-
Notifications
You must be signed in to change notification settings - Fork 2
/
Copy pathclassCGAL_1_1Eigen__solver__traits.html
525 lines (499 loc) · 37 KB
/
classCGAL_1_1Eigen__solver__traits.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
<!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>
<link rel="canonical" href="https://doc.cgal.org/latest/Solver_interface/classCGAL_1_1Eigen__solver__traits.html"/>
<link rel="icon" type="image/png" href="../Manual/g-196x196-doc.png">
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8">
<meta http-equiv="X-UA-Compatible" content="IE=11">
<meta name="generator" content="Doxygen 1.9.6">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>CGAL 6.1 - CGAL and Solvers: CGAL::Eigen_solver_traits< EigenSolverT > Class Template Reference</title>
<!-- <link href="../Manual/tabs.css" rel="stylesheet" type="text/css"/> -->
<script type="text/javascript" src="../Manual/jquery.js"></script>
<script type="text/javascript" src="../Manual/dynsections.js"></script>
<script src="../Manual/hacks.js" type="text/javascript"></script>
<!-- Manually include treeview and search to avoid bloat and to fix
paths to the directory Manual . -->
<!-- $.treeview -->
<!-- $.search -->
<link href="navtree.css" rel="stylesheet" type="text/css">
<script type="text/javascript" src="../Manual/resize.js"></script>
<script type="text/javascript" src="navtreedata.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<script type="text/javascript">
$(document).ready(initResizable);
</script>
<link href="../Manual/search/search.css" rel="stylesheet" type="text/css">
<script type="text/javascript" src="../Manual/search/searchdata.js"></script>
<script type="text/javascript" src="../Manual/search/search.js"></script>
<script type="text/javascript">
$(document).ready(function() { init_search(); });
</script>
<link href="../Manual/search/search.css" rel="stylesheet" type="text/css">
<script type="text/javascript" src="../Manual/search/search.js"></script>
<!-- Manually done below. -->
<link href="../Manual/doxygen.css" rel="stylesheet" type="text/css">
<link href="../Manual/cgal_stylesheet.css" rel="stylesheet" type="text/css">
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
jax: ["input/TeX","output/HTML-CSS"],
});
//<![CDATA[
MathJax.Hub.Config(
{
TeX: {
Macros: {
qprel: [ "{\\gtreqless}", 0],
qpx: [ "{\\mathbf{x}}", 0],
qpl: [ "{\\mathbf{l}}", 0],
qpu: [ "{\\mathbf{u}}", 0],
qpc: [ "{\\mathbf{c}}", 0],
qpb: [ "{\\mathbf{b}}", 0],
qpy: [ "{\\mathbf{y}}", 0],
qpw: [ "{\\mathbf{w}}", 0],
qplambda: [ "{\\mathbf{\\lambda}}", 0],
ssWpoint: [ "{\\bf #1}", 1],
ssWeight: [ "{w_{#1}}", 1],
dabs: [ "{\\parallel\\! #1 \\!\\parallel}", 1],
E: [ "{\\mathrm{E}}", 0],
A: [ "{\\mathrm{A}}", 0],
R: [ "{\\mathrm{R}}", 0],
N: [ "{\\mathrm{N}}", 0],
Q: [ "{\\mathrm{Q}}", 0],
Z: [ "{\\mathrm{Z}}", 0],
ccSum: [ "{\\sum_{#1}^{#2}{#3}}", 3],
ccProd: [ "{\\prod_{#1}^{#2}{#3}}", 3],
pyr: [ "{\\operatorname{Pyr}}", 0],
aff: [ "{\\operatorname{aff}}", 0],
Ac: [ "{\\cal A}", 0],
Sc: [ "{\\cal S}", 0],
},
equationNumbers: { autoNumber: "AMS" }
}
}
);
MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () {
var PARSE = MathJax.InputJax.TeX.Parse,
TEXT = PARSE.prototype.InternalText;
PARSE.Augment({
InternalText: function (text,def) {
text = text.replace(/\\/g,"");
return TEXT.call(this,text,def);
}
});
});
//]]>
</script>
<script type="text/javascript" async="async" src="https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js"></script>
<script src="modules.js" type="text/javascript"></script>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="back-nav">
<ul>
<li><a href="https://www.cgal.org/">cgal.org</a></li>
<li><a href="../Manual/index.html">Top</a></li>
<li><a href="../Manual/general_intro.html">Getting Started</a></li>
<li><a href="../Manual/tutorials.html">Tutorials</a></li>
