-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathATSolver2D_8h_source.html
936 lines (934 loc) · 219 KB
/
ATSolver2D_8h_source.html
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
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://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 1.9.1"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>DGtal: ATSolver2D.h 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="navtreedata.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
jax: ["input/TeX","output/HTML-CSS"],
});
</script>
<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.3/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
<link href="doxygen-awesome.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 id="projectalign" style="padding-left: 0.5em;">
<div id="projectname">DGtal
 <span id="projectnumber">1.4.2</span>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.9.1 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
var searchBox = new SearchBox("searchBox", "search",false,'Search','.html');
/* @license-end */
</script>
<script type="text/javascript" src="menudata.js"></script>
<script type="text/javascript" src="menu.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
$(function() {
initMenu('',true,false,'search.php','Search');
$(document).ready(function() { init_search(); });
});
/* @license-end */</script>
<div id="main-nav"></div>
</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">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
$(document).ready(function(){initNavTree('ATSolver2D_8h_source.html',''); initResizable(); });
/* @license-end */
</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)">
</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">ATSolver2D.h</div> </div>
</div><!--header-->
<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span>  </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#pragma once</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>  </div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#if defined(ATSolver2D_RECURSES)</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#error Recursive header files inclusion detected in ATSolver2D.h</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor">#else </span><span class="comment">// defined(ATSolver2D_RECURSES)</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment"></span>#define ATSolver2D_RECURSES</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="preprocessor">#if !defined ATSolver2D_h</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="preprocessor">#define ATSolver2D_h</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// Inclusions</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#include <iostream></span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="preprocessor">#include <sstream></span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="preprocessor">#include <tuple></span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="preprocessor">#include "DGtal/base/Common.h"</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="preprocessor">#include "DGtal/base/ConstAlias.h"</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="preprocessor">#include "DGtal/math/linalg/EigenSupport.h"</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="preprocessor">#include "DGtal/dec/DiscreteExteriorCalculus.h"</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="preprocessor">#include "DGtal/dec/DiscreteExteriorCalculusSolver.h"</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="preprocessor">#include "DGtal/dec/DECHelpers.h"</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  </div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="keyword">namespace </span><a class="code" href="namespaceDGtal.html">DGtal</a></div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> {</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="comment">// template class ATSolver2D</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment"></span> <span class="keyword">template</span> < <span class="keyword">typename</span> TKSpace,</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keyword">typename</span> TLinearAlgebra = EigenLinearAlgebraBackend ></div>
<div class="line"><a name="l00090"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html"> 90</a></span>  <span class="keyword">class </span><a class="code" href="classDGtal_1_1ATSolver2D.html">ATSolver2D</a></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="comment">// ----------------------- Standard services ------------------------------</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  </div>
<div class="line"><a name="l00095"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#afa2b4116a2bcc862b6df458ae067eb4b"> 95</a></span>  <span class="keyword">typedef</span> TKSpace <a class="code" href="classDGtal_1_1ATSolver2D.html#afa2b4116a2bcc862b6df458ae067eb4b">KSpace</a>;</div>
<div class="line"><a name="l00096"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a55bca79bf2ef4b57d3f14bf74e00cd5e"> 96</a></span>  <span class="keyword">typedef</span> TLinearAlgebra <a class="code" href="classDGtal_1_1ATSolver2D.html#a55bca79bf2ef4b57d3f14bf74e00cd5e">LinearAlgebra</a>;</div>
<div class="line"><a name="l00097"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#ac48f83d74c760279204aad8cb1ce3205"> 97</a></span>  <span class="keyword">typedef</span> <a class="code" href="classDGtal_1_1ATSolver2D.html">ATSolver2D< KSpace, LinearAlgebra ></a> <a class="code" href="classDGtal_1_1ATSolver2D.html#ac48f83d74c760279204aad8cb1ce3205">Self</a>;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  </div>
<div class="line"><a name="l00099"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a25191de161019d127bbbcc82c6dcffe2"> 99</a></span>  <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a25191de161019d127bbbcc82c6dcffe2">dimension</a> = KSpace::dimension;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  </div>
<div class="line"><a name="l00103"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aede4e265e44ce612075bb3c15f8690daadb00ed33d4644ea0a15d240658b90d16"> 103</a></span>  <span class="keyword">enum</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#aede4e265e44ce612075bb3c15f8690da">CellOutputPolicy</a> { <a class="code" href="classDGtal_1_1ATSolver2D.html#aede4e265e44ce612075bb3c15f8690daadb00ed33d4644ea0a15d240658b90d16">Average</a>, </div>
<div class="line"><a name="l00104"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aede4e265e44ce612075bb3c15f8690daaf5b10e5f87cc7b7839257bab531fb74a"> 104</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#aede4e265e44ce612075bb3c15f8690daaf5b10e5f87cc7b7839257bab531fb74a">Minimum</a>, </div>
<div class="line"><a name="l00105"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aede4e265e44ce612075bb3c15f8690daa1cfa7b862062261bcc5cfe4fbe5ccc94"> 105</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#aede4e265e44ce612075bb3c15f8690daa1cfa7b862062261bcc5cfe4fbe5ccc94">Maximum</a>, </div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  };</div>
<div class="line"><a name="l00107"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a17b53da8cc48bf5d3da9e94cf3d7c51f"> 107</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1SpaceND.html">KSpace::Space</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a17b53da8cc48bf5d3da9e94cf3d7c51f">Space</a>;</div>
<div class="line"><a name="l00108"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aa5901cc63f4066bea0a57f21600e685a"> 108</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1PointVector.html">Space::RealVector</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#aa5901cc63f4066bea0a57f21600e685a">RealVector</a>;</div>
<div class="line"><a name="l00109"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a47214523de8fccd4ec0436b85be4d3cb"> 109</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1PointVector.html#ab5f7548d4edc0d8edb4b64cc332db8f2">RealVector::Component</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a47214523de8fccd4ec0436b85be4d3cb">Scalar</a>;</div>
<div class="line"><a name="l00110"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a4fd154d5f3f9a31d16f812b9e9602fbd"> 110</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structDGtal_1_1SignedKhalimskyCell.html">KSpace::SCell</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a4fd154d5f3f9a31d16f812b9e9602fbd">SCell</a>;</div>
<div class="line"><a name="l00111"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#ad57b159c5d672171e2d321d243464b3a"> 111</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">KSpace::Cell</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#ad57b159c5d672171e2d321d243464b3a">Cell</a>;</div>
<div class="line"><a name="l00112"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a0c80067d705837a6cbd45ef54778433d"> 112</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structDGtal_1_1SignedKhalimskyCell.html">KSpace::Surfel</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a0c80067d705837a6cbd45ef54778433d">Surfel</a>;</div>
<div class="line"><a name="l00113"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a423dedbfb78fa3d29b947360a2fa1abf"> 113</a></span>  <span class="keyword">typedef</span> <a class="code" href="classDGtal_1_1HyperRectDomain.html">HyperRectDomain<Space></a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a423dedbfb78fa3d29b947360a2fa1abf">Domain</a>;</div>
<div class="line"><a name="l00114"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a966e9e7334baff72542aa5ffd50fb670"> 114</a></span>  <span class="keyword">typedef</span> <a class="code" href="classDGtal_1_1DiscreteExteriorCalculus.html">DiscreteExteriorCalculus<2,dimension, LinearAlgebra></a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a966e9e7334baff72542aa5ffd50fb670">Calculus</a>;</div>
<div class="line"><a name="l00115"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a9fc1d6faa1e173efa7d3490e39abf403"> 115</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> KSpace::template SurfelMap<double>::Type <a class="code" href="classDGtal_1_1ATSolver2D.html#a9fc1d6faa1e173efa7d3490e39abf403">SmallestEpsilonMap</a>;</div>
<div class="line"><a name="l00116"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36"> 116</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1DiscreteExteriorCalculus.html#ab4367cb06a628fc96e6c637d0f822df0">Calculus::Index</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a>;</div>
<div class="line"><a name="l00117"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a4276d97eaa8663a0689d50c0cdda46bb"> 117</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1KForm.html">Calculus::PrimalForm0</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a4276d97eaa8663a0689d50c0cdda46bb">PrimalForm0</a>;</div>
<div class="line"><a name="l00118"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a6f50e5d7dee9c71461130c1548c1edc1"> 118</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1KForm.html">Calculus::PrimalForm1</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a6f50e5d7dee9c71461130c1548c1edc1">PrimalForm1</a>;</div>
<div class="line"><a name="l00119"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#ab8b5510ecfe47577444bd8bbe56fdfb8"> 119</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1KForm.html">Calculus::PrimalForm2</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#ab8b5510ecfe47577444bd8bbe56fdfb8">PrimalForm2</a>;</div>
<div class="line"><a name="l00120"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aaa633904ce76ed3a46428243ef909f6c"> 120</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1LinearOperator.html">Calculus::PrimalIdentity0</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#aaa633904ce76ed3a46428243ef909f6c">PrimalIdentity0</a>;</div>
<div class="line"><a name="l00121"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a3ce0376a76b6b7c28d0483193ba76714"> 121</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1LinearOperator.html">Calculus::PrimalIdentity1</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a3ce0376a76b6b7c28d0483193ba76714">PrimalIdentity1</a>;</div>
<div class="line"><a name="l00122"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a7a4bba850da56d1718eb2d860e3e0eaa"> 122</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1LinearOperator.html">Calculus::PrimalIdentity2</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a7a4bba850da56d1718eb2d860e3e0eaa">PrimalIdentity2</a>;</div>
<div class="line"><a name="l00123"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a1ece7aebeff8a3eec8941d091474eb53"> 123</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1LinearOperator.html">Calculus::PrimalDerivative0</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a1ece7aebeff8a3eec8941d091474eb53">PrimalDerivative0</a>;</div>
<div class="line"><a name="l00124"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a85c07dbe94ccebc4796eddbe9dcbcd4b"> 124</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1LinearOperator.html">Calculus::PrimalDerivative1</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a85c07dbe94ccebc4796eddbe9dcbcd4b">PrimalDerivative1</a>;</div>
<div class="line"><a name="l00125"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a51b87e769d2450bccd86bdc45d792c9c"> 125</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1LinearOperator.html">Calculus::PrimalAntiderivative1</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a51b87e769d2450bccd86bdc45d792c9c">PrimalAntiderivative1</a>;</div>
<div class="line"><a name="l00126"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a9c2c3aef54916e26a9532602adedc594"> 126</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1LinearOperator.html">Calculus::PrimalAntiderivative2</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a9c2c3aef54916e26a9532602adedc594">PrimalAntiderivative2</a>;</div>
<div class="line"><a name="l00127"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a25b7904c9073c351c31051900374aae9"> 127</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1LinearOperator.html">Calculus::PrimalHodge0</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a25b7904c9073c351c31051900374aae9">PrimalHodge0</a>;</div>
<div class="line"><a name="l00128"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aa505567d0cbde4340e447f31cabca9d8"> 128</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1LinearOperator.html">Calculus::PrimalHodge1</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#aa505567d0cbde4340e447f31cabca9d8">PrimalHodge1</a>;</div>
<div class="line"><a name="l00129"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a120ac6c13bc482b8a7f21fe25c96fa96"> 129</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classDGtal_1_1LinearOperator.html">Calculus::PrimalHodge2</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a120ac6c13bc482b8a7f21fe25c96fa96">PrimalHodge2</a>;</div>
<div class="line"><a name="l00130"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aa7ade8239ac530e34ff0405cc5c8f46f"> 130</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> KSpace::template SurfelMap<Index>::Type <a class="code" href="classDGtal_1_1ATSolver2D.html#aa7ade8239ac530e34ff0405cc5c8f46f">Surfel2IndexMap</a>;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="comment">// SparseLU is so much faster than SparseQR</span></div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="comment">// SimplicialLLT is much faster than SparseLU</span></div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="comment">// SimplicialLDLT is as fast as SimplicialLLT but more robust</span></div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="comment">// typedef EigenLinearAlgebraBackend::SolverSparseQR LinearAlgebraSolver;</span></div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="comment">// typedef EigenLinearAlgebraBackend::SolverSparseLU LinearAlgebraSolver;</span></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="comment">// typedef EigenLinearAlgebraBackend::SolverSimplicialLLT LinearAlgebraSolver;</span></div>
<div class="line"><a name="l00138"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a559189aa3b4834e4af30439ab7796aba"> 138</a></span>  <span class="keyword">typedef</span> <a class="code" href="structDGtal_1_1EigenLinearAlgebraBackend.html#a164f5eddcb81f4d6fd688fefc91057c9">EigenLinearAlgebraBackend::SolverSimplicialLDLT</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a559189aa3b4834e4af30439ab7796aba">LinearAlgebraSolver</a>;</div>
<div class="line"><a name="l00139"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#ad62971b62a4601b991db67ed2ef69fb6"> 139</a></span>  <span class="keyword">typedef</span> <a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html">DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 2, PRIMAL, 2, PRIMAL></a> <a class="code" href="classDGtal_1_1ATSolver2D.html#ad62971b62a4601b991db67ed2ef69fb6">SolverU2</a>;</div>
<div class="line"><a name="l00140"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#abb06d49e7ede42c74b9768b2387156ad"> 140</a></span>  <span class="keyword">typedef</span> <a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html">DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL></a> <a class="code" href="classDGtal_1_1ATSolver2D.html#abb06d49e7ede42c74b9768b2387156ad">SolverV0</a>;</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  </div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00144"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e"> 144</a></span>  <a class="code" href="classDGtal_1_1CountedConstPtrOrConstPtr.html">CountedConstPtrOrConstPtr< Calculus ></a> <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>;</div>
<div class="line"><a name="l00146"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aecc1cb13fbf576486331e9cbda695eca"> 146</a></span>  <a class="code" href="classDGtal_1_1LinearOperator.html">PrimalDerivative0</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#aecc1cb13fbf576486331e9cbda695eca">primal_D0</a>;</div>
<div class="line"><a name="l00148"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#ab9b12aea6bd78758f5f05aeb256916e1"> 148</a></span>  <a class="code" href="classDGtal_1_1LinearOperator.html">PrimalDerivative1</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#ab9b12aea6bd78758f5f05aeb256916e1">primal_D1</a>;</div>
<div class="line"><a name="l00150"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#af04301709ce9ba5dd2233acde8642301"> 150</a></span>  <a class="code" href="classDGtal_1_1LinearOperator.html">PrimalDerivative0</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#af04301709ce9ba5dd2233acde8642301">M01</a>; </div>
<div class="line"><a name="l00152"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a68577ab02e5f3f631739243a437cffd7"> 152</a></span>  <a class="code" href="classDGtal_1_1LinearOperator.html">PrimalDerivative1</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a68577ab02e5f3f631739243a437cffd7">M12</a>; </div>
<div class="line"><a name="l00154"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a78262d79c4f40544ec8eac15c68fa712"> 154</a></span>  <a class="code" href="classDGtal_1_1LinearOperator.html">PrimalAntiderivative2</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a78262d79c4f40544ec8eac15c68fa712">primal_AD2</a>;</div>
<div class="line"><a name="l00156"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a37f5070cd69ec86f319d04546236c3e2"> 156</a></span>  <a class="code" href="classDGtal_1_1LinearOperator.html">PrimalIdentity2</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a37f5070cd69ec86f319d04546236c3e2">alpha_Id2</a>;</div>
<div class="line"><a name="l00158"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#abd1939fe7e7775c22a381f07306b8104"> 158</a></span>  <a class="code" href="classDGtal_1_1LinearOperator.html">PrimalIdentity0</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#abd1939fe7e7775c22a381f07306b8104">l_1_over_4e_Id0</a>;</div>
