd772d3d0157d7">solve_impl</a>(<a class="code" href="classviennacl_1_1compressed__matrix.html">viennacl::compressed_matrix<NumericT></a> <span class="keyword">const</span> & A,</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <span class="keyword">const</span> & rhs,</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> <span class="keyword">const</span> & tag,</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  <a class="code" href="classviennacl_1_1linalg_1_1no__precond.html">viennacl::linalg::no_precond</a>,</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <span class="keywordtype">bool</span> (*monitor)(<a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <span class="keyword">const</span> &, <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>, <span class="keywordtype">void</span>*) = NULL,</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  <span class="keywordtype">void</span> *monitor_data = NULL)</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  {</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a173ef3bf1e3cf75985fbd3989e37290f">pipelined_solve</a>(A, rhs, tag, <a class="code" href="classviennacl_1_1linalg_1_1no__precond.html">viennacl::linalg::no_precond</a>(), monitor, monitor_data);</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  }</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span> </div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span> </div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><a name="l00384"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#aada551fe82155e6dc10f49ddabb02972"> 384</a></span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ae33ca2ea245229d9d1cd772d3d0157d7">solve_impl</a>(<a class="code" href="classviennacl_1_1coordinate__matrix.html">viennacl::coordinate_matrix<NumericT></a> <span class="keyword">const</span> & A,</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <span class="keyword">const</span> & rhs,</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> <span class="keyword">const</span> & tag,</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  <a class="code" href="classviennacl_1_1linalg_1_1no__precond.html">viennacl::linalg::no_precond</a>,</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <span class="keywordtype">bool</span> (*monitor)(<a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <span class="keyword">const</span> &, <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>, <span class="keywordtype">void</span>*) = NULL,</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <span class="keywordtype">void</span> *monitor_data = NULL)</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  {</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a173ef3bf1e3cf75985fbd3989e37290f">detail::pipelined_solve</a>(A, rhs, tag, <a class="code" href="classviennacl_1_1linalg_1_1no__precond.html">viennacl::linalg::no_precond</a>(), monitor, monitor_data);</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  }</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span> </div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span> </div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span> </div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><a name="l00398"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#ab78281bce494282ee783cd0001cd0be2"> 398</a></span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ae33ca2ea245229d9d1cd772d3d0157d7">solve_impl</a>(<a class="code" href="classviennacl_1_1ell__matrix.html">viennacl::ell_matrix<NumericT></a> <span class="keyword">const</span> & A,</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <span class="keyword">const</span> & rhs,</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> <span class="keyword">const</span> & tag,</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  <a class="code" href="classviennacl_1_1linalg_1_1no__precond.html">viennacl::linalg::no_precond</a>,</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  <span class="keywordtype">bool</span> (*monitor)(<a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <span class="keyword">const</span> &, <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>, <span class="keywordtype">void</span>*) = NULL,</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  <span class="keywordtype">void</span> *monitor_data = NULL)</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  {</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a173ef3bf1e3cf75985fbd3989e37290f">detail::pipelined_solve</a>(A, rhs, tag, <a class="code" href="classviennacl_1_1linalg_1_1no__precond.html">viennacl::linalg::no_precond</a>(), monitor, monitor_data);</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  }</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> </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> </div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  <span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><a name="l00412"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a304f63e39f16978a014caa3ce2dc9a01"> 412</a></span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ae33ca2ea245229d9d1cd772d3d0157d7">solve_impl</a>(<a class="code" href="classviennacl_1_1sliced__ell__matrix.html">viennacl::sliced_ell_matrix<NumericT></a> <span class="keyword">const</span> & A,</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <span class="keyword">const</span> & rhs,</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> <span class="keyword">const</span> & tag,</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  <a class="code" href="classviennacl_1_1linalg_1_1no__precond.html">viennacl::linalg::no_precond</a>,</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  <span class="keywordtype">bool</span> (*monitor)(<a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <span class="keyword">const</span> &, <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>, <span class="keywordtype">void</span>*) = NULL,</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <span class="keywordtype">void</span> *monitor_data = NULL)</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="keywordflow">return</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a173ef3bf1e3cf75985fbd3989e37290f">detail::pipelined_solve</a>(A, rhs, tag, <a class="code" href="classviennacl_1_1linalg_1_1no__precond.html">viennacl::linalg::no_precond</a>(), monitor, monitor_data);</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  }</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> </div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><a name="l00425"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#ae9e2cd3c427dad87c8dbc4da4303dbe5"> 425</a></span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ae33ca2ea245229d9d1cd772d3d0157d7">solve_impl</a>(<a class="code" href="classviennacl_1_1hyb__matrix.html">viennacl::hyb_matrix<NumericT></a> <span class="keyword">const</span> & A,</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <span class="keyword">const</span> & rhs,</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> <span class="keyword">const</span> & tag,</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  <a class="code" href="classviennacl_1_1linalg_1_1no__precond.html">viennacl::linalg::no_precond</a>,</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  <span class="keywordtype">bool</span> (*monitor)(<a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> <span class="keyword">const</span> &, <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>, <span class="keywordtype">void</span>*) = NULL,</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="keywordtype">void</span> *monitor_data = NULL)</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="keywordflow">return</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a173ef3bf1e3cf75985fbd3989e37290f">detail::pipelined_solve</a>(A, rhs, tag, <a class="code" href="classviennacl_1_1linalg_1_1no__precond.html">viennacl::linalg::no_precond</a>(), monitor, monitor_data);</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  }</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> </div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT, <span class="keyword">typename</span> VectorT, <span class="keyword">typename</span> PreconditionerT></div>