<li><a href="../Manual/packages.html">Package Overview</a></li>
<li><a href="../Manual/how_to_cite_cgal.html">Acknowledging CGAL</a></li>
</ul>
<!-- In a package SEARCHENGINE = false, so we cannot use
insertion. That's why we have to do it manually here. Notice
that we also take pngs from the Manual. -->
<div id="MSearchBox" class="MSearchBoxInactive">
<span class="left">
<span id="MSearchSelect" onmouseover="return searchBox.OnSearchSelectShow()" onmouseout="return searchBox.OnSearchSelectHide()">
</span>
<input type="text" id="MSearchField" value="" placeholder="Search" accesskey="S" onfocus="searchBox.OnSearchFieldFocus(true)" onblur="searchBox.OnSearchFieldFocus(false)" onkeyup="searchBox.OnSearchFieldChange(event)">
</span>
<span class="right">
<a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="../Manual/search/close.svg" alt=""></a>
</span>
</div>
</div>
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr id="projectrow">
<td id="projectalign">
<div id="projectname">CGAL 6.1 - CGAL and Solvers
</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- Code below is usually inserted by doxygen when SEARCHENGINE =
true. Notice that the path to the search directory is adjusted to
the top-level.-->
<script type="text/javascript">
var searchBox = new SearchBox("searchBox", "../Manual/search/",'.html');
</script>
<!-- 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">
<div id="MSearchResults">
<div class="SRPage">
<div id="SRIndex">
<div id="SRResults"></div>
<div class="SRStatus" id="Loading">Loading...</div>
<div class="SRStatus" id="Searching">Searching...</div>
<div class="SRStatus" id="NoMatches">No Matches</div>
</div>
</div>
</div>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.9.6 -->
</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" style="display: none"></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:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
$(document).ready(function(){initNavTree('classCGAL_1_1Eigen__solver__traits.html',''); initResizable(); });
/* @license-end */
</script>
<div id="doc-content">
<div class="header">
<div class="summary">
<a href="classCGAL_1_1Eigen__solver__traits-members.html">List of all members</a> |
<a href="#pub-methods">Public Member Functions</a> |
<a href="#pro-attribs">Protected Attributes</a> </div>
<div class="headertitle"><div class="title">CGAL::Eigen_solver_traits< EigenSolverT > Class Template Reference<div class="ingroups"><a class="el" href="group__PkgSolverInterfaceRef.html">CGAL and Solvers Reference</a> » <a class="el" href="group__PkgSolverInterfaceLS.html">Linear Systems</a></div></div></div>
</div><!--header-->
<div class="contents">
<p><code>#include <CGAL/Eigen_solver_traits.h></code></p>
<a name="details" id="details"></a><h2 class="groupheader">Definition</h2>
<div class="textblock"><div class="compoundTemplParams">template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>><br>
class CGAL::Eigen_solver_traits< EigenSolverT ></div><p>The class <code><a class="el" href="classCGAL_1_1Eigen__solver__traits.html" title="The class Eigen_solver_traits provides an interface to the sparse solvers of Eigen.">Eigen_solver_traits</a></code> provides an interface to the sparse solvers of <a class="elRef" href="../Manual/thirdparty.html#thirdpartyEigen">Eigen</a>. </p>
<p><a class="elRef" href="../Manual/thirdparty.html#thirdpartyEigen">Eigen</a> version 3.1 (or later) must be available on the system.</p>
<dl>
<dt>Is model of</dt>
<dd><code><a class="el" href="classSparseLinearAlgebraWithFactorTraits__d.html" title="Concept describing the set of requirements for a direct sparse linear system solver with factorizatio...">SparseLinearAlgebraWithFactorTraits_d</a></code> </dd>
<dt></dt>