<div class="line"><a name="l00160"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7"> 160</a></span>  std::vector<PrimalForm2> <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>;</div>
<div class="line"><a name="l00162"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c"> 162</a></span>  std::vector<PrimalForm2> <a class="code" href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c">alpha_g2</a>;</div>
<div class="line"><a name="l00164"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a362e088d0dc6e3230fc7ff2cea53d247"> 164</a></span>  std::vector<PrimalForm2> <a class="code" href="classDGtal_1_1ATSolver2D.html#a362e088d0dc6e3230fc7ff2cea53d247">u2</a>;</div>
<div class="line"><a name="l00167"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a93f2d93034f48846c70d8ba848a79795"> 167</a></span>  <a class="code" href="classDGtal_1_1KForm.html">PrimalForm0</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a93f2d93034f48846c70d8ba848a79795">v0</a>;</div>
<div class="line"><a name="l00169"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#acf4463f93c45c3b40f5c921a5914312e"> 169</a></span>  <a class="code" href="classDGtal_1_1KForm.html">PrimalForm0</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#acf4463f93c45c3b40f5c921a5914312e">former_v0</a>;</div>
<div class="line"><a name="l00171"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a7332a00eda9c5a8f2cca3283df4fb97c"> 171</a></span>  <a class="code" href="classDGtal_1_1KForm.html">PrimalForm0</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a7332a00eda9c5a8f2cca3283df4fb97c">l_1_over_4e</a>;</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  </div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="comment">// The map Surfel -> Index that gives the index of the surfel in 2-forms.</span></div>
<div class="line"><a name="l00175"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aa10fb1c8ee0c9873a9abe3d6cd04eea1"> 175</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#aa7ade8239ac530e34ff0405cc5c8f46f">Surfel2IndexMap</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#aa10fb1c8ee0c9873a9abe3d6cd04eea1">surfel2idx</a>; </div>
<div class="line"><a name="l00178"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a6934e9269b94e7c454824cff61bda4b2"> 178</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a9fc1d6faa1e173efa7d3490e39abf403">SmallestEpsilonMap</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a6934e9269b94e7c454824cff61bda4b2">smallest_epsilon_map</a>;</div>
<div class="line"><a name="l00181"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a5aea21e7b14b68c9d0e74acdc39b73a8"> 181</a></span>  <span class="keywordtype">double</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a5aea21e7b14b68c9d0e74acdc39b73a8">alpha</a>;</div>
<div class="line"><a name="l00184"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aceea9eaa1d4e48105f531cb288bf4fef"> 184</a></span>  <span class="keywordtype">double</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#aceea9eaa1d4e48105f531cb288bf4fef">lambda</a>;</div>
<div class="line"><a name="l00187"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#afe7dfc2d191ecdf4b86ee43220fc6dc7"> 187</a></span>  <span class="keywordtype">double</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#afe7dfc2d191ecdf4b86ee43220fc6dc7">epsilon</a>;</div>
<div class="line"><a name="l00189"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#acd57ddea1029fe4bbd9cc3b946c66034"> 189</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#acd57ddea1029fe4bbd9cc3b946c66034">normalize_u2</a>;</div>
<div class="line"><a name="l00191"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0"> 191</a></span>  <span class="keywordtype">int</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a>;</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  </div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="comment">// ----------------------- Standard services ------------------------------</span></div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment"></span> </div>
<div class="line"><a name="l00202"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a3d53f156dd63e507459e1e6f90bee138"> 202</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a3d53f156dd63e507459e1e6f90bee138">ATSolver2D</a>( <a class="code" href="classDGtal_1_1ConstAlias.html">ConstAlias< Calculus ></a> aCalculus, <span class="keywordtype">int</span> aVerbose = 0 )</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  : <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>( aCalculus ),</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#aecc1cb13fbf576486331e9cbda695eca">primal_D0</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ), <a class="code" href="classDGtal_1_1ATSolver2D.html#ab9b12aea6bd78758f5f05aeb256916e1">primal_D1</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ),</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#af04301709ce9ba5dd2233acde8642301">M01</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ), <a class="code" href="classDGtal_1_1ATSolver2D.html#a68577ab02e5f3f631739243a437cffd7">M12</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ), <a class="code" href="classDGtal_1_1ATSolver2D.html#a78262d79c4f40544ec8eac15c68fa712">primal_AD2</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ),</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a37f5070cd69ec86f319d04546236c3e2">alpha_Id2</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ), <a class="code" href="classDGtal_1_1ATSolver2D.html#abd1939fe7e7775c22a381f07306b8104">l_1_over_4e_Id0</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ),</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>(), <a class="code" href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c">alpha_g2</a>(), u2(), v0( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ), <a class="code" href="classDGtal_1_1ATSolver2D.html#acf4463f93c45c3b40f5c921a5914312e">former_v0</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ),</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a7332a00eda9c5a8f2cca3283df4fb97c">l_1_over_4e</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ), <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a>( aVerbose )</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  {</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 )</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"[ATSolver::ATSolver] "</span> << *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> << std::endl;</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a9adf8bd493312d3a4feb100575fa5146">initOperators</a>();</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keyword">const</span> <span class="keyword">auto</span> size2 = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->kFormLength( 2, <a class="code" href="namespaceDGtal.html#ab8007ddbb5627666913e18c3b951745da7b7d86a1d82efbe8b9bc0ad3c7c80bd7">PRIMAL</a> );</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keywordflow">for</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> index = 0; index < size2; ++<a class="code" href="testBits_8cpp.html#abf1224ffcf053d0b7990122fcef93bc9">index</a>) {</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keyword">const</span> <span class="keyword">auto</span>& calculus_cell = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->getSCell( 2, <a class="code" href="namespaceDGtal.html#ab8007ddbb5627666913e18c3b951745da7b7d86a1d82efbe8b9bc0ad3c7c80bd7">PRIMAL</a>, index );</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#aa10fb1c8ee0c9873a9abe3d6cd04eea1">surfel2idx</a>[ calculus_cell ] = <a class="code" href="testBits_8cpp.html#abf1224ffcf053d0b7990122fcef93bc9">index</a>;</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  }</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  }</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  </div>
<div class="line"><a name="l00223"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aebd65b0edd0d5018015092e8aa74141c"> 223</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#aebd65b0edd0d5018015092e8aa74141c">ATSolver2D</a>() = <span class="keyword">delete</span>;</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  </div>
<div class="line"><a name="l00228"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#ad8ef0a982f30c949beb422687931a428"> 228</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ad8ef0a982f30c949beb422687931a428">~ATSolver2D</a>() = <span class="keywordflow">default</span>;</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  </div>
<div class="line"><a name="l00234"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#af39a545e086dbe2509ac81c72c46f3e8"> 234</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#af39a545e086dbe2509ac81c72c46f3e8">ATSolver2D</a> ( <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html">ATSolver2D</a> & other ) = <span class="keywordflow">default</span>;</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  </div>
<div class="line"><a name="l00240"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a9cd935c7278fa1c6a413908565952638"> 240</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a9cd935c7278fa1c6a413908565952638">ATSolver2D</a> ( <a class="code" href="classDGtal_1_1ATSolver2D.html">ATSolver2D</a> && other ) = <span class="keywordflow">default</span>;</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  </div>
<div class="line"><a name="l00247"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aa5666abdbf81ceecf6802d754233c6c3"> 247</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html">ATSolver2D</a> & <a class="code" href="classDGtal_1_1ATSolver2D.html#aa5666abdbf81ceecf6802d754233c6c3">operator= </a>( <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html">ATSolver2D</a> & other ) = <span class="keywordflow">default</span>;</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  </div>
<div class="line"><a name="l00254"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#abf19584bcfe4c44a73c0610f50be9243"> 254</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html">ATSolver2D</a> & <a class="code" href="classDGtal_1_1ATSolver2D.html#aa5666abdbf81ceecf6802d754233c6c3">operator= </a>( <a class="code" href="classDGtal_1_1ATSolver2D.html">ATSolver2D</a> && other ) = <span class="keywordflow">default</span>;</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  </div>
<div class="line"><a name="l00258"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a7853f33b9a33d2744130cc29ab7cbfea"> 258</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a7853f33b9a33d2744130cc29ab7cbfea">size</a>( <span class="keyword">const</span> <span class="keywordtype">int</span> order )<span class="keyword"> const</span></div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="keywordflow">return</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->kFormLength(order, <a class="code" href="namespaceDGtal.html#ab8007ddbb5627666913e18c3b951745da7b7d86a1d82efbe8b9bc0ad3c7c80bd7">PRIMAL</a>);</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>  </div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  </div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  </div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="comment">// ----------------------- Initialization services ------------------------------</span></div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  </div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> VectorFieldInput, <span class="keyword">typename</span> SurfelRangeConstIterator></div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keywordtype">void</span></div>
<div class="line"><a name="l00288"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a639bc75c1b8c9d67a5002c960c579aec"> 288</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a639bc75c1b8c9d67a5002c960c579aec">initInputVectorFieldU2</a>( <span class="keyword">const</span> VectorFieldInput& input,</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  SurfelRangeConstIterator itB, SurfelRangeConstIterator itE,</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="keywordtype">bool</span> normalize = <span class="keyword">false</span> )</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  {</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 )</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">"[ATSolver2D::initInputVectorFieldU2] Initializing input data"</span> );</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  ASSERT( ! input.empty() );</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="keyword">const</span> <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> N = input[ 0 ].size();</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"input g as "</span> << N << <span class="stringliteral">" 2-forms."</span> << std::endl;</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a> = std::vector<PrimalForm2>( N, <a class="code" href="classDGtal_1_1ATSolver2D.html#ab8b5510ecfe47577444bd8bbe56fdfb8">PrimalForm2</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ) );</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c">alpha_g2</a> = std::vector<PrimalForm2>( N, <a class="code" href="classDGtal_1_1ATSolver2D.html#ab8b5510ecfe47577444bd8bbe56fdfb8">PrimalForm2</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ) );</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> i = 0;</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="keywordflow">for</span> ( <span class="keyword">auto</span> it = itB; it != itE; ++it, ++i )</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  {</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> idx = <a class="code" href="classDGtal_1_1ATSolver2D.html#aa10fb1c8ee0c9873a9abe3d6cd04eea1">surfel2idx</a>[ *it ];</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="keywordflow">for</span> ( <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> k = 0; k < N; ++k )</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>[ k ].myContainer( idx ) = input[ i ][ k ]; </div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  }</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <span class="comment">// u = g at the beginning</span></div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 )</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Unknown u[:] = g[:] at beginning."</span> << std::endl;</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  u2 = <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>;</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="comment">// v = 1 at the beginning</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Unknown v = 1"</span> << std::endl;</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  v0 = <a class="code" href="classDGtal_1_1KForm.html#a0f34f82e9a9dbc012dfb727b552806a6">PrimalForm0::ones</a>(*<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>);</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#acd57ddea1029fe4bbd9cc3b946c66034">normalize_u2</a> = normalize;</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="l00328"></a><span class="lineno"> 328</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ScalarFieldInput, <span class="keyword">typename</span> SurfelRangeConstIterator></div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="keywordtype">void</span></div>
<div class="line"><a name="l00330"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a2f154cab3aed8a87209a940db41b8364"> 330</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a2f154cab3aed8a87209a940db41b8364">initInputScalarFieldU2</a>( <span class="keyword">const</span> ScalarFieldInput& input,</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  SurfelRangeConstIterator itB, SurfelRangeConstIterator itE )</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="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 )</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">"[ATSolver2D::initInputVectorFieldU2] Initializing input data"</span> );</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  ASSERT( ! input.empty() );</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"input g as one 2-form."</span> << std::endl;</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a> = std::vector<PrimalForm2>( 1, <a class="code" href="classDGtal_1_1ATSolver2D.html#ab8b5510ecfe47577444bd8bbe56fdfb8">PrimalForm2</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ) );</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c">alpha_g2</a> = std::vector<PrimalForm2>( 1, <a class="code" href="classDGtal_1_1ATSolver2D.html#ab8b5510ecfe47577444bd8bbe56fdfb8">PrimalForm2</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ) );</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> i = 0;</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="keywordflow">for</span> ( <span class="keyword">auto</span> it = itB; it != itE; ++it, ++i )</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  {</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> idx = <a class="code" href="classDGtal_1_1ATSolver2D.html#aa10fb1c8ee0c9873a9abe3d6cd04eea1">surfel2idx</a>[ *it ];</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>[ 0 ].myContainer( idx ) = input[ i ]; </div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  }</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <span class="comment">// u = g at the beginning</span></div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 )</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Unknown u[:] = g[:] at beginning."</span> << std::endl;</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  u2 = <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>;</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="comment">// v = 1 at the beginning</span></div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Unknown v = 1"</span> << std::endl;</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  v0 = <a class="code" href="classDGtal_1_1KForm.html#a0f34f82e9a9dbc012dfb727b552806a6">PrimalForm0::ones</a>(*<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>);</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#acd57ddea1029fe4bbd9cc3b946c66034">normalize_u2</a> = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  }</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  </div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  </div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ScalarVector></div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  <a class="code" href="fullConvexitySphereGeodesics_8cpp.html#ab053a8ae7537e4f87fa9a46962f7617a">Index</a></div>