<div class="line"><a name="l00450"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a3c3ba2040dfb1b25894bb1314b2b95c9"> 450</a></span>  VectorT <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ae33ca2ea245229d9d1cd772d3d0157d7">solve_impl</a>(MatrixT <span class="keyword">const</span> & <a class="code" href="classviennacl_1_1matrix.html">matrix</a>,</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  VectorT <span class="keyword">const</span> & rhs,</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> <span class="keyword">const</span> & tag,</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  PreconditionerT <span class="keyword">const</span> & precond,</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="keywordtype">bool</span> (*monitor)(VectorT <span class="keyword">const</span> &, <span class="keyword">typename</span> <a class="code" href="structviennacl_1_1result__of_1_1cpu__value__type.html">viennacl::result_of::cpu_value_type</a><<span class="keyword">typename</span> <a class="code" href="structviennacl_1_1result__of_1_1value__type.html#a1fccdddb6d57eaba8f19506cea2051a3">viennacl::result_of::value_type<VectorT>::type</a>>::type, <span class="keywordtype">void</span>*) = NULL,</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <span class="keywordtype">void</span> *monitor_data = NULL)</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  {</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structviennacl_1_1result__of_1_1value__type.html#a1fccdddb6d57eaba8f19506cea2051a3">viennacl::result_of::value_type<VectorT>::type</a> NumericType;</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structviennacl_1_1result__of_1_1cpu__value__type.html#aa015d93f419985879a7c13b09633c5c6">viennacl::result_of::cpu_value_type<NumericType>::type</a> CPU_NumericType;</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>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> problem_size = <span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span> <span class="keywordtype">int</span><span class="keyword">></span>(<a class="code" href="namespaceviennacl_1_1traits.html#aa2344ea20469f55fbc15a8e9526494d0">viennacl::traits::size</a>(rhs));</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  VectorT result = rhs;</div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  <a class="code" href="namespaceviennacl_1_1traits.html#a22ab64b1df12a9da0423e5cad52ea367">viennacl::traits::clear</a>(result);</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>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> krylov_dim = <span class="keyword">static_cast<</span><a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a><span class="keyword">></span>(tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>());</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="keywordflow">if</span> (problem_size < krylov_dim)</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  krylov_dim = problem_size; <span class="comment">//A Krylov space larger than the matrix would lead to seg-faults (mathematically, error is certain to be zero already)</span></div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span> </div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  VectorT res = rhs;</div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  VectorT v_k_tilde = rhs;</div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  VectorT v_k_tilde_temp = rhs;</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span> </div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  std::vector< std::vector<CPU_NumericType> > R(krylov_dim, std::vector<CPU_NumericType>(tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">krylov_dim</a>()));</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  std::vector<CPU_NumericType> projection_rhs(krylov_dim);</div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span> </div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  std::vector<VectorT> householder_reflectors(krylov_dim, rhs);</div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  std::vector<CPU_NumericType> betas(krylov_dim);</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span> </div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  CPU_NumericType norm_rhs = <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(rhs);</div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span> </div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  <span class="keywordflow">if</span> (norm_rhs <= tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a8df40f7ba3716b9b5594ff5c3d8b415f">abs_tolerance</a>()) <span class="comment">//solution is zero if RHS norm is zero</span></div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span> </div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a4eb47bfc797a70a4db76d629f18f456a">iters</a>(0);</div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span> </div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> it = 0; it <= tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aceaecb48094fac8123d3be0a636ce6df">max_restarts</a>(); ++it)</div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  {</div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  <span class="comment">// (Re-)Initialize residual: r = b - A*x (without temporary for the result of A*x)</span></div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  res = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(matrix, result); <span class="comment">//initial guess zero</span></div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  res = rhs - res;</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  precond.apply(res);</div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span> </div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  CPU_NumericType rho_0 = <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(res);</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span> </div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  <span class="comment">// Check for premature convergence</span></div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  <span class="keywordflow">if</span> (rho_0 / norm_rhs < tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa055ac8c0bc4144295c4ac2c176a6c0a">tolerance</a>() || rho_0 < tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a8df40f7ba3716b9b5594ff5c3d8b415f">abs_tolerance</a>()) <span class="comment">// norm_rhs is known to be nonzero here</span></div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  {</div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa9bd21a63747c3f3a2ffe3b726a2a9bb">error</a>(rho_0 / norm_rhs);</div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  }</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span> </div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  <span class="comment">// Normalize residual and set 'rho' to 1 as requested in 'A Simpler GMRES' by Walker and Zhou.</span></div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  res /= rho_0;</div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  CPU_NumericType rho = <span class="keyword">static_cast<</span>CPU_NumericType<span class="keyword">></span>(1.0);</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span> </div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span> </div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  <span class="comment">// Iterate up until maximal Krylove space dimension is reached:</span></div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = 0;</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  <span class="keywordflow">for</span> (k = 0; k < krylov_dim; ++k)</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  {</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a4eb47bfc797a70a4db76d629f18f456a">iters</a>( tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#a4eb47bfc797a70a4db76d629f18f456a">iters</a>() + 1 ); <span class="comment">//increase iteration counter</span></div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span> </div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  <span class="comment">// prepare storage:</span></div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  <a class="code" href="namespaceviennacl_1_1traits.html#a22ab64b1df12a9da0423e5cad52ea367">viennacl::traits::clear</a>(R[k]);</div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  <a class="code" href="namespaceviennacl_1_1traits.html#a22ab64b1df12a9da0423e5cad52ea367">viennacl::traits::clear</a>(householder_reflectors[k]);</div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span> </div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <span class="comment">//compute v_k = A * v_{k-1} via Householder matrices</span></div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  <span class="keywordflow">if</span> (k == 0)</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  {</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  v_k_tilde = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(matrix, res);</div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  precond.apply(v_k_tilde);</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>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  {</div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  <a class="code" href="namespaceviennacl_1_1traits.html#a22ab64b1df12a9da0423e5cad52ea367">viennacl::traits::clear</a>(v_k_tilde);</div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  v_k_tilde[k-1] = CPU_NumericType(1);</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">//Householder rotations, part 1: Compute P_1 * P_2 * ... * P_{k-1} * e_{k-1}</span></div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = static_cast<int>(k)-1; i > -1; --i)</div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ad2b2c8a343124143d1ddc2fee8b2ce73">detail::gmres_householder_reflect</a>(v_k_tilde, householder_reflectors[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)], betas[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)]);</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span> </div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  v_k_tilde_temp = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(matrix, v_k_tilde);</div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  precond.apply(v_k_tilde_temp);</div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  v_k_tilde = v_k_tilde_temp;</div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span> </div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  <span class="comment">//Householder rotations, part 2: Compute P_{k-1} * ... * P_{1} * v_k_tilde</span></div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i = 0; i < k; ++i)</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ad2b2c8a343124143d1ddc2fee8b2ce73">detail::gmres_householder_reflect</a>(v_k_tilde, householder_reflectors[i], betas[i]);</div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  }</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>  <span class="comment">//</span></div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  <span class="comment">// Compute Householder reflection for v_k_tilde such that all entries below k-th entry are zero:</span></div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  CPU_NumericType rho_k_k = 0;</div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a29d6b53b3a99961196a859fa7ef46537">detail::gmres_setup_householder_vector</a>(v_k_tilde, householder_reflectors[k], betas[k], rho_k_k, k);</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span> </div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  <span class="comment">// copy first k entries from v_k_tilde to R[k] in order to fill k-th column with result of</span></div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  <span class="comment">// P_k * v_k_tilde = (v[0], ... , v[k-1], norm(v), 0, 0, ...) =: (rho_{1,k}, rho_{2,k}, ..., rho_{k,k}, 0, ..., 0);</span></div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a9dace8e3f8cafdc7c5b56282860e5a97">detail::gmres_copy_helper</a>(v_k_tilde, R[k], k);</div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  R[k][k] = rho_k_k;</div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span> </div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  <span class="comment">// Update residual: r = P_k r</span></div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  <span class="comment">// Set zeta_k = r[k] including machine precision considerations: mathematically we have |r[k]| <= rho</span></div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  <span class="comment">// Set rho *= sin(acos(r[k] / rho))</span></div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ad2b2c8a343124143d1ddc2fee8b2ce73">detail::gmres_householder_reflect</a>(res, householder_reflectors[k], betas[k]);</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="keywordflow">if</span> (res[k] > rho) <span class="comment">//machine precision reached</span></div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  res[k] = rho;</div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  <span class="keywordflow">if</span> (res[k] < -rho) <span class="comment">//machine precision reached</span></div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  res[k] = -rho;</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  projection_rhs[k] = res[k];</div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span> </div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  rho *= std::sin( std::acos(projection_rhs[k] / rho) );</div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span> </div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  <span class="keywordflow">if</span> (std::fabs(rho * rho_0 / norm_rhs) < tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa055ac8c0bc4144295c4ac2c176a6c0a">tolerance</a>()) <span class="comment">// Residual is sufficiently reduced, stop here</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>  tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa9bd21a63747c3f3a2ffe3b726a2a9bb">error</a>( std::fabs(rho*rho_0 / norm_rhs) );</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  ++k;</div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  }</div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  } <span class="comment">// for k</span></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="comment">//</span></div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  <span class="comment">// Triangular solver stage:</span></div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span> </div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i2=static_cast<int>(k)-1; i2>-1; --i2)</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  {</div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i = <span class="keyword">static_cast<</span><a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a><span class="keyword">></span>(i2);</div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=i+1; j<k; ++j)</div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  projection_rhs[i] -= R[j][i] * projection_rhs[j]; <span class="comment">//R is transposed</span></div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span> </div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  projection_rhs[i] /= R[i][i];</div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  }</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span> </div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  <span class="comment">// Note: 'projection_rhs' now holds the solution (eta_1, ..., eta_k)</span></div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00600"></a><span class="lineno"> 600</span> </div>
<div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  res *= projection_rhs[0];</div>
<div class="line"><a name="l00602"></a><span class="lineno"> 602</span> </div>
<div class="line"><a name="l00603"></a><span class="lineno"> 603</span>  <span class="keywordflow">if</span> (k > 0)</div>
<div class="line"><a name="l00604"></a><span class="lineno"> 604</span>  {</div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < k-1; ++i)</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  res[i] += projection_rhs[i+1];</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  }</div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span> </div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  <span class="comment">// Form z inplace in 'res' by applying P_1 * ... * P_{k}</span></div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=static_cast<int>(k)-1; i>=0; --i)</div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ad2b2c8a343124143d1ddc2fee8b2ce73">detail::gmres_householder_reflect</a>(res, householder_reflectors[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)], betas[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)]);</div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span> </div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  res *= rho_0;</div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  result += res; <span class="comment">// x += rho_0 * z in the paper</span></div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span> </div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span>  <span class="comment">// Check for convergence:</span></div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span>  tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa9bd21a63747c3f3a2ffe3b726a2a9bb">error</a>(std::fabs(rho*rho_0 / norm_rhs));</div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span> </div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  <span class="keywordflow">if</span> (monitor && monitor(result, std::fabs(rho*rho_0 / norm_rhs), monitor_data))</div>