<dd><code><a class="el" href="classNormalEquationSparseLinearAlgebraTraits__d.html" title="Concept describing the set of requirements for solving the normal equation , being a matrix,...">NormalEquationSparseLinearAlgebraTraits_d</a></code> </dd>
</dl>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">EigenSolverT</td><td>A sparse solver of <a class="elRef" href="../Manual/thirdparty.html#thirdpartyEigen">Eigen</a>. The default solver is the iterative bi-conjugate gradient stabilized solver <code>Eigen::BiCGSTAB</code> for <code>double</code>.</td></tr>
</table>
</dd>
</dl>
<dl class="section see"><dt>See also</dt><dd><code><a class="el" href="structCGAL_1_1Eigen__sparse__matrix.html" title="The class Eigen_sparse_matrix is a wrapper around Eigen matrix type Eigen::SparseMatrix that represen...">CGAL::Eigen_sparse_matrix</a><T></code> </dd>
<dd>
<code><a class="el" href="structCGAL_1_1Eigen__sparse__symmetric__matrix.html" title="The class Eigen_sparse_symmetric_matrix is a wrapper around Eigen matrix type Eigen::SparseMatrix">CGAL::Eigen_sparse_symmetric_matrix</a><T></code> </dd>
<dd>
<code><a class="el" href="classCGAL_1_1Eigen__vector.html" title="The class Eigen_vector is a wrapper around Eigen vector type, which is a simple array of numbers.">CGAL::Eigen_vector</a><T></code> </dd>
<dd>
<a href="https://eigen.tuxfamily.org/index.php?title=Main_Page">https://eigen.tuxfamily.org/index.php?title=Main_Page</a></dd></dl>
<p><b>Instantiation Example</b><br>
</p>
<p>The instantiation of this class assumes an <a class="elRef" href="../Manual/thirdparty.html#thirdpartyEigen">Eigen</a> sparse solver is provided. Here are few examples:</p>
<div class="fragment"><div class="line"><span class="keyword">typedef</span> <a class="code hl_typedef" href="structCGAL_1_1Eigen__sparse__matrix.html#a4b43cacc467d285c11a39f4eef7a55ae">CGAL::Eigen_sparse_matrix<double>::EigenType</a> EigenMatrix;</div>
<div class="line"> </div>
<div class="line"><span class="comment">//iterative general solver</span></div>
<div class="line"><span class="keyword">typedef</span> <a class="code hl_class" href="classCGAL_1_1Eigen__solver__traits.html">CGAL::Eigen_solver_traits< Eigen::BiCGSTAB<EigenMatrix></a> > Iterative_general_solver;</div>
<div class="line"> </div>
<div class="line"><span class="comment">//iterative symmetric solver</span></div>
<div class="line"><span class="keyword">typedef</span> <a class="code hl_class" href="classCGAL_1_1Eigen__solver__traits.html">CGAL::Eigen_solver_traits< Eigen::ConjugateGradient<EigenMatrix></a> > Iterative_symmetric_solver;</div>
<div class="line"> </div>
<div class="line"><span class="comment">//direct symmetric solver</span></div>
<div class="line"><span class="keyword">typedef</span> <a class="code hl_class" href="classCGAL_1_1Eigen__solver__traits.html">CGAL::Eigen_solver_traits< Eigen::SimplicialCholesky<EigenMatrix></a> > Direct_symmetric_solver;</div>
<div class="ttc" id="aclassCGAL_1_1Eigen__solver__traits_html"><div class="ttname"><a href="classCGAL_1_1Eigen__solver__traits.html">CGAL::Eigen_solver_traits</a></div><div class="ttdoc">The class Eigen_solver_traits provides an interface to the sparse solvers of Eigen.</div><div class="ttdef"><b>Definition:</b> Eigen_solver_traits.h:101</div></div>
<div class="ttc" id="astructCGAL_1_1Eigen__sparse__matrix_html_a4b43cacc467d285c11a39f4eef7a55ae"><div class="ttname"><a href="structCGAL_1_1Eigen__sparse__matrix.html#a4b43cacc467d285c11a39f4eef7a55ae">CGAL::Eigen_sparse_matrix::EigenType</a></div><div class="ttdeci">Eigen::SparseMatrix< T > EigenType</div><div class="ttdoc">The internal matrix type from Eigen.</div><div class="ttdef"><b>Definition:</b> Eigen_sparse_matrix.h:44</div></div>
</div><!-- fragment --> <dl class="section examples"><dt>Examples</dt><dd><a class="el" href="Solver_interface_2sparse_solvers_8cpp-example.html#_a0">Solver_interface/sparse_solvers.cpp</a>.</dd>