<div class="line"><a name="l00371"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a0b9e41763b2efad4573222df2ac75016"> 371</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a0b9e41763b2efad4573222df2ac75016">initInputVectorFieldU2</a>( <span class="keyword">const</span> std::map<Surfel,ScalarVector>& input,</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <span class="keywordtype">bool</span> normalize = <span class="keyword">false</span> )</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  {</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">"[ATSolver2D::initVectorInput] Initializing input data"</span> );</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"discontinuity 0-form v = 1."</span> << std::endl;</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  <span class="keyword">const</span> <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> N = ScalarVector().size();</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"input g as "</span> << N << <span class="stringliteral">" 2-forms."</span> << std::endl;</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a> = std::vector<PrimalForm2>( N, <a class="code" href="classDGtal_1_1ATSolver2D.html#ab8b5510ecfe47577444bd8bbe56fdfb8">PrimalForm2</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ) );</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c">alpha_g2</a> = std::vector<PrimalForm2>( N, <a class="code" href="classDGtal_1_1ATSolver2D.html#ab8b5510ecfe47577444bd8bbe56fdfb8">PrimalForm2</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ) );</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  <span class="keyword">const</span> ScalarVector zero;</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> nbok = 0;</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="keywordflow">for</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> index = 0; index < <a class="code" href="classDGtal_1_1ATSolver2D.html#a7853f33b9a33d2744130cc29ab7cbfea">size</a>(2); index++)</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  {</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1SignedKhalimskyCell.html">SCell</a>& cell = <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>[ 0 ].getSCell( index );</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <span class="keyword">const</span> <span class="keyword">auto</span> it = input.find( cell ); </div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  <span class="keyword">const</span> <span class="keyword">auto</span> n = ( it != input.end() ) ? it->second : zero;</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  nbok += ( it != input.end() ) ? 1 : 0;</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <span class="keywordflow">for</span> ( <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> k = 0; k < N; ++k )</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>[ k ].myContainer( index ) = n[ k ];</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="comment">// u = g at the beginning</span></div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 )</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Unknown u[:] = g[:] at beginning."</span> << std::endl;</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  u2 = <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>;</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  <span class="comment">// v = 1 at the beginning</span></div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Unknown v = 1"</span> << std::endl;</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  v0 = <a class="code" href="classDGtal_1_1KForm.html#a0f34f82e9a9dbc012dfb727b552806a6">PrimalForm0::ones</a>(*<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>);</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#acd57ddea1029fe4bbd9cc3b946c66034">normalize_u2</a> = normalize;</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  <span class="keywordflow">return</span> nbok;</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  }</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  </div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  <a class="code" href="fullConvexitySphereGeodesics_8cpp.html#ab053a8ae7537e4f87fa9a46962f7617a">Index</a></div>
<div class="line"><a name="l00411"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a14527d6ddd86aa606d6a23cb20b786ad"> 411</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a14527d6ddd86aa606d6a23cb20b786ad">initInputScalarFieldU2</a>( <span class="keyword">const</span> std::map<Surfel,Scalar>& input )</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  {</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">"[ATSolver2D::initScalarInput] Initializing input data"</span> );</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"discontinuity 0-form v = 1."</span> << std::endl;</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  v0 = <a class="code" href="classDGtal_1_1KForm.html#a0f34f82e9a9dbc012dfb727b552806a6">PrimalForm0::ones</a>(*<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>);</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"input g as one 2-form."</span> << std::endl;</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a> = std::vector<PrimalForm2>( 1, <a class="code" href="classDGtal_1_1ATSolver2D.html#ab8b5510ecfe47577444bd8bbe56fdfb8">PrimalForm2</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ) );</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c">alpha_g2</a> = std::vector<PrimalForm2>( 1, <a class="code" href="classDGtal_1_1ATSolver2D.html#ab8b5510ecfe47577444bd8bbe56fdfb8">PrimalForm2</a>( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> ) );</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a47214523de8fccd4ec0436b85be4d3cb">Scalar</a> zero;</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> nbok = 0;</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="keywordflow">for</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> index = 0; index < <a class="code" href="classDGtal_1_1ATSolver2D.html#a7853f33b9a33d2744130cc29ab7cbfea">size</a>(2); index++)</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  {</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1SignedKhalimskyCell.html">SCell</a>& cell = <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>[ 0 ].getSCell( index );</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <span class="keyword">const</span> <span class="keyword">auto</span> it = input.find( cell ); </div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  <span class="keyword">const</span> <span class="keyword">auto</span> n = ( it != input.end() ) ? *it : zero;</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  nbok += ( it != input.end() ) ? 1 : 0;</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>[ 0 ].myContainer( index ) = n;</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  }</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  <span class="comment">// u = g at the beginning</span></div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Unknown u[:] = g[:] at beginning."</span> << std::endl;</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  u2 = <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>;</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  <span class="comment">// v = 1 at the beginning</span></div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Unknown v = 1"</span> << std::endl;</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  v0 = <a class="code" href="classDGtal_1_1KForm.html#a0f34f82e9a9dbc012dfb727b552806a6">PrimalForm0::ones</a>(*<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>);</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#acd57ddea1029fe4bbd9cc3b946c66034">normalize_u2</a> = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  <span class="keywordflow">return</span> nbok;</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  }</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  </div>
<div class="line"><a name="l00444"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a368accf722d9e6d3ed3f02e7b2c350f3"> 444</a></span>  <span class="keywordtype">void</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a368accf722d9e6d3ed3f02e7b2c350f3">setUp</a>( <span class="keywordtype">double</span> a, <span class="keywordtype">double</span> l )</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  {</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  <span class="keyword">const</span> <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> N = (<a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a>)<a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>.size();</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  alpha = a;</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#aceea9eaa1d4e48105f531cb288bf4fef">lambda</a> = l;</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a37f5070cd69ec86f319d04546236c3e2">alpha_Id2</a> = alpha * <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->template identity<2, PRIMAL>();</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  <span class="keywordflow">for</span> ( <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> k = 0; k < N; ++k )</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c">alpha_g2</a>[ k ] = alpha * <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>[ k ];</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  }</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  </div>
<div class="line"><a name="l00463"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a9b11764a4db07a8d2c66a9ddd645667b"> 463</a></span>  <span class="keywordtype">void</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a9b11764a4db07a8d2c66a9ddd645667b">setUp</a>( <span class="keywordtype">double</span> a, <span class="keywordtype">double</span> l, <span class="keyword">const</span> std::map<Surfel,Scalar>& weights )</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  {</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="keyword">const</span> <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> N = <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>.size();</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  alpha = a;</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#aceea9eaa1d4e48105f531cb288bf4fef">lambda</a> = l;</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  <a class="code" href="classDGtal_1_1KForm.html">PrimalForm2</a> w_form( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> );</div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 )</div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Using variable weights for fitting (alpha term)"</span> << std::endl;</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  <span class="keywordflow">for</span> ( <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> k = 0; k < N; ++k )</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c">alpha_g2</a>[ k ] = alpha * <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>[ k ];</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  <span class="keywordflow">for</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> index = 0; index < <a class="code" href="classDGtal_1_1ATSolver2D.html#a7853f33b9a33d2744130cc29ab7cbfea">size</a>( 2 ); index++)</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>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1SignedKhalimskyCell.html">SCell</a>& cell = <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>[ 0 ].getSCell( index );</div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a47214523de8fccd4ec0436b85be4d3cb">Scalar</a>& w = weights[ cell ];</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  w_form.<a class="code" href="classDGtal_1_1KForm.html#a19e859f462f1d851550465b7fcc2c68d">myContainer</a>( index ) = w;</div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  <span class="keywordflow">for</span> ( <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> k = 0; k < N; ++k )</div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c">alpha_g2</a>[ k ].myContainer( index ) *= w;</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  }</div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a37f5070cd69ec86f319d04546236c3e2">alpha_Id2</a> = alpha * diagonal( w_form );</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>  </div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> AlphaWeights, <span class="keyword">typename</span> SurfelRangeConstIterator></div>
<div class="line"><a name="l00499"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a1820dfbc6f093ed24e6911707c75404a"> 499</a></span>  <span class="keywordtype">void</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a1820dfbc6f093ed24e6911707c75404a">setUp</a>( <span class="keywordtype">double</span> a, <span class="keywordtype">double</span> l,</div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  <span class="keyword">const</span> AlphaWeights& weights,</div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  SurfelRangeConstIterator itB, SurfelRangeConstIterator itE )</div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  {</div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  <span class="keyword">const</span> <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> N = <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>.size();</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  alpha = a;</div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#aceea9eaa1d4e48105f531cb288bf4fef">lambda</a> = l;</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  <a class="code" href="classDGtal_1_1KForm.html">PrimalForm2</a> w_form( *<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a> );</div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 )</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Using variable weights for fitting (alpha term)"</span> << std::endl;</div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  <span class="keywordflow">for</span> ( <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> k = 0; k < N; ++k )</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c">alpha_g2</a>[ k ] = alpha * <a class="code" href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">g2</a>[ k ];</div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> i = 0;</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  <span class="keywordflow">for</span> ( <span class="keyword">auto</span> it = itB; it != itE; ++it, ++i )</div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  {</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> idx = <a class="code" href="classDGtal_1_1ATSolver2D.html#aa10fb1c8ee0c9873a9abe3d6cd04eea1">surfel2idx</a>[ *it ];</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a47214523de8fccd4ec0436b85be4d3cb">Scalar</a> w = weights[ i ];</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  w_form.<a class="code" href="classDGtal_1_1KForm.html#a19e859f462f1d851550465b7fcc2c68d">myContainer</a>( idx ) = w;</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  <span class="keywordflow">for</span> ( <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> k = 0; k < N; ++k )</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c">alpha_g2</a>[ k ].myContainer( idx ) *= w;</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>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a37f5070cd69ec86f319d04546236c3e2">alpha_Id2</a> = alpha * diagonal( w_form );</div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  }</div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  </div>
<div class="line"><a name="l00525"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a6122683e9eaf0a7c08cacf81dc253131"> 525</a></span>  <span class="keywordtype">void</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a6122683e9eaf0a7c08cacf81dc253131">setEpsilon</a>( <span class="keywordtype">double</span> e )</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>  <a class="code" href="classDGtal_1_1ATSolver2D.html#afe7dfc2d191ecdf4b86ee43220fc6dc7">epsilon</a> = e;</div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a7332a00eda9c5a8f2cca3283df4fb97c">l_1_over_4e</a> = (<a class="code" href="classDGtal_1_1ATSolver2D.html#aceea9eaa1d4e48105f531cb288bf4fef">lambda</a>/4./<a class="code" href="classDGtal_1_1ATSolver2D.html#afe7dfc2d191ecdf4b86ee43220fc6dc7">epsilon</a>)*<a class="code" href="classDGtal_1_1KForm.html#a0f34f82e9a9dbc012dfb727b552806a6">PrimalForm0::ones</a>(*<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>);</div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#abd1939fe7e7775c22a381f07306b8104">l_1_over_4e_Id0</a> = (<a class="code" href="classDGtal_1_1ATSolver2D.html#aceea9eaa1d4e48105f531cb288bf4fef">lambda</a>/4./<a class="code" href="classDGtal_1_1ATSolver2D.html#afe7dfc2d191ecdf4b86ee43220fc6dc7">epsilon</a>)*<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->template identity<0, PRIMAL>();</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  }</div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  </div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  </div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  <span class="comment">// ----------------------- Optimization services ------------------------------</span></div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  </div>
<div class="line"><a name="l00546"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a26e5a500532d1a80d4a0b89f1462f4ff"> 546</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a26e5a500532d1a80d4a0b89f1462f4ff">solveOneAlternateStep</a>()</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="keywordtype">bool</span> solve_ok = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>(<span class="stringliteral">"Solving for u as a 2-form"</span>);</div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <a class="code" href="classDGtal_1_1KForm.html">PrimalForm1</a> v1_squared = <a class="code" href="classDGtal_1_1ATSolver2D.html#af04301709ce9ba5dd2233acde8642301">M01</a>*<a class="code" href="classDGtal_1_1ATSolver2D.html#a93f2d93034f48846c70d8ba848a79795">v0</a>;</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  v1_squared.<a class="code" href="classDGtal_1_1KForm.html#a19e859f462f1d851550465b7fcc2c68d">myContainer</a>.array() = v1_squared.<a class="code" href="classDGtal_1_1KForm.html#a19e859f462f1d851550465b7fcc2c68d">myContainer</a>.array().square();</div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1LinearOperator.html">PrimalIdentity2</a> ope_u2 = <a class="code" href="classDGtal_1_1ATSolver2D.html#a37f5070cd69ec86f319d04546236c3e2">alpha_Id2</a></div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  + <a class="code" href="classDGtal_1_1ATSolver2D.html#a78262d79c4f40544ec8eac15c68fa712">primal_AD2</a>.<a class="code" href="classDGtal_1_1LinearOperator.html#aeee5924a3cc7b145068dacb48611157c">transpose</a>() * <a class="code" href="namespaceDGtal_1_1dec__helper.html#a6b01f3b8906df8056bf147dd40935738">dec_helper::diagonal</a>( v1_squared ) * <a class="code" href="classDGtal_1_1ATSolver2D.html#a78262d79c4f40544ec8eac15c68fa712">primal_AD2</a>;</div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  </div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Prefactoring matrix U associated to u"</span> << std::endl;</div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  <a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html">SolverU2</a> solver_u2;</div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  solver_u2.<a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#a90f2a9e43a13293e6368b63298363b60">compute</a>( ope_u2 );</div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <span class="keywordflow">for</span> ( <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> d = 0; d < u2.size(); ++d )</div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  {</div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Solving U u["</span> << d << <span class="stringliteral">"] = a g["</span> << d << <span class="stringliteral">"]"</span> << std::endl;</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  u2[ d ] = solver_u2.<a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#a7673281a29a04ef2978bad9b373c2382">solve</a>( <a class="code" href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c">alpha_g2</a>[ d ] );</div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">" => "</span> << ( solver_u2.<a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#a073f1c0cdb349421b1a6d499fefc6052">isValid</a>() ? <span class="stringliteral">"OK"</span> : <span class="stringliteral">"ERROR"</span> )</div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  << <span class="stringliteral">" "</span> << solver_u2.<a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#ab26e3418601a9779709cf92f4366cefe">myLinearAlgebraSolver</a>.info() << std::endl;</div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  solve_ok = solve_ok && solver_u2.