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span> </div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span>  <span class="keywordflow">if</span> ( tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa9bd21a63747c3f3a2ffe3b726a2a9bb">error</a>() < tag.<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html#aa055ac8c0bc4144295c4ac2c176a6c0a">tolerance</a>() )</div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  }</div>
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span> </div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  }</div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span> </div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span> }</div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span> </div>
<div class="line"><a name="l00635"></a><span class="lineno"> 635</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT, <span class="keyword">typename</span> VectorT, <span class="keyword">typename</span> PreconditionerT></div>
<div class="line"><a name="l00636"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg.html#af6c0a087d090d74573763d9dd48c9074"> 636</a></span> VectorT <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">solve</a>(MatrixT <span class="keyword">const</span> & matrix, VectorT <span class="keyword">const</span> & rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> <span class="keyword">const</span> & tag, PreconditionerT <span class="keyword">const</span> & precond)</div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span> {</div>
<div class="line"><a name="l00638"></a><span class="lineno"> 638</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ae33ca2ea245229d9d1cd772d3d0157d7">detail::solve_impl</a>(matrix, rhs, tag, precond);</div>
<div class="line"><a name="l00639"></a><span class="lineno"> 639</span> }</div>
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span> </div>
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span> <span class="keyword">template</span><<span class="keyword">typename</span> IndexT, <span class="keyword">typename</span> NumericT, <span class="keyword">typename</span> PreconditionerT></div>
<div class="line"><a name="l00647"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg.html#a70c979c1bdf04f724d1b32c7789b563d"> 647</a></span> std::vector<NumericT> <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">solve</a>(std::vector< std::map<IndexT, NumericT> > <span class="keyword">const</span> & A, std::vector<NumericT> <span class="keyword">const</span> & rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> <span class="keyword">const</span> & tag, PreconditionerT <span class="keyword">const</span> & precond)</div>
<div class="line"><a name="l00648"></a><span class="lineno"> 648</span> {</div>
<div class="line"><a name="l00649"></a><span class="lineno"> 649</span>  <a class="code" href="classviennacl_1_1compressed__matrix.html">viennacl::compressed_matrix<NumericT></a> vcl_A;</div>
<div class="line"><a name="l00650"></a><span class="lineno"> 650</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(A, vcl_A);</div>
<div class="line"><a name="l00651"></a><span class="lineno"> 651</span> </div>
<div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> vcl_rhs(rhs.size());</div>
<div class="line"><a name="l00653"></a><span class="lineno"> 653</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(rhs, vcl_rhs);</div>
<div class="line"><a name="l00654"></a><span class="lineno"> 654</span> </div>
<div class="line"><a name="l00655"></a><span class="lineno"> 655</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">solve</a>(vcl_A, vcl_rhs, tag, precond);</div>
<div class="line"><a name="l00656"></a><span class="lineno"> 656</span> </div>
<div class="line"><a name="l00657"></a><span class="lineno"> 657</span>  std::vector<NumericT> result(vcl_result.<a class="code" href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">size</a>());</div>
<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(vcl_result, result);</div>
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span> }</div>
<div class="line"><a name="l00661"></a><span class="lineno"> 661</span> </div>
<div class="line"><a name="l00669"></a><span class="lineno"> 669</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT, <span class="keyword">typename</span> VectorT></div>
<div class="line"><a name="l00670"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg.html#ac34f2a4be7c82ecf4fd10e05ecc24273"> 670</a></span> VectorT <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">solve</a>(MatrixT <span class="keyword">const</span> & A, VectorT <span class="keyword">const</span> & rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> <span class="keyword">const</span> & tag)</div>
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span> {</div>
<div class="line"><a name="l00672"></a><span class="lineno"> 672</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">solve</a>(A, rhs, tag, <a class="code" href="classviennacl_1_1linalg_1_1no__precond.html">no_precond</a>());</div>
<div class="line"><a name="l00673"></a><span class="lineno"> 673</span> }</div>
<div class="line"><a name="l00674"></a><span class="lineno"> 674</span> </div>
<div class="line"><a name="l00675"></a><span class="lineno"> 675</span> </div>
<div class="line"><a name="l00676"></a><span class="lineno"> 676</span> </div>
<div class="line"><a name="l00677"></a><span class="lineno"> 677</span> <span class="keyword">template</span><<span class="keyword">typename</span> VectorT></div>
<div class="line"><a name="l00678"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__solver.html"> 678</a></span> <span class="keyword">class </span><a class="code" href="classviennacl_1_1linalg_1_1gmres__solver.html">gmres_solver</a></div>
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span> {</div>
<div class="line"><a name="l00680"></a><span class="lineno"> 680</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00681"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__solver.html#a4bd467e9c847e8454c0ac7823e4d688c"> 681</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structviennacl_1_1result__of_1_1cpu__value__type.html#aa015d93f419985879a7c13b09633c5c6">viennacl::result_of::cpu_value_type<VectorT>::type</a> <a class="code" href="classviennacl_1_1linalg_1_1gmres__solver.html#a4bd467e9c847e8454c0ac7823e4d688c">numeric_type</a>;</div>
<div class="line"><a name="l00682"></a><span class="lineno"> 682</span> </div>
<div class="line"><a name="l00683"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__solver.html#a43d4224ee3c3aa42581f1c871562fb5c"> 683</a></span>  <a class="code" href="classviennacl_1_1linalg_1_1gmres__solver.html#a43d4224ee3c3aa42581f1c871562fb5c">gmres_solver</a>(<a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> <span class="keyword">const</span> & tag) : tag_(tag), monitor_callback_(NULL), user_data_(NULL) {}</div>
<div class="line"><a name="l00684"></a><span class="lineno"> 684</span> </div>
<div class="line"><a name="l00685"></a><span class="lineno"> 685</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT, <span class="keyword">typename</span> PreconditionerT></div>
<div class="line"><a name="l00686"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__solver.html#ad92194cbf315cf813ca45c98df206144"> 686</a></span>  VectorT <a class="code" href="classviennacl_1_1linalg_1_1gmres__solver.html#ad92194cbf315cf813ca45c98df206144">operator()</a>(MatrixT <span class="keyword">const</span> & A, VectorT <span class="keyword">const</span> & b, PreconditionerT <span class="keyword">const</span> & precond)<span class="keyword"> const</span></div>
<div class="line"><a name="l00687"></a><span class="lineno"> 687</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span>  <span class="keywordflow">if</span> (<a class="code" href="namespaceviennacl_1_1traits.html#aa2344ea20469f55fbc15a8e9526494d0">viennacl::traits::size</a>(init_guess_) > 0) <span class="comment">// take initial guess into account</span></div>
<div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  {</div>
<div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  VectorT mod_rhs = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(A, init_guess_);</div>
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span>  mod_rhs = b - mod_rhs;</div>
<div class="line"><a name="l00692"></a><span class="lineno"> 692</span>  VectorT y = <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ae33ca2ea245229d9d1cd772d3d0157d7">detail::solve_impl</a>(A, mod_rhs, tag_, precond, monitor_callback_, user_data_);</div>