</dl>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:addb131ecd843f7a34875eba7b5084566"><td class="memItemLeft" align="right" valign="top"><a id="addb131ecd843f7a34875eba7b5084566" name="addb131ecd843f7a34875eba7b5084566"></a>
</td><td class="memItemRight" valign="bottom"><b>Eigen_solver_traits</b> ()</td></tr>
<tr class="memdesc:addb131ecd843f7a34875eba7b5084566"><td class="mdescLeft"> </td><td class="mdescRight">Constructor. <br></td></tr>
<tr class="separator:addb131ecd843f7a34875eba7b5084566"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a4c4555c432106f6c91a5dc1b5243ba60"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a4c4555c432106f6c91a5dc1b5243ba60">linear_solver</a> (const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a58120f2edd7c2262b6179d83bfa139cb">Matrix</a> &A, const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> &B, <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> &X, <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aab771bce9303d78604f4d91246694f76">NT</a> &D)</td></tr>
<tr class="memdesc:a4c4555c432106f6c91a5dc1b5243ba60"><td class="mdescLeft"> </td><td class="mdescRight">Solve the sparse linear system \( A \times X = B \). <br></td></tr>
<tr class="separator:a4c4555c432106f6c91a5dc1b5243ba60"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a8cfb87e76fb8bd8985c770b212723394"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a8cfb87e76fb8bd8985c770b212723394">factor</a> (const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a58120f2edd7c2262b6179d83bfa139cb">Matrix</a> &A, <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aab771bce9303d78604f4d91246694f76">NT</a> &D)</td></tr>
<tr class="memdesc:a8cfb87e76fb8bd8985c770b212723394"><td class="mdescLeft"> </td><td class="mdescRight">Factorize the sparse matrix \( A \). <br></td></tr>
<tr class="separator:a8cfb87e76fb8bd8985c770b212723394"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a7fcc09d5dc4ddf72a09894835dfad9e3"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a7fcc09d5dc4ddf72a09894835dfad9e3">linear_solver</a> (const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> &B, <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> &X)</td></tr>
<tr class="memdesc:a7fcc09d5dc4ddf72a09894835dfad9e3"><td class="mdescLeft"> </td><td class="mdescRight">Solve the sparse linear system \( A \times X = B\), with \( A \) being the matrix provided in <code><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a8cfb87e76fb8bd8985c770b212723394" title="Factorize the sparse matrix .">factor()</a></code>. <br></td></tr>
<tr class="separator:a7fcc09d5dc4ddf72a09894835dfad9e3"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a8f2c24d24f29d2b9615a89785d7ed899"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a8f2c24d24f29d2b9615a89785d7ed899">linear_solver</a> (const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a58120f2edd7c2262b6179d83bfa139cb">Matrix</a> &B, <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> &X)</td></tr>
<tr class="memdesc:a8f2c24d24f29d2b9615a89785d7ed899"><td class="mdescLeft"> </td><td class="mdescRight">Solve the sparse linear system \( A \times X = B\), with \( A \) being the matrix provided in <code><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a8cfb87e76fb8bd8985c770b212723394" title="Factorize the sparse matrix .">factor()</a></code>. <br></td></tr>
<tr class="separator:a8f2c24d24f29d2b9615a89785d7ed899"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a58ad3fc8fcc441e0c331d101bb7c37a1"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a58ad3fc8fcc441e0c331d101bb7c37a1">normal_equation_factor</a> (const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a58120f2edd7c2262b6179d83bfa139cb">Matrix</a> &A)</td></tr>