<a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#a073f1c0cdb349421b1a6d499fefc6052">isValid</a>();</div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  }</div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#acd57ddea1029fe4bbd9cc3b946c66034">normalize_u2</a> ) <a class="code" href="classDGtal_1_1ATSolver2D.html#ad64e8fed55c3206e409844e78b64b076">normalizeU2</a>();</div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>(<span class="stringliteral">"Solving for v"</span>);</div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#acf4463f93c45c3b40f5c921a5914312e">former_v0</a> = <a class="code" href="classDGtal_1_1ATSolver2D.html#a93f2d93034f48846c70d8ba848a79795">v0</a>;</div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  <a class="code" href="classDGtal_1_1KForm.html">PrimalForm1</a> squared_norm_d_u2 = <a class="code" href="classDGtal_1_1KForm.html#afbd7ecc8d2c3eb5ec5d0f7c187c33ba0">PrimalForm1::zeros</a>(*<a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>);</div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  <span class="keywordflow">for</span> ( <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> d = 0; d < u2.size(); ++d )</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  squared_norm_d_u2.<a class="code" href="classDGtal_1_1KForm.html#a19e859f462f1d851550465b7fcc2c68d">myContainer</a>.array() += (<a class="code" href="classDGtal_1_1ATSolver2D.html#a78262d79c4f40544ec8eac15c68fa712">primal_AD2</a> * u2[ d ] ).myContainer.array().square();</div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"build metric u2"</span> << std::endl;</div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1LinearOperator.html">PrimalIdentity0</a> ope_v0 = <a class="code" href="classDGtal_1_1ATSolver2D.html#abd1939fe7e7775c22a381f07306b8104">l_1_over_4e_Id0</a></div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  + (<a class="code" href="classDGtal_1_1ATSolver2D.html#aceea9eaa1d4e48105f531cb288bf4fef">lambda</a> * <a class="code" href="classDGtal_1_1ATSolver2D.html#afe7dfc2d191ecdf4b86ee43220fc6dc7">epsilon</a>) * <a class="code" href="classDGtal_1_1ATSolver2D.html#aecc1cb13fbf576486331e9cbda695eca">primal_D0</a>.<a class="code" href="classDGtal_1_1LinearOperator.html#aeee5924a3cc7b145068dacb48611157c">transpose</a>() * <a class="code" href="classDGtal_1_1ATSolver2D.html#aecc1cb13fbf576486331e9cbda695eca">primal_D0</a></div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  + <a class="code" href="classDGtal_1_1ATSolver2D.html#af04301709ce9ba5dd2233acde8642301">M01</a>.<a class="code" href="classDGtal_1_1LinearOperator.html#aeee5924a3cc7b145068dacb48611157c">transpose</a>() * <a class="code" href="namespaceDGtal_1_1dec__helper.html#a6b01f3b8906df8056bf147dd40935738">dec_helper::diagonal</a>( squared_norm_d_u2 ) * <a class="code" href="classDGtal_1_1ATSolver2D.html#af04301709ce9ba5dd2233acde8642301">M01</a>;</div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  </div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Prefactoring matrix V associated to v"</span> << std::endl;</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  <a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html">SolverV0</a> solver_v0;</div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  solver_v0.<a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#a90f2a9e43a13293e6368b63298363b60">compute</a>( ope_v0 );</div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Solving V v = l/4e * 1"</span> << std::endl;</div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  v0 = solver_v0.<a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#a7673281a29a04ef2978bad9b373c2382">solve</a>( <a class="code" href="classDGtal_1_1ATSolver2D.html#a7332a00eda9c5a8f2cca3283df4fb97c">l_1_over_4e</a> );</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">" => "</span> << ( solver_v0.<a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#a073f1c0cdb349421b1a6d499fefc6052">isValid</a>() ? <span class="stringliteral">"OK"</span> : <span class="stringliteral">"ERROR"</span> )</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  << <span class="stringliteral">" "</span> << solver_v0.<a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#ab26e3418601a9779709cf92f4366cefe">myLinearAlgebraSolver</a>.info() << std::endl;</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  solve_ok = solve_ok && solver_v0.<a class="code" href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#a073f1c0cdb349421b1a6d499fefc6052">isValid</a>();</div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  <span class="keywordflow">return</span> solve_ok;</div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  }</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  </div>
<div class="line"><a name="l00605"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a013806c87253a7ac556fe256efcfc7a7"> 605</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a013806c87253a7ac556fe256efcfc7a7">solveForEpsilon</a>( <span class="keywordtype">double</span> eps,</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  <span class="keywordtype">double</span> n_oo_max = 1e-4,</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> iter_max = 10 )</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>  (void)n_oo_max;<span class="comment">//paramerter not used</span></div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  </div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  <span class="keywordtype">bool</span> ok = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) {</div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  std::ostringstream sstr;</div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  sstr << <span class="stringliteral">"******* Solving AT for epsilon = "</span> << eps << <span class="stringliteral">" **********"</span>;</div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( sstr.str() ); </div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  }</div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a6122683e9eaf0a7c08cacf81dc253131">setEpsilon</a>( eps );</div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  <span class="keywordflow">for</span> ( <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < iter_max; ++i )</div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span>  {</div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 )</div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"---------- Iteration "</span></div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span>  << i << <span class="stringliteral">"/"</span> << iter_max << <span class="stringliteral">" ---------------"</span> << std::endl;</div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a26e5a500532d1a80d4a0b89f1462f4ff">solveOneAlternateStep</a>( );</div>
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span>  <span class="keyword">auto</span> diffs_v = <a class="code" href="classDGtal_1_1ATSolver2D.html#adb0834940772ba408ed86d9b34a57a6a">diffV0</a>();</div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) {</div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Variation |v^k+1 - v^k|_oo = "</span> << std::get<0>( diffs_v )</div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  << std::endl;</div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) {</div>
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Variation |v^k+1 - v^k|_2 = "</span> << std::get<1>( diffs_v )</div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  << std::endl;</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"Variation |v^k+1 - v^k|_1 = "</span> << std::get<2>( diffs_v )</div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span>  << std::endl;</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="keywordflow">if</span> ( std::get<0>( diffs_v ) < 1e-4 ) <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span>  }</div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00638"></a><span class="lineno"> 638</span>  <span class="keywordflow">return</span> ok;</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="l00657"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#ab1fba42ea868fa2959c8ae6f17884d06"> 657</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#ab1fba42ea868fa2959c8ae6f17884d06">solveGammaConvergence</a>( <span class="keywordtype">double</span> eps1 = 2.0,</div>
<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  <span class="keywordtype">double</span> eps2 = 0.25,</div>
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  <span class="keywordtype">double</span> epsr = 2.0,</div>
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span>  <span class="keywordtype">bool</span> compute_smallest_epsilon_map = <span class="keyword">false</span>,</div>
<div class="line"><a name="l00661"></a><span class="lineno"> 661</span>  <span class="keywordtype">double</span> n_oo_max = 1e-4,</div>
<div class="line"><a name="l00662"></a><span class="lineno"> 662</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> iter_max = 10 )</div>
<div class="line"><a name="l00663"></a><span class="lineno"> 663</span>  {</div>
<div class="line"><a name="l00664"></a><span class="lineno"> 664</span>  <span class="keywordtype">bool</span> ok = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00665"></a><span class="lineno"> 665</span>  <span class="keywordflow">if</span> ( epsr <= 1.0 ) epsr = 2.0;</div>
<div class="line"><a name="l00666"></a><span class="lineno"> 666</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 )</div>
<div class="line"><a name="l00667"></a><span class="lineno"> 667</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">"#### Solve AT by Gamma-convergence ##########"</span> );</div>
<div class="line"><a name="l00668"></a><span class="lineno"> 668</span>  <span class="keywordflow">if</span> ( compute_smallest_epsilon_map ) <a class="code" href="classDGtal_1_1ATSolver2D.html#a6934e9269b94e7c454824cff61bda4b2">smallest_epsilon_map</a>.clear();</div>
<div class="line"><a name="l00669"></a><span class="lineno"> 669</span>  <span class="keywordflow">for</span> ( <span class="keywordtype">double</span> eps = eps1; eps >= eps2; eps /= epsr )</div>
<div class="line"><a name="l00670"></a><span class="lineno"> 670</span>  {</div>
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a013806c87253a7ac556fe256efcfc7a7">solveForEpsilon</a>( eps, n_oo_max, iter_max );</div>
<div class="line"><a name="l00672"></a><span class="lineno"> 672</span>  <span class="keywordflow">if</span> ( compute_smallest_epsilon_map )</div>
<div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a46bf0b98ceaaa27eebf2949cea702f30">updateSmallestEpsilonMap</a>( 0.5 );</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>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 )</div>
<div class="line"><a name="l00676"></a><span class="lineno"> 676</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00677"></a><span class="lineno"> 677</span>  <span class="keywordflow">return</span> ok;</div>
<div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  }</div>
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  </div>
<div class="line"><a name="l00684"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#ad64e8fed55c3206e409844e78b64b076"> 684</a></span>  <span class="keywordtype">void</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#ad64e8fed55c3206e409844e78b64b076">normalizeU2</a>()</div>
<div class="line"><a name="l00685"></a><span class="lineno"> 685</span>  {</div>
<div class="line"><a name="l00686"></a><span class="lineno"> 686</span>  <span class="keywordflow">for</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> index = 0; index < <a class="code" href="classDGtal_1_1ATSolver2D.html#a7853f33b9a33d2744130cc29ab7cbfea">size</a>( 2 ); index++)</div>
<div class="line"><a name="l00687"></a><span class="lineno"> 687</span>  {</div>
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span>  <span class="keywordtype">double</span> n2 = 0.0;</div>
<div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  <span class="keywordflow">for</span> ( <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> d = 0; d < u2.size(); ++d )</div>
<div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  n2 += u2[ d ].myContainer( index ) * u2[ d ].myContainer( index );</div>
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span>  <span class="keywordtype">double</span> norm = sqrt( n2 );</div>
<div class="line"><a name="l00692"></a><span class="lineno"> 692</span>  <span class="keywordflow">if</span> (norm == 0.0) <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span>  <span class="keywordflow">for</span> ( <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> d = 0; d < u2.size(); ++d )</div>
<div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  u2[ d ].myContainer( index ) /= norm;</div>
<div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  }</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="l00702"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#adb0834940772ba408ed86d9b34a57a6a"> 702</a></span>  std::tuple<double,double,double> <a class="code" href="classDGtal_1_1ATSolver2D.html#adb0834940772ba408ed86d9b34a57a6a">diffV0</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00703"></a><span class="lineno"> 703</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00704"></a><span class="lineno"> 704</span>  <a class="code" href="classDGtal_1_1KForm.html">PrimalForm0</a> delta = v0 - <a class="code" href="classDGtal_1_1ATSolver2D.html#acf4463f93c45c3b40f5c921a5914312e">former_v0</a>;</div>
<div class="line"><a name="l00705"></a><span class="lineno"> 705</span>  delta.<a class="code" href="classDGtal_1_1KForm.html#a19e859f462f1d851550465b7fcc2c68d">myContainer</a> = delta.<a class="code" href="classDGtal_1_1KForm.html#a19e859f462f1d851550465b7fcc2c68d">myContainer</a>.cwiseAbs();</div>
<div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> n_oo = delta.<a class="code" href="classDGtal_1_1KForm.html#a19e859f462f1d851550465b7fcc2c68d">myContainer</a>.maxCoeff();</div>
<div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> n_2 = std::sqrt(delta.<a class="code" href="classDGtal_1_1KForm.html#a19e859f462f1d851550465b7fcc2c68d">myContainer</a>.squaredNorm()/delta.<a class="code" href="classDGtal_1_1KForm.html#a19e859f462f1d851550465b7fcc2c68d">myContainer</a>.size());</div>
<div class="line"><a name="l00708"></a><span class="lineno"> 708</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> n_1 = delta.<a class="code" href="classDGtal_1_1KForm.html#a19e859f462f1d851550465b7fcc2c68d">myContainer</a>.mean();</div>
<div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  <span class="keywordflow">return</span> std::make_tuple( n_oo, n_2, n_1 );</div>
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span>  }</div>
<div class="line"><a name="l00711"></a><span class="lineno"> 711</span>  </div>
<div class="line"><a name="l00713"></a><span class="lineno"> 713</span>  </div>
<div class="line"><a name="l00714"></a><span class="lineno"> 714</span>  </div>
<div class="line"><a name="l00715"></a><span class="lineno"> 715</span>  <span class="comment">// ----------------------- Access services ------------------------------</span></div>
<div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  </div>
<div class="line"><a name="l00723"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a92f43a60c3f47ef37e451c23ef790f40"> 723</a></span>  std::tuple<double,double,double> <a class="code" href="classDGtal_1_1ATSolver2D.html#a92f43a60c3f47ef37e451c23ef790f40">checkV0</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00724"></a><span class="lineno"> 724</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00725"></a><span class="lineno"> 725</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> m1 = v0.myContainer.minCoeff();</div>
<div class="line"><a name="l00726"></a><span class="lineno"> 726</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> m2 = v0.myContainer.maxCoeff();</div>
<div class="line"><a name="l00727"></a><span class="lineno"> 727</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> ma = v0.myContainer.mean();</div>
<div class="line"><a name="l00728"></a><span class="lineno"> 728</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 )</div>
<div class="line"><a name="l00729"></a><span class="lineno"> 729</span>  <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"0-form v (should be in [0,1]): min="</span> << m1 << <span class="stringliteral">" avg="</span> << ma << <span class="stringliteral">" max="</span> << m2 << std::endl;</div>
<div class="line"><a name="l00730"></a><span class="lineno"> 730</span>  <span class="keywordflow">return</span> std::make_tuple( m1, m2, ma );</div>
<div class="line"><a name="l00731"></a><span class="lineno"> 731</span>  }</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="l00735"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a75240fe17b67bfdb7c34170c92413596"> 735</a></span>  <a class="code" href="classDGtal_1_1KForm.html">PrimalForm0</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a75240fe17b67bfdb7c34170c92413596">getV0</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00736"></a><span class="lineno"> 736</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00737"></a><span class="lineno"> 737</span>  <span class="keywordflow">return</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a93f2d93034f48846c70d8ba848a79795">v0</a>;</div>
<div class="line"><a name="l00738"></a><span class="lineno"> 738</span>  }</div>
<div class="line"><a name="l00739"></a><span class="lineno"> 739</span>  </div>
<div class="line"><a name="l00741"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a7f3e5bf3b47fb86dfccaa98ca7bb2e66"> 741</a></span>  <a class="code" href="classDGtal_1_1KForm.html">PrimalForm1</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a7f3e5bf3b47fb86dfccaa98ca7bb2e66">getV1</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00742"></a><span class="lineno"> 742</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00743"></a><span class="lineno"> 743</span>  <span class="keywordflow">return</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#af04301709ce9ba5dd2233acde8642301">M01</a>*<a class="code" href="classDGtal_1_1ATSolver2D.html#a93f2d93034f48846c70d8ba848a79795">v0</a>;</div>
<div class="line"><a name="l00744"></a><span class="lineno"> 744</span>  }</div>
<div class="line"><a name="l00745"></a><span class="lineno"> 745</span>  </div>
<div class="line"><a name="l00747"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#ab8bd483b502f6e0808db55a17d2f234f"> 747</a></span>  <a class="code" href="classDGtal_1_1KForm.html">PrimalForm2</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#ab8bd483b502f6e0808db55a17d2f234f">getV2</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00748"></a><span class="lineno"> 748</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00749"></a><span class="lineno"> 749</span>  <span class="keywordflow">return</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a68577ab02e5f3f631739243a437cffd7">M12</a>*<a class="code" href="classDGtal_1_1ATSolver2D.html#af04301709ce9ba5dd2233acde8642301">M01</a>*<a class="code" href="classDGtal_1_1ATSolver2D.html#a93f2d93034f48846c70d8ba848a79795">v0</a>;</div>
<div class="line"><a name="l00750"></a><span class="lineno"> 750</span>  }</div>
<div class="line"><a name="l00751"></a><span class="lineno"> 751</span>  </div>
<div class="line"><a name="l00754"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a2d1ba909007c68eba2c95c69d1549ca6"> 754</a></span>  <a class="code" href="classDGtal_1_1KForm.html">PrimalForm2</a> <a class="code" href="classDGtal_1_1ATSolver2D.html#a2d1ba909007c68eba2c95c69d1549ca6">getU2</a>( <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> k )<span class="keyword"> const</span></div>
<div class="line"><a name="l00755"></a><span class="lineno"> 755</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00756"></a><span class="lineno"> 756</span>  <span class="keywordflow">return</span> u2[ k ];</div>