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span>  <span class="keywordflow">return</span> init_guess_ + y;</div>
<div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  }</div>
<div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ae33ca2ea245229d9d1cd772d3d0157d7">detail::solve_impl</a>(A, b, tag_, precond, monitor_callback_, user_data_);</div>
<div class="line"><a name="l00696"></a><span class="lineno"> 696</span>  }</div>
<div class="line"><a name="l00697"></a><span class="lineno"> 697</span> </div>
<div class="line"><a name="l00698"></a><span class="lineno"> 698</span> </div>
<div class="line"><a name="l00699"></a><span class="lineno"> 699</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT></div>
<div class="line"><a name="l00700"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__solver.html#a68a580b281256dca581b6b596eb8dc57"> 700</a></span>  VectorT <a class="code" href="classviennacl_1_1linalg_1_1gmres__solver.html#a68a580b281256dca581b6b596eb8dc57">operator()</a>(MatrixT <span class="keyword">const</span> & A, VectorT <span class="keyword">const</span> & b)<span class="keyword"> const</span></div>
<div class="line"><a name="l00701"></a><span class="lineno"> 701</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00702"></a><span class="lineno"> 702</span>  <span class="keywordflow">return</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__solver.html#ad92194cbf315cf813ca45c98df206144">operator()</a>(A, b, <a class="code" href="classviennacl_1_1linalg_1_1no__precond.html">viennacl::linalg::no_precond</a>());</div>
<div class="line"><a name="l00703"></a><span class="lineno"> 703</span>  }</div>
<div class="line"><a name="l00704"></a><span class="lineno"> 704</span> </div>
<div class="line"><a name="l00709"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__solver.html#a73984f2ec1f3e4b5d9398e4b457b3efb"> 709</a></span>  <span class="keywordtype">void</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__solver.html#a73984f2ec1f3e4b5d9398e4b457b3efb">set_initial_guess</a>(VectorT <span class="keyword">const</span> & x) { init_guess_ = x; }</div>
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span> </div>
<div class="line"><a name="l00718"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__solver.html#a5a0e1b4766423935abc49d93029baddc"> 718</a></span>  <span class="keywordtype">void</span> <a class="code" href="classviennacl_1_1linalg_1_1gmres__solver.html#a5a0e1b4766423935abc49d93029baddc">set_monitor</a>(<span class="keywordtype">bool</span> (*monitor_fun)(VectorT <span class="keyword">const</span> &, <a class="code" href="classviennacl_1_1linalg_1_1gmres__solver.html#a4bd467e9c847e8454c0ac7823e4d688c">numeric_type</a>, <span class="keywordtype">void</span> *), <span class="keywordtype">void</span> *user_data)</div>
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  {</div>
<div class="line"><a name="l00720"></a><span class="lineno"> 720</span>  monitor_callback_ = monitor_fun;</div>
<div class="line"><a name="l00721"></a><span class="lineno"> 721</span>  user_data_ = user_data;</div>
<div class="line"><a name="l00722"></a><span class="lineno"> 722</span>  }</div>
<div class="line"><a name="l00723"></a><span class="lineno"> 723</span> </div>
<div class="line"><a name="l00725"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1gmres__solver.html#adf0c22fd8e2fb3734d4f0545b0b97b5c"> 725</a></span>  <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> <span class="keyword">const</span> & <a class="code" href="classviennacl_1_1linalg_1_1gmres__solver.html#adf0c22fd8e2fb3734d4f0545b0b97b5c">tag</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> tag_; }</div>
<div class="line"><a name="l00726"></a><span class="lineno"> 726</span> </div>
<div class="line"><a name="l00727"></a><span class="lineno"> 727</span> <span class="keyword">private</span>:</div>
<div class="line"><a name="l00728"></a><span class="lineno"> 728</span>  <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">gmres_tag</a> tag_;</div>
<div class="line"><a name="l00729"></a><span class="lineno"> 729</span>  VectorT init_guess_;</div>
<div class="line"><a name="l00730"></a><span class="lineno"> 730</span>  bool (*monitor_callback_)(VectorT <span class="keyword">const</span> &, <a class="code" href="classviennacl_1_1linalg_1_1gmres__solver.html#a4bd467e9c847e8454c0ac7823e4d688c">numeric_type</a>, <span class="keywordtype">void</span> *);</div>
<div class="line"><a name="l00731"></a><span class="lineno"> 731</span>  <span class="keywordtype">void</span> *user_data_;</div>
<div class="line"><a name="l00732"></a><span class="lineno"> 732</span> };</div>
<div class="line"><a name="l00733"></a><span class="lineno"> 733</span> </div>
<div class="line"><a name="l00734"></a><span class="lineno"> 734</span> </div>
<div class="line"><a name="l00735"></a><span class="lineno"> 735</span> }</div>
<div class="line"><a name="l00736"></a><span class="lineno"> 736</span> }</div>
<div class="line"><a name="l00737"></a><span class="lineno"> 737</span> </div>
<div class="line"><a name="l00738"></a><span class="lineno"> 738</span> <span class="preprocessor">#endif</span></div>
<div class="ttc" id="classviennacl_1_1hyb__matrix_html"><div class="ttname"><a href="classviennacl_1_1hyb__matrix.html">viennacl::hyb_matrix</a></div><div class="ttdoc">Sparse matrix class using a hybrid format composed of the ELL and CSR format for storing the nonzeros...</div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00406">forwards.h:406</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__tag_html_aceaecb48094fac8123d3be0a636ce6df"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__tag.html#aceaecb48094fac8123d3be0a636ce6df">viennacl::linalg::gmres_tag::max_restarts</a></div><div class="ttdeci">unsigned int max_restarts() const </div><div class="ttdoc">Returns the maximum number of GMRES restarts. </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00074">gmres.hpp:74</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_ae46f15d01c01f92a153b3f555a15096b"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a></div><div class="ttdeci">T norm_2(std::vector< T, A > const &v1)</div><div class="ttdef"><b>Definition:</b> <a href="norm__2_8hpp_source.html#l00096">norm_2.hpp:96</a></div></div>
<div class="ttc" id="norm__2_8hpp_html"><div class="ttname"><a href="norm__2_8hpp.html">norm_2.hpp</a></div><div class="ttdoc">Generic interface for the l^2-norm. See viennacl/linalg/vector_operations.hpp for implementations...</div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__solver_html_a4bd467e9c847e8454c0ac7823e4d688c"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__solver.html#a4bd467e9c847e8454c0ac7823e4d688c">viennacl::linalg::gmres_solver::numeric_type</a></div><div class="ttdeci">viennacl::result_of::cpu_value_type< VectorT >::type numeric_type</div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00681">gmres.hpp:681</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__tag_html_a14c5e80e1d5da7563e333337b13bd922"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__tag.html#a14c5e80e1d5da7563e333337b13bd922">viennacl::linalg::gmres_tag::max_iterations</a></div><div class="ttdeci">unsigned int max_iterations() const </div><div class="ttdoc">Returns the maximum number of iterations. </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00070">gmres.hpp:70</a></div></div>
<div class="ttc" id="size_8hpp_html"><div class="ttname"><a href="size_8hpp.html">size.hpp</a></div><div class="ttdoc">Generic size and resize functionality for different vector and matrix types. </div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__tag_html_a4eb47bfc797a70a4db76d629f18f456a"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__tag.html#a4eb47bfc797a70a4db76d629f18f456a">viennacl::linalg::gmres_tag::iters</a></div><div class="ttdeci">unsigned int iters() const </div><div class="ttdoc">Return the number of solver iterations: </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00083">gmres.hpp:83</a></div></div>
<div class="ttc" id="prod_8hpp_html"><div class="ttname"><a href="prod_8hpp.html">prod.hpp</a></div><div class="ttdoc">Generic interface for matrix-vector and matrix-matrix products. See viennacl/linalg/vector_operations...</div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__tag_html_aeed1d3814b1ec24110228ffb9307569d"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__tag.html#aeed1d3814b1ec24110228ffb9307569d">viennacl::linalg::gmres_tag::abs_tolerance</a></div><div class="ttdeci">void abs_tolerance(double new_tol)</div><div class="ttdoc">Sets the absolute tolerance. </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00067">gmres.hpp:67</a></div></div>