<tr class="memdesc:a58ad3fc8fcc441e0c331d101bb7c37a1"><td class="mdescLeft"> </td><td class="mdescRight">Factorize the sparse matrix \( A^t \times A\), where \( A^t \) is the transpose matrix of \( A \). <br></td></tr>
<tr class="separator:a58ad3fc8fcc441e0c331d101bb7c37a1"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a135da70b77a8a17ae47264474dc94b1d"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a135da70b77a8a17ae47264474dc94b1d">normal_equation_solver</a> (const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> &B, <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> &X)</td></tr>
<tr class="memdesc:a135da70b77a8a17ae47264474dc94b1d"><td class="mdescLeft"> </td><td class="mdescRight">Solve the sparse linear system \( A^t \times A \times X = A^t \times B \), with \( A \) being the matrix provided in <code>#<a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a58ad3fc8fcc441e0c331d101bb7c37a1" title="Factorize the sparse matrix , where is the transpose matrix of .">normal_equation_factor()</a></code>, and \( A^t \) its transpose matrix. <br></td></tr>
<tr class="separator:a135da70b77a8a17ae47264474dc94b1d"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a9bbcd0e4f6bf80799b02fc4df39dc1ff"><td class="memItemLeft" align="right" valign="top"><a id="a9bbcd0e4f6bf80799b02fc4df39dc1ff" name="a9bbcd0e4f6bf80799b02fc4df39dc1ff"></a>
bool </td><td class="memItemRight" valign="bottom"><b>normal_equation_solver</b> (const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a58120f2edd7c2262b6179d83bfa139cb">Matrix</a> &A, const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> &B, <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> &X)</td></tr>
<tr class="memdesc:a9bbcd0e4f6bf80799b02fc4df39dc1ff"><td class="mdescLeft"> </td><td class="mdescRight">Equivalent to a call to <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a58ad3fc8fcc441e0c331d101bb7c37a1"><code>normal_equation_factor(A)</code> </a> followed by a call to <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a135da70b77a8a17ae47264474dc94b1d"><code>normal_equation_solver(B, X)</code> </a> . <br></td></tr>
<tr class="separator:a9bbcd0e4f6bf80799b02fc4df39dc1ff"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pro-attribs" name="pro-attribs"></a>
Protected Attributes</h2></td></tr>
<tr class="memitem:a45e0998ec6903d5368a4ddcbcaff4d60"><td class="memItemLeft" align="right" valign="top"><a id="a45e0998ec6903d5368a4ddcbcaff4d60" name="a45e0998ec6903d5368a4ddcbcaff4d60"></a>
const Matrix::EigenType * </td><td class="memItemRight" valign="bottom"><b>m_mat</b></td></tr>
<tr class="separator:a45e0998ec6903d5368a4ddcbcaff4d60"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af1e87beb9f1a96c1b3bbc6fbbbda0b31"><td class="memItemLeft" align="right" valign="top"><a id="af1e87beb9f1a96c1b3bbc6fbbbda0b31" name="af1e87beb9f1a96c1b3bbc6fbbbda0b31"></a>
std::shared_ptr< EigenSolverT > </td><td class="memItemRight" valign="bottom"><b>m_solver_sptr</b></td></tr>
<tr class="separator:af1e87beb9f1a96c1b3bbc6fbbbda0b31"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader">Types</h2></td></tr>
<tr class="memitem:a285f003cd0b894658bf28bf54fa02876"><td class="memItemLeft" align="right" valign="top"><a id="a285f003cd0b894658bf28bf54fa02876" name="a285f003cd0b894658bf28bf54fa02876"></a>
typedef EigenSolverT </td><td class="memItemRight" valign="bottom"><b>Solver</b></td></tr>
<tr class="separator:a285f003cd0b894658bf28bf54fa02876"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aab771bce9303d78604f4d91246694f76"><td class="memItemLeft" align="right" valign="top"><a id="aab771bce9303d78604f4d91246694f76" name="aab771bce9303d78604f4d91246694f76"></a>
typedef Scalar </td><td class="memItemRight" valign="bottom"><b>NT</b></td></tr>