<div class="line"><a name="l00757"></a><span class="lineno"> 757</span>  }</div>
<div class="line"><a name="l00758"></a><span class="lineno"> 758</span>  </div>
<div class="line"><a name="l00770"></a><span class="lineno"> 770</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> VectorFieldOutput, <span class="keyword">typename</span> SurfelRangeConstIterator></div>
<div class="line"><a name="l00771"></a><span class="lineno"> 771</span>  <span class="keywordtype">void</span></div>
<div class="line"><a name="l00772"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#adead3da234dde032d7a2e5bd76573507"> 772</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#adead3da234dde032d7a2e5bd76573507">getOutputVectorFieldU2</a>( VectorFieldOutput& output,</div>
<div class="line"><a name="l00773"></a><span class="lineno"> 773</span>  SurfelRangeConstIterator itB, SurfelRangeConstIterator itE )</div>
<div class="line"><a name="l00774"></a><span class="lineno"> 774</span>  {</div>
<div class="line"><a name="l00775"></a><span class="lineno"> 775</span>  <span class="keyword">const</span> <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> N = u2.size();</div>
<div class="line"><a name="l00776"></a><span class="lineno"> 776</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> i = 0;</div>
<div class="line"><a name="l00777"></a><span class="lineno"> 777</span>  <span class="keywordflow">for</span> ( <span class="keyword">auto</span> it = itB; it != itE; ++it, ++i )</div>
<div class="line"><a name="l00778"></a><span class="lineno"> 778</span>  {</div>
<div class="line"><a name="l00779"></a><span class="lineno"> 779</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> idx = <a class="code" href="classDGtal_1_1ATSolver2D.html#aa10fb1c8ee0c9873a9abe3d6cd04eea1">surfel2idx</a>[ *it ];</div>
<div class="line"><a name="l00780"></a><span class="lineno"> 780</span>  ASSERT( output[ i ].<a class="code" href="classDGtal_1_1ATSolver2D.html#a7853f33b9a33d2744130cc29ab7cbfea">size</a>() >= N );</div>
<div class="line"><a name="l00781"></a><span class="lineno"> 781</span>  <span class="keywordflow">for</span> ( <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> k = 0; k < N; ++k )</div>
<div class="line"><a name="l00782"></a><span class="lineno"> 782</span>  output[ i ][ k ] = u2[ k ].myContainer( idx );</div>
<div class="line"><a name="l00783"></a><span class="lineno"> 783</span>  }</div>
<div class="line"><a name="l00784"></a><span class="lineno"> 784</span>  }</div>
<div class="line"><a name="l00785"></a><span class="lineno"> 785</span>  </div>
<div class="line"><a name="l00796"></a><span class="lineno"> 796</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ScalarFieldOutput, <span class="keyword">typename</span> SurfelRangeConstIterator></div>
<div class="line"><a name="l00797"></a><span class="lineno"> 797</span>  <span class="keywordtype">void</span></div>
<div class="line"><a name="l00798"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a17412769bb50ec129b201b7624122a2d"> 798</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a17412769bb50ec129b201b7624122a2d">getOutputScalarFieldU2</a>( ScalarFieldOutput& output,</div>
<div class="line"><a name="l00799"></a><span class="lineno"> 799</span>  SurfelRangeConstIterator itB, SurfelRangeConstIterator itE )</div>
<div class="line"><a name="l00800"></a><span class="lineno"> 800</span>  {</div>
<div class="line"><a name="l00801"></a><span class="lineno"> 801</span>  ASSERT( u2.size() == 1 && <span class="stringliteral">"[ATSolver2D::getOutputScalarFieldU2] "</span></div>
<div class="line"><a name="l00802"></a><span class="lineno"> 802</span>  <span class="stringliteral">"You try to output a scalar field from a vector field."</span> );</div>
<div class="line"><a name="l00803"></a><span class="lineno"> 803</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> i = 0;</div>
<div class="line"><a name="l00804"></a><span class="lineno"> 804</span>  <span class="keywordflow">for</span> ( <span class="keyword">auto</span> it = itB; it != itE; ++it, ++i )</div>
<div class="line"><a name="l00805"></a><span class="lineno"> 805</span>  {</div>
<div class="line"><a name="l00806"></a><span class="lineno"> 806</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> idx = <a class="code" href="classDGtal_1_1ATSolver2D.html#aa10fb1c8ee0c9873a9abe3d6cd04eea1">surfel2idx</a>[ *it ];</div>
<div class="line"><a name="l00807"></a><span class="lineno"> 807</span>  output[ i ] = u2[ 0 ].myContainer( idx );</div>
<div class="line"><a name="l00808"></a><span class="lineno"> 808</span>  }</div>
<div class="line"><a name="l00809"></a><span class="lineno"> 809</span>  }</div>
<div class="line"><a name="l00810"></a><span class="lineno"> 810</span>  </div>
<div class="line"><a name="l00822"></a><span class="lineno"> 822</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ScalarFieldOutput, <span class="keyword">typename</span> CellRangeConstIterator></div>
<div class="line"><a name="l00823"></a><span class="lineno"> 823</span>  <span class="keywordtype">void</span></div>
<div class="line"><a name="l00824"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a1dd71a81f0afc69ef73ec2a41326f16e"> 824</a></span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a1dd71a81f0afc69ef73ec2a41326f16e">getOutputScalarFieldV0</a>( ScalarFieldOutput& output,</div>
<div class="line"><a name="l00825"></a><span class="lineno"> 825</span>  CellRangeConstIterator itB, CellRangeConstIterator itE,</div>
<div class="line"><a name="l00826"></a><span class="lineno"> 826</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#aede4e265e44ce612075bb3c15f8690da">CellOutputPolicy</a> policy = CellOutputPolicy::Average )</div>
<div class="line"><a name="l00827"></a><span class="lineno"> 827</span>  {</div>
<div class="line"><a name="l00828"></a><span class="lineno"> 828</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#afa2b4116a2bcc862b6df458ae067eb4b">KSpace</a>& <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a> = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->myKSpace;</div>
<div class="line"><a name="l00829"></a><span class="lineno"> 829</span>  <span class="keyword">const</span> <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> k = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uDim( *itB );</div>
<div class="line"><a name="l00830"></a><span class="lineno"> 830</span>  ASSERT( k <= 2 );</div>
<div class="line"><a name="l00831"></a><span class="lineno"> 831</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> i = 0;</div>
<div class="line"><a name="l00832"></a><span class="lineno"> 832</span>  <span class="keywordflow">if</span> ( k == 0 )</div>
<div class="line"><a name="l00833"></a><span class="lineno"> 833</span>  {</div>
<div class="line"><a name="l00834"></a><span class="lineno"> 834</span>  <span class="keywordflow">for</span> ( <span class="keyword">auto</span> it = itB; it != itE; ++it, ++i )</div>
<div class="line"><a name="l00835"></a><span class="lineno"> 835</span>  {</div>
<div class="line"><a name="l00836"></a><span class="lineno"> 836</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> pointel = *it;</div>
<div class="line"><a name="l00837"></a><span class="lineno"> 837</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> idx = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->getCellIndex( pointel );</div>
<div class="line"><a name="l00838"></a><span class="lineno"> 838</span>  output[ i ] = v0.myContainer( idx );</div>
<div class="line"><a name="l00839"></a><span class="lineno"> 839</span>  }</div>
<div class="line"><a name="l00840"></a><span class="lineno"> 840</span>  }</div>
<div class="line"><a name="l00841"></a><span class="lineno"> 841</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( k == 1 )</div>
<div class="line"><a name="l00842"></a><span class="lineno"> 842</span>  {</div>
<div class="line"><a name="l00843"></a><span class="lineno"> 843</span>  <span class="keywordflow">for</span> ( <span class="keyword">auto</span> it = itB; it != itE; ++it, ++i )</div>
<div class="line"><a name="l00844"></a><span class="lineno"> 844</span>  {</div>
<div class="line"><a name="l00845"></a><span class="lineno"> 845</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> linel = *it;</div>
<div class="line"><a name="l00846"></a><span class="lineno"> 846</span>  <span class="keyword">const</span> <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> d = * <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uDirs( linel );</div>
<div class="line"><a name="l00847"></a><span class="lineno"> 847</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> p0 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( linel, d, <span class="keyword">false</span> );</div>
<div class="line"><a name="l00848"></a><span class="lineno"> 848</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> p1 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( linel, d, <span class="keyword">true</span> );</div>
<div class="line"><a name="l00849"></a><span class="lineno"> 849</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> idx0 = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->getCellIndex( p0 );</div>
<div class="line"><a name="l00850"></a><span class="lineno"> 850</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> idx1 = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->getCellIndex( p1 );</div>
<div class="line"><a name="l00851"></a><span class="lineno"> 851</span>  <span class="keywordflow">switch</span> (policy) {</div>
<div class="line"><a name="l00852"></a><span class="lineno"> 852</span>  <span class="keywordflow">case</span> CellOutputPolicy::Average: output[ i ] = 0.5 * ( v0.myContainer( idx0 ) + v0.myContainer( idx1 ) );</div>
<div class="line"><a name="l00853"></a><span class="lineno"> 853</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00854"></a><span class="lineno"> 854</span>  <span class="keywordflow">case</span> CellOutputPolicy::Minimum: output[ i ] = std::min( v0.myContainer( idx0 ), v0.myContainer( idx1 ) );</div>
<div class="line"><a name="l00855"></a><span class="lineno"> 855</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00856"></a><span class="lineno"> 856</span>  <span class="keywordflow">case</span> CellOutputPolicy::Maximum: output[ i ] = <a class="code" href="testArithmeticalDSS_8cpp.html#af082905f7eac6d03e92015146bbc1925">std::max</a>( v0.myContainer( idx0 ), v0.myContainer( idx1 ) );</div>
<div class="line"><a name="l00857"></a><span class="lineno"> 857</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00858"></a><span class="lineno"> 858</span>  }</div>
<div class="line"><a name="l00859"></a><span class="lineno"> 859</span>  }</div>
<div class="line"><a name="l00860"></a><span class="lineno"> 860</span>  }</div>
<div class="line"><a name="l00861"></a><span class="lineno"> 861</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( k == 2 )</div>
<div class="line"><a name="l00862"></a><span class="lineno"> 862</span>  {</div>
<div class="line"><a name="l00863"></a><span class="lineno"> 863</span>  <span class="keywordflow">for</span> ( <span class="keyword">auto</span> it = itB; it != itE; ++it, ++i )</div>
<div class="line"><a name="l00864"></a><span class="lineno"> 864</span>  {</div>
<div class="line"><a name="l00865"></a><span class="lineno"> 865</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> face = *it;</div>
<div class="line"><a name="l00866"></a><span class="lineno"> 866</span>  <span class="keyword">const</span> <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> d = * <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uDirs( face );</div>
<div class="line"><a name="l00867"></a><span class="lineno"> 867</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> l0 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( face, d, <span class="keyword">false</span> );</div>
<div class="line"><a name="l00868"></a><span class="lineno"> 868</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> l1 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( face, d, <span class="keyword">true</span> );</div>
<div class="line"><a name="l00869"></a><span class="lineno"> 869</span>  <span class="keyword">const</span> <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> j = * <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uDirs( l0 );</div>
<div class="line"><a name="l00870"></a><span class="lineno"> 870</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> p00 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( l0, j, <span class="keyword">false</span> );</div>
<div class="line"><a name="l00871"></a><span class="lineno"> 871</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> p01 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( l0, j, <span class="keyword">true</span> );</div>
<div class="line"><a name="l00872"></a><span class="lineno"> 872</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> p10 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( l1, j, <span class="keyword">false</span> );</div>
<div class="line"><a name="l00873"></a><span class="lineno"> 873</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> p11 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( l1, j, <span class="keyword">true</span> );</div>
<div class="line"><a name="l00874"></a><span class="lineno"> 874</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> idx00 = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->getCellIndex( p00 );</div>
<div class="line"><a name="l00875"></a><span class="lineno"> 875</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> idx01 = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->getCellIndex( p01 );</div>
<div class="line"><a name="l00876"></a><span class="lineno"> 876</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> idx10 = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->getCellIndex( p10 );</div>
<div class="line"><a name="l00877"></a><span class="lineno"> 877</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">Index</a> idx11 = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->getCellIndex( p11 );</div>
<div class="line"><a name="l00878"></a><span class="lineno"> 878</span>  <span class="keywordflow">switch</span> (policy) {</div>
<div class="line"><a name="l00879"></a><span class="lineno"> 879</span>  <span class="keywordflow">case</span> CellOutputPolicy::Average:</div>
<div class="line"><a name="l00880"></a><span class="lineno"> 880</span>  output[ i ] = 0.25 * ( v0.myContainer( idx00 ) + v0.myContainer( idx01 )</div>
<div class="line"><a name="l00881"></a><span class="lineno"> 881</span>  + v0.myContainer( idx10 ) + v0.myContainer( idx11 ) );</div>
<div class="line"><a name="l00882"></a><span class="lineno"> 882</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00883"></a><span class="lineno"> 883</span>  <span class="keywordflow">case</span> CellOutputPolicy::Minimum:</div>
<div class="line"><a name="l00884"></a><span class="lineno"> 884</span>  output[ i ] = std::min( std::min( v0.myContainer( idx00 ), v0.myContainer( idx01 ) ),</div>
<div class="line"><a name="l00885"></a><span class="lineno"> 885</span>  std::min( v0.myContainer( idx10 ), v0.myContainer( idx11 ) ) );</div>
<div class="line"><a name="l00886"></a><span class="lineno"> 886</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00887"></a><span class="lineno"> 887</span>  <span class="keywordflow">case</span> CellOutputPolicy::Maximum:</div>
<div class="line"><a name="l00888"></a><span class="lineno"> 888</span>  output[ i ] = <a class="code" href="testArithmeticalDSS_8cpp.html#af082905f7eac6d03e92015146bbc1925">std::max</a>( <a class="code" href="testArithmeticalDSS_8cpp.html#af082905f7eac6d03e92015146bbc1925">std::max</a>( v0.myContainer( idx00 ), v0.myContainer( idx01 ) ),</div>
<div class="line"><a name="l00889"></a><span class="lineno"> 889</span>  <a class="code" href="testArithmeticalDSS_8cpp.html#af082905f7eac6d03e92015146bbc1925">std::max</a>( v0.myContainer( idx10 ), v0.myContainer( idx11 ) ) );</div>
<div class="line"><a name="l00890"></a><span class="lineno"> 890</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00891"></a><span class="lineno"> 891</span>  }</div>
<div class="line"><a name="l00892"></a><span class="lineno"> 892</span>  }</div>
<div class="line"><a name="l00893"></a><span class="lineno"> 893</span>  }</div>
<div class="line"><a name="l00894"></a><span class="lineno"> 894</span>  }</div>
<div class="line"><a name="l00895"></a><span class="lineno"> 895</span>  </div>
<div class="line"><a name="l00903"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a46bf0b98ceaaa27eebf2949cea702f30"> 903</a></span>  <span class="keywordtype">void</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a46bf0b98ceaaa27eebf2949cea702f30">updateSmallestEpsilonMap</a>( <span class="keyword">const</span> <span class="keywordtype">double</span> threshold = .5 )</div>
<div class="line"><a name="l00904"></a><span class="lineno"> 904</span>  {</div>
<div class="line"><a name="l00905"></a><span class="lineno"> 905</span>  <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#afa2b4116a2bcc862b6df458ae067eb4b">KSpace</a>& <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a> = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->myKSpace;</div>
<div class="line"><a name="l00906"></a><span class="lineno"> 906</span>  <span class="keywordflow">for</span> ( <span class="keyword">const</span> <a class="code" href="structDGtal_1_1SignedKhalimskyCell.html">SCell</a> surfel : <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->template getIndexedSCells<2, PRIMAL>() )</div>
<div class="line"><a name="l00907"></a><span class="lineno"> 907</span>  {</div>
<div class="line"><a name="l00908"></a><span class="lineno"> 908</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> face = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.unsigns( surfel );</div>
<div class="line"><a name="l00909"></a><span class="lineno"> 909</span>  <span class="keyword">const</span> <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> k1 = * <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uDirs( face );</div>
<div class="line"><a name="l00910"></a><span class="lineno"> 910</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> l0 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( face, k1, <span class="keyword">false</span> );</div>
<div class="line"><a name="l00911"></a><span class="lineno"> 911</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> l1 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( face, k1, <span class="keyword">true</span> );</div>
<div class="line"><a name="l00912"></a><span class="lineno"> 912</span>  <span class="keyword">const</span> <a class="code" href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> k2 = * <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uDirs( l0 );</div>
<div class="line"><a name="l00913"></a><span class="lineno"> 913</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> ll0 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( face, k2, <span class="keyword">false</span> );</div>
<div class="line"><a name="l00914"></a><span class="lineno"> 914</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> ll1 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( face, k2, <span class="keyword">true</span> );</div>
<div class="line"><a name="l00915"></a><span class="lineno"> 915</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> p00 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( l0, k2, <span class="keyword">false</span> );</div>
<div class="line"><a name="l00916"></a><span class="lineno"> 916</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> p01 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( l0, k2, <span class="keyword">true</span> );</div>