<div class="ttc" id="tools_8hpp_html"><div class="ttname"><a href="tools_8hpp.html">tools.hpp</a></div><div class="ttdoc">Various little tools used here and there in ViennaCL. </div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a26e6e73c2c27a83fa958ca25e468b8ad"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a26e6e73c2c27a83fa958ca25e468b8ad">viennacl::linalg::pipelined_gmres_gram_schmidt_stage1</a></div><div class="ttdeci">void pipelined_gmres_gram_schmidt_stage1(vector_base< T > const &device_krylov_basis, vcl_size_t v_k_size, vcl_size_t v_k_internal_size, vcl_size_t k, vector_base< T > &vi_in_vk_buffer, vcl_size_t buffer_chunk_size)</div><div class="ttdoc">Computes the first reduction stage for multiple inner products <v_i, v_k>, i=0..k-1. </div><div class="ttdef"><b>Definition:</b> <a href="iterative__operations_8hpp_source.html#l00286">iterative_operations.hpp:286</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__solver_html_ad92194cbf315cf813ca45c98df206144"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__solver.html#ad92194cbf315cf813ca45c98df206144">viennacl::linalg::gmres_solver::operator()</a></div><div class="ttdeci">VectorT operator()(MatrixT const &A, VectorT const &b, PreconditionerT const &precond) const </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00686">gmres.hpp:686</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a8783d68cc82f47d4862d7bb77bed2bab"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a8783d68cc82f47d4862d7bb77bed2bab">viennacl::linalg::pipelined_gmres_update_result</a></div><div class="ttdeci">void pipelined_gmres_update_result(vector_base< T > &result, vector_base< T > const &residual, vector_base< T > const &krylov_basis, vcl_size_t v_k_size, vcl_size_t v_k_internal_size, vector_base< T > const &coefficients, vcl_size_t k)</div><div class="ttdoc">Computes x += eta_0 r + sum_{i=1}^{k-1} eta_i v_{i-1}. </div><div class="ttdef"><b>Definition:</b> <a href="iterative__operations_8hpp_source.html#l00356">iterative_operations.hpp:356</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a39b768f9d8385b980d2e5e9073d09530"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a39b768f9d8385b980d2e5e9073d09530">viennacl::linalg::pipelined_gmres_gram_schmidt_stage2</a></div><div class="ttdeci">void pipelined_gmres_gram_schmidt_stage2(vector_base< T > &device_krylov_basis, vcl_size_t v_k_size, vcl_size_t v_k_internal_size, vcl_size_t k, vector_base< T > const &vi_in_vk_buffer, vector_base< T > &R_buffer, vcl_size_t krylov_dim, vector_base< T > &inner_prod_buffer, vcl_size_t buffer_chunk_size)</div><div class="ttdoc">Computes the second reduction stage for multiple inner products <v_i, v_k>, i=0..k-1, then updates v_k -= <v_i, v_k> v_i and computes the first reduction stage for ||v_k||. </div><div class="ttdef"><b>Definition:</b> <a href="iterative__operations_8hpp_source.html#l00321">iterative_operations.hpp:321</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_ae33ca2ea245229d9d1cd772d3d0157d7"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#ae33ca2ea245229d9d1cd772d3d0157d7">viennacl::linalg::detail::solve_impl</a></div><div class="ttdeci">viennacl::vector< NumericT > solve_impl(viennacl::compressed_matrix< NumericT > const &A, viennacl::vector< NumericT > const &rhs, bicgstab_tag const &tag, viennacl::linalg::no_precond, bool(*monitor)(viennacl::vector< NumericT > const &, NumericT, void *)=NULL, void *monitor_data=NULL)</div><div class="ttdoc">Overload for the pipelined CG implementation for the ViennaCL sparse matrix types. </div><div class="ttdef"><b>Definition:</b> <a href="bicgstab_8hpp_source.html#l00219">bicgstab.hpp:219</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__tag_html_a8df40f7ba3716b9b5594ff5c3d8b415f"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__tag.html#a8df40f7ba3716b9b5594ff5c3d8b415f">viennacl::linalg::gmres_tag::abs_tolerance</a></div><div class="ttdeci">double abs_tolerance() const </div><div class="ttdoc">Returns the absolute tolerance. </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00065">gmres.hpp:65</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__tag_html_ab1c7ce4738a05af039a23889d98a09c4"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__tag.html#ab1c7ce4738a05af039a23889d98a09c4">viennacl::linalg::gmres_tag::iters</a></div><div class="ttdeci">void iters(unsigned int i) const </div><div class="ttdoc">Set the number of solver iterations (should only be modified by the solver) </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00085">gmres.hpp:85</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1traits_html_a22ab64b1df12a9da0423e5cad52ea367"><div class="ttname"><a href="namespaceviennacl_1_1traits.html#a22ab64b1df12a9da0423e5cad52ea367">viennacl::traits::clear</a></div><div class="ttdeci">void clear(VectorType &vec)</div><div class="ttdoc">Generic routine for setting all entries of a vector to zero. This is the version for non-ViennaCL obj...</div><div class="ttdef"><b>Definition:</b> <a href="clear_8hpp_source.html#l00043">clear.hpp:43</a></div></div>
<div class="ttc" id="forwards_8h_html"><div class="ttname"><a href="forwards_8h.html">forwards.h</a></div><div class="ttdoc">This file provides the forward declarations for the main types used within ViennaCL. </div></div>
<div class="ttc" id="structviennacl_1_1zero__vector_html"><div class="ttname"><a href="structviennacl_1_1zero__vector.html">viennacl::zero_vector</a></div><div class="ttdef"><b>Definition:</b> <a href="vector__def_8hpp_source.html#l00093">vector_def.hpp:93</a></div></div>
<div class="ttc" id="classviennacl_1_1matrix_html"><div class="ttname"><a href="classviennacl_1_1matrix.html">viennacl::matrix</a></div><div class="ttdoc">A dense matrix class. </div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00375">forwards.h:375</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_ab35950c4374eb3be08a03d852508c01a"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#ab35950c4374eb3be08a03d852508c01a">viennacl::linalg::inner_prod</a></div><div class="ttdeci">viennacl::enable_if< viennacl::is_stl< typename viennacl::traits::tag_of< VectorT1 >::type >::value, typename VectorT1::value_type >::type inner_prod(VectorT1 const &v1, VectorT2 const &v2)</div><div class="ttdef"><b>Definition:</b> <a href="inner__prod_8hpp_source.html#l00100">inner_prod.hpp:100</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__tag_html_a2ad9dac58a4cef0fea4e6b6ce3799b5d"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__tag.html#a2ad9dac58a4cef0fea4e6b6ce3799b5d">viennacl::linalg::gmres_tag::error</a></div><div class="ttdeci">void error(double e) const </div><div class="ttdoc">Sets the estimated relative error at the end of the solver run. </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00090">gmres.hpp:90</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__solver_html"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__solver.html">viennacl::linalg::gmres_solver</a></div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00678">gmres.hpp:678</a></div></div>
<div class="ttc" id="structviennacl_1_1result__of_1_1value__type_html_a1fccdddb6d57eaba8f19506cea2051a3"><div class="ttname"><a href="structviennacl_1_1result__of_1_1value__type.html#a1fccdddb6d57eaba8f19506cea2051a3">viennacl::result_of::value_type::type</a></div><div class="ttdeci">T::value_type type</div><div class="ttdef"><b>Definition:</b> <a href="result__of_8hpp_source.html#l00213">result_of.hpp:213</a></div></div>