<tr class="separator:aab771bce9303d78604f4d91246694f76"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa857cc5434a376c8cd6e5fd18b6edf26"><td class="memItemLeft" align="right" valign="top"><a id="aa857cc5434a376c8cd6e5fd18b6edf26" name="aa857cc5434a376c8cd6e5fd18b6edf26"></a>
typedef <a class="el" href="classCGAL_1_1Eigen__vector.html">CGAL::Eigen_vector</a>< <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aab771bce9303d78604f4d91246694f76">NT</a> > </td><td class="memItemRight" valign="bottom"><b>Vector</b></td></tr>
<tr class="separator:aa857cc5434a376c8cd6e5fd18b6edf26"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ad7a0ad82c87dc211ee5836fde06195ea"><td class="memItemLeft" align="right" valign="top"><a id="ad7a0ad82c87dc211ee5836fde06195ea" name="ad7a0ad82c87dc211ee5836fde06195ea"></a>
typedef Eigen::DenseIndex </td><td class="memItemRight" valign="bottom"><b>Index</b></td></tr>
<tr class="separator:ad7a0ad82c87dc211ee5836fde06195ea"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a58120f2edd7c2262b6179d83bfa139cb"><td class="memItemLeft" align="right" valign="top"><a id="a58120f2edd7c2262b6179d83bfa139cb" name="a58120f2edd7c2262b6179d83bfa139cb"></a>
typedef <a class="elRef" href="../Manual/classunspecified__type.html">unspecified_type</a> </td><td class="memItemRight" valign="bottom"><b>Matrix</b></td></tr>
<tr class="memdesc:a58120f2edd7c2262b6179d83bfa139cb"><td class="mdescLeft"> </td><td class="mdescRight">If <code>T</code> is <code>Eigen::ConjugateGradient<M></code> or <code>Eigen::SimplicialCholesky<M></code>, <code>Matrix</code> is <code><a class="el" href="structCGAL_1_1Eigen__sparse__symmetric__matrix.html" title="The class Eigen_sparse_symmetric_matrix is a wrapper around Eigen matrix type Eigen::SparseMatrix">CGAL::Eigen_sparse_symmetric_matrix</a><T></code>, and <code><a class="el" href="structCGAL_1_1Eigen__sparse__matrix.html" title="The class Eigen_sparse_matrix is a wrapper around Eigen matrix type Eigen::SparseMatrix that represen...">CGAL::Eigen_sparse_matrix</a><T></code> otherwise. <br></td></tr>
<tr class="separator:a58120f2edd7c2262b6179d83bfa139cb"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader">Operations</h2></td></tr>
<tr class="memitem:a32307b241c57f08649fa3bd48cd82098"><td class="memItemLeft" align="right" valign="top">EigenSolverT & </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a32307b241c57f08649fa3bd48cd82098">solver</a> ()</td></tr>
<tr class="memdesc:a32307b241c57f08649fa3bd48cd82098"><td class="mdescLeft"> </td><td class="mdescRight">Returns a reference to the internal <a class="elRef" href="../Manual/thirdparty.html#thirdpartyEigen">Eigen</a> solver. <br></td></tr>
<tr class="separator:a32307b241c57f08649fa3bd48cd82098"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<h2 class="groupheader">Member Function Documentation</h2>
<a id="a8cfb87e76fb8bd8985c770b212723394" name="a8cfb87e76fb8bd8985c770b212723394"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a8cfb87e76fb8bd8985c770b212723394">◆ </a></span>factor()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>> </div>
<table class="memname">
<tr>
<td class="memname">bool <a class="el" href="classCGAL_1_1Eigen__solver__traits.html">CGAL::Eigen_solver_traits</a>< EigenSolverT >::factor </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a58120f2edd7c2262b6179d83bfa139cb">Matrix</a> & </td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aab771bce9303d78604f4d91246694f76">NT</a> & </td>
<td class="paramname"><em>D</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Factorize the sparse matrix \( A \). </p>
<p>This factorization is used in <code><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a4c4555c432106f6c91a5dc1b5243ba60" title="Solve the sparse linear system .">linear_solver()</a></code> to solve the system for different right-hand side vectors. See <code><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a4c4555c432106f6c91a5dc1b5243ba60" title="Solve the sparse linear system .">linear_solver()</a></code> for the description of \( D \). </p><dl class="section return"><dt>Returns</dt><dd><code>true</code> if the factorization is successful and <code>false</code> otherwise. </dd></dl>