<div class="line"><a name="l00917"></a><span class="lineno"> 917</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> p10 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( l1, k2, <span class="keyword">false</span> );</div>
<div class="line"><a name="l00918"></a><span class="lineno"> 918</span>  <span class="keyword">const</span> <a class="code" href="structDGtal_1_1KhalimskyCell.html">Cell</a> p11 = <a class="code" href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a>.uIncident( l1, k2, <span class="keyword">true</span> );</div>
<div class="line"><a name="l00919"></a><span class="lineno"> 919</span>  </div>
<div class="line"><a name="l00920"></a><span class="lineno"> 920</span>  std::vector<double> features( 4 );</div>
<div class="line"><a name="l00921"></a><span class="lineno"> 921</span>  features[ 0 ] = v0.myContainer( <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->getCellIndex( p00 ) );</div>
<div class="line"><a name="l00922"></a><span class="lineno"> 922</span>  features[ 1 ] = v0.myContainer( <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->getCellIndex( p01 ) );</div>
<div class="line"><a name="l00923"></a><span class="lineno"> 923</span>  features[ 2 ] = v0.myContainer( <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->getCellIndex( p10 ) );</div>
<div class="line"><a name="l00924"></a><span class="lineno"> 924</span>  features[ 3 ] = v0.myContainer( <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->getCellIndex( p11 ) );</div>
<div class="line"><a name="l00925"></a><span class="lineno"> 925</span>  std::sort( features.begin(), features.end() );</div>
<div class="line"><a name="l00926"></a><span class="lineno"> 926</span>  </div>
<div class="line"><a name="l00927"></a><span class="lineno"> 927</span>  <span class="keywordflow">if</span> ( features[ 1 ] <= threshold )</div>
<div class="line"><a name="l00928"></a><span class="lineno"> 928</span>  {</div>
<div class="line"><a name="l00929"></a><span class="lineno"> 929</span>  <span class="keyword">auto</span> it = <a class="code" href="classDGtal_1_1ATSolver2D.html#a6934e9269b94e7c454824cff61bda4b2">smallest_epsilon_map</a>.find( surfel );</div>
<div class="line"><a name="l00930"></a><span class="lineno"> 930</span>  <span class="keywordflow">if</span> ( it != <a class="code" href="classDGtal_1_1ATSolver2D.html#a6934e9269b94e7c454824cff61bda4b2">smallest_epsilon_map</a>.end() )</div>
<div class="line"><a name="l00931"></a><span class="lineno"> 931</span>  it->second = std::min( <a class="code" href="classDGtal_1_1ATSolver2D.html#afe7dfc2d191ecdf4b86ee43220fc6dc7">epsilon</a>, it->second );</div>
<div class="line"><a name="l00932"></a><span class="lineno"> 932</span>  <span class="keywordflow">else</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a6934e9269b94e7c454824cff61bda4b2">smallest_epsilon_map</a>[ surfel ] = <a class="code" href="classDGtal_1_1ATSolver2D.html#afe7dfc2d191ecdf4b86ee43220fc6dc7">epsilon</a>;</div>
<div class="line"><a name="l00933"></a><span class="lineno"> 933</span>  }</div>
<div class="line"><a name="l00934"></a><span class="lineno"> 934</span>  }</div>
<div class="line"><a name="l00935"></a><span class="lineno"> 935</span>  }</div>
<div class="line"><a name="l00936"></a><span class="lineno"> 936</span>  </div>
<div class="line"><a name="l00938"></a><span class="lineno"> 938</span>  </div>
<div class="line"><a name="l00939"></a><span class="lineno"> 939</span>  </div>
<div class="line"><a name="l00940"></a><span class="lineno"> 940</span>  <span class="comment">// ----------------------- Interface --------------------------------------</span></div>
<div class="line"><a name="l00941"></a><span class="lineno"> 941</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00944"></a><span class="lineno"> 944</span>  </div>
<div class="line"><a name="l00949"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#ac8315ceca305aff6df624d1ac61e1db3"> 949</a></span>  <span class="keywordtype">void</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#ac8315ceca305aff6df624d1ac61e1db3">selfDisplay</a> ( std::ostream & out )<span class="keyword"> const</span></div>
<div class="line"><a name="l00950"></a><span class="lineno"> 950</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00951"></a><span class="lineno"> 951</span>  <span class="keyword">auto</span> cv = <a class="code" href="classDGtal_1_1ATSolver2D.html#a92f43a60c3f47ef37e451c23ef790f40">checkV0</a>();</div>
<div class="line"><a name="l00952"></a><span class="lineno"> 952</span>  out << <span class="stringliteral">"[ATSolver2D] v is between min/avg/max:"</span></div>
<div class="line"><a name="l00953"></a><span class="lineno"> 953</span>  << std::get<0>(cv) << <span class="stringliteral">"/"</span></div>
<div class="line"><a name="l00954"></a><span class="lineno"> 954</span>  << std::get<1>(cv) << <span class="stringliteral">"/"</span></div>
<div class="line"><a name="l00955"></a><span class="lineno"> 955</span>  << std::get<2>(cv) << std::endl;</div>
<div class="line"><a name="l00956"></a><span class="lineno"> 956</span>  }</div>
<div class="line"><a name="l00957"></a><span class="lineno"> 957</span>  </div>
<div class="line"><a name="l00962"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#aa28ebc4b0290afebeb401320c9c0d864"> 962</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#aa28ebc4b0290afebeb401320c9c0d864">isValid</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00963"></a><span class="lineno"> 963</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00964"></a><span class="lineno"> 964</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00965"></a><span class="lineno"> 965</span>  }</div>
<div class="line"><a name="l00966"></a><span class="lineno"> 966</span>  </div>
<div class="line"><a name="l00968"></a><span class="lineno"> 968</span>  </div>
<div class="line"><a name="l00969"></a><span class="lineno"> 969</span>  <span class="comment">// ------------------------- Hidden services ------------------------------</span></div>
<div class="line"><a name="l00970"></a><span class="lineno"> 970</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00971"></a><span class="lineno"> 971</span>  </div>
<div class="line"><a name="l00974"></a><span class="lineno"> 974</span>  </div>
<div class="line"><a name="l00976"></a><span class="lineno"><a class="line" href="classDGtal_1_1ATSolver2D.html#a9adf8bd493312d3a4feb100575fa5146"> 976</a></span>  <span class="keywordtype">void</span> <a class="code" href="classDGtal_1_1ATSolver2D.html#a9adf8bd493312d3a4feb100575fa5146">initOperators</a>()</div>
<div class="line"><a name="l00977"></a><span class="lineno"> 977</span>  {</div>
<div class="line"><a name="l00978"></a><span class="lineno"> 978</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">"[ATSolver2D::initOperators] Solver initialization"</span> );</div>
<div class="line"><a name="l00979"></a><span class="lineno"> 979</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"derivative of primal 0-forms: primal_D0"</span> << std::endl;</div>
<div class="line"><a name="l00980"></a><span class="lineno"> 980</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#aecc1cb13fbf576486331e9cbda695eca">primal_D0</a> = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->template derivative<0,PRIMAL>();</div>
<div class="line"><a name="l00981"></a><span class="lineno"> 981</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"derivative of primal 1-forms: primal_D1"</span> << std::endl;</div>
<div class="line"><a name="l00982"></a><span class="lineno"> 982</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#ab9b12aea6bd78758f5f05aeb256916e1">primal_D1</a> = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->template derivative<1,PRIMAL>();</div>
<div class="line"><a name="l00983"></a><span class="lineno"> 983</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"antiderivative of primal 2-forms: primal_AD2"</span> << std::endl;</div>
<div class="line"><a name="l00984"></a><span class="lineno"> 984</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a78262d79c4f40544ec8eac15c68fa712">primal_AD2</a> = <a class="code" href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">ptrCalculus</a>->template antiderivative<2,PRIMAL>();</div>
<div class="line"><a name="l00985"></a><span class="lineno"> 985</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"vertex to edge average operator: M01"</span> << std::endl;</div>
<div class="line"><a name="l00986"></a><span class="lineno"> 986</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#af04301709ce9ba5dd2233acde8642301">M01</a> = <a class="code" href="classDGtal_1_1ATSolver2D.html#aecc1cb13fbf576486331e9cbda695eca">primal_D0</a>;</div>
<div class="line"><a name="l00987"></a><span class="lineno"> 987</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#af04301709ce9ba5dd2233acde8642301">M01</a>.<a class="code" href="classDGtal_1_1LinearOperator.html#aa5696bafeed5f62de870b35ef6b9dad8">myContainer</a> = .5 * <a class="code" href="classDGtal_1_1ATSolver2D.html#af04301709ce9ba5dd2233acde8642301">M01</a>.<a class="code" href="classDGtal_1_1LinearOperator.html#aa5696bafeed5f62de870b35ef6b9dad8">myContainer</a>.cwiseAbs();</div>
<div class="line"><a name="l00988"></a><span class="lineno"> 988</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 2 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() << <span class="stringliteral">"edge to face average operator: M12"</span> << std::endl;</div>
<div class="line"><a name="l00989"></a><span class="lineno"> 989</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a68577ab02e5f3f631739243a437cffd7">M12</a> = <a class="code" href="classDGtal_1_1ATSolver2D.html#ab9b12aea6bd78758f5f05aeb256916e1">primal_D1</a>;</div>
<div class="line"><a name="l00990"></a><span class="lineno"> 990</span>  <a class="code" href="classDGtal_1_1ATSolver2D.html#a68577ab02e5f3f631739243a437cffd7">M12</a>.<a class="code" href="classDGtal_1_1LinearOperator.html#aa5696bafeed5f62de870b35ef6b9dad8">myContainer</a> = .25 * <a class="code" href="classDGtal_1_1ATSolver2D.html#a68577ab02e5f3f631739243a437cffd7">M12</a>.<a class="code" href="classDGtal_1_1LinearOperator.html#aa5696bafeed5f62de870b35ef6b9dad8">myContainer</a>.cwiseAbs();</div>
<div class="line"><a name="l00991"></a><span class="lineno"> 991</span>  <span class="keywordflow">if</span> ( <a class="code" href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">verbose</a> >= 1 ) <a class="code" href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">trace</a>.<a class="code" href="classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00992"></a><span class="lineno"> 992</span>  }</div>
<div class="line"><a name="l00993"></a><span class="lineno"> 993</span>  </div>
<div class="line"><a name="l00995"></a><span class="lineno"> 995</span>  </div>
<div class="line"><a name="l00996"></a><span class="lineno"> 996</span>  <span class="comment">// ------------------------- Internals ------------------------------------</span></div>
<div class="line"><a name="l00997"></a><span class="lineno"> 997</span>  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00998"></a><span class="lineno"> 998</span>  </div>
<div class="line"><a name="l00999"></a><span class="lineno"> 999</span>  }; <span class="comment">// end of class ATSolver2D</span></div>
<div class="line"><a name="l01000"></a><span class="lineno"> 1000</span>  </div>
<div class="line"><a name="l01001"></a><span class="lineno"> 1001</span>  </div>
<div class="line"><a name="l01008"></a><span class="lineno"> 1008</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> T></div>
<div class="line"><a name="l01009"></a><span class="lineno"><a class="line" href="namespaceDGtal.html#add8541826ace2aebbe88c8a08875cf91"> 1009</a></span>  std::ostream&</div>
<div class="line"><a name="l01010"></a><span class="lineno"> 1010</span>  <a class="codeRef" href="http://dgtal.org/doc/tools/nightly/namespaceDGtal.html#a66aca9ad97cfa71ddd5b1333a392d50d">operator<< </a>( std::ostream & out, <span class="keyword">const</span> <a class="code" href="classDGtal_1_1ATSolver2D.html">ATSolver2D<T></a> & <span class="keywordtype">object</span> );</div>
<div class="line"><a name="l01011"></a><span class="lineno"> 1011</span>  </div>
<div class="line"><a name="l01012"></a><span class="lineno"> 1012</span> } <span class="comment">// namespace DGtal</span></div>
<div class="line"><a name="l01013"></a><span class="lineno"> 1013</span>  </div>
<div class="line"><a name="l01014"></a><span class="lineno"> 1014</span>  </div>
<div class="line"><a name="l01016"></a><span class="lineno"> 1016</span> <span class="comment">// Includes inline functions.</span></div>
<div class="line"><a name="l01017"></a><span class="lineno"> 1017</span>  </div>
<div class="line"><a name="l01018"></a><span class="lineno"> 1018</span> <span class="comment">// //</span></div>
<div class="line"><a name="l01020"></a><span class="lineno"> 1020</span> <span class="comment"></span> </div>
<div class="line"><a name="l01021"></a><span class="lineno"> 1021</span> <span class="preprocessor">#endif </span><span class="comment">// !defined ATSolver2D_h</span></div>
<div class="line"><a name="l01022"></a><span class="lineno"> 1022</span>  </div>
<div class="line"><a name="l01023"></a><span class="lineno"> 1023</span> <span class="preprocessor">#undef ATSolver2D_RECURSES</span></div>
<div class="line"><a name="l01024"></a><span class="lineno"> 1024</span> <span class="preprocessor">#endif </span><span class="comment">// else defined(ATSolver2D_RECURSES)</span></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html">DGtal::ATSolver2D</a></div><div class="ttdoc">Aim: This class solves Ambrosio-Tortorelli functional on a two-dimensional digital space (a 2D grid o...</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00090">ATSolver2D.h:91</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a013806c87253a7ac556fe256efcfc7a7"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a013806c87253a7ac556fe256efcfc7a7">DGtal::ATSolver2D::solveForEpsilon</a></div><div class="ttdeci">bool solveForEpsilon(double eps, double n_oo_max=1e-4, unsigned int iter_max=10)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00605">ATSolver2D.h:605</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a0b9e41763b2efad4573222df2ac75016"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a0b9e41763b2efad4573222df2ac75016">DGtal::ATSolver2D::initInputVectorFieldU2</a></div><div class="ttdeci">Index initInputVectorFieldU2(const std::map< Surfel, ScalarVector > &input, bool normalize=false)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00371">ATSolver2D.h:371</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a0c80067d705837a6cbd45ef54778433d"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a0c80067d705837a6cbd45ef54778433d">DGtal::ATSolver2D::Surfel</a></div><div class="ttdeci">KSpace::Surfel Surfel</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00112">ATSolver2D.h:112</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a120ac6c13bc482b8a7f21fe25c96fa96"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a120ac6c13bc482b8a7f21fe25c96fa96">DGtal::ATSolver2D::PrimalHodge2</a></div><div class="ttdeci">Calculus::PrimalHodge2 PrimalHodge2</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00129">ATSolver2D.h:129</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a14527d6ddd86aa606d6a23cb20b786ad"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a14527d6ddd86aa606d6a23cb20b786ad">DGtal::ATSolver2D::initInputScalarFieldU2</a></div><div class="ttdeci">Index initInputScalarFieldU2(const std::map< Surfel, Scalar > &input)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00411">ATSolver2D.h:411</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a17412769bb50ec129b201b7624122a2d"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a17412769bb50ec129b201b7624122a2d">DGtal::ATSolver2D::getOutputScalarFieldU2</a></div><div class="ttdeci">void getOutputScalarFieldU2(ScalarFieldOutput &output, SurfelRangeConstIterator itB, SurfelRangeConstIterator itE)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00798">ATSolver2D.h:798</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a17b53da8cc48bf5d3da9e94cf3d7c51f"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a17b53da8cc48bf5d3da9e94cf3d7c51f">DGtal::ATSolver2D::Space</a></div><div class="ttdeci">KSpace::Space Space</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00107">ATSolver2D.h:107</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a1820dfbc6f093ed24e6911707c75404a"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a1820dfbc6f093ed24e6911707c75404a">DGtal::ATSolver2D::setUp</a></div><div class="ttdeci">void setUp(double a, double l, const AlphaWeights &weights, SurfelRangeConstIterator itB, SurfelRangeConstIterator itE)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00499">ATSolver2D.h:499</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a1dd71a81f0afc69ef73ec2a41326f16e"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a1dd71a81f0afc69ef73ec2a41326f16e">DGtal::ATSolver2D::getOutputScalarFieldV0</a></div><div class="ttdeci">void getOutputScalarFieldV0(ScalarFieldOutput &output, CellRangeConstIterator itB, CellRangeConstIterator itE, CellOutputPolicy policy=CellOutputPolicy::Average)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00824">ATSolver2D.h:824</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a1ece7aebeff8a3eec8941d091474eb53"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a1ece7aebeff8a3eec8941d091474eb53">DGtal::ATSolver2D::PrimalDerivative0</a></div><div class="ttdeci">Calculus::PrimalDerivative0 PrimalDerivative0</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00123">ATSolver2D.h:123</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a25191de161019d127bbbcc82c6dcffe2"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a25191de161019d127bbbcc82c6dcffe2">DGtal::ATSolver2D::dimension</a></div><div class="ttdeci">static const Dimension dimension</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00099">ATSolver2D.h:99</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a25b7904c9073c351c31051900374aae9"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a25b7904c9073c351c31051900374aae9">DGtal::ATSolver2D::PrimalHodge0</a></div><div class="ttdeci">Calculus::PrimalHodge0 PrimalHodge0</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00127">ATSolver2D.h:127</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a26e5a500532d1a80d4a0b89f1462f4ff"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a26e5a500532d1a80d4a0b89f1462f4ff">DGtal::ATSolver2D::solveOneAlternateStep</a></div><div class="ttdeci">bool solveOneAlternateStep()</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00546">ATSolver2D.h:546</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a2d1ba909007c68eba2c95c69d1549ca6"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a2d1ba909007c68eba2c95c69d1549ca6">DGtal::ATSolver2D::getU2</a></div><div class="ttdeci">PrimalForm2 getU2(Dimension k) const</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00754">ATSolver2D.h:754</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a2f154cab3aed8a87209a940db41b8364"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a2f154cab3aed8a87209a940db41b8364">DGtal::ATSolver2D::initInputScalarFieldU2</a></div><div class="ttdeci">void initInputScalarFieldU2(const ScalarFieldInput &input, SurfelRangeConstIterator itB, SurfelRangeConstIterator itE)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00330">ATSolver2D.h:330</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a3623ff997a349c7297dd7b3adf33d28c"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a3623ff997a349c7297dd7b3adf33d28c">DGtal::ATSolver2D::alpha_g2</a></div><div class="ttdeci">std::vector< PrimalForm2 > alpha_g2</div><div class="ttdoc">The alpha-weighted N-array of input primal 2-forms g.