<div class="ttc" id="inner__prod_8hpp_html"><div class="ttname"><a href="inner__prod_8hpp.html">inner_prod.hpp</a></div><div class="ttdoc">Generic interface for the computation of inner products. See viennacl/linalg/vector_operations.hpp for implementations. </div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__tag_html"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a></div><div class="ttdoc">A tag for the solver GMRES. Used for supplying solver parameters and for dispatching the solve() func...</div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00049">gmres.hpp:49</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__solver_html_a73984f2ec1f3e4b5d9398e4b457b3efb"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__solver.html#a73984f2ec1f3e4b5d9398e4b457b3efb">viennacl::linalg::gmres_solver::set_initial_guess</a></div><div class="ttdeci">void set_initial_guess(VectorT const &x)</div><div class="ttdoc">Specifies an initial guess for the iterative solver. </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00709">gmres.hpp:709</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a6e9b329b64ac782e6a5687ad2fc47a2a"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a></div><div class="ttdeci">VectorT solve(MatrixT const &matrix, VectorT const &rhs, bicgstab_tag const &tag, PreconditionerT const &precond)</div><div class="ttdef"><b>Definition:</b> <a href="bicgstab_8hpp_source.html#l00496">bicgstab.hpp:496</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__tag_html_ad6e4eb92dd1cc1ad15eada6ed1b2a8f1"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__tag.html#ad6e4eb92dd1cc1ad15eada6ed1b2a8f1">viennacl::linalg::gmres_tag::gmres_tag</a></div><div class="ttdeci">gmres_tag(double tol=1e-10, unsigned int max_iterations=300, unsigned int krylov_dim=20)</div><div class="ttdoc">The constructor. </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00058">gmres.hpp:58</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__solver_html_a68a580b281256dca581b6b596eb8dc57"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__solver.html#a68a580b281256dca581b6b596eb8dc57">viennacl::linalg::gmres_solver::operator()</a></div><div class="ttdeci">VectorT operator()(MatrixT const &A, VectorT const &b) const </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00700">gmres.hpp:700</a></div></div>
<div class="ttc" id="tests_2src_2bisect_8cpp_html_a52b5d30a2d7b064678644a3bf49b7f6c"><div class="ttname"><a href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a></div><div class="ttdeci">float NumericT</div><div class="ttdef"><b>Definition:</b> <a href="tests_2src_2bisect_8cpp_source.html#l00040">bisect.cpp:40</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_aa18d10f8a90e38bd9ff43c650fc670ef"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a></div><div class="ttdeci">VectorT prod(std::vector< std::vector< T, A1 >, A2 > const &matrix, VectorT const &vector)</div><div class="ttdef"><b>Definition:</b> <a href="prod_8hpp_source.html#l00102">prod.hpp:102</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1traits_html_aa2344ea20469f55fbc15a8e9526494d0"><div class="ttname"><a href="namespaceviennacl_1_1traits.html#aa2344ea20469f55fbc15a8e9526494d0">viennacl::traits::size</a></div><div class="ttdeci">vcl_size_t size(VectorType const &vec)</div><div class="ttdoc">Generic routine for obtaining the size of a vector (ViennaCL, uBLAS, etc.) </div><div class="ttdef"><b>Definition:</b> <a href="size_8hpp_source.html#l00239">size.hpp:239</a></div></div>
<div class="ttc" id="classviennacl_1_1vector__range_html"><div class="ttname"><a href="classviennacl_1_1vector__range.html">viennacl::vector_range</a></div><div class="ttdoc">Class for representing non-strided subvectors of a bigger vector x. </div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00434">forwards.h:434</a></div></div>
<div class="ttc" id="classviennacl_1_1ell__matrix_html"><div class="ttname"><a href="classviennacl_1_1ell__matrix.html">viennacl::ell_matrix</a></div><div class="ttdoc">Sparse matrix class using the ELLPACK format for storing the nonzeros. </div><div class="ttdef"><b>Definition:</b> <a href="ell__matrix_8hpp_source.html#l00053">ell_matrix.hpp:53</a></div></div>
<div class="ttc" id="classviennacl_1_1vector__base_html_a762d98e2f912fc534951f25555b6077f"><div class="ttname"><a href="classviennacl_1_1vector__base.html#a762d98e2f912fc534951f25555b6077f">viennacl::vector_base::begin</a></div><div class="ttdeci">iterator begin()</div><div class="ttdoc">Returns an iterator pointing to the beginning of the vector (STL like) </div><div class="ttdef"><b>Definition:</b> <a href="vector_8hpp_source.html#l00841">vector.hpp:841</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1no__precond_html"><div class="ttname"><a href="classviennacl_1_1linalg_1_1no__precond.html">viennacl::linalg::no_precond</a></div><div class="ttdoc">A tag class representing the use of no preconditioner. </div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00873">forwards.h:873</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a6faa475e03dfe776021e91f5a66f9319"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a6faa475e03dfe776021e91f5a66f9319">viennacl::linalg::pipelined_gmres_prod</a></div><div class="ttdeci">void pipelined_gmres_prod(MatrixType const &A, vector_base< T > const &p, vector_base< T > &Ap, vector_base< T > &inner_prod_buffer)</div><div class="ttdoc">Performs a joint vector update operation needed for an efficient pipelined GMRES algorithm. </div><div class="ttdef"><b>Definition:</b> <a href="iterative__operations_8hpp_source.html#l00393">iterative_operations.hpp:393</a></div></div>
<div class="ttc" id="classviennacl_1_1vector_html_a7e683e134c8aad7b3cd057776a58c4c4"><div class="ttname"><a href="classviennacl_1_1vector.html#a7e683e134c8aad7b3cd057776a58c4c4">viennacl::vector::difference_type</a></div><div class="ttdeci">base_type::difference_type difference_type</div><div class="ttdef"><b>Definition:</b> <a href="vector_8hpp_source.html#l00957">vector.hpp:957</a></div></div>
<div class="ttc" id="classviennacl_1_1implicit__vector__base_html_a56e5fd972e19933335872a11e6c48bbf"><div class="ttname"><a href="classviennacl_1_1implicit__vector__base.html#a56e5fd972e19933335872a11e6c48bbf">viennacl::implicit_vector_base::size</a></div><div class="ttdeci">vcl_size_t size() const </div><div class="ttdef"><b>Definition:</b> <a href="vector__def_8hpp_source.html#l00047">vector_def.hpp:47</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__solver_html_adf0c22fd8e2fb3734d4f0545b0b97b5c"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__solver.html#adf0c22fd8e2fb3734d4f0545b0b97b5c">viennacl::linalg::gmres_solver::tag</a></div><div class="ttdeci">gmres_tag const & tag() const </div><div class="ttdoc">Returns the solver tag containing basic configuration such as tolerances, etc. </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00725">gmres.hpp:725</a></div></div>
<div class="ttc" id="classviennacl_1_1sliced__ell__matrix_html"><div class="ttname"><a href="classviennacl_1_1sliced__ell__matrix.html">viennacl::sliced_ell_matrix</a></div><div class="ttdoc">Sparse matrix class using the sliced ELLPACK with parameters C, . </div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00403">forwards.h:403</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="traits_2context_8hpp_html"><div class="ttname"><a href="traits_2context_8hpp.html">context.hpp</a></div><div class="ttdoc">Extracts the underlying context from objects. </div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_aaca868298580acb7df97aff002bf6867"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#aaca868298580acb7df97aff002bf6867">viennacl::linalg::pipelined_gmres_normalize_vk</a></div><div class="ttdeci">void pipelined_gmres_normalize_vk(vector_base< T > &v_k, vector_base< T > const &residual, vector_base< T > &R_buffer, vcl_size_t offset_in_R, vector_base< T > const &inner_prod_buffer, vector_base< T > &r_dot_vk_buffer, vcl_size_t buffer_chunk_size, vcl_size_t buffer_chunk_offset)</div><div class="ttdoc">Performs a vector normalization needed for an efficient pipelined GMRES algorithm. </div><div class="ttdef"><b>Definition:</b> <a href="iterative__operations_8hpp_source.html#l00248">iterative_operations.hpp:248</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a29d6b53b3a99961196a859fa7ef46537"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a29d6b53b3a99961196a859fa7ef46537">viennacl::linalg::detail::gmres_setup_householder_vector</a></div><div class="ttdeci">void gmres_setup_householder_vector(VectorT const &input_vec, VectorT &hh_vec, NumericT &beta, NumericT &mu, vcl_size_t j)</div><div class="ttdoc">Computes the householder vector 'hh_vec' which rotates 'input_vec' such that all entries below the j-...</div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00131">gmres.hpp:131</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a173ef3bf1e3cf75985fbd3989e37290f"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a173ef3bf1e3cf75985fbd3989e37290f">viennacl::linalg::detail::pipelined_solve</a></div><div class="ttdeci">viennacl::vector< NumericT > pipelined_solve(MatrixT const &A, viennacl::vector_base< NumericT > const &rhs, bicgstab_tag const &tag, viennacl::linalg::no_precond, bool(*monitor)(viennacl::vector< NumericT > const &, NumericT, void *)=NULL, void *monitor_data=NULL)</div><div class="ttdoc">Implementation of a pipelined stabilized Bi-conjugate gradient solver. </div><div class="ttdef"><b>Definition:</b> <a href="bicgstab_8hpp_source.html#l00098">bicgstab.hpp:98</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__solver_html_a43d4224ee3c3aa42581f1c871562fb5c"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__solver.html#a43d4224ee3c3aa42581f1c871562fb5c">viennacl::linalg::gmres_solver::gmres_solver</a></div><div class="ttdeci">gmres_solver(gmres_tag const &tag)</div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00683">gmres.hpp:683</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a9dace8e3f8cafdc7c5b56282860e5a97"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a9dace8e3f8cafdc7c5b56282860e5a97">viennacl::linalg::detail::gmres_copy_helper</a></div><div class="ttdeci">void gmres_copy_helper(SrcVectorT const &src, DestVectorT &dest, vcl_size_t len, vcl_size_t start=0)</div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00107">gmres.hpp:107</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#l00075">forwards.h:75</a></div></div>