</div>
</div>
<a id="a4c4555c432106f6c91a5dc1b5243ba60" name="a4c4555c432106f6c91a5dc1b5243ba60"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a4c4555c432106f6c91a5dc1b5243ba60">◆ </a></span>linear_solver() <span class="overload">[1/3]</span></h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>> </div>
<table class="memname">
<tr>
<td class="memname">bool <a class="el" href="classCGAL_1_1Eigen__solver__traits.html">CGAL::Eigen_solver_traits</a>< EigenSolverT >::linear_solver </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a58120f2edd7c2262b6179d83bfa139cb">Matrix</a> & </td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> & </td>
<td class="paramname"><em>B</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> & </td>
<td class="paramname"><em>X</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aab771bce9303d78604f4d91246694f76">NT</a> & </td>
<td class="paramname"><em>D</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Solve the sparse linear system \( A \times X = B \). </p>
<p>Return <code>true</code> on success. The solution is then \( (1/D) \times X \).</p>
<dl class="section pre"><dt>Precondition</dt><dd>A.row_dimension() == B.dimension(). </dd>
<dd>
A.column_dimension() == X.dimension(). </dd></dl>
</div>
</div>
<a id="a8f2c24d24f29d2b9615a89785d7ed899" name="a8f2c24d24f29d2b9615a89785d7ed899"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a8f2c24d24f29d2b9615a89785d7ed899">◆ </a></span>linear_solver() <span class="overload">[2/3]</span></h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>> </div>
<table class="memname">
<tr>
<td class="memname">bool <a class="el" href="classCGAL_1_1Eigen__solver__traits.html">CGAL::Eigen_solver_traits</a>< EigenSolverT >::linear_solver </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a58120f2edd7c2262b6179d83bfa139cb">Matrix</a> & </td>
<td class="paramname"><em>B</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> & </td>
<td class="paramname"><em>X</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Solve the sparse linear system \( A \times X = B\), with \( A \) being the matrix provided in <code><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a8cfb87e76fb8bd8985c770b212723394" title="Factorize the sparse matrix .">factor()</a></code>. </p>
<dl class="section return"><dt>Returns</dt><dd><code>true</code> if the solver is successful and <code>false</code> otherwise. </dd></dl>
</div>
</div>
<a id="a7fcc09d5dc4ddf72a09894835dfad9e3" name="a7fcc09d5dc4ddf72a09894835dfad9e3"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7fcc09d5dc4ddf72a09894835dfad9e3">◆ </a></span>linear_solver() <span class="overload">[3/3]</span></h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>> </div>
<table class="memname">
<tr>
<td class="memname">bool <a class="el" href="classCGAL_1_1Eigen__solver__traits.html">CGAL::Eigen_solver_traits</a>< EigenSolverT >::linear_solver </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> & </td>
<td class="paramname"><em>B</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> & </td>
<td class="paramname"><em>X</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Solve the sparse linear system \( A \times X = B\), with \( A \) being the matrix provided in <code><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a8cfb87e76fb8bd8985c770b212723394" title="Factorize the sparse matrix .">factor()</a></code>. </p>
<dl class="section return"><dt>Returns</dt><dd><code>true</code> if the solver is successful and <code>false</code> otherwise. </dd></dl>
</div>
</div>