</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00162">ATSolver2D.h:162</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a362e088d0dc6e3230fc7ff2cea53d247"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a362e088d0dc6e3230fc7ff2cea53d247">DGtal::ATSolver2D::u2</a></div><div class="ttdeci">std::vector< PrimalForm2 > u2</div><div class="ttdoc">The N-array of regularized primal 2-forms u.</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00164">ATSolver2D.h:164</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a368accf722d9e6d3ed3f02e7b2c350f3"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a368accf722d9e6d3ed3f02e7b2c350f3">DGtal::ATSolver2D::setUp</a></div><div class="ttdeci">void setUp(double a, double l)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00444">ATSolver2D.h:444</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a37f5070cd69ec86f319d04546236c3e2"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a37f5070cd69ec86f319d04546236c3e2">DGtal::ATSolver2D::alpha_Id2</a></div><div class="ttdeci">PrimalIdentity2 alpha_Id2</div><div class="ttdoc">The alpha-weighted identity operator for primal 2-forms (stored for performance)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00156">ATSolver2D.h:156</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a3ce0376a76b6b7c28d0483193ba76714"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a3ce0376a76b6b7c28d0483193ba76714">DGtal::ATSolver2D::PrimalIdentity1</a></div><div class="ttdeci">Calculus::PrimalIdentity1 PrimalIdentity1</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00121">ATSolver2D.h:121</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a3d53f156dd63e507459e1e6f90bee138"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a3d53f156dd63e507459e1e6f90bee138">DGtal::ATSolver2D::ATSolver2D</a></div><div class="ttdeci">ATSolver2D(ConstAlias< Calculus > aCalculus, int aVerbose=0)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00202">ATSolver2D.h:202</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a423dedbfb78fa3d29b947360a2fa1abf"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a423dedbfb78fa3d29b947360a2fa1abf">DGtal::ATSolver2D::Domain</a></div><div class="ttdeci">HyperRectDomain< Space > Domain</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00113">ATSolver2D.h:113</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a4276d97eaa8663a0689d50c0cdda46bb"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a4276d97eaa8663a0689d50c0cdda46bb">DGtal::ATSolver2D::PrimalForm0</a></div><div class="ttdeci">Calculus::PrimalForm0 PrimalForm0</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00117">ATSolver2D.h:117</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a4441e69a1cf80754e4719ff215e14eb0"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a4441e69a1cf80754e4719ff215e14eb0">DGtal::ATSolver2D::verbose</a></div><div class="ttdeci">int verbose</div><div class="ttdoc">Tells the verbose level.</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00191">ATSolver2D.h:191</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a46bf0b98ceaaa27eebf2949cea702f30"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a46bf0b98ceaaa27eebf2949cea702f30">DGtal::ATSolver2D::updateSmallestEpsilonMap</a></div><div class="ttdeci">void updateSmallestEpsilonMap(const double threshold=.5)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00903">ATSolver2D.h:903</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a47214523de8fccd4ec0436b85be4d3cb"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a47214523de8fccd4ec0436b85be4d3cb">DGtal::ATSolver2D::Scalar</a></div><div class="ttdeci">RealVector::Component Scalar</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00109">ATSolver2D.h:109</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a4fd154d5f3f9a31d16f812b9e9602fbd"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a4fd154d5f3f9a31d16f812b9e9602fbd">DGtal::ATSolver2D::SCell</a></div><div class="ttdeci">KSpace::SCell SCell</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00110">ATSolver2D.h:110</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a51b87e769d2450bccd86bdc45d792c9c"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a51b87e769d2450bccd86bdc45d792c9c">DGtal::ATSolver2D::PrimalAntiderivative1</a></div><div class="ttdeci">Calculus::PrimalAntiderivative1 PrimalAntiderivative1</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00125">ATSolver2D.h:125</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a559189aa3b4834e4af30439ab7796aba"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a559189aa3b4834e4af30439ab7796aba">DGtal::ATSolver2D::LinearAlgebraSolver</a></div><div class="ttdeci">EigenLinearAlgebraBackend::SolverSimplicialLDLT LinearAlgebraSolver</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00138">ATSolver2D.h:138</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a55bca79bf2ef4b57d3f14bf74e00cd5e"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a55bca79bf2ef4b57d3f14bf74e00cd5e">DGtal::ATSolver2D::LinearAlgebra</a></div><div class="ttdeci">TLinearAlgebra LinearAlgebra</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00096">ATSolver2D.h:96</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a5aea21e7b14b68c9d0e74acdc39b73a8"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a5aea21e7b14b68c9d0e74acdc39b73a8">DGtal::ATSolver2D::alpha</a></div><div class="ttdeci">double alpha</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00181">ATSolver2D.h:181</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a6122683e9eaf0a7c08cacf81dc253131"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a6122683e9eaf0a7c08cacf81dc253131">DGtal::ATSolver2D::setEpsilon</a></div><div class="ttdeci">void setEpsilon(double e)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00525">ATSolver2D.h:525</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a639bc75c1b8c9d67a5002c960c579aec"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a639bc75c1b8c9d67a5002c960c579aec">DGtal::ATSolver2D::initInputVectorFieldU2</a></div><div class="ttdeci">void initInputVectorFieldU2(const VectorFieldInput &input, SurfelRangeConstIterator itB, SurfelRangeConstIterator itE, bool normalize=false)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00288">ATSolver2D.h:288</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a68577ab02e5f3f631739243a437cffd7"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a68577ab02e5f3f631739243a437cffd7">DGtal::ATSolver2D::M12</a></div><div class="ttdeci">PrimalDerivative1 M12</div><div class="ttdoc">The primal edge to face average operator.</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00152">ATSolver2D.h:152</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a6934e9269b94e7c454824cff61bda4b2"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a6934e9269b94e7c454824cff61bda4b2">DGtal::ATSolver2D::smallest_epsilon_map</a></div><div class="ttdeci">SmallestEpsilonMap smallest_epsilon_map</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00178">ATSolver2D.h:178</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a6f50e5d7dee9c71461130c1548c1edc1"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a6f50e5d7dee9c71461130c1548c1edc1">DGtal::ATSolver2D::PrimalForm1</a></div><div class="ttdeci">Calculus::PrimalForm1 PrimalForm1</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00118">ATSolver2D.h:118</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a7332a00eda9c5a8f2cca3283df4fb97c"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a7332a00eda9c5a8f2cca3283df4fb97c">DGtal::ATSolver2D::l_1_over_4e</a></div><div class="ttdeci">PrimalForm0 l_1_over_4e</div><div class="ttdoc">The primal 0-form lambda/(4epsilon) (stored for performance)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00171">ATSolver2D.h:171</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a75240fe17b67bfdb7c34170c92413596"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a75240fe17b67bfdb7c34170c92413596">DGtal::ATSolver2D::getV0</a></div><div class="ttdeci">PrimalForm0 getV0() const</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00735">ATSolver2D.h:735</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a78262d79c4f40544ec8eac15c68fa712"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a78262d79c4f40544ec8eac15c68fa712">DGtal::ATSolver2D::primal_AD2</a></div><div class="ttdeci">PrimalAntiderivative2 primal_AD2</div><div class="ttdoc">The antiderivative of primal 2-forms.</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00154">ATSolver2D.h:154</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a7853f33b9a33d2744130cc29ab7cbfea"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a7853f33b9a33d2744130cc29ab7cbfea">DGtal::ATSolver2D::size</a></div><div class="ttdeci">Index size(const int order) const</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00258">ATSolver2D.h:258</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a7a4bba850da56d1718eb2d860e3e0eaa"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a7a4bba850da56d1718eb2d860e3e0eaa">DGtal::ATSolver2D::PrimalIdentity2</a></div><div class="ttdeci">Calculus::PrimalIdentity2 PrimalIdentity2</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00122">ATSolver2D.h:122</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a7f3e5bf3b47fb86dfccaa98ca7bb2e66"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a7f3e5bf3b47fb86dfccaa98ca7bb2e66">DGtal::ATSolver2D::getV1</a></div><div class="ttdeci">PrimalForm1 getV1() const</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00741">ATSolver2D.h:741</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a85c07dbe94ccebc4796eddbe9dcbcd4b"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a85c07dbe94ccebc4796eddbe9dcbcd4b">DGtal::ATSolver2D::PrimalDerivative1</a></div><div class="ttdeci">Calculus::PrimalDerivative1 PrimalDerivative1</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00124">ATSolver2D.h:124</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a92f43a60c3f47ef37e451c23ef790f40"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a92f43a60c3f47ef37e451c23ef790f40">DGtal::ATSolver2D::checkV0</a></div><div class="ttdeci">std::tuple< double, double, double > checkV0() const</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00723">ATSolver2D.h:723</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a93f2d93034f48846c70d8ba848a79795"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a93f2d93034f48846c70d8ba848a79795">DGtal::ATSolver2D::v0</a></div><div class="ttdeci">PrimalForm0 v0</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00167">ATSolver2D.h:167</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a966e9e7334baff72542aa5ffd50fb670"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a966e9e7334baff72542aa5ffd50fb670">DGtal::ATSolver2D::Calculus</a></div><div class="ttdeci">DiscreteExteriorCalculus< 2, dimension, LinearAlgebra > Calculus</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00114">ATSolver2D.h:114</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a9adf8bd493312d3a4feb100575fa5146"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a9adf8bd493312d3a4feb100575fa5146">DGtal::ATSolver2D::initOperators</a></div><div class="ttdeci">void initOperators()</div><div class="ttdoc">Initializes the operators.</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00976">ATSolver2D.h:976</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a9b11764a4db07a8d2c66a9ddd645667b"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a9b11764a4db07a8d2c66a9ddd645667b">DGtal::ATSolver2D::setUp</a></div><div class="ttdeci">void setUp(double a, double l, const std::map< Surfel, Scalar > &weights)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00463">ATSolver2D.h:463</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a9c2c3aef54916e26a9532602adedc594"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a9c2c3aef54916e26a9532602adedc594">DGtal::ATSolver2D::PrimalAntiderivative2</a></div><div class="ttdeci">Calculus::PrimalAntiderivative2 PrimalAntiderivative2</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00126">ATSolver2D.h:126</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a9cd935c7278fa1c6a413908565952638"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a9cd935c7278fa1c6a413908565952638">DGtal::ATSolver2D::ATSolver2D</a></div><div class="ttdeci">ATSolver2D(ATSolver2D &&other)=default</div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_a9fc1d6faa1e173efa7d3490e39abf403"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#a9fc1d6faa1e173efa7d3490e39abf403">DGtal::ATSolver2D::SmallestEpsilonMap</a></div><div class="ttdeci">KSpace::template SurfelMap< double >::Type SmallestEpsilonMap</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00115">ATSolver2D.h:115</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aa10fb1c8ee0c9873a9abe3d6cd04eea1"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aa10fb1c8ee0c9873a9abe3d6cd04eea1">DGtal::ATSolver2D::surfel2idx</a></div><div class="ttdeci">Surfel2IndexMap surfel2idx</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00175">ATSolver2D.h:175</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aa28ebc4b0290afebeb401320c9c0d864"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aa28ebc4b0290afebeb401320c9c0d864">DGtal::ATSolver2D::isValid</a></div><div class="ttdeci">bool isValid() const</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00962">ATSolver2D.h:962</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aa505567d0cbde4340e447f31cabca9d8"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aa505567d0cbde4340e447f31cabca9d8">DGtal::ATSolver2D::PrimalHodge1</a></div><div class="ttdeci">Calculus::PrimalHodge1 PrimalHodge1</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00128">ATSolver2D.h:128</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aa5666abdbf81ceecf6802d754233c6c3"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aa5666abdbf81ceecf6802d754233c6c3">DGtal::ATSolver2D::operator=</a></div><div class="ttdeci">ATSolver2D & operator=(const ATSolver2D &other)=default</div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aa5901cc63f4066bea0a57f21600e685a"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aa5901cc63f4066bea0a57f21600e685a">DGtal::ATSolver2D::RealVector</a></div><div class="ttdeci">Space::RealVector RealVector</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00108">ATSolver2D.h:108</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aa7ade8239ac530e34ff0405cc5c8f46f"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aa7ade8239ac530e34ff0405cc5c8f46f">DGtal::ATSolver2D::Surfel2IndexMap</a></div><div class="ttdeci">KSpace::template SurfelMap< Index >::Type Surfel2IndexMap</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00130">ATSolver2D.h:130</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aaa633904ce76ed3a46428243ef909f6c"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aaa633904ce76ed3a46428243ef909f6c">DGtal::ATSolver2D::PrimalIdentity0</a></div><div class="ttdeci">Calculus::PrimalIdentity0 PrimalIdentity0</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00120">ATSolver2D.h:120</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_ab1fba42ea868fa2959c8ae6f17884d06"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#ab1fba42ea868fa2959c8ae6f17884d06">DGtal::ATSolver2D::solveGammaConvergence</a></div><div class="ttdeci">bool solveGammaConvergence(double eps1=2.0, double eps2=0.25, double epsr=2.0, bool compute_smallest_epsilon_map=false, double n_oo_max=1e-4, unsigned int iter_max=10)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00657">ATSolver2D.h:657</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_ab8b5510ecfe47577444bd8bbe56fdfb8"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#ab8b5510ecfe47577444bd8bbe56fdfb8">DGtal::ATSolver2D::PrimalForm2</a></div><div class="ttdeci">Calculus::PrimalForm2 PrimalForm2</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00119">ATSolver2D.h:119</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_ab8bd483b502f6e0808db55a17d2f234f"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#ab8bd483b502f6e0808db55a17d2f234f">DGtal::ATSolver2D::getV2</a></div><div class="ttdeci">PrimalForm2 getV2() const</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00747">ATSolver2D.h:747</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_ab9b12aea6bd78758f5f05aeb256916e1"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#ab9b12aea6bd78758f5f05aeb256916e1">DGtal::ATSolver2D::primal_D1</a></div><div class="ttdeci">PrimalDerivative1 primal_D1</div><div class="ttdoc">the derivative operator for primal 1-forms</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00148">ATSolver2D.h:148</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_abb06d49e7ede42c74b9768b2387156ad"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#abb06d49e7ede42c74b9768b2387156ad">DGtal::ATSolver2D::SolverV0</a></div><div class="ttdeci">DiscreteExteriorCalculusSolver< Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL > SolverV0</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00140">ATSolver2D.h:140</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_abd1939fe7e7775c22a381f07306b8104"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#abd1939fe7e7775c22a381f07306b8104">DGtal::ATSolver2D::l_1_over_4e_Id0</a></div><div class="ttdeci">PrimalIdentity0 l_1_over_4e_Id0</div><div class="ttdoc">The 1/(4epsilon)-weighted identity operator for primal 0-forms (stored for performance)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00158">ATSolver2D.h:158</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_ac48f83d74c760279204aad8cb1ce3205"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#ac48f83d74c760279204aad8cb1ce3205">DGtal::ATSolver2D::Self</a></div><div class="ttdeci">ATSolver2D< KSpace, LinearAlgebra > Self</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00097">ATSolver2D.h:97</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_ac8315ceca305aff6df624d1ac61e1db3"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#ac8315ceca305aff6df624d1ac61e1db3">DGtal::ATSolver2D::selfDisplay</a></div><div class="ttdeci">void selfDisplay(std::ostream &out) const</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00949">ATSolver2D.h:949</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_acd57ddea1029fe4bbd9cc3b946c66034"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#acd57ddea1029fe4bbd9cc3b946c66034">DGtal::ATSolver2D::normalize_u2</a></div><div class="ttdeci">bool normalize_u2</div><div class="ttdoc">Indicates whether to normalize U (unit norm) at each iteration or not.</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00189">ATSolver2D.h:189</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_ace1d921c6ca6be396640de3a1601fc36"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#ace1d921c6ca6be396640de3a1601fc36">DGtal::ATSolver2D::Index</a></div><div class="ttdeci">Calculus::Index Index</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00116">ATSolver2D.h:116</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aceea9eaa1d4e48105f531cb288bf4fef"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aceea9eaa1d4e48105f531cb288bf4fef">DGtal::ATSolver2D::lambda</a></div><div class="ttdeci">double lambda</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00184">ATSolver2D.h:184</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_acf4463f93c45c3b40f5c921a5914312e"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#acf4463f93c45c3b40f5c921a5914312e">DGtal::ATSolver2D::former_v0</a></div><div class="ttdeci">PrimalForm0 former_v0</div><div class="ttdoc">The primal 0-form v at the previous iteration.