<div class="ttc" id="clear_8hpp_html"><div class="ttname"><a href="clear_8hpp.html">clear.hpp</a></div><div class="ttdoc">Generic clear functionality for different vector and matrix types. </div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__solver_html_a5a0e1b4766423935abc49d93029baddc"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__solver.html#a5a0e1b4766423935abc49d93029baddc">viennacl::linalg::gmres_solver::set_monitor</a></div><div class="ttdeci">void set_monitor(bool(*monitor_fun)(VectorT const &, numeric_type, void *), void *user_data)</div><div class="ttdoc">Sets a monitor function pointer to be called in each iteration. Set to NULL to run without monitor...</div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00718">gmres.hpp:718</a></div></div>
<div class="ttc" id="classviennacl_1_1vector_html"><div class="ttname"><a href="classviennacl_1_1vector.html">viennacl::vector< NumericT ></a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__tag_html_aa055ac8c0bc4144295c4ac2c176a6c0a"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__tag.html#aa055ac8c0bc4144295c4ac2c176a6c0a">viennacl::linalg::gmres_tag::tolerance</a></div><div class="ttdeci">double tolerance() const </div><div class="ttdoc">Returns the relative tolerance. </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00062">gmres.hpp:62</a></div></div>
<div class="ttc" id="structviennacl_1_1result__of_1_1cpu__value__type_html_aa015d93f419985879a7c13b09633c5c6"><div class="ttname"><a href="structviennacl_1_1result__of_1_1cpu__value__type.html#aa015d93f419985879a7c13b09633c5c6">viennacl::result_of::cpu_value_type::type</a></div><div class="ttdeci">T::ERROR_CANNOT_DEDUCE_CPU_SCALAR_TYPE_FOR_T type</div><div class="ttdef"><b>Definition:</b> <a href="result__of_8hpp_source.html#l00271">result_of.hpp:271</a></div></div>
<div class="ttc" id="vector__proxy_8hpp_html"><div class="ttname"><a href="vector__proxy_8hpp.html">vector_proxy.hpp</a></div><div class="ttdoc">Proxy classes for vectors. </div></div>
<div class="ttc" id="iterative__operations_8hpp_html"><div class="ttname"><a href="iterative__operations_8hpp.html">iterative_operations.hpp</a></div><div class="ttdoc">Implementations of specialized routines for the iterative solvers. </div></div>
<div class="ttc" id="namespaceviennacl_1_1traits_html_a6707f5dab8f482170d2046a605f46ef8"><div class="ttname"><a href="namespaceviennacl_1_1traits.html#a6707f5dab8f482170d2046a605f46ef8">viennacl::traits::context</a></div><div class="ttdeci">viennacl::context context(T const &t)</div><div class="ttdoc">Returns an ID for the currently active memory domain of an object. </div><div class="ttdef"><b>Definition:</b> <a href="traits_2context_8hpp_source.html#l00040">context.hpp:40</a></div></div>
<div class="ttc" id="structviennacl_1_1result__of_1_1cpu__value__type_html"><div class="ttname"><a href="structviennacl_1_1result__of_1_1cpu__value__type.html">viennacl::result_of::cpu_value_type</a></div><div class="ttdoc">Helper meta function for retrieving the main RAM-based value type. Particularly important to obtain T...</div><div class="ttdef"><b>Definition:</b> <a href="result__of_8hpp_source.html#l00269">result_of.hpp:269</a></div></div>
<div class="ttc" id="namespaceviennacl_html_a10b7f8cf6b8864a7aa196d670481a453"><div class="ttname"><a href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a></div><div class="ttdeci">void copy(std::vector< NumericT > &cpu_vec, circulant_matrix< NumericT, AlignmentV > &gpu_mat)</div><div class="ttdoc">Copies a circulant matrix from the std::vector to the OpenCL device (either GPU or multi-core CPU) ...</div><div class="ttdef"><b>Definition:</b> <a href="circulant__matrix_8hpp_source.html#l00150">circulant_matrix.hpp:150</a></div></div>
<div class="ttc" id="classviennacl_1_1vector__base_html_a15c47ae4326098aeaa4ed6b91fc6df9b"><div class="ttname"><a href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">viennacl::vector_base::size</a></div><div class="ttdeci">size_type size() const </div><div class="ttdoc">Returns the length of the vector (cf. std::vector) </div><div class="ttdef"><b>Definition:</b> <a href="vector__def_8hpp_source.html#l00118">vector_def.hpp:118</a></div></div>
<div class="ttc" id="classviennacl_1_1basic__range_html"><div class="ttname"><a href="classviennacl_1_1basic__range.html">viennacl::basic_range</a></div><div class="ttdoc">A range class that refers to an interval [start, stop), where 'start' is included, and 'stop' is excluded. </div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00424">forwards.h:424</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="classviennacl_1_1compressed__matrix_html"><div class="ttname"><a href="classviennacl_1_1compressed__matrix.html">viennacl::compressed_matrix< NumericT ></a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__tag_html_aa9bd21a63747c3f3a2ffe3b726a2a9bb"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__tag.html#aa9bd21a63747c3f3a2ffe3b726a2a9bb">viennacl::linalg::gmres_tag::error</a></div><div class="ttdeci">double error() const </div><div class="ttdoc">Returns the estimated relative error at the end of the solver run. </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00088">gmres.hpp:88</a></div></div>
<div class="ttc" id="classviennacl_1_1vector__base_html_a47350ccdc4b0a24eaea0e8d5f9fe7fec"><div class="ttname"><a href="classviennacl_1_1vector__base.html#a47350ccdc4b0a24eaea0e8d5f9fe7fec">viennacl::vector_base::internal_size</a></div><div class="ttdeci">size_type internal_size() const </div><div class="ttdoc">Returns the internal length of the vector, which is given by size() plus the extra memory due to padd...</div><div class="ttdef"><b>Definition:</b> <a href="vector__def_8hpp_source.html#l00120">vector_def.hpp:120</a></div></div>
<div class="ttc" id="result__of_8hpp_html"><div class="ttname"><a href="result__of_8hpp.html">result_of.hpp</a></div><div class="ttdoc">A collection of compile time type deductions. </div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1gmres__tag_html_afec21365bfdf6b200e6387b898b9c899"><div class="ttname"><a href="classviennacl_1_1linalg_1_1gmres__tag.html#afec21365bfdf6b200e6387b898b9c899">viennacl::linalg::gmres_tag::krylov_dim</a></div><div class="ttdeci">unsigned int krylov_dim() const </div><div class="ttdoc">Returns the maximum dimension of the Krylov space before restart. </div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00072">gmres.hpp:72</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_ad2b2c8a343124143d1ddc2fee8b2ce73"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#ad2b2c8a343124143d1ddc2fee8b2ce73">viennacl::linalg::detail::gmres_householder_reflect</a></div><div class="ttdeci">void gmres_householder_reflect(VectorT &x, VectorT const &h, NumericT beta)</div><div class="ttdef"><b>Definition:</b> <a href="gmres_8hpp_source.html#l00162">gmres.hpp:162</a></div></div>
<div class="ttc" id="classviennacl_1_1coordinate__matrix_html"><div class="ttname"><a href="classviennacl_1_1coordinate__matrix.html">viennacl::coordinate_matrix</a></div><div class="ttdoc">A sparse square matrix, where entries are stored as triplets (i,j, val), where i and j are the row an...</div><div class="ttdef"><b>Definition:</b> <a href="coordinate__matrix_8hpp_source.html#l00186">coordinate_matrix.hpp:186</a></div></div>
<div class="ttc" id="namespaceviennacl_html_aaa5c8726b45bc89a523ca2fa8c42107a"><div class="ttname"><a href="namespaceviennacl.html#aaa5c8726b45bc89a523ca2fa8c42107a">viennacl::fast_copy</a></div><div class="ttdeci">void fast_copy(const const_vector_iterator< SCALARTYPE, ALIGNMENT > &gpu_begin, const const_vector_iterator< SCALARTYPE, ALIGNMENT > &gpu_end, CPU_ITERATOR cpu_begin)</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="gmres_8hpp.html">gmres.hpp</a></li>
<li class="footer">Generated on Wed Jan 20 2016 22:32:42 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>
|