<a id="a58ad3fc8fcc441e0c331d101bb7c37a1" name="a58ad3fc8fcc441e0c331d101bb7c37a1"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a58ad3fc8fcc441e0c331d101bb7c37a1">◆ </a></span>normal_equation_factor()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>> </div>
<table class="memname">
<tr>
<td class="memname">bool <a class="el" href="classCGAL_1_1Eigen__solver__traits.html">CGAL::Eigen_solver_traits</a>< EigenSolverT >::normal_equation_factor </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a58120f2edd7c2262b6179d83bfa139cb">Matrix</a> & </td>
<td class="paramname"><em>A</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Factorize the sparse matrix \( A^t \times A\), where \( A^t \) is the transpose matrix of \( A \). </p>
<p>This factorization is used in <code><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a135da70b77a8a17ae47264474dc94b1d" title="Solve the sparse linear system , with being the matrix provided in #normal_equation_factor(),...">normal_equation_solver()</a></code> to solve the system for different right-hand side vectors. </p><dl class="section return"><dt>Returns</dt><dd><code>true</code> if the factorization is successful and <code>false</code> otherwise. </dd></dl>
</div>
</div>
<a id="a135da70b77a8a17ae47264474dc94b1d" name="a135da70b77a8a17ae47264474dc94b1d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a135da70b77a8a17ae47264474dc94b1d">◆ </a></span>normal_equation_solver()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>> </div>
<table class="memname">
<tr>
<td class="memname">bool <a class="el" href="classCGAL_1_1Eigen__solver__traits.html">CGAL::Eigen_solver_traits</a>< EigenSolverT >::normal_equation_solver </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> & </td>
<td class="paramname"><em>B</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html#aa857cc5434a376c8cd6e5fd18b6edf26">Vector</a> & </td>
<td class="paramname"><em>X</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Solve the sparse linear system \( A^t \times A \times X = A^t \times B \), with \( A \) being the matrix provided in <code>#<a class="el" href="classCGAL_1_1Eigen__solver__traits.html#a58ad3fc8fcc441e0c331d101bb7c37a1" title="Factorize the sparse matrix , where is the transpose matrix of .">normal_equation_factor()</a></code>, and \( A^t \) its transpose matrix. </p>
<dl class="section return"><dt>Returns</dt><dd><code>true</code> if the solver is successful and <code>false</code> otherwise. </dd></dl>
</div>
</div>
<a id="a32307b241c57f08649fa3bd48cd82098" name="a32307b241c57f08649fa3bd48cd82098"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a32307b241c57f08649fa3bd48cd82098">◆ </a></span>solver()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<class EigenSolverT = Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType>> </div>
<table class="memname">
<tr>
<td class="memname">EigenSolverT & <a class="el" href="classCGAL_1_1Eigen__solver__traits.html">CGAL::Eigen_solver_traits</a>< EigenSolverT >::solver </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Returns a reference to the internal <a class="elRef" href="../Manual/thirdparty.html#thirdpartyEigen">Eigen</a> solver. </p>
<p>This function can be used for example to set specific parameters of the solver. </p>
</div>
</div>
</div><!-- contents -->
</div><!-- doc-content -->
<!-- HTML footer for doxygen 1.9.6-->
<!-- start footer part -->
<!-- The footer div is not part of the default but we require it to
move the footer to the bottom of the page. -->
<div id="footer">
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><b>CGAL</b></li><li class="navelem"><a class="el" href="classCGAL_1_1Eigen__solver__traits.html">Eigen_solver_traits</a></li>
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"></a> 1.9.6 </li>
</ul>
</div>
</div>
</body>
</html>