</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00169">ATSolver2D.h:169</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_ad57b159c5d672171e2d321d243464b3a"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#ad57b159c5d672171e2d321d243464b3a">DGtal::ATSolver2D::Cell</a></div><div class="ttdeci">KSpace::Cell Cell</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00111">ATSolver2D.h:111</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_ad62971b62a4601b991db67ed2ef69fb6"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#ad62971b62a4601b991db67ed2ef69fb6">DGtal::ATSolver2D::SolverU2</a></div><div class="ttdeci">DiscreteExteriorCalculusSolver< Calculus, LinearAlgebraSolver, 2, PRIMAL, 2, PRIMAL > SolverU2</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00139">ATSolver2D.h:139</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_ad64e8fed55c3206e409844e78b64b076"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#ad64e8fed55c3206e409844e78b64b076">DGtal::ATSolver2D::normalizeU2</a></div><div class="ttdeci">void normalizeU2()</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00684">ATSolver2D.h:684</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_ad6746ffd0e041d8c9e3634d9ecd66ac7"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#ad6746ffd0e041d8c9e3634d9ecd66ac7">DGtal::ATSolver2D::g2</a></div><div class="ttdeci">std::vector< PrimalForm2 > g2</div><div class="ttdoc">The N-array of input primal 2-forms g.</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00160">ATSolver2D.h:160</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_ad8ef0a982f30c949beb422687931a428"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#ad8ef0a982f30c949beb422687931a428">DGtal::ATSolver2D::~ATSolver2D</a></div><div class="ttdeci">~ATSolver2D()=default</div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_adb0834940772ba408ed86d9b34a57a6a"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#adb0834940772ba408ed86d9b34a57a6a">DGtal::ATSolver2D::diffV0</a></div><div class="ttdeci">std::tuple< double, double, double > diffV0() const</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00702">ATSolver2D.h:702</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_adead3da234dde032d7a2e5bd76573507"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#adead3da234dde032d7a2e5bd76573507">DGtal::ATSolver2D::getOutputVectorFieldU2</a></div><div class="ttdeci">void getOutputVectorFieldU2(VectorFieldOutput &output, SurfelRangeConstIterator itB, SurfelRangeConstIterator itE)</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00772">ATSolver2D.h:772</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aebd65b0edd0d5018015092e8aa74141c"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aebd65b0edd0d5018015092e8aa74141c">DGtal::ATSolver2D::ATSolver2D</a></div><div class="ttdeci">ATSolver2D()=delete</div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aecc1cb13fbf576486331e9cbda695eca"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aecc1cb13fbf576486331e9cbda695eca">DGtal::ATSolver2D::primal_D0</a></div><div class="ttdeci">PrimalDerivative0 primal_D0</div><div class="ttdoc">the derivative operator for primal 0-forms</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00146">ATSolver2D.h:146</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aede4e265e44ce612075bb3c15f8690da"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aede4e265e44ce612075bb3c15f8690da">DGtal::ATSolver2D::CellOutputPolicy</a></div><div class="ttdeci">CellOutputPolicy</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00103">ATSolver2D.h:103</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aede4e265e44ce612075bb3c15f8690daa1cfa7b862062261bcc5cfe4fbe5ccc94"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aede4e265e44ce612075bb3c15f8690daa1cfa7b862062261bcc5cfe4fbe5ccc94">DGtal::ATSolver2D::Maximum</a></div><div class="ttdeci">@ Maximum</div><div class="ttdoc">compute maximum value at cell vertices</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00105">ATSolver2D.h:105</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aede4e265e44ce612075bb3c15f8690daadb00ed33d4644ea0a15d240658b90d16"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aede4e265e44ce612075bb3c15f8690daadb00ed33d4644ea0a15d240658b90d16">DGtal::ATSolver2D::Average</a></div><div class="ttdeci">@ Average</div><div class="ttdoc">compute average values at cell vertices</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00103">ATSolver2D.h:103</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aede4e265e44ce612075bb3c15f8690daaf5b10e5f87cc7b7839257bab531fb74a"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aede4e265e44ce612075bb3c15f8690daaf5b10e5f87cc7b7839257bab531fb74a">DGtal::ATSolver2D::Minimum</a></div><div class="ttdeci">@ Minimum</div><div class="ttdoc">compute minimum value at cell vertices,</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00104">ATSolver2D.h:104</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_aee83b3ac462fb907f43d57a9124e8e7e"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#aee83b3ac462fb907f43d57a9124e8e7e">DGtal::ATSolver2D::ptrCalculus</a></div><div class="ttdeci">CountedConstPtrOrConstPtr< Calculus > ptrCalculus</div><div class="ttdoc">A smart (or not) pointer to a calculus object.</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00144">ATSolver2D.h:144</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_af04301709ce9ba5dd2233acde8642301"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#af04301709ce9ba5dd2233acde8642301">DGtal::ATSolver2D::M01</a></div><div class="ttdeci">PrimalDerivative0 M01</div><div class="ttdoc">The primal vertex to edge average operator.</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00150">ATSolver2D.h:150</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_af39a545e086dbe2509ac81c72c46f3e8"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#af39a545e086dbe2509ac81c72c46f3e8">DGtal::ATSolver2D::ATSolver2D</a></div><div class="ttdeci">ATSolver2D(const ATSolver2D &other)=default</div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_afa2b4116a2bcc862b6df458ae067eb4b"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#afa2b4116a2bcc862b6df458ae067eb4b">DGtal::ATSolver2D::KSpace</a></div><div class="ttdeci">TKSpace KSpace</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00095">ATSolver2D.h:95</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ATSolver2D_html_afe7dfc2d191ecdf4b86ee43220fc6dc7"><div class="ttname"><a href="classDGtal_1_1ATSolver2D.html#afe7dfc2d191ecdf4b86ee43220fc6dc7">DGtal::ATSolver2D::epsilon</a></div><div class="ttdeci">double epsilon</div><div class="ttdef"><b>Definition:</b> <a href="ATSolver2D_8h_source.html#l00187">ATSolver2D.h:187</a></div></div>
<div class="ttc" id="aclassDGtal_1_1ConstAlias_html"><div class="ttname"><a href="classDGtal_1_1ConstAlias.html">DGtal::ConstAlias</a></div><div class="ttdoc">Aim: This class encapsulates its parameter class so that to indicate to the user that the object/poin...</div><div class="ttdef"><b>Definition:</b> <a href="ConstAlias_8h_source.html#l00186">ConstAlias.h:187</a></div></div>
<div class="ttc" id="aclassDGtal_1_1CountedConstPtrOrConstPtr_html"><div class="ttname"><a href="classDGtal_1_1CountedConstPtrOrConstPtr.html">DGtal::CountedConstPtrOrConstPtr</a></div><div class="ttdoc">Aim: Smart or simple const pointer on T. It can be a smart pointer based on reference counts or a sim...</div><div class="ttdef"><b>Definition:</b> <a href="CountedConstPtrOrConstPtr_8h_source.html#l00094">CountedConstPtrOrConstPtr.h:95</a></div></div>
<div class="ttc" id="aclassDGtal_1_1DiscreteExteriorCalculusSolver_html"><div class="ttname"><a href="classDGtal_1_1DiscreteExteriorCalculusSolver.html">DGtal::DiscreteExteriorCalculusSolver< Calculus, LinearAlgebraSolver, 2, PRIMAL, 2, PRIMAL ></a></div></div>
<div class="ttc" id="aclassDGtal_1_1DiscreteExteriorCalculusSolver_html_a073f1c0cdb349421b1a6d499fefc6052"><div class="ttname"><a href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#a073f1c0cdb349421b1a6d499fefc6052">DGtal::DiscreteExteriorCalculusSolver::isValid</a></div><div class="ttdeci">bool isValid() const</div></div>
<div class="ttc" id="aclassDGtal_1_1DiscreteExteriorCalculusSolver_html_a7673281a29a04ef2978bad9b373c2382"><div class="ttname"><a href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#a7673281a29a04ef2978bad9b373c2382">DGtal::DiscreteExteriorCalculusSolver::solve</a></div><div class="ttdeci">SolutionKForm solve(const InputKForm &input_kform) const</div></div>
<div class="ttc" id="aclassDGtal_1_1DiscreteExteriorCalculusSolver_html_a90f2a9e43a13293e6368b63298363b60"><div class="ttname"><a href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#a90f2a9e43a13293e6368b63298363b60">DGtal::DiscreteExteriorCalculusSolver::compute</a></div><div class="ttdeci">DiscreteExteriorCalculusSolver & compute(const Operator &linear_operator)</div></div>
<div class="ttc" id="aclassDGtal_1_1DiscreteExteriorCalculusSolver_html_ab26e3418601a9779709cf92f4366cefe"><div class="ttname"><a href="classDGtal_1_1DiscreteExteriorCalculusSolver.html#ab26e3418601a9779709cf92f4366cefe">DGtal::DiscreteExteriorCalculusSolver::myLinearAlgebraSolver</a></div><div class="ttdeci">LinearAlgebraSolver myLinearAlgebraSolver</div><div class="ttdef"><b>Definition:</b> <a href="DiscreteExteriorCalculusSolver_8h_source.html#l00100">DiscreteExteriorCalculusSolver.h:100</a></div></div>
<div class="ttc" id="aclassDGtal_1_1DiscreteExteriorCalculus_html"><div class="ttname"><a href="classDGtal_1_1DiscreteExteriorCalculus.html">DGtal::DiscreteExteriorCalculus</a></div><div class="ttdoc">Aim: DiscreteExteriorCalculus represents a calculus in the dec package. This is the main structure in...</div><div class="ttdef"><b>Definition:</b> <a href="DiscreteExteriorCalculus_8h_source.html#l00097">DiscreteExteriorCalculus.h:98</a></div></div>
<div class="ttc" id="aclassDGtal_1_1DiscreteExteriorCalculus_html_ab4367cb06a628fc96e6c637d0f822df0"><div class="ttname"><a href="classDGtal_1_1DiscreteExteriorCalculus.html#ab4367cb06a628fc96e6c637d0f822df0">DGtal::DiscreteExteriorCalculus::Index</a></div><div class="ttdeci">LinearAlgebraBackend::DenseVector::Index Index</div><div class="ttdef"><b>Definition:</b> <a href="DiscreteExteriorCalculus_8h_source.html#l00107">DiscreteExteriorCalculus.h:107</a></div></div>
<div class="ttc" id="aclassDGtal_1_1HyperRectDomain_html"><div class="ttname"><a href="classDGtal_1_1HyperRectDomain.html">DGtal::HyperRectDomain< Space ></a></div></div>
<div class="ttc" id="aclassDGtal_1_1KForm_html"><div class="ttname"><a href="classDGtal_1_1KForm.html">DGtal::KForm</a></div><div class="ttdoc">Aim: KForm represents discrete kforms in the dec package.</div><div class="ttdef"><b>Definition:</b> <a href="KForm_8h_source.html#l00065">KForm.h:66</a></div></div>
<div class="ttc" id="aclassDGtal_1_1KForm_html_a0f34f82e9a9dbc012dfb727b552806a6"><div class="ttname"><a href="classDGtal_1_1KForm.html#a0f34f82e9a9dbc012dfb727b552806a6">DGtal::KForm::ones</a></div><div class="ttdeci">static KForm< TCalculus, order, duality > ones(ConstAlias< Calculus > calculus)</div></div>
<div class="ttc" id="aclassDGtal_1_1KForm_html_a19e859f462f1d851550465b7fcc2c68d"><div class="ttname"><a href="classDGtal_1_1KForm.html#a19e859f462f1d851550465b7fcc2c68d">DGtal::KForm::myContainer</a></div><div class="ttdeci">Container myContainer</div><div class="ttdef"><b>Definition:</b> <a href="KForm_8h_source.html#l00131">KForm.h:131</a></div></div>
<div class="ttc" id="aclassDGtal_1_1KForm_html_afbd7ecc8d2c3eb5ec5d0f7c187c33ba0"><div class="ttname"><a href="classDGtal_1_1KForm.html#afbd7ecc8d2c3eb5ec5d0f7c187c33ba0">DGtal::KForm::zeros</a></div><div class="ttdeci">static KForm< TCalculus, order, duality > zeros(ConstAlias< Calculus > calculus)</div></div>
<div class="ttc" id="aclassDGtal_1_1LinearOperator_html"><div class="ttname"><a href="classDGtal_1_1LinearOperator.html">DGtal::LinearOperator</a></div><div class="ttdoc">Aim: LinearOperator represents discrete linear operator between discrete kforms in the DEC package.</div><div class="ttdef"><b>Definition:</b> <a href="LinearOperator_8h_source.html#l00068">LinearOperator.h:69</a></div></div>
<div class="ttc" id="aclassDGtal_1_1LinearOperator_html_aa5696bafeed5f62de870b35ef6b9dad8"><div class="ttname"><a href="classDGtal_1_1LinearOperator.html#aa5696bafeed5f62de870b35ef6b9dad8">DGtal::LinearOperator::myContainer</a></div><div class="ttdeci">Container myContainer</div><div class="ttdef"><b>Definition:</b> <a href="LinearOperator_8h_source.html#l00117">LinearOperator.h:117</a></div></div>
<div class="ttc" id="aclassDGtal_1_1LinearOperator_html_aeee5924a3cc7b145068dacb48611157c"><div class="ttname"><a href="classDGtal_1_1LinearOperator.html#aeee5924a3cc7b145068dacb48611157c">DGtal::LinearOperator::transpose</a></div><div class="ttdeci">TransposedLinearOperator transpose() const</div></div>
<div class="ttc" id="aclassDGtal_1_1PointVector_html"><div class="ttname"><a href="classDGtal_1_1PointVector.html">DGtal::PointVector</a></div><div class="ttdoc">Aim: Implements basic operations that will be used in Point and Vector classes.</div><div class="ttdef"><b>Definition:</b> <a href="PointVector_8h_source.html#l00592">PointVector.h:593</a></div></div>
<div class="ttc" id="aclassDGtal_1_1PointVector_html_ab5f7548d4edc0d8edb4b64cc332db8f2"><div class="ttname"><a href="classDGtal_1_1PointVector.html#ab5f7548d4edc0d8edb4b64cc332db8f2">DGtal::PointVector::Component</a></div><div class="ttdeci">TEuclideanRing Component</div><div class="ttdoc">Type for Vector elements.</div><div class="ttdef"><b>Definition:</b> <a href="PointVector_8h_source.html#l00614">PointVector.h:614</a></div></div>
<div class="ttc" id="aclassDGtal_1_1SpaceND_html"><div class="ttname"><a href="classDGtal_1_1SpaceND.html">DGtal::SpaceND</a></div><div class="ttdef"><b>Definition:</b> <a href="SpaceND_8h_source.html#l00095">SpaceND.h:96</a></div></div>
<div class="ttc" id="aclassDGtal_1_1Trace_html_a352b7160bf722e2f0bcbee5d0bad6ef3"><div class="ttname"><a href="classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">DGtal::Trace::beginBlock</a></div><div class="ttdeci">void beginBlock(const std::string &keyword="")</div></div>
<div class="ttc" id="aclassDGtal_1_1Trace_html_ad054990834d2763627166540087a2980"><div class="ttname"><a href="classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">DGtal::Trace::info</a></div><div class="ttdeci">std::ostream & info()</div></div>
<div class="ttc" id="aclassDGtal_1_1Trace_html_afa3a2874289734884107b1ce68ccb93d"><div class="ttname"><a href="classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">DGtal::Trace::endBlock</a></div><div class="ttdeci">double endBlock()</div></div>
<div class="ttc" id="afullConvexitySphereGeodesics_8cpp_html_ab053a8ae7537e4f87fa9a46962f7617a"><div class="ttname"><a href="fullConvexitySphereGeodesics_8cpp.html#ab053a8ae7537e4f87fa9a46962f7617a">Index</a></div><div class="ttdeci">SMesh::Index Index</div><div class="ttdef"><b>Definition:</b> <a href="fullConvexitySphereGeodesics_8cpp_source.html#l00117">fullConvexitySphereGeodesics.cpp:117</a></div></div>
<div class="ttc" id="anamespaceDGtal_1_1dec__helper_html_a6b01f3b8906df8056bf147dd40935738"><div class="ttname"><a href="namespaceDGtal_1_1dec__helper.html#a6b01f3b8906df8056bf147dd40935738">DGtal::dec_helper::diagonal</a></div><div class="ttdeci">DGtal::LinearOperator< Calculus, dim, duality, dim, duality > diagonal(const DGtal::KForm< Calculus, dim, duality > &kform)</div><div class="ttdef"><b>Definition:</b> <a href="DECHelpers_8h_source.html#l00060">DECHelpers.h:60</a></div></div>
<div class="ttc" id="anamespaceDGtal_html"><div class="ttname"><a href="namespaceDGtal.html">DGtal</a></div><div class="ttdoc">DGtal is the top-level namespace which contains all DGtal functions and types.</div></div>
<div class="ttc" id="anamespaceDGtal_html_a66aca9ad97cfa71ddd5b1333a392d50d"><div class="ttname"><a href="http://dgtal.org/doc/tools/nightly/namespaceDGtal.html#a66aca9ad97cfa71ddd5b1333a392d50d">DGtal::operator<<</a></div><div class="ttdeci">std::ostream & operator<<(std::ostream &out, const ATu0v1< TKSpace, TLinearAlgebra > &object)</div></div>
<div class="ttc" id="anamespaceDGtal_html_a8fbe8c8d47ca5c36ced14284ac62613d"><div class="ttname"><a href="namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">DGtal::Dimension</a></div><div class="ttdeci">DGtal::uint32_t Dimension</div><div class="ttdef"><b>Definition:</b> <a href="Common_8h_source.html#l00136">Common.h:136</a></div></div>
<div class="ttc" id="anamespaceDGtal_html_a8fc7012708b0416880a5c8b12dfdf9dd"><div class="ttname"><a href="namespaceDGtal.html#a8fc7012708b0416880a5c8b12dfdf9dd">DGtal::trace</a></div><div class="ttdeci">Trace trace</div><div class="ttdef"><b>Definition:</b> <a href="Common_8h_source.html#l00153">Common.h:153</a></div></div>
<div class="ttc" id="anamespaceDGtal_html_ab8007ddbb5627666913e18c3b951745da7b7d86a1d82efbe8b9bc0ad3c7c80bd7"><div class="ttname"><a href="namespaceDGtal.html#ab8007ddbb5627666913e18c3b951745da7b7d86a1d82efbe8b9bc0ad3c7c80bd7">DGtal::PRIMAL</a></div><div class="ttdeci">@ PRIMAL</div><div class="ttdef"><b>Definition:</b> <a href="Duality_8h_source.html#l00061">Duality.h:61</a></div></div>
<div class="ttc" id="astructDGtal_1_1EigenLinearAlgebraBackend_html_a164f5eddcb81f4d6fd688fefc91057c9"><div class="ttname"><a href="structDGtal_1_1EigenLinearAlgebraBackend.html#a164f5eddcb81f4d6fd688fefc91057c9">DGtal::EigenLinearAlgebraBackend::SolverSimplicialLDLT</a></div><div class="ttdeci">Eigen::SimplicialLDLT< SparseMatrix > SolverSimplicialLDLT</div><div class="ttdef"><b>Definition:</b> <a href="EigenSupport_8h_source.html#l00106">EigenSupport.h:106</a></div></div>
<div class="ttc" id="astructDGtal_1_1KhalimskyCell_html"><div class="ttname"><a href="structDGtal_1_1KhalimskyCell.html">DGtal::KhalimskyCell< dim, Integer ></a></div></div>
<div class="ttc" id="astructDGtal_1_1SignedKhalimskyCell_html"><div class="ttname"><a href="structDGtal_1_1SignedKhalimskyCell.html">DGtal::SignedKhalimskyCell</a></div><div class="ttdoc">Represents a signed cell in a cellular grid space by its Khalimsky coordinates and a boolean value.</div><div class="ttdef"><b>Definition:</b> <a href="KhalimskySpaceND_8h_source.html#l00208">KhalimskySpaceND.h:209</a></div></div>
<div class="ttc" id="atestArithmeticalDSS_8cpp_html_af082905f7eac6d03e92015146bbc1925"><div class="ttname"><a href="testArithmeticalDSS_8cpp.html#af082905f7eac6d03e92015146bbc1925">max</a></div><div class="ttdeci">int max(int a, int b)</div><div class="ttdef"><b>Definition:</b> <a href="testArithmeticalDSS_8cpp_source.html#l01108">testArithmeticalDSS.cpp:1108</a></div></div>
<div class="ttc" id="atestBits_8cpp_html_abf1224ffcf053d0b7990122fcef93bc9"><div class="ttname"><a href="testBits_8cpp.html#abf1224ffcf053d0b7990122fcef93bc9">index</a></div><div class="ttdeci">unsigned int index(DGtal::uint32_t n, unsigned int b)</div><div class="ttdef"><b>Definition:</b> <a href="testBits_8cpp_source.html#l00044">testBits.cpp:44</a></div></div>
<div class="ttc" id="atestCubicalComplex_8cpp_html_a2b87ed989d2519d025bd5d4fbcbac062"><div class="ttname"><a href="testCubicalComplex_8cpp.html#a2b87ed989d2519d025bd5d4fbcbac062">K</a></div><div class="ttdeci">KSpace K</div><div class="ttdef"><b>Definition:</b> <a href="testCubicalComplex_8cpp_source.html#l00062">testCubicalComplex.cpp:62</a></div></div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="dir_68267d1309a1af8e8297ef4c3efbcdba.html">src</a></li><li class="navelem"><a class="el" href="dir_f2cd1aeea1cfa982bb13a5f95fa4218c.html">DGtal</a></li><li class="navelem"><a class="el" href="dir_dff551b9dd3c14b106f4789fe844a7f9.html">dec</a></li><li class="navelem"><b>ATSolver2D.h</b></li>
<li class="footer">Generated on Mon Dec 23 2024 13:18:27 for DGtal by <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.1 </li>
</ul>
</div>
</body>
</html>